Texture mapping progressive meshes

TLDR

The paper proposes a method to build progressive meshes that share a common texture parametrization while simultaneously minimizing texture stretch and deviation. The approach partitions the mesh into charts, generates stretch‑minimizing parametrizations per chart, resizes charts, simplifies the mesh while respecting chart boundaries, re‑optimizes the parametrization across the sequence, and finally packs the charts into a texture atlas. Experiments show that the resulting atlases enable effective sampling of color and normal maps on multiple models.

Abstract

Given an arbitrary mesh, we present a method to construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. Our method considers two important goals simultaneously. It minimizes texture stretch (small texture distances mapped onto large surface distances) to balance sampling rates over all locations and directions on the surface. It also minimizes texture deviation (“slippage” error based on parametric correspondence) to obtain accurate textured mesh approximations. The method begins by partitioning the mesh into charts using planarity and compactness heuristics. It creates a stretch-minimizing parametrization within each chart, and resizes the charts based on the resulting stretch. Next, it simplifies the mesh while respecting the chart boundaries. The parametrization is re-optimized to reduce both stretch and deviation over the whole PM sequence. Finally, the charts are packed into a texture atlas. We demonstrate using such atlases to sample color and normal maps over several models.