I just want to know in detail about a certain type of parametric surface which could exactly interpolate its control points (say 4x4) as what Catmull-Rom spline did in 2D. Can anyone tell me if there is such a type of parametric surface? And detailed documents are preferred. ThanX in advance.

quote:Original post by Nik02
Catmull-Rom interpolation works in 3d, also - I think it could be used to interpolate the surface.

-Nik

I''ve tried the following code. But the result is disappointing.

MB is the Catmull-Rom basis matrix.

D3DXMatrixTranspose(&MBt,&MB);
Mx=MB*Gx*MBt;
My=MB*Gy*MBt;
Mz=MB*Gz*MBt;

void Calc(float fu, float fv, D3DXMATRIX Mx, D3DXMATRIX My,
D3DXMATRIX Mz, D3DXVECTOR3 &r)
{
D3DXVECTOR4 tu,tv,tx,ty,tz;

tu=D3DXVECTOR4(fu*fu*fu,fu*fu,fu,1.0f);
tv=D3DXVECTOR4(fv*fv*fv,fv*fv,fv,1.0f);

tx=D3DXVECTOR4(tu.x*Mx._11+tu.y*Mx._12+tu.z*Mx._13+tu.w*Mx._14,
tu.x*Mx._21+tu.y*Mx._22+tu.z*Mx._23+tu.w*Mx._24,
tu.x*Mx._31+tu.y*Mx._32+tu.z*Mx._33+tu.w*Mx._34,
tu.x*Mx._41+tu.y*Mx._42+tu.z*Mx._43+tu.w*Mx._44);
ty=D3DXVECTOR4(tu.x*My._11+tu.y*My._12+tu.z*My._13+tu.w*My._14,
tu.x*My._21+tu.y*My._22+tu.z*My._23+tu.w*My._24,
tu.x*My._31+tu.y*My._32+tu.z*My._33+tu.w*My._34,
tu.x*My._41+tu.y*My._42+tu.z*My._43+tu.w*My._44);
tz=D3DXVECTOR4(tu.x*Mz._11+tu.y*Mz._12+tu.z*Mz._13+tu.w*Mz._14,
tu.z*Mz._21+tu.y*Mz._22+tu.z*Mz._23+tu.w*Mz._24,
tu.z*Mz._31+tu.y*Mz._32+tu.z*Mz._33+tu.w*Mz._34,
tu.z*Mz._41+tu.y*Mz._42+tu.z*Mz._43+tu.w*Mz._44);

r=D3DXVECTOR3(D3DXVec4Dot(&tx,&tv),
D3DXVec4Dot(&ty,&tv),
D3DXVec4Dot(&tz,&tv));
}

Suppose control point 0 is (-8.250,0.0469,-8.250)

when I sent (fu=0.0f, fv=0.0f) into Calc, I got ridiculus result in r=(-8.000,0.0469,8.000)

They didn''t match at all!

Any one can help me figure this out?