I have a sort of unrelated question to the question in the slide. Say someone makes a triangle mesh that looks like a person's head like in this slide (but actually like a real person's head), and then a 3D artist makes a texture map of a person's head / face to put over that mesh. But then, someone else decides that they actually want to change the facial structure, i.e. make the nose bigger, shorten the chin, etc. Wouldn't that distort the texture map / force people to rewrite texture maps every time they want to change a mesh? Or is there a way to make sure that textures look okay after transforming a mesh?
Well, Texture maps are usually anchored to vertices on the mesh, in that every vertex knows its location in texture space in addition to world space.
Changing the locations of the vertices would indeed distort the texture map, but they would only need to correct it at the changed locations, because the unchanged locations are still good. It they made an obscenely large nose, they could even decided to map the nose coordinates to an alternative nose dedicated texture and just keep the original vertices pointing to locations in the original texture outside of the nose region, in this way a model designer can stitch pieces of art together.
You can also compute new texture locations automatically in many mesh operations such as subdivision, which we will be doing for week 2 of assignment 2.
Here is a link to a digital art project where a mesh is used to represent the user's hand, where texture coordinates needed to be mapped judiciously to the underlying mesh structure: Augmented Hand Series
We redesigned the mesh several times for aesthetic and performance reasons. We used a very simple mesh for the rigid as possible mesh deformation procedure and then subdivided the mesh after being deformed to display a smooth aesthetically pleasing image of the hand to the user. The subdivided vertices acquired their texture coordinates from the texture coordinates of the vertices in the stencil in much the same way as they acquired their positions.
(A stencil is the local set of interesting features that are used in mesh processing operations, we will likely talk more about it next week in preparation for part 2 of assignment 2.)
@dvernet Good point! And actually Professor Crane has some related work on the subject. Click me.