deCasteljau2dai

[liuyuanhao]

Dear canitesc,
Thank you for your previous help!May you tell me the method of the function deCasteljau2dai?Or may you give me the relevant paper of it?
Thank you so much!
Deeply grateful,
Jim

[canitesc]

Dear Jim,

There are several parts to that function, but in the first part it applies the deCasteljau algorithm ( https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm ) to calculate the Bezier coefficients of the basis functions on the refined 2x2 mesh. The 1D algorithm is applied in both the u and v directions to produce the 2D refinement.

In the second part, the basis functions are truncated to ensure the linear dependence of the basis, in the lines 85-99.

Finally, in the last part, the Bezier coefficients for the new basis functions are calculated. This part is a little bit more involved, because it involves checking whether some of the old basis functions can be removed from the mesh. The resulting Bezier coefficients are stored in the matrices Ce1, ..., Ce4, and the basis function indices are stored in in1, ..., in4. A somewhat simplified description of the procedure is given in the original paper on PHT splines: https://doi.org/10.1016/j.gmod.2008.03.001

[shuyiyang-code]

Dear canitesc,
Thank you very much for your help. When I run blade.m, the function recoverDerivEstGal will give an error message. Is there something wrong with this function?