⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task}} {{requires|Graphics}} [[Category:3D]]
;Task: Draw a sphere.
The sphere can be represented graphically, or in ASCII art, depending on the language capabilities.
Either static or rotational projection is acceptable for this task.
Ada
{{libheader|GtkAda}} Translation from the C code at http://cairographics.org/samples/gradient Uses the Cairo component of GtkAda to create and save as png [[File:SphereAda.png|thumb|right]]
with Glib; use Glib;
with Cairo; use Cairo;
with Cairo.Png; use Cairo.Png;
with Cairo.Pattern; use Cairo.Pattern;
with Cairo.Image_Surface; use Cairo.Image_Surface;
with Ada.Numerics;
procedure Sphere is
subtype Dub is Glib.Gdouble;
Surface : Cairo_Surface;
Cr : Cairo_Context;
Pat : Cairo_Pattern;
Status_Out : Cairo_Status;
M_Pi : constant Dub := Dub (Ada.Numerics.Pi);
begin
Surface := Create (Cairo_Format_ARGB32, 512, 512);
Cr := Create (Surface);
Pat :=
Cairo.Pattern.Create_Radial (230.4, 204.8, 51.1, 204.8, 204.8, 256.0);
Cairo.Pattern.Add_Color_Stop_Rgba (Pat, 0.0, 1.0, 1.0, 1.0, 1.0);
Cairo.Pattern.Add_Color_Stop_Rgba (Pat, 1.0, 0.0, 0.0, 0.0, 1.0);
Cairo.Set_Source (Cr, Pat);
Cairo.Arc (Cr, 256.0, 256.0, 153.6, 0.0, 2.0 * M_Pi);
Cairo.Fill (Cr);
Cairo.Pattern.Destroy (Pat);
Status_Out := Write_To_Png (Surface, "SphereAda.png");
pragma Assert (Status_Out = Cairo_Status_Success);
end Sphere;
{{libheader|Display}} This uses a very loose binding to SDL as found in any GPS installation. For it to work, you must choose New Project From Templte|Empty Game
with Display; use Display;
with Display.Basic; use Display.Basic;
procedure Main is
Ball : Shape_Id := New_Circle
(X => 0.0,
Y => 0.0,
Radius => 20.0,
Color => Blue);
begin
null;
end Main;
Arendelle
[ #j ,
[ #i ,
{ ( #x - 19 ) ^ 2 +
( #y - 14 ) ^ 2 < 125 , p
} r
] [ #i , l ] d
]
ATS
(* ****** ****** ) // #include "share/atspre_define.hats" // defines some names #include "share/atspre_staload.hats" // for targeting C #include "share/HATS/atspre_staload_libats_ML.hats" // for ... #include "share/HATS/atslib_staload_libats_libc.hats" // for libc // ( ****** ****** *)
extern fun Draw_a_sphere ( R: double, k: double, ambient: double ) : void // end of [Draw_a_sphere]
(* ****** ****** *)
implement Draw_a_sphere ( R: double, k: double, ambient: double ) = let fun normalize(v0: double, v1: double, v2: double): (double, double, double) = let val len = sqrt(v0v0+v1v1+v2*v2) in (v0/len, v1/len, v2/len) end // end of [normalize]
fun dot(v0: double, v1: double, v2: double, x0: double, x1: double, x2: double): double = let val d = v0*x0+v1*x1+v2*x2 val sgn = gcompare_val_val<double> (d, 0.0) in if sgn < 0 then ~d else 0.0 end // end of [dot] fun print_char(i: int): void = if i = 0 then print!(".") else if i = 1 then print!(":") else if i = 2 then print!("!") else if i = 3 then print!("*") else if i = 4 then print!("o") else if i = 5 then print!("e") else if i = 6 then print!("&") else if i = 7 then print!("#") else if i = 8 then print!("%") else if i = 9 then print!("@") else print!(" ") val i_start = floor(~R) val i_end = ceil(R) val j_start = floor(~2 * R) val j_end = ceil(2 * R) val (l0, l1, l2) = normalize(30.0, 30.0, ~50.0) fun loopj(j: int, j_end: int, x: double): void = let val y = j / 2.0 + 0.5; val sgn = gcompare_val_val<double> (x*x + y*y, R*R) val (v0, v1, v2) = normalize(x, y, sqrt(R*R - x*x - y*y)) val b = pow(dot(l0, l1, l2, v0, v1, v2), k) + ambient val intensity = 9.0 - 9.0*b val sgn2 = gcompare_val_val<double> (intensity, 0.0) val sgn3 = gcompare_val_val<double> (intensity, 9.0) in ( if sgn > 0 then print_char(10) else if sgn2 < 0 then print_char(0) else if sgn3 >= 0 then print_char(8) else print_char(g0float2int(intensity)); if j < j_end then loopj(j+1, j_end, x) ) end // end of [loopj] fun loopi(i: int, i_end: int, j: int, j_end: int): void = let val x = i + 0.5 val () = loopj(j, j_end, x) val () = println!() in if i < i_end then loopi(i+1, i_end, j, j_end) end // end of [loopi]
in loopi(g0float2int(i_start), g0float2int(i_end), g0float2int(j_start), g0float2int(j_end)) end
(* ****** ****** *)
implement main0() = () where { val () = DrawSphere(20.0, 4.0, .1) val () = DrawSphere(10.0, 2.0, .4) } (* end of [main0] *)
(* ****** ****** *)
## AutoHotkey
{{libheader|GDIP}}
```ahk
#NoEnv
SetBatchLines, -1
#SingleInstance, Force
; Uncomment if Gdip.ahk is not in your standard library
#Include, Gdip.ahk
; Settings
X := 200, Y := 200, Width := 200, Height := 200 ; Location and size of sphere
rotation := -30 ; degrees
ARGB := 0xFFFF0000 ; Color=Solid Red
If !pToken := Gdip_Startup() ; Start gdi+
{
MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
ExitApp
}
OnExit, Exit
Gui, -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs ; Create GUI
Gui, Show, NA ; Show GUI
hwnd1 := WinExist() ; Get a handle to this window we have created in order to update it later
hbm := CreateDIBSection(A_ScreenWidth, A_ScreenHeight) ; Create a gdi bitmap drawing area
hdc := CreateCompatibleDC() ; Get a device context compatible with the screen
obm := SelectObject(hdc, hbm) ; Select the bitmap into the device context
pGraphics := Gdip_GraphicsFromHDC(hdc) ; Get a pointer to the graphics of the bitmap, for use with drawing functions
Gdip_SetSmoothingMode(pGraphics, 4) ; Set the smoothing mode to antialias = 4 to make shapes appear smother
Gdip_TranslateWorldTransform(pGraphics, X, Y)
Gdip_RotateWorldTransform(pGraphics, rotation)
; Base ellipse
pBrush := Gdip_CreateLineBrushFromRect(0, 0, Width, Height, ARGB, 0xFF000000)
Gdip_FillEllipse(pGraphics, pBrush, 0, 0, Width, Height)
; First highlight ellipse
pBrush := Gdip_CreateLineBrushFromRect(Width*0.1, Height*0.01, Width*0.8, Height*0.6, 0x33FFFFFF, 0x00FFFFFF)
Gdip_FillEllipse(pGraphics, pBrush, Width*0.1, Height*0.01, Width*0.8, Height*0.6)
; Second highlight ellipse
pBrush := Gdip_CreateLineBrushFromRect(Width*0.3, Height*0.02, Width*0.3, Height*0.2, 0xBBFFFFFF, 0x00FFFFFF)
Gdip_FillEllipse(pGraphics, pBrush, Width*0.3, Height*0.02, Width*0.3, Height*0.2)
UpdateLayeredWindow(hwnd1, hdc, 0, 0, A_ScreenWidth, A_ScreenHeight)
SelectObject(hdc, obm) ; Select the object back into the hdc
Gdip_DeletePath(Path)
Gdip_DeleteBrush(pBrush)
DeleteObject(hbm) ; Now the bitmap may be deleted
DeleteDC(hdc) ; Also the device context related to the bitmap may be deleted
Gdip_DeleteGraphics(G) ; The graphics may now be deleted
Return
Exit:
; gdi+ may now be shutdown on exiting the program
Gdip_Shutdown(pToken)
ExitApp
AWK
# syntax: GAWK -f DRAW_A_SPHERE.AWK
# converted from VBSCRIPT
BEGIN {
draw_sphere(20,4,0.1)
draw_sphere(10,2,0.4)
exit(0)
}
function draw_sphere(radius,k,ambient, b,i,intensity,j,leng_shades,light,line,shades,vec,x,y) {
leng_shades = split0(".:!*oe&#%@",shades,"")
split("30,30,-50",light,",")
normalize(light)
for (i=int(-radius); i<=ceil(radius); i++) {
x = i + 0.5
line = ""
for (j=int(-2*radius); j<=ceil(2*radius); j++) {
y = j / 2 + 0.5
if (x*x + y*y <= radius*radius) {
vec[1] = x
vec[2] = y
vec[3] = sqrt(radius*radius - x*x - y*y)
normalize(vec)
b = dot(light,vec) ^ k + ambient
intensity = int((1-b) * leng_shades)
if (intensity < 0) {
intensity = 0
}
if (intensity >= leng_shades) {
intensity = leng_shades
}
line = line shades[intensity]
}
else {
line = line " "
}
}
printf("%s\n",line)
}
}
function ceil(x, tmp) {
tmp = int(x)
return (tmp != x) ? tmp+1 : tmp
}
function dot(x,y, tmp) {
tmp = x[1]*y[1] + x[2]*y[2] + x[3]*y[3]
return (tmp < 0) ? -tmp : 0
}
function normalize(v, tmp) {
tmp = sqrt(v[1]*v[1] + v[2]*v[2] + v[3]*v[3])
v[1] /= tmp
v[2] /= tmp
v[3] /= tmp
}
function split0(str,array,fs, arr,i,n) { # same as split except indices start at zero
n = split(str,arr,fs)
for (i=1; i<=n; i++) {
array[i-1] = arr[i]
}
return(n)
}
{{out}}
############%%%%%
#&&&eeeeeeeee&&&&&&#####%%%%%%%
&eeeoooooooooooooeeeee&&&&#####%%%%%%%%
&eoo***************oooooeeee&&&&####%%%%%%%%%
&eo***!!!!!:::!!!!!!!****ooooeee&&&&#####%%%%%%%%%%
eoo*!!!::::::::::::::!!!!****oooeeee&&&#####%%%%%%%%%%%
eo**!!:::............::::!!!!***oooeeee&&&#####%%%%%%%%%%%%
&eo*!!::.................:::!!!!***oooeee&&&&#####%%%%%%%%%%%%%
eo*!!::...................::::!!!***oooeeee&&&#####%%%%%%%%%%%%%%
#eo*!!::.....................:::!!!***oooeeee&&&&####%%%%%%%%%%%%%%%@
&eo*!!::......................:::!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%@
&eo*!!::......................::::!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%@@
#eo**!!::......................:::!!!****oooeee&&&&#####%%%%%%%%%%%%%%%%%@@
&eo**!:::....................::::!!!!***oooeeee&&&&#####%%%%%%%%%%%%%%%%%@@
&eoo**!!::...................::::!!!!***ooooeee&&&&######%%%%%%%%%%%%%%%%%@@@
&eoo**!!:::................::::!!!!****ooooeee&&&&&#####%%%%%%%%%%%%%%%%%%@@@
#&eoo**!!!::::...........:::::!!!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%%%%@@@@
#&eeoo**!!!!::::::::::::::::!!!!!****ooooeeee&&&&&######%%%%%%%%%%%%%%%%%%%@@@@
#&eeooo***!!!!!::::::::!!!!!!!*****ooooeeeee&&&&&######%%%%%%%%%%%%%%%%%%%@@@@@
#&&eeooo****!!!!!!!!!!!!!!!******oooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%@@@@@
##&&eeoooo********************oooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%@@@@@
##&&&eeeoooooo***********oooooooeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%@@@@@@
%##&&&eeeeeooooooooooooooooooeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@
%%###&&&&eeeeeeeeeeoeeeeeeeeeeee&&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@
%%###&&&&&&eeeeeeeeeeeeeeee&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@
%%%#####&&&&&&&&&&&&&&&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@
%%%%#######&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@
%%%%%%#############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@
%%%%%%%%######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@
%%%%%%%%%%%%%%%#####%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@
@%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@
@@@@%%%%%%%%%%%%@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@@@@@@@@@@@@@@@@@
::..::::!!**o
.............::!!**oe
..................::!!*ooee
.....................::!!*ooeee
.......................:!!**ooeee
........................:!!**ooeeee
........................::!!**ooeeee&
:........................::!!**ooeeee&&
........................::!!**oooeeee&&
:......................::!!***ooeeeee&&
:....................::!!!***ooeeeee&&&
!::................:::!!***oooeeeeee&&&
*!!::..........::::!!!****oooeeeeee&&&&
**!!::::::::::!!!!!***ooooeeeeee&&&&&
o***!!!!!!!!!!*****ooooeeeeeee&&&&&
eooo*********ooooooeeeeeeee&&&&&&
eeeoooooooooooeeeeeeeeee&&&&&&&
eeeeeeeeeeeeeeeeeee&&&&&&&&
&eeeeeeeeee&&&&&&&&&&
&&&&&&&&&&&&&
BASIC
=
BASIC256
= This is modeled after the [http://rosettacode.org/wiki/Draw_a_sphere#Tcl Tcl] implementation. Thus, the output of this is almost the same to the output of Tcl implementation below.
clg
color white
rect 0,0,graphwidth, graphheight
For n = 1 to 100
color rgb(2*n,2*n,2*n)
circle 150-2*n/3,150-n/2,150-n
next n
=
BBC BASIC
= {{works with|BBC BASIC for Windows}} Using Direct3D.
MODE 8
INSTALL @lib$+"D3DLIB"
D3DTS_VIEW = 2
D3DTS_PROJECTION = 3
D3DRS_SPECULARENABLE = 29
SYS "LoadLibrary", @lib$+"D3DX8BBC.DLL" TO d3dx%
IF d3dx%=0 ERROR 100, "Couldn't load D3DX8BBC.DLL"
SYS "GetProcAddress", d3dx%, "D3DXCreateSphere" TO `D3DXCreateSphere`
SYS "GetProcAddress", d3dx%, "D3DXMatrixLookAtLH" TO `D3DXMatrixLookAtLH`
SYS "GetProcAddress", d3dx%, "D3DXMatrixPerspectiveFovLH" TO `D3DXMatrixPerspectiveFovLH`
DIM eyepos%(2), lookat%(2), up%(2), mat%(3,3)
DIM D3Dlight8{Type%, Diffuse{r%,g%,b%,a%}, Specular{r%,g%,b%,a%}, \
\ Ambient{r%,g%,b%,a%}, Position{x%,y%,z%}, Direction{x%,y%,z%}, \
\ Range%, Falloff%, Attenuation0%, Attenuation1%, Attenuation2%, \
\ Theta%, Phi%}
DIM D3Dmaterial8{Diffuse{r%,g%,b%,a%}, Ambient{r%,g%,b%,a%}, \
\ Specular{r%,g%,b%,a%}, Emissive{r%,g%,b%,a%}, Power%}
DIM D3Dbasemesh8{QueryInterface%, Addref%, Release%, \
\ DrawSubset%, GetNumFaces%, GetNumVertices%, GetFVF%, \
\ GetDeclaration%, GetOptions%, GetDevice%, \
\ CloneMeshFVF%, CloneMesh%, GetVertexBuffer%, GetIndexBuffer%, \
\ LockVertexBuffer%, UnlockVertexBuffer%, LockIndexBuffer%, \
\ UnlockIndexBuffer%, GetAttributeTable%}
DIM D3Ddevice8{QueryInterface%, AddRef%, Release%, TestCooperativeLevel%, \
\ GetAvailableTextureMem%, ResourceManagerDiscardBytes%, GetDirect3D%, \
\ GetDeviceCaps%, GetDisplayMode%, GetCreationParameters%, SetCursorProperties%, \
\ SetCursorPosition%, ShowCursor%, CreateAdditionalSwapChain%, Reset%, \
\ Present%, GetBackBuffer%, GetRasterStatus%, SetGammaRamp%, GetGammaRamp%, \
\ CreateTexture%, CreateVolumeTexture%, CreateCubeTexture%, CreateVertexBuffer%, \
\ CreateIndexBuffer%, CreateRenderTarget%, CreateDepthStencilSurface%, \
\ CreateImageSurface%, CopyRects%, UpdateTexture%, GetFrontBuffer%, \
\ SetRenderTarget%, GetRenderTarget%, GetDepthStencilSurface%, BeginScene%, \
\ EndScene%, Clear%, SetTransform%, GetTransform%, MultiplyTransform%, \
\ SetViewport%, GetViewport%, SetMaterial%, GetMaterial%, SetLight%, GetLight%, \
\ LightEnable%, GetLightEnable%, SetClipPlane%, GetClipPlane%, SetRenderState%, \
\ GetRenderState%, BeginStateBlock%, EndStateBlock%, ApplyStateBlock%, \
\ CaptureStateBlock%, DeleteStateBlock%, CreateStateBlock%, SetClipStatus%, \
\ GetClipStatus%, GetTexture%, SetTexture%, GetTextureStageState%, \
\ SetTextureStageState%, ValidateDevice%, GetInfo%, SetPaletteEntries%, \
\ GetPaletteEntries%, SetCurrentTexturePalette%, GetCurrentTexturePalette%, \
\ DrawPrimitive%, DrawIndexedPrimitive%, DrawPrimitiveUP%, \
\ DrawIndexedPrimitiveUP%, ProcessVertices%, CreateVertexShader%, \
\ SetVertexShader%, GetVertexShader%, DeleteVertexShader%, \
\ SetVertexShaderConstant%, GetVertexShaderConstant%, GetVertexShaderDeclaration%, \
\ GetVertexShaderFunction%, SetStreamSource%, GetStreamSource%, SetIndices%, \
\ GetIndices%, CreatePixelShader%, SetPixelShader%, GetPixelShader%, \
\ DeletePixelShader%, SetPixelShaderConstant%, GetPixelShaderConstant%, \
\ GetPixelShaderFunction%, DrawRectPatch%, DrawTriPatch%, DeletePatch%}
pDevice%=FN_initd3d(@hwnd%, 1, 1)
IF pDevice%=0 ERROR 100, "Couldn't create Direct3D8 device"
!(^D3Ddevice8{}+4) = !pDevice%
SYS `D3DXCreateSphere`, pDevice%, FN_f4(1), 50, 50, ^meshSphere%, 0
IF meshSphere% = 0 ERROR 100, "D3DXCreateSphere failed"
!(^D3Dbasemesh8{}+4) = !meshSphere%
REM. Point-source light:
D3Dlight8.Type%=1 : REM. point source
D3Dlight8.Diffuse.r% = FN_f4(1)
D3Dlight8.Diffuse.g% = FN_f4(1)
D3Dlight8.Diffuse.b% = FN_f4(1)
D3Dlight8.Specular.r% = FN_f4(1)
D3Dlight8.Specular.g% = FN_f4(1)
D3Dlight8.Specular.b% = FN_f4(1)
D3Dlight8.Position.x% = FN_f4(2)
D3Dlight8.Position.y% = FN_f4(1)
D3Dlight8.Position.z% = FN_f4(4)
D3Dlight8.Range% = FN_f4(10)
D3Dlight8.Attenuation0% = FN_f4(1)
REM. Material:
D3Dmaterial8.Diffuse.r% = FN_f4(0.2)
D3Dmaterial8.Diffuse.g% = FN_f4(0.6)
D3Dmaterial8.Diffuse.b% = FN_f4(1.0)
D3Dmaterial8.Specular.r% = FN_f4(0.4)
D3Dmaterial8.Specular.g% = FN_f4(0.4)
D3Dmaterial8.Specular.b% = FN_f4(0.4)
D3Dmaterial8.Power% = FN_f4(100)
fovy = RAD(30)
aspect = 5/4
znear = 1
zfar = 1000
bkgnd% = &7F7F7F
eyepos%() = 0, 0, FN_f4(6)
lookat%() = 0, 0, 0
up%() = 0, FN_f4(1), 0
SYS D3Ddevice8.Clear%, pDevice%, 0, 0, 3, bkgnd%, FN_f4(1), 0
SYS D3Ddevice8.BeginScene%, pDevice%
SYS D3Ddevice8.SetLight%, pDevice%, 0, D3Dlight8{}
SYS D3Ddevice8.LightEnable%, pDevice%, 0, 1
SYS D3Ddevice8.SetMaterial%, pDevice%, D3Dmaterial8{}
SYS D3Ddevice8.SetRenderState%, pDevice%, D3DRS_SPECULARENABLE, 1
SYS `D3DXMatrixLookAtLH`, ^mat%(0,0), ^eyepos%(0), ^lookat%(0), ^up%(0)
SYS D3Ddevice8.SetTransform%, pDevice%, D3DTS_VIEW, ^mat%(0,0)
SYS `D3DXMatrixPerspectiveFovLH`, ^mat%(0,0), FN_f4(fovy), \
\ FN_f4(aspect), FN_f4(znear), FN_f4(zfar)
SYS D3Ddevice8.SetTransform%, pDevice%, D3DTS_PROJECTION, ^mat%(0,0)
SYS D3Dbasemesh8.DrawSubset%, meshSphere%, 0
SYS D3Ddevice8.EndScene%, pDevice%
SYS D3Ddevice8.Present%, pDevice%, 0, 0, 0, 0
SYS D3Ddevice8.Release%, pDevice%
SYS D3Dbasemesh8.Release%, meshSphere%
SYS "FreeLibrary", d3dx%
END
{{out}} [[File:Sphere_BBC.jpeg]]
===[[DarkBASIC]]===
Some simple 3D objects are built into DarkBASIC. Creating a sphere only takes 1 line:
MAKE OBJECT SPHERE 1,1
=
FreeBASIC
=
' "\" = a integer division (CPU)
' "/" = a floating point division (FPU)
' the compiler takes care of the conversion between floating point and integer
' compile with: FBC -s console "filename.bas" or FBC -s GUI "filename.bas"
' filename is whatever name you give it, .bas is mandatory
' Sphere using XPL0 code from rosetacode sphere page
' Altered freebasic version to compile in default mode
' version 17-06-2015
' compile with: fbc -s console or fbc -s gui
#Define W 640
#Define H 480
ScreenRes W, H, 32 ' set 640x480x32 graphics mode, 32 bits color mode
WindowTitle "32 bpp Cyan Sphere FreeBASIC"
' wait until keypress
' Color(RGB(255,255,255),RGB(0,0,0)) ' default white foreground, black background
Locate 50,2
Print "Enter any key to start"
Sleep
Dim As UInteger R = 100, R2 = R * R ' radius, in pixels; radius squared
Dim As UInteger X0 = W \ 2, Y0 = H \ 2 ' coordinates of center of screen
Dim As Integer X, Y, C, D2 ' coords, color, distance from center squared
For Y = -R To R ' for all the coordinates near the circle
For X = -R To R ' which is under the sphere
D2 = X * X + Y * Y
If D2 <= R2 Then ' coordinate is inside circle under sphere
' height of point on surface of sphere above X,Y
C = Sqr(R2 - D2) - ( X + Y) / 2 + 130 ' color is proportional; offset X and Y, and
Color C Shl 8 + C ' = color RGB(0, C, C)
' green + blue = cyan
PSet(X + X0, Y + Y0)
End If
Next
Next
' wait until keypress
Locate 50,2
Color(RGB(255,255,255),RGB(0,0,0)) ' foreground color is changed
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
{{works with|FreeBASIC}} needs #Lang "fblite", #Lang "qb" or #Lang "deprecated" to compile.
