Code archives/3D Graphics - Maths/Wheel rolling example
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| Shows how to roll a wheel, unlike a ball it cannot go in any direction. |
;wheel rolling physics example by Jeppe Nielsen 2003 ;email: nielsen_jeppe@hotmail.com Const gravity#=-0.04;-0.02 ;gravity constant Graphics3D 800,600,16,2 Const wheel_col=1 Const world_col=2 Collisions wheel_col,world_col,2,3 ;create old amiga texture :-) Global texture texture=CreateTexture(16,16) SetBuffer TextureBuffer(texture) Color 255,255,255 Rect 0,0,16,16,1 Color 255,0,0 Rect 0,0,8,8,1 Rect 8,8,8,8,1 ScaleTexture texture,0.5,0.5 Global groundtexture=CreateTexture(32,32,1+8) SetBuffer TextureBuffer(groundtexture) Color 0,0,0 Rect 0,0,32,32,1 Color 0,0,255 Rect 0,0,32,32,0 ScaleTexture groundtexture,2,2 SetBuffer BackBuffer() Color 255,255,255 plane=CreatePlane() EntityTexture plane,groundtexture EntityType plane,world_col EntityAlpha plane,0.5 light=CreateLight(1) RotateEntity light,30,20,0 obj=CreateCube() EntityType obj,world_col PositionEntity obj,0,-20,-175 ScaleEntity obj,10,140,40 RotateEntity obj,75,0,0 EntityTexture obj,texture sphere=CreateSphere(32) EntityType sphere,world_col ScaleEntity sphere,40,40,40 EntityTexture sphere,texture Dim VertArray(0) sphere1=AdjustTriangles(sphere,0.5,False) sphere2=AdjustTriangles(Sphere,0.5,True) FlipMesh sphere2 PositionEntity sphere1,0,35,0 RotateEntity sphere1,180,0,0 ScaleEntity sphere1,40,40,40 EntityTexture sphere1,texture EntityType sphere1,world_col RotateEntity sphere2,180,0,0 PositionEntity sphere2,0,35,0 ScaleEntity sphere2,40,40,40 EntityTexture sphere2,texture EntityType sphere2,world_col camera=CreateCamera() CameraClsColor camera,0,0,255 PositionEntity camera,0,600,-40 wheel.wheel=wheelnew(0,4,0,2) zoom#=14 Repeat zoom#=zoom#-MouseZSpeed() wheelcamera(camera,wheel,0,zoom#,-zoom#,0,5,0) wheelcontrol(wheel) wheelupdate() RenderWorld() Color 255,255,255 Text 10,10,"Arrow keys to control wheel" Text 10,20,"Space to lift wheel" Text 10,30,"Scroll on mouse to zoom" Flip Until KeyDown(1) End Type wheel Field e ;entity Field cylinder Field pivot Field x#,y#,z# ; position in 3d-space Field vx#,vy#,vz# ; velocity Field ax#,ay#,az# ; acceleration Field size# Field vel# Field vx2#,vy2#,vz2# ; temp velocity Field collided End Type Function wheelnew.wheel(x#,y#,z#,size#=1) c.wheel=New wheel c\x#=x# c\y#=y# c\z#=z# c\size=size c\e=CreatePivot() c\cylinder=CreateCylinder(64) RotateMesh c\cylinder,0,0,90 c\pivot=CreatePivot() EntityType c\e,wheel_col EntityRadius c\e,c\size PositionEntity c\e,c\x,c\y,c\z ScaleEntity c\cylinder,c\size,c\size,c\size EntityTexture c\cylinder,texture Return c End Function Function wheelupdate() For c.wheel=Each wheel c\vy#=c\vy#+gravity# c\vx#=c\vx#+c\ax# c\vy#=c\vy#+c\ay# c\vz#=c\vz#+c\az# c\x#=EntityX(c\e) c\y#=EntityY(c\e) c\z#=EntityZ(c\e) TranslateEntity c\e,c\vx,c\vy,c\vz Next UpdateWorld() For c.wheel=Each wheel ;correct velocity if collided c\vx2=(EntityX(c\e)-c\x) c\vy2=(EntityY(c\e)-c\y) c\vz2=(EntityZ(c\e)-c\z) c\x#=EntityX(c\e) c\y#=EntityY(c\e) c\z#=EntityZ(c\e) PositionEntity c\cylinder,c\x,c\y,c\z PositionEntity c\pivot,c\x,c\y,c\z TFormVector 1,0,0,c\e,0 AlignToVector c\cylinder,TFormedX(),TFormedY(),TFormedZ(),1,0.6 c\collided=0 If EntityCollided(c\e,world_col) c\collided=1 avnx#=0 avny#=0 avnz#=0 count=CountCollisions(c\e) For i = 1 To count ; Get the normal of the surface which the entity collided with. Nx# = CollisionNX(c\e, i) Ny# = CollisionNY(c\e, i) Nz# = CollisionNZ(c\e, i) avnx#=avnx+Nx avny#=avny+Ny avnz#=avnz+Nz ; Compute the dot product of the entity's motion vector and the normal of the surface collided with. VdotN# = c\vx#*Nx# + c\vy#*Ny# + c\vz#*Nz# ; Calculate