Quadrangle Collapse Mesh Simplification with Regularity and Angular Deviation Bias and Probabilistic Heap Updating

This paper describes using a bias based on shape regularity and angular deviation after collapse to improve the quality of meshes reduced using a quadric-based metric with quadrangle collapse. After calculating the error score from the metric, we then calculate the compactness of the resulting faces and their angular deviation from their original orientations, and derive a bias to weight the error score with. The bias aims to reduce sliver faces and maintain the orientation of the faces. We also attempt to improve the updating of the heap, with an probabilistic heap updating procedure that only performs full updates when necessary and partial updates otherwise.