'Sphere for FreeBASIC May 2015
'spherefb4.bas
'Sphere using XPL0 code from rosetacode sphere page
'
screenres 640,480,32 '\set 640x480x32 graphics mode
windowtitle "32 bpp Blue Sphere FreeBASIC"
'
' wait until keypress
locate 50,2
color(rgb(255,255,255),rgb(0,0,0))
Print "Enter any key to start"
sleep
R=100 : R2=R*R '\radius, in pixels; radius squared
X0=640/2 : Y0=480/2 '\coordinates of center of screen
dim as integer X, Y, Z, C, D2 '\coords, color, distance from center squared
'
for Y= -R to +R '\for all the coordinates near the circle
for X = -R to +R '\ which is under the sphere
D2 = X*X + Y*Y '
C = 0 '\default color is black
if D2 <= R2 then '\coordinate is inside circle under sphere
Z = sqr(R2-D2) '\height of point on surface of sphere above X,Y
C = Z-(X+Y)/2+130 ' \color is proportional; offset X and Y, and
endif
color c ' \ shift color to upper limit of its range
'\green + blue = cyan orginal line don't understand
Pset(X+X0, Y+Y0)
next x
next y
'
' wait until keypress
locate 50,2
color(rgb(255,255,255),rgb(0,0,0))
Print "Enter any key to exit "
sleep
END
=
Liberty BASIC
=
WindowWidth =420
WindowHeight =460
nomainwin
open "Sphere" for graphics_nsb_nf as #w
#w "down ; fill lightgray"
xS =200
yS =200
for radius =150 to 0 step -1
level$ =str$( int( 256 -256 *radius /150))
c$ =level$ +" " +level$ +" " +level$
#w "color "; c$
#w "backcolor "; c$
#w "place "; xS; " "; yS
xS =xS -0.5
yS =yS -0.2
#w "circlefilled "; radius
next radius
#w "flush"
wait
close #w
end
=
Locomotive Basic
= Translated from ERRE version, this will print a 39x20 text sphere onscreen. The variables in line 80 can be used to adjust size (r), spotlight (k), reflective light (ambient).
10 MODE 2:s$=".:!*oe&#%@"
20 DIM v(2),vec(2)
30 v(0)=30:v(1)=30:v(2)=-50
40 lung=SQR(v(0)*v(0)+v(1)*v(1)+v(2)*v(2))
50 v(0)=v(0)/lung
60 v(1)=v(1)/lung
70 v(2)=v(2)/lung
80 r=10:k=2:ambient=0.4
90 FOR i=INT(-r) TO INT(r)
100 x=i+0.5
110 FOR j=INT(-2*r) TO INT(2*r)
120 y=j/2+0.5
130 IF (x*x+y*y<=r*r) THEN GOSUB 1000 ELSE PRINT" ";
140 NEXT j
150 PRINT
160 NEXT i
170 END
1000 vec(0)=x
1010 vec(1)=y
1020 vec(2)=SQR(r*r-x*x-y*y)
1030 GOSUB 2000
1040 GOSUB 3000
1050 b=d^k+ambient
1060 intensity%=(1-b)*(LEN(s$)-1)
1070 IF (intensity%<0) THEN intensity%=0
1080 IF (intensity%>LEN(s$)-1) THEN intensity%=LEN(s$)-2
1090 PRINT MID$(s$,intensity%+1,1);
1100 RETURN
2000 lung=SQR(vec(0)*vec(0)+vec(1)*vec(1)+vec(2)*vec(2))
2010 vec(0)=vec(0)/lung
2020 vec(1)=vec(1)/lung
2030 vec(2)=vec(2)/lung
2040 RETURN
3000 d=v(0)*vec(0)+v(1)*vec(1)+v(2)*vec(2)
3010 IF d<0 THEN d=-d ELSE d=0
3020 RETURN
=
PureBasic
= 3D Sphere animation.
; Original by Comtois @ 28/03/06
;
; Updated/Formated by Fluid Byte @ March.24,2009
;
; http://www.purebasic.fr/english/viewtopic.php?p=281258#p281258
Declare CreateSphere(M,P)
Declare UpdateMesh()
#_SIZEVERT = 36
#_SIZETRIS = 6
#FULLSCREEN = 0
Structure VECTOR
X.f
Y.f
Z.f
EndStructure
Structure VERTEX
X.f
Y.f
Z.f
NX.f
NY.f
NZ.f
Color.l
U.f
V.f
EndStructure
Structure TRIANGLE
V1.w
V2.w
V3.w
EndStructure
Macro CALC_NORMALS
*PtrV\NX = *PtrV\X
*PtrV\NY = *PtrV\Y
*PtrV\NZ = *PtrV\Z
EndMacro
Global *VBuffer, *IBuffer
Global Meridian = 50, Parallele = 50, PasLength = 4, Length
Define EventID, i, NbSommet, CameraMode, Angle.f, Pas.f = 0.5
InitEngine3D() : InitSprite() : InitKeyboard()
Add3DArchive(GetTemporaryDirectory(),#PB_3DArchive_FileSystem)
Add3DArchive(#PB_Compiler_Home + "Examples\Sources\Data\",#PB_3DArchive_FileSystem)
If #FULLSCREEN
OpenScreen(800,600,32,"Sphere 3D")
Else
OpenWindow(0,0,0,800,600,"Sphere 3D",#PB_Window_SystemMenu | 1)
OpenWindowedScreen(WindowID(0),0,0,800,600,0,0,0)
EndIf
;-Texture
CreateImage(0,128,128)
StartDrawing(ImageOutput(0))
For i = 0 To 127 Step 4
Box(0,i,ImageWidth(0),2,RGB(255,255,255))
Box(0,i + 2,ImageWidth(0),2,RGB(0,0,155))
Next i
StopDrawing()
SaveImage(0,GetTemporaryDirectory() + "temp.bmp") : FreeImage(0)
;-Material
CreateMaterial(0,LoadTexture(0,"temp.bmp"))
RotateMaterial(0,0.1,#PB_Material_Animated)
;-Mesh
CreateSphere(Meridian,Parallele)
;-Entity
CreateEntity(0,MeshID(0),MaterialID(0))
ScaleEntity(0,60,60,60)
;-Camera
CreateCamera(0,0,0,100,100)
MoveCamera(0,0,0,-200)
CameraLookAt(0,EntityX(0),EntityY(0),EntityZ(0))
;-Light
AmbientColor(RGB(105, 105, 105))
CreateLight(0, RGB(255, 255, 55), EntityX(0) + 150, EntityY(0) , EntityZ(0))
CreateLight(1, RGB( 55, 255, 255), EntityX(0) - 150, EntityY(0) , EntityZ(0))
CreateLight(2, RGB( 55, 55, 255), EntityX(0) , EntityY(0) + 150, EntityZ(0))
CreateLight(3, RGB(255, 55, 255), EntityX(0) , EntityY(0) - 150, EntityZ(0))
; ----------------------------------------------------------------------------------------------------
; MAINLOOP
; ----------------------------------------------------------------------------------------------------
Repeat
If #FULLSCREEN = 0
Repeat
EventID = WindowEvent()
Select EventID
Case #PB_Event_CloseWindow : End
EndSelect
Until EventID = 0
EndIf
Angle + Pas
RotateEntity(0, Angle, Angle,Angle)
If PasLength > 0 : UpdateMesh() : EndIf
If ExamineKeyboard()
If KeyboardReleased(#PB_Key_F1)
CameraMode = 1 - CameraMode
CameraRenderMode(0, CameraMode)
EndIf
EndIf
RenderWorld()
FlipBuffers()
Until KeyboardPushed(#PB_Key_Escape)
; ----------------------------------------------------------------------------------------------------
; FUNCTIONS
; ----------------------------------------------------------------------------------------------------
Procedure CreateSphere(M,P)
; M = Meridian
; P = Parallele
; The radius is 1. Front to remove it later, it's just for the demo.
If M < 3 Or P < 2 : ProcedureReturn 0 : EndIf
Protected Normale.VECTOR, NbSommet, i, j, Theta.f, cTheta.f, sTheta.f
Protected Alpha.f, cAlpha.f, sAlpha.f, *PtrV.VERTEX, *PtrF.TRIANGLE, NbTriangle
NbSommet = 2 + ((M + 1) * P)
*VBuffer = AllocateMemory(#_SIZEVERT * Nbsommet)
For i = 0 To M
Theta = i * #PI * 2.0 / M
cTheta = Cos(theta)
sTheta = Sin(theta)
For j = 1 To P
Alpha = j * #PI / (P + 1)
cAlpha = Cos(Alpha)
sAlpha = Sin(Alpha)
*PtrV = *VBuffer + #_SIZEVERT * ((i * P) + (j - 1))
*PtrV\X = sAlpha * cTheta
*PtrV\Y = sAlpha * sTheta
*PtrV\Z = cAlpha
*PtrV\U = Theta / (2.0 * #PI)
*PtrV\V = Alpha / #PI
CALC_NORMALS
Next j
Next i
; Southpole
*PtrV = *VBuffer + #_SIZEVERT * ((M + 1) * P)
*PtrV\X = 0
*PtrV\Y = 0
*PtrV\Z = -1
*PtrV\U = 0
*PtrV\V = 0
CALC_NORMALS
; Northpole
*PtrV + #_SIZEVERT
*PtrV\X = 0
*PtrV\Y = 0
*PtrV\Z = 1
*PtrV\U = 0
*PtrV\V = 0
CALC_NORMALS
; Les facettes
NbTriangle = 4 * M * P
*IBuffer = AllocateMemory(#_SIZETRIS * NbTriangle)
*PtrF = *IBuffer
For i = 0 To M - 1
For j = 1 To P - 1
*PtrF\V1 = ((i + 1) * P) + j
*PtrF\V2 = ((i + 1) * P) + (j - 1)
*PtrF\V3 = (i * P) + (j - 1)
*PtrF + #_SIZETRIS
*PtrF\V3 = ((i + 1) * P) + j ;Recto
*PtrF\V2 = ((i + 1) * P) + (j - 1) ;Recto
*PtrF\V1 = (i * P) + (j - 1) ;Recto
*PtrF + #_SIZETRIS
*PtrF\V1 = i * P + j
*PtrF\V2 = ((i + 1) * P) + j
*PtrF\V3 = (i * P) + (j - 1)
*PtrF + #_SIZETRIS
*PtrF\V3 = i * P + j ;Recto
*PtrF\V2 = ((i + 1) * P) + j ;Recto
*PtrF\V1 = (i * P) + (j - 1) ;Recto
*PtrF + #_SIZETRIS
Next j
Next i
; The Poles
For i = 0 To M - 1
*PtrF\V3 = (M + 1) * P + 1
*PtrF\V2 = (i + 1) * P
*PtrF\V1 = i * P
*PtrF + #_SIZETRIS
*PtrF\V1 = (M + 1) * P + 1 ;Recto
*PtrF\V2 = (i + 1) * P ;Recto
*PtrF\V3 = i * P ;Recto
*PtrF + #_SIZETRIS
Next i
For i = 0 To M - 1
*PtrF\V3 = (M + 1) * P
*PtrF\V2 = i * P + (P - 1)
*PtrF\V1 = (i + 1) * P + (P - 1)
*PtrF + #_SIZETRIS
*PtrF\V1 = (M + 1) * P ;Recto
*PtrF\V2 = i * P + (P - 1) ;Recto
*PtrF\V3 = (i + 1) * P + (P - 1) ;Recto
*PtrF + #_SIZETRIS
Next i
If CreateMesh(0,100)
Protected Flag = #PB_Mesh_Vertex | #PB_Mesh_Normal | #PB_Mesh_UVCoordinate | #PB_Mesh_Color
SetMeshData(0,Flag,*VBuffer,NbSommet)
SetMeshData(0,#PB_Mesh_Face,*IBuffer,NbTriangle)
ProcedureReturn 1
EndIf
ProcedureReturn 0
EndProcedure
; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Procedure UpdateMesh()
Protected NbTriangle = 4 * Meridian * Parallele
Length + PasLength
If Length >= NbTriangle
PasLength = 0
Length = Nbtriangle
EndIf
SetMeshData(0,#PB_Mesh_Face,*IBuffer,Length)
EndProcedure
[[image:PB_Animated_sphere.png]]
===[[QBasic]]===
SCREEN 13 ' enter high-color graphic mode
' sets palette colors B/N
FOR i = 0 TO 255
PALETTE 255 - i, INT(i / 4) + INT(i / 4) * 256 + INT(i / 4) * 65536
NEXT i
PALETTE 0, 0
' draw the sphere
FOR i = 255 TO 0 STEP -1
x = 50 + i / 3
y = 99
CIRCLE (x, y), i / 3, i
PAINT (x, y), i
NEXT i
' wait until keypress
DO: LOOP WHILE INKEY$ = ""
END
=
Run BASIC
=
'Run BASIC White Sphere, Black background
'runbasic.com
graphic #win, 300, 300
#win size(1)
R=100
R2=R*R
X0=300/2
Y0=300/2
for Y = -150 to 150
for X = -150 to 150
D2 = X*X + Y*Y
C = 0
if D2 <= R2 then Z = sqr(R2-D2) : C = int(Z-(X+Y)/2+130)
#win color(C,C,C)
#win set(X+X0, Y+Y0)
next X
next Y
render #win
'This is a simple Circle
graphic #g, 300, 300 'create a graphic object
#g place(100,100) 'place the drawing pen at 100,100
#g circle(75) 'make a circle with radius 75
render #g 'show it
=
Sinclair ZX81 BASIC
= Works with 1k of RAM. A screenshot of the output is [http://www.edmundgriffiths.com/zx81sphere.jpg here].
10 LET I=21
20 LET J=2
30 FOR K=-PI TO PI STEP 0.07
40 PLOT 21+I*SIN K,22+21*COS K
50 PLOT 21+21*SIN K,22+(I-1)*COS K
60 NEXT K
70 LET I=I-J
80 LET J=J+1
90 IF I>0 THEN GOTO 30
Batch File
In my console the sphere looked more or less spheric, but this site has a larger interval between lines, so the result looks more like an egg. The code of this sample is not ported from the C sample. Integer square root by Aacini.
@echo off
setlocal enabledelayedexpansion
mode con cols=80
set /a r=220,cent=340,r2=r/2
set "spaces= "
set "block1=MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM"
set "block2=#########"
set "block3=XXXXXXXXX"
set "block4=ooooooooo"
set "block5=?????????"
set "block6=*********"
set "block7=~~~~~~~~~"
set "block8=---------"
set wy=0
set linea=
echo Batch-File ASCII Ball
echo.
for /L %%y in (-%r%,10,%r%) do (
set /a "w1=r*r-%%y*%%y"
call:sqrt2 w1 w1
set /a "w1=14*w1/10,wy=(cent-w1),cnt=0,sp=wy/10,centre=cent/10-sp"
call set "linea=%%spaces:~0,!sp!%%%%block1:~0,!centre!%%
set /a wy=0,sum=0
for %%i in (30 80 120 150 170 185 195 200) do (
set /a "cnt+=1,wy2=(%%i+r2)*w1/r,ww=(wy2+5)/10-sum,wy=wy2,sum+=ww"
call set miblock=%%block!cnt!%%
call set "Linea=%%linea%%%%miblock:~0,!ww!%%"
)
call echo(!linea!
