Abstract:
Geometric data plays an increasingly vital role in tasks ranging from computational fabrication to augmented reality to autonomous driving. Triangle meshes are a basic representation for 3D geometry, playing the same central role as pixel arrays in image processing. Hence, even seemingly small shifts in the way we think about triangle meshes can have major consequences for a wide variety of applications. In this talk we explore what happens if we replace the ordinary extrinsic encoding of mesh geometry, via vertex positions in R n , with an alternative intrinsic description, via lengths associated with edges. The resulting intrinsic triangulations are far more flexible than their traditional extrinsic counterparts, yet still provide the geometric information needed to execute many fundamental geometry processing tasks. I will be covering the basic theory surrounding intrinsic triangulations, followed by an introduction to recently proposed data structures to utilize these structures and an algorithm for generating intrinsic Delaunay triangulations.
This work is a culmination of recent work by Keenan Crane’s group at CMU which was compiled into a course at SIGGRAPH 2021. The course notes can be found here: https://markjgillespie.com/Research/int-tri-course/int_tri_course.pdf