Intrinsic Mesh Simplification

TL;DR

This paper introduces a new intrinsic mesh simplification technique that selectively removes vertices based on Gaussian curvature, using local intrinsic edge flips and barycentric coordinates to maintain mesh integrity.

Contribution

The method is novel in its curvature-based vertex removal approach combined with intrinsic edge flips and coordinate updates for mesh simplification.

Findings

Effective on the Thingi10k dataset

Robustness demonstrated across various curvature thresholds

Impacts PDE solutions on simplified meshes

Abstract

This paper presents a novel simplification method for removing vertices from an intrinsic triangulation corresponding to extrinsic vertices lying on near-developable (i.e., with limited Gaussian curvature) and general surfaces. We greedily process all intrinsic vertices with an absolute Gaussian curvature below a user selected threshold. For each vertex, we repeatedly perform local intrinsic edge flips until the vertex reaches the desired valence (three for internal vertices or two for boundary vertices) such that removal of the vertex and incident edges can be locally performed in the intrinsic triangulation. Each removed vertex's intrinsic location is tracked via (intrinsic) barycentric coordinates that are updated to reflect changes in the intrinsic triangulation. We demonstrate the robustness and effectiveness of our method on the Thingi10k dataset and analyze the effect of the curvature threshold on the solutions of PDEs.