)
echo.
exit /b
:sqrt2 [num] calculates integer square root . By AAcini
set "s=!%~1!"
set /A "x=s/(11*1024)+40,x=(s/x+x)>>1,x=(s/x+x)>>1,x=(s/x+x)>>1,x=(s/x+x)>>1,x=(s/x+x)>>1,x+=(s-x*x)>>31
set %~2=%x%
exit /b
{{Out}}
Batch-File ASCII Ball
MMMMMMMMMMMMMMMM##XXo?~
MMMMMMMMMMMMMMMMMMMMM###XXoo?*~
MMMMMMMMMMMMMMMMMMMMMMMMMM###XXXoo??*-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMM####XXXooo?**-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXooo??*~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXooo??*~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXooo???*~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXXooo??**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXXooo??**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXooo???*~~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXoooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXoooo??**~~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo??**~~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXoooo???**~~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXXoooo??**~~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXoooo???**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXoooo??**~~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXoooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#######XXXXXooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXooo???**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM######XXXXXooo???*~~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXXooo??**~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXXooo??**~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXooo???*~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXXooo??*~-
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#####XXXooo??*~
MMMMMMMMMMMMMMMMMMMMMMMMMMMMM####XXXooo?**-
MMMMMMMMMMMMMMMMMMMMMMMMMM###XXXoo??*-
MMMMMMMMMMMMMMMMMMMMM###XXoo?*~
MMMMMMMMMMMMMMMM##XXo?~
Befunge
{{trans|C}} While based on the C implementation, the algorithm has been considerably simplified to try and avoid floating point (which Befunge doesn't support) and minimise the need for sqrt calculations (which we approximate using the Babylonian method).
The first four values on the stack define the radius (45* = 20) and the light vector (6565"2" = 30;30;50). The ''k'' parameter has been hardcoded to 2, and the ambient light is approximated by adjusting the shade characters (defined on the last line).
Also note that the z-coordinate of the light vector is negated at runtime to more closely match the C defaults. This is preferable to making the initial constant negative since negative data values aren't supported across all Befunge implementations.
45*65*65*"2"30p20p10p::00p2*40p4*5vv<
>60p140g->:::*00g50g*60g40g-:*-\-v0>1
^_@#`\g0<|`\g04:+1, <*84$$_v#`\0:<>p^
>v>g2+:5^$>g:*++*/7g^>*:9$#<"~"/:"~"v
g:^06,+55<^03*<v09p07%"~"p09/"~"p08%<
^>#0 *#12#<0g:^>+::"~~"90g*80g+*70gv|
g-10g*+:9**00gv|!*`\2\`-20::/2-\/\+<>
%#&eo*!:..^g05<>$030g-*9/\20g*+60g40^
{{out}}
eeeeeeeeeee&&&&&#
eooo********oooooooeeee&&&&###%
oo****!!!!!!!!********ooooeeeee&&&###%%
o**!!!!!!!!!!!!!!!!!!!*****oooooeeee&&&####%%
o*!!!!:::::::::::::::!!!!!!*****ooooeeee&&&&####%%%
**!!:::::::....::::::::::!!!!!!****ooooeeeee&&&####%%%%
**!!::::.............::::::::!!!!!****ooooeeee&&&&####%%%%%
o*!!::::.................::::::!!!!!!****ooooeeee&&&&####%%%%%%
*!!::::....................::::::!!!!!****ooooeeeee&&&&####%%%%%%
e*!!:::......................::::::!!!!!*****ooooeeee&&&&####%%%%%%%%
o*!!:::.......................::::::!!!!!*****ooooeeee&&&&#####%%%%%%%%
o*!!::::.......................::::::!!!!!****oooooeeee&&&&#####%%%%%%%%%
e**!!:::.......................::::::!!!!!*****ooooeeeee&&&&#####%%%%%%%%%%
o*!!!:::......................:::::::!!!!!*****ooooeeeee&&&&#####%%%%%%%%%%
o**!!!::::...................::::::::!!!!!*****oooooeeee&&&&&#####%%%%%%%%%%%
o**!!!:::::................::::::::!!!!!!*****oooooeeeee&&&&#####%%%%%%%%%%%%
eo**!!!:::::::............:::::::::!!!!!!*****oooooeeeee&&&&&#####%%%%%%%%%%%%%
eo***!!!:::::::::::::::::::::::::!!!!!!******oooooeeeee&&&&&#####%%%%%%%%%%%%%%
eoo**!!!!!::::::::::::::::::::!!!!!!!!******oooooeeeee&&&&&######%%%%%%%%%%%%%%
eoo***!!!!!!:::::::::::::::!!!!!!!!!******ooooooeeeee&&&&&######%%%%%%%%%%%%%%%
eeoo****!!!!!!!!!!!!!!!!!!!!!!!!!*******ooooooeeeeee&&&&&######%%%%%%%%%%%%%%%%
&eooo*****!!!!!!!!!!!!!!!!!!!!********ooooooeeeeee&&&&&&######%%%%%%%%%%%%%%%%%
&eeoooo*******!!!!!!!!!!***********oooooooeeeeeee&&&&&&######%%%%%%%%%%%%%%%%%#
&&eeeoooo***********************ooooooooeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%#
&&eeeooooooo**************ooooooooooeeeeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%#
#&&eeeeeoooooooooooooooooooooooooeeeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%##
#&&&eeeeeeeooooooooooooooooeeeeeeeeee&&&&&&&&########%%%%%%%%%%%%%%%%%%%%##
%##&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&########%%%%%%%%%%%%%%%%%%%%%##&
%###&&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%##&
%####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%##&
%%######&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%##e
%%%################################%%%%%%%%%%%%%%%%%%%%%%%%%%%##&
%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%###########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##&&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###&
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%####&
%%%%%%%%%%%%%%%%%%%%%%%%%%####&
%%%%%%%%%%%%#####
Brlcad
opendb balls.g y # Create a database to hold our shapes
units cm # Set the unit of measure
in ball.s sph 0 0 0 3 # Create a sphere of radius 3 cm named ball.s with its centre at 0,0,0
C
The lighting calculation is somewhere between crude and bogus, but hey, I'm shading it with ASCII characters, don't expect too much.
#include <stdio.h> #include <stdlib.h> #include <string.h> #include <ctype.h> #include <math.h> const char *shades = ".:!*oe&#%@"; double light[3] = { 30, 30, -50 }; void normalize(double * v) { double len = sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= len; v[1] /= len; v[2] /= len; } double dot(double *x, double *y) { double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2]; return d < 0 ? -d : 0; } void draw_sphere(double R, double k, double ambient) { int i, j, intensity; double b; double vec[3], x, y; for (i = floor(-R); i <= ceil(R); i++) { x = i + .5; for (j = floor(-2 * R); j <= ceil(2 * R); j++) { y = j / 2. + .5; if (x * x + y * y <= R * R) { vec[0] = x; vec[1] = y; vec[2] = sqrt(R * R - x * x - y * y); normalize(vec); b = pow(dot(light, vec), k) + ambient; intensity = (1 - b) * (sizeof(shades) - 1); if (intensity < 0) intensity = 0; if (intensity >= sizeof(shades) - 1) intensity = sizeof(shades) - 2; putchar(shades[intensity]); } else putchar(' '); } putchar('\n'); } } int main() { normalize(light); draw_sphere(20, 4, .1); draw_sphere(10, 2, .4); return 0; }
{{out}}
#############%%%%
##&&eeeeeeeeee&&&&&&&####%%%%%%%%
&&eeooooooooooooooeeeee&&&&######%%%%%%%%
eeoo**************oooooooeeee&&&&####%%%%%%%%
&&oo**!!!!!!::!!!!!!!!****oooooee&&&&######%%%%%%%%%%
eeoo!!!!::::::::::::::!!!!*****ooeeee&&&&####%%%%%%%%%%%%
ee**!!::::............::::!!!!***ooooeeee&&######%%%%%%%%%%%%
&&oo!!::..................::!!!!*****ooeeee&&&&####%%%%%%%%%%%%%%
oo!!::....................::::!!*****ooeeee&&&&####%%%%%%%%%%%%%%
ee**!!::....................::::!!*****ooeeee&&&&####%%%%%%%%%%%%%%%%
&&oo!!::......................::::!!*****ooeeee&&&&######%%%%%%%%%%%%%%%%
ee**!!::......................::::!!*****ooeeee&&&&######%%%%%%%%%%%%%%%%
##oo**!!::......................::!!!!*****ooeeee&&&&####%%%%%%%%%%%%%%%%%%%%
&&oo**::::....................::::!!!!***ooooeeee&&&&####%%%%%%%%%%%%%%%%%%%%
eeoo**!!::..................::::!!!!*****ooooee&&&&######%%%%%%%%%%%%%%%%%%%%
eeoo**!!::................::::!!!!****oooooeeee&&&&######%%%%%%%%%%%%%%%%%%%%
#eeoo**!!::::............::::!!!!!!****oooeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%
#eeoo**!!!!::::::::::::::::!!!!!!****oooooeeee&&&&######%%%%%%%%%%%%%%%%%%%%%%%%
#eeoooo**!!!!!!::::::::!!!!!!******ooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%
#&&eeoo****!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%%%
#&&eeoooo********************ooooooeeee&&&&&&&######%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#&&&&eeoooooo************ooooooeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%##&&eeeeeeooooooooooooooooooeeeeee&&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&eeeeeeeeeeeeeeeeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%##&&&&&&eeeeeeeeeeeeeeee&&&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%######&&&&&&&&&&&&&&&&&&&&&&&&###########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%########&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%####%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::..:::::!!**
.............::!!**oo
...................::!!**ooee
.......................::!!ooeeee
.......................::!!**ooee
.........................::!!**ooeeee
.........................::!!**ooeeee
:.........................::!!**ooeeeeee
........................::!!**ooooeeeeee
:.......................::!!**ooeeeeeeee
:.....................::!!****ooeeeeeeee
!::................:::!!****ooeeeeeeeeee
*!!::..........::::!!!****ooooeeeeeeeeee
**!!::::::::::!!!!*****ooooeeeeeeeeee
oo**!!!!!!!!!!*******ooooeeeeeeeeeeee
oooo********oooooooeeeeeeeeeeeeee
eeeeooooooooooeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Fun with 3D noise texture
[[file:sphere-perlin.png]]
#include <stdio.h> #include <stdlib.h> #include <math.h> #define MAXD 8 int g[] = { -1, 1, -1, 1 }; /* Perlin-like noise */ inline void hashed(int *data, int *out, int len) { # define ror(a, d) ((a << (d)) | (a >> (32 - d))) register unsigned int h = 0x12345678, tmp; unsigned int *d = (void*)data; int i = len; while (i--) { tmp = *d++; h += ror(h, 15) ^ ror(tmp, 5); } h ^= ror(h, 7); h += ror(h, 23); h ^= ror(h, 19); h += ror(h, 11); h ^= ror(h, 13); h += ror(h, 17); # undef ror for (i = len; i--; ) { out[i] = g[h & 3]; h >>= 2; } } double scale[MAXD], scale_u[MAXD]; void noise_init() { int i; for (i = 1; i < MAXD; i++) { scale[i] = 1 / (1 + sqrt(i + 1)); scale_u[i] = scale[i] / sqrt(i + 1); } } double noise(double *x, int d) { # define sum(s, x) for (s = 0, j = 0; j < d; j++) s += x register int i, j; int n[MAXD], o[MAXD], g[MAXD], tmp; double s, r, t, w, ret, u[MAXD]; sum(s, x[j]); s *= scale[d]; for (i = 0; i < d; i++) { o[i] = i; t = x[i] + s; u[i] = t - (n[i] = floor(t)); } o[d] = 0; for (i = 0; i < d - 1; i++) for (j = i; j < d; j++) if (u[o[i]] < u[o[j]]) tmp = o[i], o[i] = o[j], o[j] = tmp; ret = w = 0, r = 1; for (s = 0, j = 0; j < d; j++) s += n[j]; s *= scale_u[d]; for (i = 0; i <= d; i++) { for (j = 0; j < d; j++) u[j] = x[j] + s - n[j]; for (t = (d + 1.) / (2 * d), j = 0; j < d; j++) { t -= u[j] * u[j]; if (t <= 0) break; } if (t >= 0) { r = 0; hashed(n, g, d); for (j = 0; j < d; j++) if (g[j]) r += (g[j] == 1 ? u[j] : -u[j]); t *= t; ret += r * t * t; } if (i < d) { n[o[i]]++; s += scale_u[d]; } } return ret * (d * d); } double get_noise2(double x, double y) { int i, ws; double r = 0, v[2]; for (i = 1, ws = 0; i <= 128; i <<= 1) { v[0] = x * i, v[1] = y * i; r += noise(v, 2); ws ++; } r /= ws; return r; } double get_noise3(double x, double y, double z) { int i, ws; double r = 0, v[3], w; for (i = 1, ws = 0; i <= 32; i <<= 1) { v[0] = x * i, v[1] = y * i, v[2] = z * i; w = 1./sqrt(i); r += noise(v, 3) * w; ws += w; } return r / ws; } int main(int c, char** v) { unsigned char pix[256 * 256], *p; int i, j; double x, y, z, w; FILE *fp; noise_init(); for (p = pix, i = 0; i < 256 * 256; i++) *p++ = 0; for (p = pix, i = 0; i < 256; i++) { y = (i - 128) / 125.; for (j = 0; j < 256; j++, p++) { x = (j - 128) / 125.; *p = (get_noise2(i/256., j/256.) + 1) / 6 * i; z = 1- x*x - y*y; if (z < 0) continue; z = sqrt(z); w = get_noise3(x, y, z); w = (w + 1) / 2; w *= (1 + x - y + z) / 3.5; if (w < 0) w = 0; *p = w * 255; } } fp = fopen("out.pgm", "w+"); fprintf(fp, "P5\n256 256\n255\n"); fwrite(pix, 1, 256 * 256, fp); fclose(fp); return 0; }
C#
{{trans|C}}
using System; namespace Sphere { internal class Program { private const string Shades = ".:!*oe%&#@"; private static readonly double[] Light = {30, 30, -50}; private static void Normalize(double[] v) { double len = Math.Sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= len; v[1] /= len; v[2] /= len; } private static double Dot(double[] x, double[] y) { double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2]; return d < 0 ? -d : 0; } public static void DrawSphere(double r, double k, double ambient) { var vec = new double[3]; for(var i = (int)Math.Floor(-r); i <= (int)Math.Ceiling(r); i++) { double x = i + .5; for(var j = (int)Math.Floor(-2*r); j <= (int)Math.Ceiling(2*r); j++) { double y = j/2.0 + .5; if(x*x + y*y <= r*r) { vec[0] = x; vec[1] = y; vec[2] = Math.Sqrt(r*r - x*x - y*y); Normalize(vec); double b = Math.Pow(Dot(Light, vec), k) + ambient; int intensity = (b <= 0) ? Shades.Length - 2 : (int)Math.Max((1 - b)*(Shades.Length - 1), 0); Console.Write(Shades[intensity]); } else Console.Write(' '); } Console.WriteLine(); } } private static void Main() { Normalize(Light); DrawSphere(6, 4, .1); DrawSphere(10, 2, .4); Console.ReadKey(); } } }
Clojure
{{libheader|quil}}
(use 'quil.core) (def w 500) (def h 400) (defn setup [] (background 0)) (defn draw [] (push-matrix) (translate 250 200 0) (sphere 100) (pop-matrix)) (defsketch main :title "sphere" :setup setup :size [w h] :draw draw :renderer :opengl)
{{out}} [http://i.imgur.com/fkzH5wM.png]
D
{{trans|C}}
import std.stdio, std.math, std.algorithm, std.numeric; alias V3 = double[3]; immutable light = normalize([30.0, 30.0, -50.0]); V3 normalize(V3 v) pure @nogc { v[] /= dotProduct(v, v) ^^ 0.5; return v; } double dot(in ref V3 x, in ref V3 y) pure nothrow @nogc { immutable double d = dotProduct(x, y); return d < 0 ? -d : 0; } void drawSphere(in double R, in double k, in double ambient) @nogc { enum shades = ".:!*oe&#%@"; foreach (immutable i; cast(int)floor(-R) .. cast(int)ceil(R) + 1) { immutable double x = i + 0.5; foreach (immutable j; cast(int)floor(-2 * R) .. cast(int)ceil(2 * R) + 1) { immutable double y = j / 2. + 0.5; if (x ^^ 2 + y ^^ 2 <= R ^^ 2) { immutable vec = [x, y, (R^^2 - x^^2 - y^^2) ^^ 0.5] .normalize; immutable double b = dot(light, vec) ^^ k + ambient; int intensity = cast(int)((1 - b) * (shades.length-1)); intensity = min(shades.length - 1, max(intensity, 0)); shades[intensity].putchar; } else ' '.putchar; } '\n'.putchar; } } void main() { drawSphere(20, 4, 0.1); drawSphere(10, 2, 0.4); }
Delphi
{{trans|C}} '''Under Microsoft Windows:''' If you notice the big sphere loses its roundness, then try increasing the width of the Windows console. By default it’s 80; so put it to something bigger, let’s say 90.
'''Steps:''' Run the CMD Windows shell. Then follow this path to setup the new width: '''Main Menu-> Properties -> Layout -> Window Size -> Width'''.
program DrawASphere;
{$APPTYPE CONSOLE}
uses
SysUtils,
Math;
type
TDouble3 = array[0..2] of Double;
TChar10 = array[0..9] of Char;
var
shades: TChar10 = ('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@');
light: TDouble3 = (30, 30, -50 );
procedure normalize(var v: TDouble3);
var
len: Double;
begin
len:= sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] := v[0] / len;
v[1] := v[1] / len;
v[2] := v[2] / len;
end;
function dot(x, y: TDouble3): Double;
begin
Result:= x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
Result:= IfThen(Result < 0, -Result, 0 );
end;
procedure drawSphere(R, k, ambient: Double);
var
vec: TDouble3;
x, y, b: Double;
i, j,
intensity: Integer;
begin
for i:= Floor(-R) to Ceil(R) do
begin
x := i + 0.5;
for j:= Floor(-2*R) to Ceil(2 * R) do
begin
y:= j / 2 + 0.5;
if(x * x + y * y <= R * R) then
begin
vec[0]:= x;
vec[1]:= y;
vec[2]:= sqrt(R * R - x * x - y * y);
normalize(vec);
b:= Power(dot(light, vec), k) + ambient;
intensity:= IfThen(b <= 0,
Length(shades) - 2,
Trunc(max( (1 - b) * (Length(shades) - 1), 0 )));
Write(shades[intensity]);
end
else
Write(' ');
end;
Writeln;
end;
end;
begin
normalize(light);
drawSphere(19, 4, 0.1);
drawSphere(10, 2, 0.4);
Readln;
end.
