Spline surface interpolation
Hello,
I try to interpole a spline Surface.
I have a grid of N*M points.
I need to compute (N-1)*(M-1) spline patchs.
I impose that these patchs are udegree=vdegree=3.
So a patch equation is like that :
a + bu + cu*u + d*u*u*u + v*(e + fu + gu*u + h*u*u*u) + v*v*(i + ju + ku*u + l*u*u*u) + v*v*v*(m + nu + ou*u + p*u*u*u)
16 unknow parameters to get.
I can get, for each point, the utan, and vtan.
I also know the value on uvtan on the 4 corners of the whole surface.
Now, what I need is the uvtan on each point.
If I have that, for each patch, I will have 16 equations, and it will be perfect to finish computing the surface patch per patch. Actually, with points, utan, and vtan, I have only 12.
I think the missing constraints are, if P is a patch, and Q its right patch, Puv(1,0) = Quv(0,0) and Puv(1,1) = Quv(0,1) (assuming all patch have urange=vrange = 0..1)
But anyway, I don't manage to make a matrix to compute all my uvtan.
I bet the matrix will be width = height = M*N, but if I could have a smallest matrix, or astuces to inverse it faster, it should be better.
If someone can give me clues to get my uvtan, it should help me a lot !
Thank you !
* sorry for my english, this is not my main language...
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