| Bezier Interpolation BlitzBasic 3D Example von Markus |
| [code:1:8b1bcd8c09] ;Bezier Interpolation BlitzBasic 3D Example from Markus Rauch ;MR 14.04.2003 ;-------------------------------------------------------- Graphics3D 800,600,16,0 SetBuffer BackBuffer() AppTitle " Bezier Interpolation BlitzBasic 3D Example from Markus Rauch" ;-------------------------------------------------------- Global camp=CreatePivot() Global cam=CreateCamera(camp) CameraZoom cam,1 CameraRange cam,1,10000 PositionEntity camp,0,0,-200 ;-------------------------------------------------------- Type Vector3D Field x#,y#,z# Field Pitch# Field Yaw# Field Roll# End Type Dim ve.Vector3D(100) ve.Vector3D(0)=New Vector3D ve.Vector3D(1)=New Vector3D ve.Vector3D(2)=New Vector3D ve.Vector3D(3)=New Vector3D Global VectorMax=4 Global p.Vector3D=New Vector3D ve(0)x=-50 ve(0)y=50 ve(0)z=0 ve(1)x=-25 ve(1)y=0 ve(1)z=0 ve(2)x=25 ve(2)y=50 ve(2)z=0 ve(3)x=0 ;Moving ve(3)y=0 ve(3)z=0 While Not KeyHit(1) RenderWorld ;-------------------- Moving Point (3) Local w# ve(3)x=50+Sin(w)*100 ve(3)y= 0+Cos(w)*100 w#=w#+1 :If w>360.0 Then w=w-360.0 ;-------------------- Color 255,255,0 Local mu# Local st#=0.01 mu=0.0 Repeat Bezier4 p,ve(0),ve(1),ve(2),ve(3),mu ;Only 4 Points ;Bezier p,mu ;All Points Plot3D p mu=mu+st If mu>1.0 Then Exit Forever ;Show all Points For v=0 To VectorMax-1 Color 128,128,128 Text3D ve(v),"V "+V Color 255,0,0 Plot3D ve(v) Next Flip Wend End ;########################################################################## Function Bezier3(p.Vector3D,p1.Vector3D,p2.Vector3D,p3.Vector3D,mu#) ;MR 13.04.2003 ;Three control point Bezier interpolation ;mu ranges from 0 To 1, start To End of curve Local mum1#,mum12#,mu2# mu2 = mu * mu mum1 = 1 - mu mum12 = mum1 * mum1 px = p1x * mum12 + 2 * p2x * mum1 * mu + p3x * mu2 py = p1y * mum12 + 2 * p2y * mum1 * mu + p3y * mu2 pz = p1z * mum12 + 2 * p2z * mum1 * mu + p3z * mu2 End Function Function Bezier4(p.Vector3D,p1.Vector3D,p2.Vector3D,p3.Vector3D,p4.Vector3D,mu#) ;MR 13.04.2003 ;Four control point Bezier interpolation ;mu ranges from 0 To 1, start To End of curve Local mum1#,mum13#,mu3# mum1 = 1.0 - mu mum13 = mum1 * mum1 * mum1 mu3 = mu * mu * mu px = mum13*p1x + 3.0*mu*mum1*mum1*p2x + 3.0*mu*mu*mum1*p3x + mu3*p4x py = mum13*p1y + 3.0*mu*mum1*mum1*p2y + 3.0*mu*mu*mum1*p3y + mu3*p4y pz = mum13*p1z + 3.0*mu*mum1*mum1*p2z + 3.0*mu*mu*mum1*p3z + mu3*p4z End Function ;########################################################################## Function Bezier(p.Vector3D,mu#) ;MR 14.04.2003 ;General Bezier curve ;Number of control points is n+1 ;mu 0 bis 1 IMPORTANT, the Last point is Not computed Local k,kn,nn,nkn Local blend#,muk#,munk# Local px#,py#,pz# Local n=VectorMax-1 px=0.0 py=0.0 pz=0.0 muk = 1.0 munk = pow(1.0-mu,Float(n)) For k=0 To n nn = n kn = k nkn = n - k blend = muk * munk muk =muk * mu munk = munk / (1.0-mu) While nn => 1 blend=blend * nn nn=nn-1 If kn > 1 Then blend=blend / Float(kn) kn=kn-1 EndIf If nkn > 1 Then blend=blend / Float(nkn) nkn=nkn-1 EndIf Wend px=px+ve(k)x * blend py=py+ve(k)y * blend pz=pz+ve(k)z * blend Next End Function ;########################################################################## Function pow#(a#,b#) ;MR 14.04.2003 ;C Like :-) Return a^b End Function ;########################################################################## Function Plot3D(p.Vector3D) ;MR 14.04.2003 ;cam ist Global und das Handle der Camera Local x,y CameraProject cam,px,py,pz x=ProjectedX() y=ProjectedY() Plot x,y End Function ;########################################################################## Function Text3D(p.Vector3D,t$) ;MR 14.04.2003 ;cam ist Global und das Handle der Camera Local x,y CameraProject cam,px,py,pz x=ProjectedX() y=ProjectedY() Text x,y,t$,True,True End Function ;########################################################################## Function CubicInterpolate#(y0#,y1#,y2#,y3#,mu#) ;MR 13.04.2003 Local a0#,a1#,a2#,a3#,mu2# mu2 = mu*mu a0 = y3 - y2 - y0 + y1 a1 = y0 - y1 - a0 a2 = y2 - y0 a3 = y1 Return (a0*mu*mu2+a1*mu2+a2*mu+a3) End Function ;########################################################################## [/code:1:8b1bcd8c09] |