{{out}}
&&&&&&&&&&#######
&eeeeeooeeeeeeee&&&&&&#######
eeooo*********oooooeeeee&&&&&#######%
eo***!!!!!!!!!!!*****ooooeeee&&&&&#######%%
eo**!!!::::::::::!!!!!****ooooeeee&&&&########%%%
eo*!!::::........:::::!!!!****oooeeee&&&&########%%%%
eo*!!::..............:::::!!!***ooooeeee&&&&#########%%%%
eo*!!::..................:::!!!!***oooeeee&&&&&########%%%%%%
eo*!::....................::::!!!***ooooeeee&&&&#########%%%%%%
o**!::.....................::::!!!***ooooeeee&&&&#########%%%%%%%
eo*!::......................::::!!!***ooooeeee&&&&##########%%%%%%%
eo*!!::......................:::!!!!***ooooeee&&&&&##########%%%%%%%%
eo**!!::.....................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo**!!::...................::::!!!!****oooeeeee&&&&&##########%%%%%%%%%%
eeo**!!:::................:::::!!!!****ooooeeee&&&&&##########%%%%%%%%%%%
&eoo**!!!::::............:::::!!!!****oooooeeee&&&&&###########%%%%%%%%%%%%
&eeo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&&##########%%%%%%%%%%%%%
&eeoo***!!!!::::::::::::!!!!!!*****oooooeeeee&&&&&&###########%%%%%%%%%%%%%
&&eeoo****!!!!!!!!!!!!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeeooo*****!!!!!!!!!!*******ooooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
#&&eeeoooo*****************oooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&&eeeeoooooooooooooooooooooooeeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
##&&&&eeeeeoooooooooooooooeeeeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%
###&&&&eeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
####&&&&&&&eeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%
########&&&&&&&&&&&&&&&&&&&####################%%%%%%%%%%%%%%%%%%%%%%
############################################%%%%%%%%%%%%%%%%%%%%%%%
%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%
%%##################################%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%###########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%#################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
DWScript
[[image:DWScript-sphere.pbm.png|thumb|right|PBM output magnified 5 times]] {{trans|C}} but adapted to spit out a [[wp:Netpbm_format|PGM]] image
type
TFloat3 = array[0..2] of Float;
var
light : TFloat3 = [ 30, 30, -50 ];
procedure normalize(var v : TFloat3);
var
len: Float;
begin
len := sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
v[0] /= len;
v[1] /= len;
v[2] /= len;
end;
function dot(x, y : TFloat3) : Float;
begin
Result := x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
if Result<0 then
Result:=-Result
else Result:=0;
end;
procedure drawSphere(R, k, ambient : Float);
var
vec : TFloat3;
x, y, b : Float;
i, j, size, intensity : Integer;
begin
size:=Trunc(Ceil(R)-Floor(-R)+1);
PrintLn('P2');
PrintLn(IntToStr(size)+' '+IntToStr(size));
PrintLn('255');
for i := Floor(-R) to Ceil(R) do begin
x := i + 0.5;
for j := Floor(-R) to Ceil(R) do begin
y := j + 0.5;
if (x * x + y * y <= R * R) then begin
vec[0] := x;
vec[1] := y;
vec[2] := sqrt(R * R - x * x - y * y);
normalize(vec);
b := Power(dot(light, vec), k) + ambient;
intensity := ClampInt( Round(b*255), 0, 255);
Print(intensity);
Print(' ')
end else Print('0 ');
end;
PrintLn('');
end;
end;
normalize(light);
drawSphere(19, 4, 0.1);
ERRE
Using ASCII art: output is written to 'SPHERE.PRN' sequential file.
PROGRAM SPHERE
CONST SHADES$=".:!*oe&#%@"
DIM LIGHT[2],X[2],Y[2],V[2],VEC[2]
PROCEDURE DOT(X[],Y[]->D)
D=X[0]*Y[0]+X[1]*Y[1]+X[2]*Y[2]
IF D<0 THEN D=-D ELSE D=0 END IF
END PROCEDURE
PROCEDURE NORMALIZE(V[]->V[])
LUNG=SQR(V[0]*V[0]+V[1]*V[1]+V[2]*V[2])
V[0]=V[0]/LUNG
V[1]=V[1]/LUNG
V[2]=V[2]/LUNG
END PROCEDURE
PROCEDURE PDRAW(R,K,AMBIENT)
FOR I=INT(-R) TO INT(R) DO
X=I+0.5
FOR J=INT(-2*R) TO INT(2*R) DO
Y=J/2+0.5
IF (X*X+Y*Y<=R*R) THEN
VEC[0]=X
VEC[1]=Y
VEC[2]=SQR(R*R-X*X-Y*Y)
NORMALIZE(VEC[]->VEC[])
DOT(LIGHT[],VEC[]->D)
B=D^K+AMBIENT
INTENSITY%=(1-B)*(LEN(SHADES$)-1)
IF (INTENSITY%<0) THEN INTENSITY%=0 END IF
IF (INTENSITY%>=LEN(SHADES$)-1) THEN
INTENSITY%=LEN(SHADES$)-2
END IF
PRINT(#1,MID$(SHADES$,INTENSITY%+1,1);)
ELSE
PRINT(#1,(" ");)
END IF
END FOR
PRINT(#1,)
END FOR
END PROCEDURE
BEGIN
LIGHT[]=(30,30,-50)
OPEN("O",1,"SPHERE.PRN")
NORMALIZE(LIGHT[]->LIGHT[])
PDRAW(10,2,0.4)
PRINT(#1,STRING$(79,"="))
PDRAW(20,4,0.1)
CLOSE(1)
END PROGRAM
{{out}}
!::::::!!!**o
............:::!!**oe
:................::!!**ooee
:...................::!!**ooeee
......................::!!**ooeee
.......................::!!**ooeeee
.......................:::!!**ooeeeee
:.......................::!!***ooeeeeee
:......................::!!!**oooeeeeee
:....................:::!!!**oooeeeeeee
!:..................:::!!***oooeeeeeeee
!!:..............::::!!!***oooeeeeeeeee
*!!::::.....::::::!!!!***ooooeeeeeeeeee
o*!!!!::::::!!!!!!****ooooeeeeeeeeeee
o****!!!!!!!******oooooeeeeeeeeeeee
eooo********oooooooeeeeeeeeeeeeee
eeeoooooooooooeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
### =========================================================================
##############%%%
#&&eeeeeeeeeee&&&&&&######%%%%%
&eeeoooooooooooooeeeee&&&&&######%%%%%%
&eooo**************oooooeeee&&&&&#####%%%%%%%
&eoo**!!!!!!!!!!!!!!*****ooooeeee&&&&######%%%%%%%%
eoo**!!!::::::::::::!!!!****ooooeeee&&&&######%%%%%%%%%
eoo*!!!::::.......::::::!!!!****oooeeee&&&&######%%%%%%%%%%
&eo*!!:::..............::::!!!!***ooooeeee&&&&######%%%%%%%%%%%
eo**!!::.................::::!!!****oooeeee&&&&######%%%%%%%%%%%%
&eo*!!:::..................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%
&eo*!!:::...................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%%
&eo**!!::....................::::!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%
#eoo*!!:::...................::::!!!!***ooooeeee&&&&#######%%%%%%%%%%%%%%%%
&eo**!!:::.................:::::!!!!****oooeeee&&&&&#######%%%%%%%%%%%%%%%%
&eoo**!!::::...............:::::!!!!****ooooeeee&&&&#######%%%%%%%%%%%%%%%%%%
&eoo**!!!::::...........::::::!!!!*****ooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%
#&eoo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%
#&eeoo***!!!!::::::::::::!!!!!!!*****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%%
#&eeooo****!!!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%
#&&eeooo******!!!!!!!!!!!*******ooooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%
#&&&eeooooo******************ooooooeeeeee&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%
##&&&eeeooooooo********oooooooooeeeeeee&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%
###&&&eeeeeooooooooooooooooooeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%
%###&&&&eeeeeeeeeeeoeeeeeeeeeeeee&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#####&&&&&&&&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######&&&&&&&&&&&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%############&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%#######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
FutureBasic
include "Tlbx agl.incl"
include "Tlbx glut.incl"
output file "Rotating Sphere"
local fn SphereDraw
'~'1
begin globals
dim as double sRotation // 'static' var
end globals
// Speed of rotation
sRotation += 2.9
glMatrixMode( _GLMODELVIEW )
glLoadIdentity()
// Position parameters: x axis, y axis, z axis
// Set to center of screen:
glTranslated( 0.0, 0.0, 0.0 )
// Rotation (wobble) parameters: angle, x, y
glRotated( sRotation, -0.45, -0.8, -0.6 )
// Set color of sphere's wireframe
glColor3d( 1.0, 0.0, 0.3 )
// Set width of sphere's wireframe lines
glLineWidth( 1.5 )
// Apply above to GLUT's built-in sphere wireframe
// Size & frame parameters: radius, slices, stack
fn glutWireSphere( 0.8, 25, 25 )
end fn
// main program
dim as GLint attrib(2)
dim as CGrafPtr port
dim as AGLPixelFormat fmt
dim as AGLContext glContext
dim as EventRecord ev
dim as GLboolean yesOK
// Make a window
window 1, @"Rotating Sphere", (0,0) - (500,500)
// Minimal setup of OpenGL
attrib(0) = _AGLRGBA
attrib(1) = _AGLDOUBLEBUFFER
attrib(2) = _AGLNONE
fmt = fn aglChoosePixelFormat( 0, 0, attrib(0) )
glContext = fn aglCreateContext( fmt, 0 )
aglDestroyPixelFormat( fmt )
// Set the FB window as port for drawing
port = window( _wndPort )
yesOK = fn aglSetDrawable( glContext, port )
yesOK = fn aglSetCurrentContext( glContext )
// Background color: red, green, blue, alpha
glClearColor( 0.0, 0.0, 0.0, 0.0 )
// 60/s HandleEvents Trigger
poke long event - 8, 1
do
// Clear window
glClear( _GLCOLORBUFFERBIT )
// Run animation
fn SphereDraw
aglSwapBuffers( glContext )
HandleEvents
until gFBquit
Go
[[file:GoSphere.png|right|thumb|Output png]] {{trans|C}} Using image library rather than ASCII art.
package main import ( "fmt" "image" "image/color" "image/png" "math" "os" ) type vector [3]float64 func normalize(v *vector) { invLen := 1 / math.Sqrt(dot(v, v)) v[0] *= invLen v[1] *= invLen v[2] *= invLen } func dot(x, y *vector) float64 { return x[0]*y[0] + x[1]*y[1] + x[2]*y[2] } func drawSphere(r int, k, amb float64, dir *vector) *image.Gray { w, h := r*4, r*3 img := image.NewGray(image.Rect(-w/2, -h/2, w/2, h/2)) vec := new(vector) for x := -r; x < r; x++ { for y := -r; y < r; y++ { if z := r*r - x*x - y*y; z >= 0 { vec[0] = float64(x) vec[1] = float64(y) vec[2] = math.Sqrt(float64(z)) normalize(vec) s := dot(dir, vec) if s < 0 { s = 0 } lum := 255 * (math.Pow(s, k) + amb) / (1 + amb) if lum < 0 { lum = 0 } else if lum > 255 { lum = 255 } img.SetGray(x, y, color.Gray{uint8(lum)}) } } } return img } func main() { dir := &vector{-30, -30, 50} normalize(dir) img := drawSphere(200, 1.5, .2, dir) f, err := os.Create("sphere.png") if err != nil { fmt.Println(err) return } if err = png.Encode(f, img); err != nil { fmt.Println(err) } if err = f.Close(); err != nil { fmt.Println(err) } }
HTML
See [[Draw_a_sphere#Javascript]]
Haskell
[[File:Sphere_Haskell.png|thumb|right]]
import Graphics.Rendering.OpenGL.GL import Graphics.UI.GLUT.Objects import Graphics.UI.GLUT setProjection :: IO () setProjection = do matrixMode $= Projection ortho (-1) 1 (-1) 1 0 (-1) grey1,grey9,red,white :: Color4 GLfloat grey1 = Color4 0.1 0.1 0.1 1 grey9 = Color4 0.9 0.9 0.9 1 red = Color4 1 0 0 1 white = Color4 1 1 1 1 setLights :: IO () setLights = do let l = Light 0 ambient l $= grey1 diffuse l $= white specular l $= white position l $= Vertex4 (-4) 4 3 (0 :: GLfloat) light l $= Enabled lighting $= Enabled setMaterial :: IO () setMaterial = do materialAmbient Front $= grey1 materialDiffuse Front $= red materialSpecular Front $= grey9 materialShininess Front $= (32 :: GLfloat) display :: IO() display = do clear [ColorBuffer] renderObject Solid $ Sphere' 0.8 64 64 swapBuffers main :: IO() main = do _ <- getArgsAndInitialize _ <- createWindow "Sphere" clearColor $= Color4 0.0 0.0 0.0 0.0 setProjection setLights setMaterial displayCallback $= display mainLoop
==Icon and {{header|Unicon}}== Unicon provides a built-in interface to openGL including some higher level abstractions (for more information see [[Icon%2BUnicon/Intro#Graphics.2C_Network_Messaging.2C_etc.|Unicon Technical References, 3D Graphics]]). The example below draws a blue sphere on a black background and waits for input to quit.[[File:Sphere_unicon.PNG|thumb|Unicon Sphere]]
procedure main()
W := open("Demo", "gl", "size=400,400", "bg=black") | stop("can't open window!")
WAttrib(W, "slices=40", "rings=40", "light0=on, ambient white; diffuse gold; specular gold; position 5, 0, 0" )
Fg(W, "emission blue")
DrawSphere(W, 0, 0, -5, 1)
Event(W)
end
J
[[File:J-sphere.png|thumb|J Sphere]]
The simplest way to draw a sphere is to run the sphere demo code from J's simple demos. (This assumes J version 6.)
Normally you would bring up this demo by using the menu system:
Studio
Demos... opengl simple... [ok] > sphere [Run]
But bringing up the example with a line of code is trivial enough:
load 'system/examples/graphics/opengl/simple/sphere.ijs'
Raytracing Solution
Here's a version using raytracing computed in J. luminosity is an array of luminosity values with theoretical maximum 1 and minimum 0, and viewmat is used to display this.
'R k ambient' =. 10 2 0.4
light =. (% +/&.:*:) 30 30 _50
pts =. (0&*^:(0={:))@:(,,(0>.(*:R)-+)&.*:)"0/~ i:15j200
luminosity =. (>:ambient) %~ (ambient * * +/&.:*:"1 pts) + k^~ 0>. R%~ pts +/@:*"1 -light
load 'viewmat'
torgb =. 256 #. [: <. 255 255 255 *"1 0 ]
'rgb' viewmat torgb luminosity
Java
{{trans|C}}
public class Sphere{ static char[] shades = {'.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'}; static double[] light = { 30, 30, -50 }; private static void normalize(double[] v){ double len = Math.sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] /= len; v[1] /= len; v[2] /= len; } private static double dot(double[] x, double[] y){ double d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2]; return d < 0 ? -d : 0; } public static void drawSphere(double R, double k, double ambient){ double[] vec = new double[3]; for(int i = (int)Math.floor(-R); i <= (int)Math.ceil(R); i++){ double x = i + .5; for(int j = (int)Math.floor(-2 * R); j <= (int)Math.ceil(2 * R); j++){ double y = j / 2. + .5; if(x * x + y * y <= R * R) { vec[0] = x; vec[1] = y; vec[2] = Math.sqrt(R * R - x * x - y * y); normalize(vec); double b = Math.pow(dot(light, vec), k) + ambient; int intensity = (b <= 0) ? shades.length - 2 : (int)Math.max((1 - b) * (shades.length - 1), 0); System.out.print(shades[intensity]); } else System.out.print(' '); } System.out.println(); } } public static void main(String[] args){ normalize(light); drawSphere(20, 4, .1); drawSphere(10, 2, .4); } }
{{out}}
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
JavaScript
{{trans|C}}
This Javascript entry uses an HTML wrapper to offer easy running and some interactivity. It is made as such, though, that the entire HTML wrapper can be removed (except for a canvas with id c) and still work. If you remove the HTML, call the draw_sphere function to draw the thing.
<!DOCTYPE html> <html> <head> <meta charset="utf-8"> <title>Draw a sphere</title> <script> var light=[30,30,-50],gR,gk,gambient; function normalize(v){ var len=Math.sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]); v[0]/=len; v[1]/=len; v[2]/=len; return v; } function dot(x,y){ var d=x[0]*y[0]+x[1]*y[1]+x[2]*y[2]; return d<0?-d:0; } function draw_sphere(R,k,ambient){ var i,j,intensity,b,vec,x,y,cvs,ctx,imgdata,idx; cvs=document.getElementById("c"); ctx=cvs.getContext("2d"); cvs.width=cvs.height=2*Math.ceil(R)+1; imgdata=ctx.createImageData(2*Math.ceil(R)+1,2*Math.ceil(R)+1); idx=0; for(i=Math.floor(-R);i<=Math.ceil(R);i++){ x=i+.5; for(j=Math.floor(-R);j<=Math.ceil(R);j++){ y=j+.5; if(x*x+y*y<=R*R){ vec=[x,y,Math.sqrt(R*R-x*x-y*y)]; vec=normalize(vec); b=Math.pow(dot(light,vec),k)+ambient; intensity=(1-b)*256; if(intensity<0)intensity=0; if(intensity>=256)intensity=255; imgdata.data[idx++]=imgdata.data[idx++]=255-~~(intensity); //RG imgdata.data[idx++]=imgdata.data[idx++]=255; //BA } else { imgdata.data[idx++]=imgdata.data[idx++]=imgdata.data[idx++]=imgdata.data[idx++]=255; //RGBA } } } ctx.putImageData(imgdata,0,0); } light=normalize(light); </script> </head> <body onload="gR=200;gk=4;gambient=.2;draw_sphere(gR,gk,gambient)"> R=<input type="range" id="R" name="R" min="5" max="500" value="200" step="5" onchange="document.getElementById('lR').innerHTML=gR=parseFloat(this.value);draw_sphere(gR,gk,gambient)"> <label for="R" id="lR">200</label> k=<input type="range" id="k" name="k" min="0" max="10" value="4" step=".25" onchange="document.getElementById('lk').innerHTML=gk=parseFloat(this.value);draw_sphere(gR,gk,gambient)"> <label for="k" id="lk">4</label> ambient=<input type="range" id="ambient" name="ambient" min="0" max="1" value=".2" step=".05" onchange="document.getElementById('lambient').innerHTML=gambient=parseFloat(this.value);draw_sphere(gR,gk,gambient)"> <label for="ambient" id="lambient">0.2</label> <canvas id="c">Unsupportive browser...</canvas> </body> </html>
jq
{{works with|jq|1.4}} The approach adopted here is to generate an SVG file, which may then be viewed, for example, in a web browser.
def svg:
"<svg width='100%' height='100%' version='1.1'
xmlns='http://www.w3.org/2000/svg'
xmlns:xlink='http://www.w3.org/1999/xlink'>" ;
# A radial gradient to make a circle look like a sphere.
# "colors" should be [startColor, intermediateColor, endColor]
# or null for ["white", "teal", "black"]
def sphericalGradient(id; colors):
"<defs>
<radialGradient id = '\(id)' cx = '30%' cy = '30%' r = '100%' fx='10%' fy='10%' >
<stop stop-color = '\(colors[0]//"white")' offset = '0%'/>
<stop stop-color = '\(colors[1]//"teal")' offset = '50%'/>
<stop stop-color = '\(colors[1]//"black")' offset = '100%'/>
</radialGradient>
</defs>" ;
def sphere(cx; cy; r; gradientId):
"<circle fill='url(#\(gradientId))' cx='\(cx)' cy='\(cy)' r='\(r)' />" ;
'''Example:'''
def draw_sphere:
svg,
"<title>Teal sphere</title>",
sphericalGradient("tealGradient"; null), # define the gradient to use
sphere(100;100;100; "tealGradient"), # draw a sphere using the gradient
sphere(100;300;100; "tealGradient"), # draw another sphere using the same gradient
"</svg>" ;
draw_sphere
{{out}}
$ jq -r -n -f spheres.jq > spheres.svg
One way to view the output as an image is to point your browser to the generated SVG.