the normal force. NFx# = -2.0 * Nx# * VdotN# NFy# = -2.0 * Ny# * VdotN# NFz# = -2.0 * Nz# * VdotN# ; Add the normal force to the direction vector. c\vx# = c\vx# + NFx# c\vy# = c\vy# + NFy# c\vz# = c\vz# + NFz# Next If count>0 ;average collision normals avnx#=avnx/count avny#=avny/count avnz#=avnz/count ;align controlpivot to averaged collision normals AlignToVector c\e,avnx,avny,avnz,2 ;calculate length of motion vector, or total velocity. l#=Sqr(c\vx*c\vx+c\vy*c\vy+c\vz*c\vz) ;get normalized direction of motion, the vector will have a length of one. ;the +0.00001 is there to aviod NaN (not a number) numbers. This happens ;if the length of the vector is 0. TFormNormal c\vx,c\vy+0.00001,c\vz,0,0 vx#=TFormedX() vy#=TFormedY() vz#=TFormedZ() ;get direction of wheel TFormNormal 0,0,1,c\e,0 ;calculate a dot product, a number between -1 and 1 to determine angle ;calculate angle like this: angle#=Acos(dot#) dot#=TFormedX()*vx+TFormedY()*vy+TFormedZ()*vz ;correct velocities, by multiplying the controlpivot´s direction with ;the dot product, followed by the original velocity vector length: c\vx=TFormedX()*dot*l c\vy=TFormedY()*dot*l c\vz=TFormedZ()*dot*l RotateEntity c\pivot,EntityPitch(c\e),EntityYaw(c\e),EntityRoll(c\e) EndIf c\vel#=Sqr(c\vx2*c\vx2+c\vy2*c\vy2+c\vz2*c\vz2) ;slow down due To friction c\vx#=c\vx*0.98 c\vy#=c\vy*0.98 c\vz#=c\vz*0.98 EndIf EntityParent c\cylinder,c\pivot TFormVector c\vx,c\vy,c\vz,0,c\e ;moving forward If TFormedZ()>0 TurnEntity c\pivot,c\vel#*(180/Pi)/c\size#,0,0 Else ;moving backwards TurnEntity c\pivot,-c\vel#*(180/Pi)/c\size#,0,0 EndIf EntityParent c\cylinder,0 ;reset acceleration c\ax#=0 c\ay#=0 c\az#=0 Next End Function Function wheelcontrol(c.wheel) If c\collided=1 If KeyDown(200) TFormVector 0,0,0.05,c\e,0 c\ax#=TFormedX() c\ay#=TFormedY() c\az#=TFormedZ() EndIf If KeyDown(208) c\vx=c\vx*0.94 c\vy=c\vy*0.94 c\vz=c\vz*0.94 EndIf EndIf If KeyDown(57) c\ay#=c\ay+0.05 EndIf If KeyDown(203) TurnEntity c\e,0,2,0 EndIf If KeyDown(205) TurnEntity c\e,0,-2,0 EndIf End Function Function wheelcamera(camera,b.wheel,camx#,camy#,camz#,aimx#=0,aimy#=0,aimz#=0,smoothcam#=0.1,roll#=0) TFormPoint camx#,camy#,camz#,b\e,0 dx#=(TFormedX()-EntityX(camera))*smoothcam# dy#=(TFormedY()-EntityY(camera))*smoothcam# dz#=(TFormedZ()-EntityZ(camera))*smoothcam# TranslateEntity camera,dx,dy,dz TFormPoint aimx#,aimy#,aimz#,b\e,0 dx# = EntityX(camera)-TFormedX() dy# = EntityY(camera)-TFormedY() dz# = EntityZ(camera)-TFormedZ() dist#=Sqr#((dx#*dx#)+(dz#*dz#)) pitch#=ATan2(dy#,dist#) yaw#=ATan2(dx#,-dz#) RotateEntity camera,pitch#,yaw#,roll# End Function ;function by Graythe Function AdjustTriangles%(EntityNo%,Triangles#,FreeSource%=True,FX%=False) Dim VertArray(2^16) Copied=CreateMesh(GetParent(EntityNo)) For SurfLoop=1 To CountSurfaces(EntityNo) NewSurface=CreateSurface(Copied) OldSurface=GetSurface(EntityNo,SurfLoop) NoVertices=CountVertices(OldSurface)-1 TotTriangles=Int(CountTriangles(OldSurface)*Triangles)-1 For TriLoop=False To TotTriangles For CornerLoop=False To 2 tri=TriangleVertex(OldSurface,TriLoop,CornerLoop) VertArray(tri)=True Next Next For VertLoop = False To NoVertices If VertArray(VertLoop) Then NewVertex=AddVertex(NewSurface,VertexX(OldSurface,VertLoop),VertexY(OldSurface,VertLoop),VertexZ(OldSurface,VertLoop),VertexU(OldSurface,VertLoop),VertexV(OldSurface,VertLoop),VertexW(OldSurface,VertLoop)) End If Next For TriLoop=False To TotTriangles AddTriangle NewSurface, TriangleVertex(OldSurface,TriLoop,False),TriangleVertex(OldSurface,TriLoop,1),TriangleVertex(OldSurface,TriLoop,2) Next Next Dim VertArray(0) UpdateNormals Copied If FX Then EntityFX Copied,FX If FreeSource Then FreeEntity EntityNo Return Copied End Function |