Mesh Simplification by Curvature-Enhanced Quadratic Error Metrics

Paolo Pellizzoni,Gianpaolo Savio

doi:10.3844/jcssp.2020.1195.1202

Abstract

Polygonal meshes have a significant role in computer graphics, design and manufacturing technology for surface representation and it is often required to reduce their complexity to save memory. An efficient algorithm for detail retaining mesh simplification is proposed; in particular, the method presented is an iterative edge contraction algorithm based on the work of Garland and Heckberts. The original algorithm is improved by enhancing the quadratic error metrics with a penalizing factor based on discrete Gaussian curvature, which is estimated efficiently through the Gauss-Bonnet theorem, to account for the presence of fine details during the edge decimation process. Experimental results show that this new algorithm helps preserve the visually salient features of the model without compromising performance.

Highlights

Nowadays, due to ever-improving computer-aided modeling in both the film industry and manufacturing, it’s easy to find ultra-detailed 3D models with millions of faces
Li et al (2010) proposed a feature-preserving simplification algorithm based on an absolute curvature weighted quadric error metric, the choice of using half-edge collapses could lead to suboptimal vertex positions (Garland and Heckbert, 1997)
Another simpler approach can be found in Yao et al (2015) where the quadratic error metrics is modified through an additive term based on a custommade curvature estimate

Summary

Introduction

Due to ever-improving computer-aided modeling in both the film industry and manufacturing, it’s easy to find ultra-detailed 3D models with millions of faces. Li et al (2010) proposed a feature-preserving simplification algorithm based on an absolute curvature weighted quadric error metric, the choice of using half-edge collapses could lead to suboptimal vertex positions (Garland and Heckbert, 1997).

Results

Conclusion