Julia
{{trans|C}}
# v0.6 function draw_sphere(r, k, ambient, light) shades = ('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@') for i in floor(Int, -r):ceil(Int, r) x = i + 0.5 line = IOBuffer() for j in floor(Int, -2r):ceil(2r) y = j / 2 + 0.5 if x ^ 2 + y ^ 2 ≤ r ^ 2 v = normalize([x, y, sqrt(r ^ 2 - x ^ 2 - y ^ 2)]) b = dot(light, v) ^ k + ambient intensity = ceil(Int, (1 - b) * (length(shades) - 1)) if intensity < 1 intensity = 1 end if intensity > length(shades) intensity = length(shades) end print(shades[intensity]) else print(' ') end end println() end end light = normalize([30, 30, -50]) draw_sphere(20, 4, 0.1, light) draw_sphere(10, 2, 0.4, light)
Kotlin
{{trans|C}}
// version 1.0.6 const val shades = ".:!*oe&#%@" val light = doubleArrayOf(30.0, 30.0, -50.0) fun normalize(v: DoubleArray) { val len = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]) v[0] /= len; v[1] /= len; v[2] /= len } fun dot(x: DoubleArray, y: DoubleArray): Double { val d = x[0] * y[0] + x[1] * y[1] + x[2] * y[2] return if (d < 0.0) -d else 0.0 } fun drawSphere(r: Double, k: Double, ambient: Double) { val vec = DoubleArray(3) var intensity: Int var b : Double var x: Double var y: Double for (i in Math.floor(-r).toInt() .. Math.ceil(r).toInt()) { x = i + 0.5 for (j in Math.floor(-2.0 * r).toInt() .. Math.ceil(2.0 * r).toInt()) { y = j / 2.0 + 0.5 if (x * x + y * y <= r * r) { vec[0] = x vec[1] = y vec[2] = Math.sqrt(r * r - x * x - y * y) normalize(vec) b = Math.pow(dot(light, vec), k) + ambient intensity = ((1.0 - b) * (shades.length - 1)).toInt() if (intensity < 0) intensity = 0 if (intensity >= shades.length - 1) intensity = shades.length - 2 print(shades[intensity]) } else print(' ') } println() } } fun main(args: Array<String>) { normalize(light) drawSphere(20.0, 4.0, 0.1) drawSphere(10.0, 2.0, 0.4) }
{{out}}
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Lingo
----------------------------------------
-- Draw a circle
-- @param {image} img
-- @param {integer} x
-- @param {integer} y
-- @param {integer} r
-- @param {integer} lineSize
-- @param {color} drawColor
----------------------------------------
on circle (img, x, y, r, lineSize, drawColor)
props = [:]
props[#shapeType] = #oval
props[#lineSize] = lineSize
props[#color] = drawColor
img.draw(x-r, y-r, x+r, y+r, props)
end
Logo
Drawing a sphere is actually very simple in logo, using the ''perspective'' function to make life easier. {{works with|MSWlogo}}
to sphere :r
cs perspective ht ;making the room ready to use
repeat 180 [polystart circle :r polyend down 1]
polyview
end
Lua
{{trans|C}} {{works with|Lua|5.1.4}}
require ("math") shades = {'.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'} function normalize (vec) len = math.sqrt(vec[1]^2 + vec[2]^2 + vec[3]^2) return {vec[1]/len, vec[2]/len, vec[3]/len} end light = normalize{30, 30, -50} function dot (vec1, vec2) d = vec1[1]*vec2[1] + vec1[2]*vec2[2] + vec1[3]*vec2[3] return d < 0 and -d or 0 end function draw_sphere (radius, k, ambient) for i = math.floor(-radius),-math.floor(-radius) do x = i + .5 local line = '' for j = math.floor(-2*radius),-math.floor(-2*radius) do y = j / 2 + .5 if x^2 + y^2 <= radius^2 then vec = normalize{x, y, math.sqrt(radius^2 - x^2 - y^2)} b = dot(light,vec) ^ k + ambient intensity = math.floor ((1 - b) * #shades) line = line .. (shades[intensity] or shades[1]) else line = line .. ' ' end end print (line) end end draw_sphere (20, 4, 0.1) draw_sphere (10, 2, 0.4)
{{out}}
&&&&&&&&&&&&#####
&eeeoooooooooeeeeee&&&&&#######
eooo*************oooooeeee&&&&&########
eo**!!!!!!!!!!!!!!!*****ooooeeee&&&&#########
eo*!!!:::::...:::::::!!!!****oooeeee&&&&&##########
o**!:::..............::::!!!!***ooooeee&&&&&###########
o*!!::...................::::!!!***ooooeee&&&&&############
eo*!::......................::::!!!***oooeeee&&&&&#############
o*!::.........................:::!!!***ooooeee&&&&&##############
&o*!::..........................:::!!!***ooooeeee&&&&###############%
eo*!::...........................:::!!!***ooooeeee&&&&&###############%
eo*!::............................:::!!!***ooooeeee&&&&&###############%%
&o*!!::...........................:::!!!!***oooeeee&&&&&#################%%
eo*!!:...........................::::!!!***ooooeeee&&&&&#################%%
eo**!!::.........................::::!!!****oooeeee&&&&&&#################%%%
eo**!!::.......................::::!!!!****oooeeeee&&&&&##################%%%
&eo**!!:::....................:::::!!!!***ooooeeeee&&&&&&##################%%%%
&eoo**!!::::................:::::!!!!****ooooeeeee&&&&&&###################%%%%
&eoo***!!!:::::........:::::::!!!!!****oooooeeeee&&&&&&###################%%%%%
&eeoo***!!!!:::::::::::::::!!!!!!*****ooooeeeee&&&&&&&####################%%%%%
&&eeoo****!!!!!!!!!!!!!!!!!!!!*****oooooeeeeee&&&&&&######################%%%%%
&&eeeooo******!!!!!!!!!!!*******ooooooeeeeee&&&&&&&######################%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#######################%%%%%%%
##&&&eeeeoooooooooo*ooooooooooooeeeeeeee&&&&&&&&#######################%%%%%%%%
##&&&eeeeeeooooooooooooooooeeeeeeeee&&&&&&&&&########################%%%%%%%%
###&&&&&eeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&##########################%%%%%%%%%
####&&&&&&&eeeeeeeeeeeeeee&&&&&&&&&&&&############################%%%%%%%%%
######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##############################%%%%%%%%%%
########&&&&&&&&&&&&&&&&&&&&&&################################%%%%%%%%%%%
###############&&&&&#######################################%%%%%%%%%%%%
#########################################################%%%%%%%%%%%%
#####################################################%%%%%%%%%%%%
#################################################%%%%%%%%%%%%%%
#############################################%%%%%%%%%%%%%%
########################################%%%%%%%%%%%%%%%
##################################%%%%%%%%%%%%%%%%%
%##########################%%%%%%%%%%%%%%%%%%
%%%%############%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
........::!!*
...............::!!*o
....................::!**oo
.......................::!**ooo
........................::!!**ooo
.........................::!!**oooo
..........................::!!**ooooe
...........................::!!**ooooee
..........................::!!***ooooee
.........................::!!!**oooooee
.......................:::!!!**oooooeee
:.....................::!!!***ooooooeee
!::................:::!!!!***ooooooeeee
!!::..........:::::!!!****ooooooeeeee
*!!!::::::::::!!!!!****oooooooeeeee
o***!!!!!!!!!******ooooooooeeeeee
ooo***********ooooooooooeeeeeee
oooooooooooooooooooeeeeeeee
eooooooooooeeeeeeeeee
eeeeeeeeeeeee
M2000 Interpreter
Module CheckIt {
Er$="Pset is a new statement"
If Version<9.4 Then Error Er$
If Version=9.4 then If revision<26 then Error Er$
Form 60, 40
Cls 0 ' Black
Gradient 0,1
Pen 14 ' Yellow
Set Fast !
Refresh 500
Module Sphere (R as long, X0 as long, Y0 as long, fun){
R2 = R * R
Def Long X, Y, D2
Let Scale=twipsx/R*13.5
For Y = -R To R step twipsx {
Move X0-R, Y+Y0
For X = -R To R step twipsy {
D2 = X **2 + Y **2
IF R2>D2 THEN Pset Fun(Max.Data(Min.Data((Sqrt(R2 - D2) - ( X + Y) / 2 )*Scale ,255),0))
Step twipsx
}
}
}
Blue=lambda (c)->{
c1=c/4+192
=Color(c,c,c1)
}
Blue1=lambda (c)->{
c1=c/4+Random(150,192)
=Color(c,c,c1)
}
Mystery=lambda m=1 (c)->{
c1=c/4+m
m+=10
if m>192 then m=1
=Color(c,c,c1)
}
Mystery2=lambda m=1, p=true (c)->{
c1=c/4+m
if p then m+=10
Else m=-10
if m>192 then m-=10 : p=false
If m<0 then m+=10: p=true
=Color(c,c,c1)
}
Buffer Alfa as byte*8
Trans =lambda Alfa (c) -> {
Return Alfa, 0:=-point as long
Return Alfa, 4:=-color(c,c, c/4+192) as long
for i=0 to 2: Return Alfa, i:=(Eval(Alfa, i)+Eval(Alfa, i+4))/2: Next i
=-Eval(Alfa, 0 as long)
}
Sphere 2400, 9000,7000, Blue
Sphere 800, 6000, 7000, Blue1
Sphere 1200, 5000,5000, Mystery
Sphere 1200, 10000,6000, Mystery2
Sphere 1200, 8000,5000, trans
}
Checkit
[[https://2.bp.blogspot.com/-ZWy2xDxXbzg/W98lAuNSY9I/AAAAAAAAHZ0/DFYluvWtz_cwwAUKfblujnW6mTC5XVs1QCLcBGAs/s1600/sphere.png]image]
Maple
[[File:Sphere_Maple.png|thumb]]
plots[display](plottools[sphere](), axes = none, style = surface);
=={{header|Mathematica}} / {{header|Wolfram Language}}== Mathematica has many 3D drawing capabilities. To create a sphere with radius one centered at (0,0,0):
Graphics3D[Sphere[{0,0,0},1]]
MATLAB
To create the unit sphere:
## Maxima
```maxima
/* Two solutions */
plot3d(1, [theta, 0, %pi], [phi, 0, 2 * %pi],
[transform_xy, spherical_to_xyz], [grid, 30, 60],
[box, false], [legend, false])$
load(draw)$
draw3d(xu_grid=30, yv_grid=60, surface_hide=true,
parametric_surface(cos(phi)*sin(theta),
sin(phi)*sin(theta),
cos(theta),
theta, 0, %pi, phi, 0, 2 * %pi))$
Nim
{{trans|C}}
import math type Point = tuple[x,y,z: float] const shades = ".:!*oe&#%@" proc normalize(x, y, z: float): Point = let len = sqrt(x*x + y*y + z*z) (x / len, y / len, z / len) proc dot(a, b: Point): float = result = max(0, - a.x*b.x - a.y*b.y - a.z*b.z) let light = normalize(30.0, 30.0, -50.0) proc drawSphere(r, k, ambient) = for i in -r .. r: let x = i.float + 0.5 for j in -2*r .. 2*r: let y = j.float / 2.0 + 0.5 if x*x + y*y <= float r*r: let v = normalize(x, y, sqrt(float(r*r) - x*x - y*y)) b = pow(dot(light, v), k) + ambient i = clamp(int((1.0 - b) * shades.high.float), 0, shades.high) stdout.write shades[i] else: stdout.write ' ' stdout.write "\n" drawSphere 20, 4.0, 0.1 drawSphere 10, 2.0, 0.4
{{out}}
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
Openscad
Drawing a sphere is easy in openscad:
// This will produce a sphere of radius 5
sphere(5);
[[Category:Geometric Primitives]]
Pascal
{{works with|Free_Pascal}} After changing "{$APPTYPE CONSOLE}" to "{$mode delphi}" or "{$mode objfpc}" the Delphi example works with FreePascal.
Perl
{{trans|Perl 6}}
This produces a PGM image which can't be uploaded on rosettacode at the moment. It looks similar as the Perl 6 solution, though.
use strict; use warnings; my $x = my $y = 255; $x |= 1; # must be odd my $depth = 255; my $light = Vector->new(rand, rand, rand)->normalized; print "P2\n$x $y\n$depth\n"; my ($r, $ambient) = (($x - 1)/2, 0); my ($r2) = $r ** 2; { for my $x (-$r .. $r) { my $x2 = $x**2; for my $y (-$r .. $r) { my $y2 = $y**2; my $pixel = 0; if ($x2 + $y2 < $r2) { my $v = Vector->new($x, $y, sqrt($r2 - $x2 - $y2))->normalized; my $I = $light . $v + $ambient; $I = $I < 0 ? 0 : $I > 1 ? 1 : $I; $pixel = int($I * $depth); } print $pixel; print $y == $r ? "\n" : " "; } } } package Vector { sub new { my $class = shift; bless ref($_[0]) eq 'Array' ? $_[0] : [ @_ ], $class; } sub normalized { my $this = shift; my $norm = sqrt($this . $this); ref($this)->new( map $_/$norm, @$this ); } use overload q{.} => sub { my ($a, $b) = @_; my $sum = 0; for (0 .. @$a - 1) { $sum += $a->[$_] * $b->[$_] } return $sum; }, q{""} => sub { sprintf "Vector:[%s]", join ' ', @{shift()} }; }
Perl 6
Pure Perl 6
{{trans|C}}
The C code is modified to output a .pgm file. {{works with|Rakudo|2018.10}}
[[File:Sphere-perl6.png|thumb]]
my $width = my $height = 255; # must be odd
my @light = normalize([ 3, 2, -5 ]);
my $depth = 255;
sub MAIN ($outfile = 'sphere-perl6.pgm') {
spurt $outfile, "P5\n$width $height\n$depth\n"; # .pgm header
my $out = open( $outfile, :a, :bin ) orelse .die;
$out.write( Blob.new(draw_sphere( ($width-1)/2, .9, .2) ) );
$out.close;
}
sub normalize (@vec) { @vec »/» ([+] @vec »*« @vec).sqrt }
sub dot (@x, @y) { -([+] @x »*« @y) max 0 }
sub draw_sphere ( $rad, $k, $ambient ) {
my @pixels[$height];
my $r2 = $rad * $rad;
my @range = -$rad .. $rad;
@range.hyper.map: -> $x {
my @row[$width];
@range.map: -> $y {
if (my $x2 = $x * $x) + (my $y2 = $y * $y) < $r2 {
my @vector = normalize([$x, $y, ($r2 - $x2 - $y2).sqrt]);
my $intensity = dot(@light, @vector) ** $k + $ambient;
my $pixel = (0 max ($intensity * $depth).Int) min $depth;
@row[$y+$rad] = $pixel;
}
else {
@row[$y+$rad] = 0;
}
}
@pixels[$x+$rad] = @row;
}
flat |@pixels.map: *.list;
}
Cairo graphics library
use Cairo;
given Cairo::Image.create(Cairo::FORMAT_ARGB32, 256, 256) {
given Cairo::Context.new($_) {
my Cairo::Pattern::Solid $bg .= create(.5,.5,.5);
.rectangle(0, 0, 256, 256);
.pattern($bg);
.fill;
$bg.destroy;
my Cairo::Pattern::Gradient::Radial $shadow .=
create(105.2, 102.4, 15.6, 102.4, 102.4, 128.0);
$shadow.add_color_stop_rgba(0, .3, .3, .3, .3);
$shadow.add_color_stop_rgba(1, .1, .1, .1, .02);
.pattern($shadow);
.arc(136.0, 134.0, 110, 0, 2 * pi);
.fill;
$shadow.destroy;
my Cairo::Pattern::Gradient::Radial $sphere .=
create(115.2, 102.4, 25.6, 102.4, 102.4, 128.0);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .923, .669, .144, 1);
.pattern($sphere);
.arc(128.0, 128.0, 110, 0, 2 * pi);
.fill;
$sphere.destroy;
};
.write_png('sphere2-perl6.png');
}
See [https://github.com/thundergnat/rc/blob/master/img/sphere2-perl6.png sphere2-perl6.png] (offsite .png image)
Phix
{{libheader|pGUI}} {{trans|Go}} (Go gets credit for the dot/normalize/drawSphere routines, but this draws on screen rather than to png file) Sphere will resize to match the window.
--
-- demo\rosetta\Draw_a_sphere.exw
--
include pGUI.e
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
function dot(sequence x, sequence y)
return sum(sq_mul(x,y))
end function
function normalize(sequence v)
atom len = sqrt(dot(v, v))
if len=0 then return {0,0,0} end if
return sq_mul(v,1/len)
end function
procedure drawSphere(integer width, height, atom k, atom amb, sequence direction)
integer r = floor((min(width,height)-20)/2)
integer cx = floor(width/2)
integer cy = floor(height/2)
integer lum
for x=-r to r do
for y=-r to r do
integer z = r*r-x*x-y*y
if z>=0 then
atom s = dot(direction, normalize({x,y,sqrt(z)}))
lum = and_bits(#FF,255*(power(iff(s<0?0:s),k)+amb)/(1+amb))
lum += lum*#100+lum*#10000
cdCanvasPixel(cddbuffer, x+cx, y+cy, lum)
end if
end for
end for
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
drawSphere(width,height,1.5,0.2,normalize({-30,-30,50}))
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_BLACK)
return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "340x340") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Draw a sphere")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()
PicoLisp
{{libheader|GLUT}} This is for the 64-bit version.
(load "@lib/openGl.l")
(glutInit)
(glutInitDisplayMode (| GLUT_RGBA GLUT_DOUBLE GLUT_ALPHA GLUT_DEPTH))
(glutInitWindowSize 400 400)
(glutCreateWindow "Sphere")
(glEnable GL_LIGHTING)
(glEnable GL_LIGHT0)
(glLightiv GL_LIGHT0 GL_POSITION (10 10 -10 0))
(glEnable GL_COLOR_MATERIAL)
(glColorMaterial GL_FRONT_AND_BACK GL_AMBIENT_AND_DIFFUSE)
(glClearColor 0.3 0.3 0.5 0)
(glColor4f 0.0 0.8 0.0 1.0)
(displayPrg
(glClear (| GL_COLOR_BUFFER_BIT GL_DEPTH_BUFFER_BIT))
(glutSolidSphere 0.9 40 32)
(glFlush)
(glutSwapBuffers) )
# Exit upon mouse click
(mouseFunc '((Btn State X Y) (bye)))
(glutMainLoop)
{{trans|C}}
(scl 24)
(setq *Shades
(list "." ":" "!" "*" "o" "e" "&" "#" "%" "@"))
(setq *Light
(list 30.0 30.0 -50.0))
(de normalize (V)
(let Len
(sqrt
(sum
(quote (X)
(** X 2))
V))
(mapcar
(quote (X)
(*/ X 1.0 Len))
V)))
(de dot (X Y)
(let D (sum (quote (A B) (*/ A B 1.0)) X Y)
(if (< D 0) (- D) 0)))
(de floor (N)
(* 1.0 (*/ (- N 0.5) 1.0)))
(de ceil (N)
(* 1.0 (*/ (+ N 0.5) 1.0)))
(de drawSphere (R K Ambient)
(let Vec NIL
(for (I (floor (- R)) (<= I (ceil R)) (+ I 1.0))
(let X (+ I 0.5)
(for (J (floor (* -2 R)) (<= J (ceil (* 2 R))) (+ J 1.0))
(let Y (+ (/ J 2) 0.5)
(if (<= (+ (*/ X X 1.0) (*/ Y Y 1.0)) (*/ R R 1.0))
(prog
(setq Vec
(list X Y
(sqrt
(* 1.0
(- (*/ R R 1.0)
(*/ X X 1.0)
(*/ Y Y 1.0))))))
(setq Vec (normalize Vec))
(let (B NIL
Intensity NIL)
(setq B (+ (/ (** (dot *Light Vec) K) (** 1.0 (- K 1))) Ambient))
(setq Intensity
(if (<= B 0)
(- (length *Shades) 2)
(max (format (round (*/ (- 1.0 B) (* (- (length *Shades) 1) 1.0) 1.0) 0)) 0)))
(prin (nth *Shades (+ Intensity 1) 1))))
(prin " "))))
(prinl)))))
(setq *Light (normalize *Light))
(drawSphere 20.0 4 0.1)
(drawSphere 10.0 2 0.4)
{{out}}
##############%%%
#&&eeeeeeeeeee&&&&&&######%%%%%
&eeeoooooooooooooeeeee&&&&&######%%%%%%
&eooo**************oooooeeee&&&&&#####%%%%%%%
&eoo**!!!!!!!!!!!!!!*****ooooeeee&&&&######%%%%%%%%
eoo**!!!::::::::::::!!!!****ooooeeee&&&&######%%%%%%%%%
eoo*!!!::::.......::::::!!!!****oooeeee&&&&######%%%%%%%%%%
&eo*!!:::..............::::!!!!***ooooeeee&&&&######%%%%%%%%%%%
eo**!!::.................::::!!!****oooeeee&&&&######%%%%%%%%%%%%
&eo*!!:::..................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%
&eo*!!:::...................::::!!!!***oooeeee&&&&&######%%%%%%%%%%%%%%
&eo**!!::....................::::!!!****oooeeee&&&&&######%%%%%%%%%%%%%%%
#eoo*!!:::...................::::!!!!***ooooeeee&&&&#######%%%%%%%%%%%%%%%%
&eo**!!:::.................:::::!!!!****oooeeee&&&&&#######%%%%%%%%%%%%%%%%
&eoo**!!::::...............:::::!!!!****ooooeeee&&&&#######%%%%%%%%%%%%%%%%%%
&eoo**!!!::::...........::::::!!!!*****ooooeeee&&&&&#######%%%%%%%%%%%%%%%%%%
#&eoo***!!!::::::::::::::::::!!!!!****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%
#&eeoo***!!!!::::::::::::!!!!!!!*****ooooeeeee&&&&&#######%%%%%%%%%%%%%%%%%%%%%
#&eeooo****!!!!!!!!!!!!!!!!!!******ooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%
#&&eeooo******!!!!!!!!!!!*******ooooooeeeee&&&&&&#######%%%%%%%%%%%%%%%%%%%%%%%
#&&&eeooooo******************ooooooeeeeee&&&&&&########%%%%%%%%%%%%%%%%%%%%%%%%
##&&&eeeooooooo********oooooooooeeeeeee&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%
###&&&eeeeeooooooooooooooooooeeeeeee&&&&&&&&#########%%%%%%%%%%%%%%%%%%%%%%%%%%
%###&&&&eeeeeeeeeeeoeeeeeeeeeeeee&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%####&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&##########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#####&&&&&&&&&&&&&&&&&&&&&&&&&&&############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######&&&&&&&&&&&&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%############&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%#######################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
!::::::!!!**o
............:::!!**oe
:................::!!**ooee
:...................::!!**ooeee
......................::!!**ooeee
.......................::!!**ooeeee
.......................:::!!**ooeeeee
:.......................::!!***ooeeeeee
:......................::!!!**oooeeeeee
:....................:::!!!**oooeeeeeee
!:..................:::!!***oooeeeeeeee
!!:..............::::!!!***oooeeeeeeeee
*!!::::.....::::::!!!!***ooooeeeeeeeeee
o*!!!!::::::!!!!!!****ooooeeeeeeeeeee
o****!!!!!!!******oooooeeeeeeeeeeee
eooo********oooooooeeeeeeeeeeeeee
eeeoooooooooooeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
PostScript
Gradient filled circle:
%!PS-Adobe-3.0
%%BoundingBox 0 0 300 300
150 150 translate 0 0 130 0 360 arc
/Pattern setcolorspace
<< /PatternType 2
/Shading <<
/ShadingType 3
/ColorSpace /DeviceRGB
/Coords [-60 60 0 0 0 100]
/Function <<
/FunctionType 2
/Domain [0 1]
/C0 [1 1 1]
/C1 [0 0 0]
/N 2
>>
>>
>> matrix makepattern setcolor fill
showpage
%%EOF
=={{header|POV-Ray}}==
This is what POVray was made for. An example with a sky, surface and transparency:
camera { location <0.0 , .8 ,-3.0> look_at 0}
light_source{< 3,3,-3> color rgb 1}
sky_sphere { pigment{ gradient <0,1,0> color_map {[0 color rgb <.2,.1,0>][.5 color rgb 1]} scale 2}}
plane {y,-2 pigment { hexagon color rgb .7 color rgb .5 color rgb .6 }}
sphere { 0,1
texture {
pigment{ color rgbft <.8,1,1,.4,.4> }
finish { phong 1 reflection {0.40 metallic 0.5} }
}
interior { ior 1.5}
}
Yields this:
[[image:PovRay-sphere.jpg]]
Processing
3D rendering is built into Processing.
