Code archives/3D Graphics - Mesh/Cube to Sphere Transformation
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| This is a demo of a Cube to Sphere transformation. The six sides (patches) of a segmented cube gets deformed until the cube looks like a sphere, with no distortion at the poles - and the patches fit perfect together! Based on a code from Birdie and some maths from "Math Proofs". Can be used for many cases, a very round sphere or even a procedural planet with fractal subdivision (I dunno how but Infinity uses this method). You can even create very high detail spheres tuning the detail variable. Screenshot:  | |||||
AppTitle "Cube to Sphere Transformation" Graphics3D 800,600,32,2 ; detail of the cube/sphere detail=10 Global transform$[1] : transform[0]="Sphere" : transform[1]="Cube" pivot=CreatePivot() ; Camera cam=CreateCamera(pivot) CameraRange cam,0.01,1000 PositionEntity cam,0,0,-3 ; create segmented Cube cube=CreateSegCube(detail) EntityColor cube,0,255,0 EntityFX cube,1+16 MoveMouse 400,300 WireFrame 1 While Not KeyHit(1) ; movement / rotating mxs#=MouseXSpeed() mys#=MouseYSpeed() TurnEntity cube,0,mxs,0 TurnEntity pivot,mys,0,0 MoveEntity cam,0,0,(KeyDown(200)-KeyDown(208))*1.0/60 ; W = Wireframe If KeyHit(17) Then wf=1-wf : WireFrame 1-wf ; SPACE = transform If KeyHit(57) Then switch=1-switch If switch=1 Then ; transforms cube to sphere Cube2Sphere(cube) Else ; creates a new cube FreeEntity cube cube=CreateSegCube(detail) EntityColor cube,0,255,0 EntityFX cube,1+16 EndIf EndIf RenderWorld Text 0,0,TrisRendered()+" Tris" Text 0,15,"W for Wireframe" Text 0,30,"SPACE for "+transform[switch] Flip Wend End ; transform a cube patch to sphere patch Function Cube2Sphere(mesh%) Local s%,surf%,v% Local vx#,vy#,vz# For s=1 To CountSurfaces(mesh) surf=GetSurface(mesh,s) For v=0 To CountVertices(surf)-1 vx=VertexX(surf,v) vy=VertexY(surf,v) vz=VertexZ(surf,v) VertexCoords surf,v,SphericalX(vx,vy,vz)*1.333333,SphericalY(vx,vy,vz)*1.333333,SphericalZ(vx,vy,vz)*1.333333 Next Next End Function ; calculate spherical X Function SphericalX#(x#,y#,z#) Return x*Sqr(1.0-y*y*0.5-z*z*0.5+y*y*z*z*1.0/3) End Function ; calculate spherical Y Function SphericalY#(x#,y#,z#) Return y*Sqr(1.0-z*z*0.5-x*x*0.5+z*z*x*x*1.0/3) End Function ; calculate spherical Z Function SphericalZ#(x#,y#,z#) Return z*Sqr(1.0-x*x*0.5-y*y*0.5+x*x*y*y*1.0/3) End Function ; creates a segmented cube Function CreateSegCube(segs=1,parent=0) Local side%,surf% Local stx#,sty#,stp#,y# Local a%,x#,v#,b%,u# Local v0%,v1%,v2%,v3% Local mesh%=CreateMesh(parent) ; sides For side=0 To 3 surf=CreateSurface( mesh ) stx=-.5 sty=stx stp=Float(1)/Float(segs) y=sty For a=0 To segs x=stx v=a/Float(segs) For b=0 To segs u=b/Float(segs) AddVertex(surf,x,y,0.5,u,v) x=x+stp Next y=y+stp Next For a=0 To segs-1 For b=0 To segs-1 v0=a*(segs+1)+b:v1=v0+1 v2=(a+1)*(segs+1)+b+1:v3=v2-1 AddTriangle( surf,v0,v1,v2 ) AddTriangle( surf,v0,v2,v3 ) Next Next RotateMesh mesh,0,90,0 Next ;top and bottom RotateMesh mesh,0,90,90 For side=0 To 1 surf=CreateSurface( mesh ) stx#=-.5 sty#=stx stp#=Float(1)/Float(segs) y#=sty For a=0 To segs x#=stx v#=a/Float(segs) For b=0 To segs u#=b/Float(segs) AddVertex(surf,x,y,0.5,u,v) x=x+stp Next y=y+stp Next For a=0 To segs-1 For b=0 To segs-1 v0=a*(segs+1)+b:v1=v0+1 v2=(a+1)*(segs+1)+b+1:v3=v2-1 AddTriangle( surf,v0,v1,v2 ) AddTriangle( surf,v0,v2,v3 ) Next Next RotateMesh mesh,180,0,0 Next ; scale uniform to -1 to +1 space in X/Y/Z dimensions FitMesh mesh,-1,-1,-1,2,2,2,1 Return mesh End Function |
Comments
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| What is the strength# variable for? |
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| Oh I forgot to delete that (did that now). You can actually multiply the vx/vy/vz values in the Cube2Sphere function before the transformation to create "rounded cubes" and very strange objects, 1.0 is a perfect sphere. |
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