I have 2 triangles ABC and PMN

I want to generalize the triangle PMN from points to lines, where any choice along that line will produce the same UV mapping for the triangle ABC

Basically i want to find all triangles that project to a given set of UV coordinates

And as the projection throws away one dimension that should be infinitely many, but they should have some ordering

So i should be able to start with one and then walk along a line to find all

i am not sure on how i could do that, any advice would be appreciated.

Formula that creates UV mapping from triangle PMN & reverse: reversing plane projection texture mapping algorithm

I am using an old Runescape model format, also used by Thief and Quake. In this format, instead of specifying UV coordinates for each vertex ABC, we specify a second trio of vertices PMN. Those vertices are then used to project UV texture coordinates onto ABC.

Some previous Q&A explains this projection algorithm and how to reverse it.

I have a mesh with UVs that I want to save in this format. To do that, I want to find a trio of vertices PMN for each triangle ABC that reproduce the correct UVs.

These PMN vertices are chosen from the collection of vertices already in my mesh.

I could search every possible ordered triangle in my mesh, but that scales as \$O(n^3)\$ and would be impractical for meshes with high vertex counts.

How can I more efficiently find a PMN triangle that produces my desired UV coordinates on each triangle ABC?

I have 2 triangles ABC and PMN

I want to generalize the triangle PMN from points to lines, where any choice along that line will produce the same UV mapping for the triangle ABC

Basically i want to find all triangles that project to a given set of UV coordinates

And as the projection throws away one dimension that should be infinitely many, but they should have some ordering

So i should be able to start with one and then walk along a line to find all

i am not sure on how i could do that, any advice would be appreciated.

I have 2 triangles ABC and PMN

I want to generalize the triangle PMN from points to lines, where any choice along that line will produce the same UV mapping for the triangle ABC

Basically i want to find all triangles that project to a given set of UV coordinates

And as the projection throws away one dimension that should be infinitely many, but they should have some ordering

So i should be able to start with one and then walk along a line to find all

i am not sure on how i could do that, any advice would be appreciated.

Formula that creates UV mapping from triangle PMN & reverse: reversing plane projection texture mapping algorithm

I have 2 triangles ABC and PMN

I want to generalize the triangle PMN from points to lines, where any choice along that line will produce the same UV mapping for the triangle ABC

i am not sure on how i could do that, any advice would be appreciated.

I have 2 triangles ABC and PMN

I want to generalize the triangle PMN from points to lines, where any choice along that line will produce the same UV mapping for the triangle ABC

Basically i want to find all triangles that project to a given set of UV coordinates

And as the projection throws away one dimension that should be infinitely many, but they should have some ordering

So i should be able to start with one and then walk along a line to find all

i am not sure on how i could do that, any advice would be appreciated.