void setup() {
size(500,500,P3D);
background(200);
}
void draw() {
stroke(200);
translate(250,250);
lights();
sphere(100);
}
Python
===Ascii-Art=== {{trans|C}}
import math shades = ('.',':','!','*','o','e','&','#','%','@') def normalize(v): len = math.sqrt(v[0]**2 + v[1]**2 + v[2]**2) return (v[0]/len, v[1]/len, v[2]/len) def dot(x,y): d = x[0]*y[0] + x[1]*y[1] + x[2]*y[2] return -d if d < 0 else 0 def draw_sphere(r, k, ambient, light): for i in range(int(math.floor(-r)),int(math.ceil(r)+1)): x = i + 0.5 line = '' for j in range(int(math.floor(-2*r)),int(math.ceil(2*r)+1)): y = j/2 + 0.5 if x*x + y*y <= r*r: vec = normalize((x,y,math.sqrt(r*r - x*x - y*y))) b = dot(light,vec)**k + ambient intensity = int((1-b)*(len(shades)-1)) line += shades[intensity] if 0 <= intensity < len(shades) else shades[0] else: line += ' ' print(line) light = normalize((30,30,-50)) draw_sphere(20,4,0.1, light) draw_sphere(10,2,0.4, light)
{{out}}
&&&&&&&&&&######
&&eeeeeeeeeeeeeeee&&&&&&######%%
&&oooo********ooooooeeeeee&&&&########%%
oo****!!!!!!!!******ooooooeeee&&&&########%%
eeoo**!!!!::::::::!!!!******ooooeeee&&&&########%%%%
ee**!!::::::....::::::!!!!!!**ooooeeee&&&&&&########%%%%
ee**!!::..............::::!!!!****ooooeeee&&&&########%%%%%%
ee**!!::..................::::!!!!**ooooeeee&&&&##########%%%%%%
oo!!::....................::::!!!!****ooeeee&&&&&&########%%%%%%
oo**::......................::::!!!!****ooeeee&&&&&&##########%%%%%%
&&**!!::......................::::!!!!****ooeeee&&&&&&##########%%%%%%%%
oo**!!::......................::::!!!!**ooooeeee&&&&&&##########%%%%%%%%
&&oo!!::........................::::!!****ooooeeee&&&&&&##########%%%%%%%%%%
ee**!!::......................::::!!!!****ooooeeee&&&&&&##########%%%%%%%%%%
ee**!!::::..................::::::!!!!****ooooeeee&&&&############%%%%%%%%%%
ee**!!::::................::::::!!!!****ooooeeee&&&&&&############%%%%%%%%%%
&&ee****!!::::............::::::!!!!****ooooooeeee&&&&&&##########%%%%%%%%%%%%%%
&&eeoo**!!!!::::::::::::::::::!!!!******ooooeeee&&&&&&############%%%%%%%%%%%%%%
&&eeoo****!!!!::::::::::::!!!!!!******ooooeeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeoooo**!!!!!!!!!!!!!!!!!!!!******ooooeeeeee&&&&&&############%%%%%%%%%%%%%%%%
&&eeeeoo******!!!!!!!!!!********ooooooeeeeee&&&&&&&&############%%%%%%%%%%%%%%%%
##&&eeoooooo******************ooooooeeeeee&&&&&&&&############%%%%%%%%%%%%%%%%%%
##&&eeeeoooooooo******ooooooooooooeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeeooooooooooooooooooeeeeeeee&&&&&&&&##############%%%%%%%%%%%%%%%%%%%%
##&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&&################%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeee&&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%
######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##################%%%%%%%%%%%%%%%%%%%%%%
%%######&&&&&&&&&&&&&&&&&&&&&&&&####################%%%%%%%%%%%%%%%%%%%%%%%%
############&&&&&&&&&&&&########################%%%%%%%%%%%%%%%%%%%%%%%%
%%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%##############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
::..::::!!**
..............::!!oo
..................::!!**ooee
......................::!!**ooee
......................::!!**ooee
........................::!!**ooooee
........................::!!**ooooee
::........................::!!**ooooeeee
........................::!!!!**ooooeeee
::......................::!!****ooeeeeee
::....................::!!!!**ooooeeeeee
!!..................::!!!!****ooeeeeeeee
**::::..........::::!!!!****ooooeeeeeeee
!!!!::::::::::!!!!!!****ooooeeeeeeee
oo**!!!!!!!!!!!!******ooooeeeeeeeeee
oo**************ooooooeeeeeeeeee
eeooooooooooooooooeeeeeeeeeeeeee
eeeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeee
eeeeeeeeeeee
==={{libheader|Pygame}}=== [[File:PythonSphere.png|thumb|Python Sphere]] Renders a sphere with random Perlin noise.
This code contains unnecessary functions which are part of a 3D graphics library I wrote.
Uses Pygame and Python 3.2.2
import pygame from pygame.locals import * import time import sys import random import math
class Tricubic: def __init__(self,pts): self.coefficients = [] for plane in pts: planecoeffs = [] for line in plane: p = (line[3]-line[2])-(line[0]-line[1]) q = (line[0]-line[1])-p r = line[2]-line[0] s = line[1] planecoeffs.append([p,q,r,s]) self.coefficients.append(planecoeff) def Eval(at): return Misc.Cubic([CoeffBicubic(coeffs[0],d),CoeffBicubic(coeffs[1],d),CoeffBicubic(coeffs[2],d),CoeffBicubic(coeffs[3],d)],d.z) def CoeffCubic(coeffs,d): return (coeffs[0]*(d.x**3))+(coeffs[1]*(d.x**2))+(coeffs[2]*d.x)+coeffs[3] def CoeffBicubic(coeffs,d): return Misc.Cubic([CoeffCubic(coeffs[0],d),CoeffCubic(coeffs[1],d),CoeffCubic(coeffs[2],d),CoeffCubic(coeffs[3],d)],d.y) class Misc: def LinePara(line,t): return Vector3.Add(line[0],Vector3.Scale(Vector3.Subtract(line[1],line[0]),t)) def LUR(at,above): look = at.Unit() right = Vector3.Cross(look,above).Unit() up = Vector3.Scale(Vector3.Cross(look,right),-1) return [look,up,right] def LinePlane(line,triangle,cp=True): try: u = Vector3.Subtract(triangle.points[1].point,triangle.points[0]) v = Vector3.Subtract(triangle.points[2],triangle.points[0]) n = Vector3.Cross(u,v) r = (Vector3.Dot(n,Vector3.Subtract(triangle.points[0],line.start))/Vector3.Dot(n,line.direction)) if stp: point = Vector3.Add(Vector3.Scale(line.direction,r),line.start) w = Vector3.Subtract(point,triangle.points[0]) udv = Vector3.Dot(u,v) wdv = Vector3.Dot(w,v) vdv = Vector3.Dot(v,v) wdu = Vector3.Dot(w,u) udu = Vector3.Dot(u,u) denominator = (udv**2)-(udu*vdv) s = ((udv*wdv)-(vdv*wdu))/denominator t = ((udv*wdu)-(udu*wdv))/denominator return [r,Vector2(s,t),point] print('hooray') else: return [r] except: return None def Cubic(pts,d): p = (pts[3]-pts[2])-(pts[0]-pts[1]) q = (pts[0]-pts[1])-p r = pts[2]-pts[0] s = pts[1] return (p*(d**3))+(q*(d**2))+(r*d)+s def Bicubic(pts,d): return Misc.Cubic([Misc.Cubic(pts[0],d.x),Misc.Cubic(pts[1],d.x),Misc.Cubic(pts[2],d.x),Misc.Cubic(pts[3],d.x)],d.y) def Tricubic(pts,d): return Misc.Cubic([Misc.Bicubic(pts[0],d),Misc.Bicubic(pts[1],d),Misc.Bicubic(pts[2],d),Misc.Bicubic(pts[3],d)],d.z) def Quadcubic(pts,d): return Misc.Cubic([Misc.Tricubic(pts[0],d),Misc.Tricubic(pts[1],d),Misc.Tricubic(pts[2],d),Misc.Tricubic(pts[3],d)],d.w) def Linear(pts,d): return (pts[2]*d)+(pts[1]*(1-d)) def Bilinear(pts,d): return Misc.Linear([0,Misc.Linear(pts[1],d.x),Misc.Linear(pts[2],d.x)],d.y) def Trilinear(pts,d): return Misc.Linear([0,Misc.Bilinear(pts[1],d),Misc.Bilinear(pts[2],d)],d.z) def LP2(line,triangle,cp=True): try: bla = triangle.points[1] bla = triangle.points[0] u = Vector3.Subtract(triangle.points[1].point,triangle.points[0].point) v = Vector3.Subtract(triangle.points[2].point,triangle.points[0].point) n = Vector3.Cross(u,v) d = Vector3.Subtract(line[1],line[0]) r = (Vector3.Dot(n,Vector3.Subtract(triangle.points[0].point,line[0]))/Vector3.Dot(n,d)) if cp: point = Vector3.Add(Vector3.Scale(d,r),line[0]) w = Vector3.Subtract(point,triangle.points[0].point) udv = Vector3.Dot(u,v) wdv = Vector3.Dot(w,v) vdv = Vector3.Dot(v,v) wdu = Vector3.Dot(w,u) udu = Vector3.Dot(u,u) denominator = (udv**2)-(udu*vdv) s = ((udv*wdv)-(vdv*wdu))/denominator t = ((udv*wdu)-(udu*wdv))/denominator return (r,Vector2(s,t),point) else: return (r) except: return None def Phong(normal,viewer,light,material,term): # light (vector_to,diffuse,specular) # material (ambient,diffuse,specular,shininess) n = normal.Unit() v = viewer.Unit() l = light[0].Unit() ldn = Vector3.Dot(l,n) #print(ldn) val = 0 if ldn > 0: val += material[1][term]*ldn*light[1][term] rdv = Vector3.Dot(Vector3.Subtract(Vector3.Scale(n,2*ldn),l),v) if rdv > 0: val += (material[2][term]*(rdv**material[3])*light[2][term]) #print(val) return val def Lighting(ambient,normal,viewer,lights,material,term): # lights [(vector_to,diffuse,specular)] # material (ambient,diffuse,specular,shininess) val = material[0][term]*ambient[term] for light in lights: val += Misc.Phong(normal,viewer,light,material,term) return val def Lighting2(start,direction,ambient,intersect,triangle,lights): coord = intersect[1] val = Color.Add(Color.Multiply(ambient,Color.Multiply(triangle.material.color['ambient'],triangle.Map('ambient',coord))), Color.Multiply(triangle.material.color['glow'],triangle.Map('glow',coord))) for light in lights: for n in range(3): val[n] += Misc.Phong(triangle.InterpolatedNormal(coord), Vector3.Scale(direction,-1), (light.To(intersect[2]),light.Diffuse(intersect[2]),light.Specular(intersect[2])), (Color(), Color.Multiply(triangle.material.color['diffuse'],triangle.Map('diffuse',coord)), Color.Multiply(triangle.material.color['specular'],triangle.Map('specular',coord)), triangle.material.shiny),n) return val def Ray(start,direction,scene,color=True,sector=None): intersect = None intersected = None col = None for triangle in scene.triangles: possible = True if sector != None: possible = False for point in triangle.points: if not(point.sector.x < sector.x): possible = True if possible: possible = False for point in triangle.points: if not(point.sector.x > sector.x): possible = True if possible: possible = False for point in triangle.points: if not(point.sector.y < sector.y): possible = True if possible: possible = False for point in triangle.points: if not(point.sector.y > sector.y): possible = True possible = True if possible: tmp = Misc.LP2([start,Vector3.Add(start,direction)],triangle,color) write = False if type(tmp) == type(5.1): tmp = None if (tmp != None): if (intersect == None): if (tmp[0] > 0) and (tmp[1].x >= 0) and (tmp[1].y >= 0) and (tmp[1].x+tmp[1].y <= 1): write = True elif (tmp[0] > 0) and (tmp[0] < intersect[0]) and (tmp[1].x >= 0) and (tmp[1].y >= 0) and (tmp[1].x+tmp[1].y <= 1): write = True if write: intersect = tmp intersected = triangle if color and (intersect != None): applicable = [] for light in scene.lights: block = Misc.Ray(intersect[2],light.To(intersect[2]),scene,False) if block == None: applicable.append(light) elif light.location != None: if Vector3.Subtract(light.location,intersect[2]).Magnitude() < block[0]: applicable.append(light) col = Misc.Lighting2(start,direction,scene.ambient,intersect,intersected,applicable) return (intersect,col) else: return intersect class DirLight: def __init__(self,direction,diffuse,specular): self.location = None self.direction = direction.Unit() self.diffuse = diffuse self.specular = specular def To(self,frm): return Vector3.Scale(self.direction,-1) def Diffuse(self,to): return self.diffuse def Specular(self,to): return self.specular class Material: def __init__(self): self.color = {'ambient':Color(1,1,1), 'diffuse':Color(1,1,1), 'specular':Color(1,1,1), 'glow':Color(1,1,1)} self.maps = {'ambient':Map(), 'diffuse':Map(), 'specular':Map(), 'glow':Map(), 'bump':Map()} self.shiny = 10 class Map: def __init__(self,surface=None): self.surface = surface if self.surface != None: self.width = self.surface.get_width() self.height = self.surface.get_height() def __getitem__(self,index): if self.surface == None: return Color(1,1,1) else: try: return Color.From255(self.surface.get_at((int(index.x*(self.width-1)),int(index.y*(self.height-1))))) except: return Color(0,0,1) class Color: def __init__(self,r=0,g=0,b=0): self.r = r self.g = g self.b = b def __getitem__(self,index): if index == 0: return self.r elif index == 1: return self.g elif index == 2: return self.b def __setitem__(self,index,value): if index == 0: self.r = value elif index == 1: self.g = value elif index == 2: self.b = value def Multiply(A,B): return Color(A.r*B.r,A.g*B.g,A.b*B.b) def Add(A,B): return Color(A.r+B.r,A.g+B.g,A.b+B.b) def From255(A): return Color(A.r/255,A.g/255,A.b/255) class Vertex: def __init__(self,point,normal,maps): self.bpoint = point self.bnormal = normal self.maps = maps for name in ['ambient','diffuse','specular','glow','bump']: try: bla = self.maps[name] except: self.maps[name] = Vector2() self.sector = None def Transform(self,points,norms): self.point = Matrix2.Multiply(self.bpoint.Horizontal(),points).Vectorize() self.normal = Matrix2.Multiply(self.bnormal.Horizontal(),norms).Vectorize() class Triangle: def __init__(self,vertices,material=Material()): self.points = vertices self.material = material def Map(self,name,coord): pts = [] for n in range(3): pts.append(self.points[n].maps[name]) loc = Vector2.Add(pts[0], Vector2.Add(Vector2.Scale(Vector2.Subtract(pts[1],pts[0]),coord.x), Vector2.Scale(Vector2.Subtract(pts[2],pts[0]),coord.y))) #print(loc.x,loc.y) return self.material.maps[name][loc] def InterpolatedNormal(self,coord): return Vector3.Add(Vector3.Scale(self.points[0].normal,1-coord.x-coord.y), Vector3.Add(Vector3.Scale(self.points[1].normal,coord.x),Vector3.Scale(self.points[2].normal,coord.y))).Unit() class Line: def __init__(self,A,B=None,direction=None): self.start = A if B != None: self.direction = Vector3.Subtract(B,A).Unit() elif direction != None: self.direction = direction else: raise RuntimeError('Neither B nor direction are specified') class Scene: def __init__(self): self.triangles = [] self.vertices = [] self.lights = [] self.exterior = [] self.ambient = 0 class Matrix2: def __init__(self,data=[[]]): self.FromData(data) def __getitem__(self,index): return self.data[index[1]][index[0]] def __setitem__(self,index,value): self.data[index[1]][index[0]]=value def Dimension(self): self.rows = len(self.data) self.cols = len(self.data[0]) def FromData(self,data): self.data = data length=len(data[0]) for row in data: if len(row)!=length: self.data=None raise RuntimeError('Data rows are not of uniform length.') self.Dimension() def Multiply(A,B): if A.cols!=B.rows: raise RuntimeError('Column count of Matrix2 \"A\" does not match row count of Matrix2 \"B\".') matrix = Matrix2.Empty(B.cols,A.rows) x=0 while x<matrix.cols: y=0 while y<matrix.rows: val=0 n=0 while n<A.cols: val+=A[(n,y)]*B[(x,n)] n+=1 matrix[(x,y)]=val y+=1 x+=1 return matrix def Scalar(A,n): pass def Empty(rows,cols): data = [] row = [0]*rows n = 0 while n < cols: data.append(row[:]) n+=1 matrix=Matrix2(data) matrix.Dimension() return matrix def Identity(cols): matrix = Matrix2.Empty(cols,cols) n = 0 while n < cols: matrix[(n,n)]=1 n += 1 return matrix def Vectorize(self): if self.cols==1: if self.rows!=4: raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.') vertical=True elif self.rows==1: if self.cols!