Tesselate do not any effect on UV Coordinate

Hello
i want to find a way to correct the zigzag texture on my mesh
i know what is the correct way ( the first solution in this forum is written by me about 7 years ago ) i know Projective Interpolation is my solution but it work on flat surface my mesh is a face(female face)

so i thinking about adding vertext between the vertext

in first of all i write an catmull-clark algorithm in c#
everything works fine but the FPS was near to die
8696097--1173618--delete.png

in second i try to use a GPU based solution (tesselate)
it works fine but didn’t change any thing in Texture just add edge and vertext in mesh is changed and uv coordinates is the same

i want a shader way to do it

is there a way to use tesselate to correct Uv texturing zigzag ?

Nope. GPU tessellation is using the same barycentric per triangle interpolation that causes the UVs to get “zigzag” in the first place.

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