=4: raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.') vertical = False else: raise RuntimeError('Only 1 by 4 or 4 by 1 Matrix2s can be cast to Vector3s.') vector=[0]*4 n=0 while n<4: if vertical: vector[n]=self[(0,n)] else: vector[n]=self[(n,0)] n+=1 return Vector3(vector[0],vector[1],vector[2],vector[3]) def Print(self,decimals,spaces): length=0 for row in self.data: for val in row: string=str(round(val,decimals)) if length<len(string): length=len(string) text='' for row in self.data: temp='' for value in row: val=str(round(float(value),decimals)) pads=length-len(val) pad=int(pads/2) temp+=(' '*pad)+val+(' '*(pads-pad))+(' '*spaces) text+=(' '*spaces)+temp[0:len(temp)-1]+(' '*spaces)+'\n' return(text[0:len(text)-1]) def RotX(angle): return Matrix2([ [1,0,0,0], [0,math.cos(angle),0-math.sin(angle),0], [0,math.sin(angle),math.cos(angle),0], [0,0,0,1]]) def RotY(angle): return Matrix2([ [math.cos(angle),0,0-math.sin(angle),0], [0,1,0,0], [math.sin(angle),0,math.cos(angle),0], [0,0,0,1]]) def RotZ(angle): return Matrix2([ [math.cos(angle),0-math.sin(angle),0,0], [math.sin(angle),math.cos(angle),0,0], [0,0,1,0], [0,0,0,1]]) def Translate(vector): return Matrix2([ [1,0,0,0], [0,1,0,0], [0,0,1,0], [vector.x,vector.y,vector.z,1]]) def Scale(vector): return Matrix2([ [vector.x,0,0,0], [0,vector.y,0,0], [0,0,vector.z,0], [0,0,0,1]]) def Clone(self): data = [] for row in self.data: data.append(row[:]) return Matrix2(data) def Inverse(self): adjoint = self.Adjoint() det = self.Determinant() if det == 0: raise RuntimeError('Cannot find the inverse of a matrix with a determinant of 0') inverse = Matrix2.Empty(self.rows,self.cols) x = 0 while x < self.cols: y = 0 while y < self.rows: inverse[(x,y)] = adjoint[(x,y)]/det y += 1 x += 1 return inverse def Transpose(self): transpose = Matrix2.Empty(self.cols,self.rows) x = 0 while x < self.cols: y = 0 while y < self.rows: transpose[(y,x)] = self[(x,y)] y += 1 x += 1 return transpose def Adjoint(self): return self.Cofactors().Transpose() def Determinant(self): if self.rows != self.cols: raise RuntimeError('Cannot find the determinant of a non-square matrix') if self.rows == 1: return self[(0,0)] cofactors = self.Cofactors() determinant = 0 n = 0 while n < self.cols: determinant += self[(n,0)]*cofactors[(n,0)] n += 1 return determinant def Minors(self): if self.rows != self.cols: raise RuntimeError('Cannot find the minors of a non-square matrix') if self.rows == 1: raise RuntimeError('Cannot find the minors of a 1 by 1 matrix') minors = Matrix2.Empty(self.rows,self.cols) lines = range(self.rows) x = 0 while x < self.cols: y = 0 while y < self.cols: tiny = Matrix2.Empty(self.rows-1,self.cols-1) ox = 0 nx = 0 while ox < self.cols: oy = 0 ny = 0 while oy < self.cols: if not((ox == x) or (oy == y)): tiny[(nx,ny)] = self[(ox,oy)] if oy != y: ny += 1 oy += 1 if ox != x: nx += 1 ox += 1 minors[(x,y)] = tiny.Determinant() y += 1 x += 1 return minors def Cofactors(self): minors = self.Minors() cofactors = Matrix2.Empty(self.rows,self.cols) x = 0 while x < self.cols: y = 0 while y < self.rows: if int((x+y)/2) == ((x+y)/2): cofactors[(x,y)] = minors[(x,y)] else: cofactors[(x,y)] = -1*minors[(x,y)] y += 1 x += 1 return cofactors def Perspective(e): return Matrix2([ [1,0,0,0], [0,1,0,0], [0,0,1,1/e[2]], [-e[0],-e[1],0,0]]) def Add(A,B): if A.rows != B.rows: RuntimeError('The row counts of Matrix \"A\" and Matrix \"B\" are not identical.') if A.cols != B.cols: RuntimeError('The column counts of Matrix \"A\" and Matrix \"B\" are not identical.') matrix = Matrix.Empty(A.rows,A.cols) for x in range(A.cols): for y in range(A.rows): matrix[(x,y)] = A[(x,y)]+B[(x,y)] return matrix def Subtract(A,B): if A.rows != B.rows: RuntimeError('The row counts of Matrix \"A\" and Matrix \"B\" are not identical.') if A.cols != B.cols: RuntimeError('The column counts of Matrix \"A\" and Matrix \"B\" are not identical.') matrix = Matrix.Empty(A.rows,A.cols) for x in range(A.cols): for y in range(A.rows): matrix[(x,y)] = A[(x,y)]+B[(x,y)] return matrix def DivHomogeneous(self): if (self.cols,self.rows) == (1,4): for y in range(3): self[(0,y)] = self[(0,y)]/self[(0,3)] self[(0,3)] = 1 if (self.cols,self.rows) == (4,1): for x in range(3): self[(x,0)] = self[(x,0)]/self[(3,0)] self[(3,0)] = 1 else: raise RuntimeError('1 by 4 or 4 by 1 Matrix2 expected') def Object(pos,look,up,right): return Matrix2([ [right.x,right.y,right.z,0], [up.x,up.y,up.z,0], [look.x,look.y,look.z,0], [pos.x,pos.y,pos.z,1]]) def Camera(eye,look,up,right): return Matrix2([ [right.x,up.x,look.x,0], [right.y,up.y,look.y,0], [right.z,up.z,look.z,0], [-Vector3.Dot(eye,right), -Vector3.Dot(eye,up), -Vector3.Dot(eye,look),1]]) def YPR(rot): return Matrix2.Multiply( Matrix2.Multiply(Matrix2.RotZ(rot.z), Matrix2.RotX(rot.x)), Matrix2.RotY(rot.y)) class Vector2: def __init__(self,data=0,y=0): if (type(data) == type(5)) or (type(data) == type(5.1)): self.x = data self.y = y else: self.x = data[0] self.y = data[1] def __getitem__(self,index): if index == 0: return self.x elif index == 1: return self.y def __setitem__(self,index,value): if index == 0: self.x = value elif index == 1: self.y = 1 def Add(A,B): return Vector2(A.x+B.x,A.y+B.y) def Subtract(A,B): return Vector2(A.x-B.x,A.y-B.y) def Scale(A,n): return Vector2(A.x*n,A.y*n) def Magnitude(self): return ((self.x**2)+(self.y**2))**.5 def Unit(self): return Vector2.Scale(self,1/self.Magnitude()) def Clone(self): return Vector2(self.x,self.y) class Vector3: def __init__(self,data=0,y=0,z=0,w=1): if (type(data) == type(5)) or (type(data) == type(5.1)): self.x = data/w self.y = y/w self.z = z/w else: try: temp = data[3] except: temp = 1 self.x = data[0]/temp self.y = data[1]/temp self.z = data[2]/temp def __getitem__(self,index): if index == 0: return self.x elif index == 1: return self.y elif index == 2: return self.z def __setitem__(self,index,value): if index == 0: self.x = value elif index == 1: self.y = value elif index == 2: self.z = value def Vertical(self): return Matrix2([[self.x],[self.y],[self.z],[1]]) def Horizontal(self): return Matrix2([[self.x,self.y,self.z,1]]) def Dot(A,B): return (A.x*B.x)+(A.y*B.y)+(A.z*B.z) def Cross(A,B): return Vector3([ (A.y*B.z)-(A.z*B.y), (A.z*B.x)-(A.x*B.z), (A.x*B.y)-(A.y*B.x)]) def Add(A,B): return Vector3(A.x+B.x,A.y+B.y,A.z+B.z) def Subtract(A,B): return Vector3(A.x-B.x,A.y-B.y,A.z-B.z) def Scale(A,n): return Vector3(A.x*n,A.y*n,A.z*n) def Magnitude(self): return ((self.x**2)+(self.y**2)+(self.z**2))**.5 def Print(self,decimals,spaces): return self.Horizontal().Print(decimals,spaces) def Same(A,B): same = False if A.x == B.x: if A.y == B.y: if A.z == B.z: same = True return same def Unit(self): return Vector3.Scale(self,1/self.Magnitude()) def Clone(self): return Vector3(self.x,self.y,self.z) class Vector4: def __init__(self,data=0,y=0,z=0,w=0): if (type(data) == type(5)) or (type(data) == type(5.1)): self.x = data self.y = y self.z = z self.w = w else: self.x = data[0] self.y = data[0] self.z = data[0] self.w = data[0] points = [Vector3([-1,-1,0]),Vector3([1,-1,0]),Vector3([0,1,0])] width = 255 height = width screen = pygame.display.set_mode((width,height),0,32) scl = 2 pos = Vector3([0,0,5]) view = Vector3([0,0,1]) frames = 0 def Transform(point,mat): return Matrix2.Multiply(point.Horizontal(),mat).Vectorize() def RV(): return Vector3([random.random(),random.random(),random.random()]) green = pygame.Color(0,255,0) def XY(bla): return (((width*bla[0])+width)/2,((height*bla[1])+width)/2) screen.fill(pygame.Color(0,0,0)) size = 255 world = Matrix2.Identity(4) inv = world.Inverse() invt = world.Inverse().Transpose() center = Vector3(0,0,2) def Texture(size): texture = [] for pa in range(size): plane = [] for pb in range(size): line = [] for pc in range(size): line.append(random.random()) plane.append(line) texture.append(plane) return texture lights = [(Vector3(-10,6,-9),[.7,.7*.9,.7*.8],[.7,.7*.9,.9*.8])] lights = [(Vector3(-10,6,-9),[.8,.8,.8],[.7,.7,.7])] depth = 3 groups = [] for n in range(1): textures = [] for n in range(depth): textures.append(Texture(4**(n+1))) groups.append(textures) def Select(texture,at): sel = [] for pa in range(4): aplane = texture[pa+math.floor(at.z)] bplane = [] for pb in range(4): aline = aplane[pb+math.floor(at.y)] bline = [] for pc in range(4): bline.append(aline[pc+math.floor(at.x)]) bplane.append(bline) sel.append(bplane) return (sel,Vector3(at.x%1,at.y%1,at.z%1)) def Round(val): return val-(val-math.floor(val)) theta = math.tan(70*math.pi/360) for x in range(width): for event in pygame.event.get(): if event.type == QUIT: pygame.quit() sys.exit() if event.type == KEYDOWN: pass for y in range(height): l = Vector3(theta*2*((x/width)-.5),theta*2*((y/width)-.5),1).Unit() ldc = Vector3.Dot(l,center) d = ldc-(((ldc**2)-Vector3.Dot(center,center)+1)**.5) if type(d) != type((-1)**.5): intersection = Vector3.Scale(l,d) normal = Vector3.Subtract(intersection,center).Unit() point = Transform(normal,world) s = Vector3.Scale(Vector3.Add(point,Vector3(1,1,1)),.5) val = 0 for i in range(depth): sel = Select(groups[0][i],Vector3.Scale(s,4**i)) val += Misc.Tricubic(sel[0],sel[1])*((1/2)**i)/4 val = (25*val)%1 vals = [0,Misc.Linear([0,.3,1],val),1] coloring = [] for i in range(3): #light = Misc.Lighting([1,1,1],normal,Vector3.Scale(intersection,-1),lights,([0,.03*val,.03],[0,.7*val,.7],[.3,.3,.3],7),i) light = Misc.Lighting([.1,.1,.1],normal,Vector3.Scale(intersection,-1),lights,(vals,vals,[1,1,1],10),i) if light > 1: light = 1 elif light < 0: light = 0 coloring.append(round(255*light)) screen.set_at((x,height-y),pygame.Color(coloring[0],coloring[1],coloring[2])) pygame.display.update() pygame.image.save(screen,"PythonSphere.png") while True: for event in pygame.event.get(): if event.type == QUIT: pygame.quit() sys.exit() if event.type == KEYDOWN: pass
==={{libheader|VPython}}=== {{works with|Python|2.7.5}} '''Short version''':
from visual import * scene.title = "VPython: Draw a sphere" sphere() # using defaults, see http://www.vpython.org/contents/docs/defaults.html
'''Regular version''', with some window-dressing:
from __future__ import print_function, division from visual import * title = "VPython: Draw a sphere" scene.title = title print( "%s\n" % title ) print( 'Drag with right mousebutton to rotate view' ) print( 'Drag up+down with middle mousebutton to zoom') scene.autocenter = True # uncomment any (or all) of those variants: S1 = sphere(pos=(0.0, 0.0, 0.0), radius=1.0, color=color.blue) #S2 = sphere(pos=(2.0, 0.0, 0.0), radius=1.0, material=materials.earth) #S3 = sphere(pos=(0.0, 2.0, 0.0), radius=1.0, material=materials.BlueMarble) #S4 = sphere(pos=(0.0, 0.0, 2.0), radius=1.0, # color=color.orange, material=materials.marble) while True: # Animation-loop rate(100) pass # no animation in this demo
Racket
[[File:Racket-sphere-plot.png|200px|thumb|right]]
Using the Typed Racket language with the plot library:
#lang typed/racket
(require plot/typed)
(plot3d (polar3d (λ (θ ρ) 1)) #:altitude 25)
REXX
This program is modeled after the '''C''' version.
The REXX language doesn't have a '''SQRT''' function, so a version is included here.
Same with the '''CEIL'''ing and '''FLOOR''' functions.
Programming note: the output will appear slightly different when executed on an EBCDIC machine (due to different dithering characters).
/*REXX program expresses a lighted sphere with simple characters used for shading. */
call drawSphere 19, 4, 2/10, '30 30 -50' /*draw a sphere with a radius of 19. */
call drawSphere 10, 2, 4/10, '30 30 -50' /* " " " " " " " ten. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
ceil: procedure; parse arg x; _= trunc(x); return _ +(x>0) * (x\=_)
floor: procedure; parse arg x; _= trunc(x); return _ -(x<0) * (x\=_)
norm: parse arg $a $b $c; _= sqrt($a**2 + $b**2 + $c**2); return $a/_ $b/_ $c/_
/*──────────────────────────────────────────────────────────────────────────────────────*/
drawSphere: procedure; parse arg r, k, ambient, lightSource /*obtain the four arguments*/
if 8=='f8'x then shading= ".:!*oe&#%@" /* EBCDIC dithering chars. */
else shading= "·:!°oe@░▒▓" /* ASCII " " */
parse value norm(lightSource) with s1 s2 s3 /*normalize light source. */
shadeLen= length(shading) - 1; rr= r**2; r2= r+r /*handy─dandy variables. */
do i=floor(-r ) to ceil(r ); x= i + .5; xx= x**2; $=
do j=floor(-r2) to ceil(r2); y= j * .5 + .5; yy= y**2; z= xx+yy
if z<=rr then do /*is point within sphere ? */
parse value norm(x y sqrt(rr - xx - yy) ) with v1 v2 v3
dot= min(0, s1*v1 + s2*v2 + s3*v3) /*the dot product of above.*/
b= -dot**k + ambient /*calculate the brightness.*/
if b<=0 then brite= shadeLen
else brite= max(0, (1-b) * shadeLen) % 1
$= $ || substr(shading, brite + 1, 1)
end /* [↑] build display line.*/
else $= $' ' /*append a blank to line. */
end /*j*/ /*[↓] strip trailing blanks*/
say strip($, 'T') /*show a line of the sphere*/
end /*i*/ /* [↑] display the sphere.*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d= digits(); numeric digits; h= d+6
numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g= g*.5'e'_%2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g
{{out|output|text= when using the default input and executed on an '''ASCII''' machine:}} (Shown at '''1/2''' size.)
eeeeeeeeee@@@@@@@
eoooooooooooooooeeeee@@@@@@@░
oo°°°!!!!!!!!°°°°°°ooooeeeee@@@@@@@░░
o°°!!!:::::::::!!!!!°°°°°ooooeeee@@@@@@@░░░
o°!!::::·········:::::!!!!°°°ooooeeeee@@@@@@@░░░░
o°!:::················::::!!!°°°°oooeeeee@@@@@@@░░░░░
o°!::····················::::!!!°°°°oooeeeee@@@@@@@░░░░░░
o°!::·······················:::!!!!°°°ooooeeee@@@@@@@@░░░░░░░
o°!::·························:::!!!°°°ooooeeeee@@@@@@@░░░░░░░░
o°!:···························:::!!!°°°°oooeeeee@@@@@@@@░░░░░░░░
o°!::··························::::!!!°°°ooooeeeee@@@@@@@@░░░░░░░░░
o°!::···························:::!!!!°°°ooooeeeee@@@@@@@@░░░░░░░░░░
o°!!::··························::::!!!°°°°ooooeeeee@@@@@@@@░░░░░░░░░░░
eo°!!::·························::::!!!°°°°ooooeeeee@@@@@@@@@░░░░░░░░░░░░
oo°!!::························::::!!!°°°°ooooeeeeee@@@@@@@@░░░░░░░░░░░░░
eoo°!!:::·····················::::!!!!°°°°oooooeeeee@@@@@@@@@░░░░░░░░░░░░░░
eoo°°!!:::·················:::::!!!!!°°°°ooooeeeeee@@@@@@@@@░░░░░░░░░░░░░░░
eoo°°!!!:::::··········:::::::!!!!!°°°°oooooeeeeee@@@@@@@@@@░░░░░░░░░░░░░░░
eeoo°°°!!!:::::::::::::::::!!!!!!°°°°°oooooeeeeee@@@@@@@@@@░░░░░░░░░░░░░░░░
eeooo°°°!!!!!!!:::::::!!!!!!!!°°°°°°oooooeeeeee@@@@@@@@@@@░░░░░░░░░░░░░░░░░
@eeooo°°°°°!!!!!!!!!!!!!!!°°°°°°°ooooooeeeeeee@@@@@@@@@@@░░░░░░░░░░░░░░░░░░
@@eeeoooo°°°°°°°°°°°°°°°°°°°°°oooooooeeeeeee@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░
@@@eeeoooooo°°°°°°°°°°°°°oooooooooeeeeeeee@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░
@@@eeeeeooooooooooooooooooooooeeeeeeeee@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░
@@@@@eeeeeeeooooooooooooeeeeeeeeeeee@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░
@@@@@@eeeeeeeeeeeeeeeeeeeeeeeee@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░
@@@@@@@@@eeeeeeeeeeeeeeeee@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░
░@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░@@@@@@@@@@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░@@@@@@@@@@@@@@@@@@░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░░
::···:::!!!°o
··············::!!°oo
··················::!!°°ooe
·····················::!!°°ooee
·······················::!!°°ooee
························::!!°°oooee
·························::!!°°oooeee
:························::!!!°°oooeeee
························::!!!°°ooooeeee
:······················::!!!°°°oooeeeee
:····················:::!!!°°°oooeeeeee
!:·················:::!!!°°°°oooeeeeeee
°!:::···········::::!!!!°°°ooooeeeeeeee
°!!!:::::::::::!!!!!°°°°oooooeeeeeeee
o°°!!!!!!!!!!!!!°°°°°oooooeeeeeeeee
oo°°°°°°°°°°°°°°ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
```
## Ruby
{{libheader|Shoes}}
Shoes comes with this sample program.
[[File:sphere.shoes.png|thumb|right]]
```ruby>Shoes.app :width =
500, :height => 500, :resizable => false do
image 400, 470, :top => 30, :left => 50 do
nostroke
fill "#127"
image :top => 230, :left => 0 do
oval 70, 130, 260, 40
blur 30
end
oval 10, 10, 380, 380
image :top => 0, :left => 0 do
fill "#46D"
oval 30, 30, 338, 338
blur 10
end
fill gradient(rgb(1.0, 1.0, 1.0, 0.7), rgb(1.0, 1.0, 1.0, 0.0))
oval 80, 14, 240, 176
image :top => 0, :left => 0 do
fill "#79F"
oval 134, 134, 130, 130
blur 40
end
image :top => 150, :left => 40, :width => 320, :height => 260 do
fill gradient(rgb(0.7, 0.9, 1.0, 0.0), rgb(0.7, 0.9, 1.0, 0.6))
oval 60, 60, 200, 136
blur 20
end
end
end
```
## Scala
```Scala
object Sphere extends App {
private val (shades, light) = (Seq('.', ':', '!', '*', 'o', 'e', '&', '#', '%', '@'), Array(30d, 30d, -50d))
private def drawSphere(r: Double, k: Double, ambient: Double): Unit = {
def dot(x: Array[Double], y: Array[Double]) = {
val d = x.head * y.head + x(1) * y(1) + x.last * y.last
if (d < 0) -d else 0D
}
for (i <- math.floor(-r).toInt to math.ceil(r).toInt; x = i + .5)
println(
(for (j <- math.floor(-2 * r).toInt to math.ceil(2 * r).toInt; y = j / 2.0 + .5)
yield if (x * x + y * y <= r * r) {
def intensity(vec: Array[Double]) = {
val b = math.pow(dot(light, vec), k) + ambient
if (b <= 0) shades.length - 2
else math.max((1 - b) * (shades.length - 1), 0).toInt
}
shades(intensity(normalize(Array(x, y, scala.math.sqrt(r * r - x * x - y * y)))))
} else ' ').mkString)
}
private def normalize(v: Array[Double]): Array[Double] = {
val len = math.sqrt(v.head * v.head + v(1) * v(1) + v.last * v.last)
v.map(_ / len)
}
normalize(light).copyToArray(light)
drawSphere(20, 4, .1)
drawSphere(10, 2, .4)
}
```
{{Out}}See it in running in your browser by [https://scalafiddle.io/sf/uSm8bJ9/0 ScalaFiddle (JavaScript)] or by [https://scastie.scala-lang.org/TtVHUp3aS0eDEB6YCW4gKg Scastie (JVM)].
## Sidef
{{trans|Perl 6}}
Produces a PGM image.
```ruby
func normalize (vec) { vec »/» (vec »*« vec -> sum.sqrt) }
func dot (x, y) { -(x »*« y -> sum) `max` 0 }
var x = var y = 255
x += 1 if x.is_even # must be odd
var light = normalize([ 3, 2, -5 ])
var depth = 255
func draw_sphere(rad, k, ambient) {
var pixels = []
var r2 = (rad * rad)
var range = (-rad .. rad)
for x,y in (range ~X range) {
if ((var x2 = x*x) + (var y2 = y*y) < r2) {
var vector = normalize([x, y, (r2 - x2 - y2).sqrt])
var intensity = (dot(light, vector)**k + ambient)
var pixel = (0 `max` (intensity*depth -> int) `min` depth)
pixels << pixel
}
else {
pixels << 0
}
}
return pixels
}
var outfile = %f'sphere-sidef.pgm'
var out = outfile.open('>:raw')
out.say("P5\n#{x} #{y}\n#{depth}") # .pgm header
out.print(draw_sphere((x-1)/2, .9, .2).map{.chr}.join)
out.close
```
## Smalltalk
there are various OpenGL bindings available; here is a translation of the bare-bones code from C/Go:
{{works with|Smalltalk/X}}
although there is a Point3 class in some loadable library, here is some self contained code, defining a local anon Point3D class.
```Smalltalk
Point3D :=
Point subclass:#Point3D
instanceVariableNames:'z'
classVariableNames:''
poolDictionaries:''
category:''
inEnvironment:nil.
Point3D compile:'z ^ z'.
Point3D compile:'z:v z := v'.
normalize := [:v | |invLen|
invLen := 1 / (dot value:v value:v) sqrt.
v x: v x * invLen.
v y: v y * invLen.
v z: v z * invLen.
].
dot := [:a :b |
(a x * b x) + (a y * b y) + (a z * b z)
].
drawSphere := [:r :k :amb :dir |
|w h imh vec img|
w := r*4. h := r*3.
img := Image width:w height:h depth:8.
img photometric:#blackIs0; createPixelStore.
vec := Point3D new.
0-r to:r do:[:x |
0-r to:r do:[:y |
|z s lum|
(z := (r*r) - (x*x) - (y*y)) >= 0 ifTrue:[
vec x: x.
vec y: y.
vec z: z sqrt.
normalize value:vec.
s := dot value:dir value:vec.
s < 0 ifTrue:[ s := 0 ].
lum := 255 * ((s raisedTo: k) + amb) / (1 + amb).
lum < 0 ifTrue:[
lum := 0
] ifFalse:[ lum > 255 ifTrue:[
lum := 255
]].
img atX:(x+(w//2)) y:(y+(h//2)) put:(Color greyByte:lum).
]
]
].
img
].
main := [
|dir img|
dir := Point3D new x:-30; y:-30; z:50; yourself.
normalize value:dir.
img := drawSphere value: 100 value: 1.5 value: 0.2 value: dir.
img displayOn:(View new extent:400@400; openAndWait).
img saveOn:'sphere.png'.
].
main value.
```
[[file:sphere-smalltalk.png]]
## SVG
Not quite a sphere.
[[file:sphere-ish.svg]]
## Swift
In Playground for example:
```Swift
class Sphere: UIView{
override func drawRect(rect: CGRect)
{
let context = UIGraphicsGetCurrentContext()
let locations: [CGFloat] = [0.0, 1.0]
let colors = [UIColor.whiteColor().CGColor,
UIColor.blueColor().CGColor]
let colorspace = CGColorSpaceCreateDeviceRGB()
let gradient = CGGradientCreateWithColors(colorspace,
colors, locations)
var startPoint = CGPoint()
var endPoint = CGPoint()
startPoint.x = self.center.x - (self.frame.width * 0.1)
startPoint.y = self.center.y - (self.frame.width * 0.15)
endPoint.x = self.center.x
endPoint.y = self.center.y
let startRadius: CGFloat = 0
let endRadius: CGFloat = self.frame.width * 0.38
CGContextDrawRadialGradient (context, gradient, startPoint,
startRadius, endPoint, endRadius,
0)
}
}
var s = Sphere(frame: CGRectMake(0, 0, 200, 200))
```
## Tcl
{{libheader|Tk}}
Assuming the task is to draw a likeness of a sphere, this would usually do:
```Tcl
proc grey {n} {format "#%2.2x%2.2x%2.2x" $n $n $n}
pack [canvas .c -height 400 -width 640 -background white]
for {set i 0} {$i < 255} {incr i} {
set h [grey $i]
.c create arc [expr {100+$i/5}] [expr {50+$i/5}] [expr {400-$i/1.5}] [expr {350-$i/1.5}] \
-start 0 -extent 359 -fill $h -outline $h
}
```
Results in this image:
[[image:Tcl-spheroid.gif]]
## TeX
{{libheader|PGF}}
The PGF shadings library includes a "ball" for a 3-D style highlight. For example with [[LaTeX]],
```TeX
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shadings}
\begin{document}
\begin{tikzpicture}
\shade[ball color=black] (0,0) circle (4);
\end{tikzpicture}
\end{document}
```
## VBScript
{{trans|C}}
```vb
shades = Array(".", ":", "!", "*", "o", "e", "&", "#", "%", "@")
light = Array(30, 30, -50)
Sub Normalize(v)
length = Sqr(v(0)*v(0) + v(1)*v(1) + v(2)*v(2))
v(0) = v(0)/length : v(1) = v(1)/length : v(2) = v(2)/length
End Sub
Function Dot(x, y)
d = x(0)*y(0) + x(1)*y(1) + x(2)*y(2)
If d < 0 Then Dot = -d Else Dot = 0 End If
End Function
'floor function is the Int function
'ceil function implementation
Function Ceil(x)
Ceil = Int(x)
If Ceil <> x Then Ceil = Ceil + 1 End if
End Function
Sub DrawSphere(R, k, ambient)
Dim i, j, intensity, inten, b, x, y
Dim vec(3)
For i = Int(-R) to Ceil(R)
x = i + 0.5
line = ""
For j = Int(-2*R) to Ceil(2*R)
y = j / 2 + 0.5
If x * x + y * y <= R*R Then
vec(0) = x
vec(1) = y
vec(2) = Sqr(R * R - x * x - y * y)
Normalize vec
b = dot(light, vec)^k + ambient
intensity = Int((1 - b) * UBound(shades))
If intensity < 0 Then intensity = 0 End If
If intensity >= UBound(shades) Then
intensity = UBound(shades)
End If
line = line & shades(intensity)
Else
line = line & " "
End If
Next
WScript.StdOut.WriteLine line
Next
End Sub
Normalize light
DrawSphere 20, 4, 0.1
DrawSphere 10,2,0.4
```
{{Out}}
```txt
&&&&&&&&&&#######
&eeeeeeeeeeeeeeee&&&&&&#######%
&eoooo*******oooooooeeeee&&&&&########%
eoo****!!!!!!!!******oooooeeee&&&&&########%%
eoo**!!!!::::::::!!!!!*****ooooeeee&&&&&########%%%
eo**!!::::::...:::::::!!!!!***ooooeeee&&&&&########%%%%
eo*!!:::.............:::::!!!!***ooooeeee&&&&&########%%%%%
eo*!!:::.................::::!!!!***ooooeeee&&&&#########%%%%%%
eo*!!::....................::::!!!****oooeeee&&&&&#########%%%%%%
&o**!::......................::::!!!****oooeeee&&&&&##########%%%%%%%
&o**!::.......................::::!!!****oooeeee&&&&&##########%%%%%%%%
&oo*!!::.......................:::!!!!***ooooeeee&&&&&##########%%%%%%%%%
&eo*!!::.......................::::!!!****ooooeeee&&&&&##########%%%%%%%%%%
eo**!!::......................::::!!!!***ooooeeeee&&&&&##########%%%%%%%%%%
&eo**!!:::...................:::::!!!!****ooooeeee&&&&&###########%%%%%%%%%%%
eeo**!!::::................:::::!!!!!****ooooeeee&&&&&&###########%%%%%%%%%%%
&eeo***!!:::::...........::::::!!!!!****oooooeeee&&&&&&###########%%%%%%%%%%%%%
&eeoo**!!!!::::::::::::::::::!!!!!*****ooooeeeee&&&&&&############%%%%%%%%%%%%%
&eeooo***!!!!::::::::::::!!!!!!!*****oooooeeeee&&&&&&############%%%%%%%%%%%%%%
&&eeooo***!!!!!!!!!!!!!!!!!!!******oooooeeeeee&&&&&&############%%%%%%%%%%%%%%%
&&eeeooo******!!!!!!!!!!********ooooooeeeeee&&&&&&&############%%%%%%%%%%%%%%%%
#&&eeeooooo******************oooooooeeeeee&&&&&&&#############%%%%%%%%%%%%%%%%%
#&&&eeeeoooooooo******oooooooooooeeeeeee&&&&&&&&#############%%%%%%%%%%%%%%%%%%
##&&&&eeeeeooooooooooooooooooeeeeeeee&&&&&&&&&##############%%%%%%%%%%%%%%%%%%%
##&&&&&eeeeeeeeeeeeeeeeeeeeeeeeee&&&&&&&&&################%%%%%%%%%%%%%%%%%%%
####&&&&&&eeeeeeeeeeeeeeeeeee&&&&&&&&&&&################%%%%%%%%%%%%%%%%%%%%%
#####&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#################%%%%%%%%%%%%%%%%%%%%%%
%#######&&&&&&&&&&&&&&&&&&&&&&&&###################%%%%%%%%%%%%%%%%%%%%%%%%
%###########&&&&&&&&&&&&&#######################%%%%%%%%%%%%%%%%%%%%%%%%%
%############################################%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#######################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%#################################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%#########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%#############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%
::...:::!!!*o
..............::!!*oo
..................::!!**ooe
.....................::!!**ooee
.......................::!!**ooee
........................::!!**oooee
.........................::!!**oooeee
:........................::!!!**oooeeee
........................::!!!**ooooeeee
:......................::!!!***oooeeeee
:....................:::!!!***oooeeeeee
!:.................:::!!!****oooeeeeeee
*!:::...........::::!!!!***ooooeeeeeeee
*!!!:::::::::::!!!!!****oooooeeeeeeee
o**!!!!!!!!!!!!!*****oooooeeeeeeeee
oo**************ooooooeeeeeeeeeee
eoooooooooooooooooeeeeeeeeeeeee
eeeooooooooeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeee
```
## XPL0
[[File:SphereXPL0.png|right]]
```XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
def R=100, R2=R*R; \radius, in pixels; radius squared
def X0=640/2, Y0=480/2; \coordinates of center of screen
int X, Y, Z, C, D2; \coords, color, distance from center squared
[SetVid($112); \set 640x480x24 graphics mode
for Y:= -R to +R do \for all the coordinates near the circle
for X:= -R to +R do \ which is under the sphere
[D2:= X*X + Y*Y;
C:= 0; \default color is black
if D2 <= R2 then \coordinate is inside circle under sphere
[Z:= sqrt(R2-D2); \height of point on surface of sphere above X,Y
C:= Z-(X+Y)/2+130; \color is proportional; offset X and Y, and
]; \ shift color to upper limit of its range
Point(X+X0, Y+Y0, C<<8+C); \green + blue = cyan
];
repeat until KeyHit; \wait for keystroke
SetVid($03); \restore normal text mode
]
```
## Yabasic
```Yabasic
ancho = 640 : alto = 480
open window 640,480
backcolor 16,16,16
clear window
sphera()
sub sphera()
local n
for n = 1 to 100
color 2*n, 2*n, 2*n
fill circle ancho/2-2*n/3, alto/2-n/2, 150-n
next n
end sub
```
## zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
{{trans|XPL0}}
[[File:Sphere.zkl.jpg|200px|thumb|right]]
```zkl
img:=PPM(640,480);
R:=100; R2:=R*R; //radius, in pixels; radius squared
X0:=640/2; Y0:=480/2; //coordinates of center of screen
foreach Y in ([-R..R]){ //for all the coordinates near the circle
foreach X in ([-R..R]){ // which is under the sphere
D2:=X*X + Y*Y;
C:=0; //default color is black
if(D2<=R2){ //coordinate is inside circle under sphere
Z:=(R2-D2).toFloat().sqrt();//height of point on surface of sphere above X,Y
C=0x82+Z-(X+Y)/2; //color is proportional; offset X and Y, and
} // shift color to upper limit of its range
img[X+X0,Y+Y0]=C.shiftLeft(8)+C; //green + blue = cyan
}
}
img.write(File("foo.ppm","wb"));
```
The radius of 100 is the max before the color calculation overflows 24 bits so for a radius (R) of, say 200, use
```zkl
img[X+X0,Y+Y0]=C*140+C;
```
Perhaps a more useful solution is to use GnuPlot (I grabbed the code from http://ayapin-film.sakura.ne.jp/Gnuplot/):
[[File:GnuplotSphere.zkl.png|250px|thumb|right]]
```zkl
#<<<
cmd:=0'|
set term wxt
set parametric
set urange [0:pi]
set vrange [0:2*pi]
set xyplane 0
set view equal xyz
set pm3d hidden3d 100 depthorder
set style line 100 lt 7 lw 0.1
set palette defined (0 "dark-blue", 1 "light-blue")
unset key
set samples 24
set isosamples 36
set title 'sphere (pm3d)' font "Times,20"
R = 3
splot R*sin(u)*cos(v), R*sin(u)*sin(v), R*cos(u) w pm3d
|;
#<<<
gnuplot:=System.popen("gnuplot","w");
gnuplot.write(cmd); gnuplot.flush();
ask("Hit return to finish"); gnuplot.close();
```
Where "term wxt" is X11 on my Linux box. A window pops up and stays until the pipe is closed.
## ZX Spectrum Basic
```zxbasic
1 REM fast
50 REM spheer with hidden lines and rotation
100 CLS
110 PRINT "sphere with lenght&wide-circles"
120 PRINT "_______________________________"''
200 INPUT "rotate x-as:";a
210 INPUT "rotate y-as:";b
220 INPUT "rotate z-as:";c
225 INPUT "distance lines(10-45):";d
230 LET u=128: LET v=87: LET r=87: LET bm=PI/180: LET h=.5
240 LET s1=SIN (a*bm): LET s2=SIN (b*bm): LET s3=SIN (c*bm)
250 LET c1=COS (a*bm): LET c2=COS (b*bm): LET c3=COS (c*bm)
260 REM calc rotate matrix
270 LET ax=c2*c3: LET ay=-c2*s3: LET az=s2
280 LET bx=c1*s3+s1*s2*c3
290 LET by=c1*c3-s1*s2*s3: LET bz=-s1*c2
300 LET cx=s1*s3-c1*s2*c3
310 LET cy=s1*c3+c1*s2*s3: LET cz=c1*c2
400 REM draw outer
410 CLS : CIRCLE u,v,r
500 REM draw lenght-circle
510 FOR l=0 TO 180-d STEP d
515 LET f1=0
520 FOR p=0 TO 360 STEP 5
530 GO SUB 1000: REM xx,yy,zz calc
540 IF yy>0 THEN LET f2=0: LET f1=0: GO TO 580
550 LET xb=INT (u+xx+h): LET yb=INT (v+zz+h): LET f2=1
560 IF f1=0 THEN LET x1=xb: LET y1=yb: LET f1=1: GO TO 580
570 PLOT x1,y1: DRAW xb-x1,yb-y1: LET x1=xb: LET y1=yb: LET f1=f2
580 NEXT p
590 NEXT l
600 REM draw wide-circle
610 FOR p=-90+d TO 90-d STEP d
615 LET f1=0
620 FOR l=0 TO 360 STEP 5
630 GO SUB 1000: REM xx,yy,zz
640 IF yy>0 THEN LET f2=0: LET f1=0: GO TO 680
650 LET xb=INT (u+xx+h): LET yb=INT (v+zz+h): LET f2=1
660 IF f1=0 THEN LET x1=xb: LET y1=yb: LET f1=1: GO TO 680
670 PLOT x1,y1: DRAW xb-x1,yb-y1: LET x1=xb: LET y1=yb: LET f1=f2
680 NEXT l
690 NEXT p
700 PRINT #0;"...press any key...": PAUSE 0: RUN
999 REM sfere-coordinates>>>Cartesis Coordinate
1000 LET x=r*COS (p*bm)*COS (l*bm)
1010 LET y=r*COS (p*bm)*SIN (l*bm)
1020 LET z=r*SIN (p*bm)
1030 REM p(x,y,z) rotate to p(xx,yy,zz)
1040 LET xx=ax*x+ay*y+az*z
1050 LET yy=bx*x+by*y+bz*z
1060 LET zz=cx*x+cy*y+cz*z
1070 RETURN
```
[[Category:Geometry]]