Structure simplification of planar quadrilateral meshes

Abstract

In this paper, we present a structure simplification framework for planar all-quad meshes with open boundaries. Our simplification framework can handle quad meshes with complex structures (e.g., quad meshes obtained via Catmull–Clark subdivision of the triangle meshes) to produce simpler meshes while preserving the boundary features. To achieve that, we introduce a set of separatrix-based semi-global operations and combine them with existing local operations to develop a new simplification framework. Additionally, we organize and order the individual simplification operations into groups and employ ranking strategies for each group to sort these operations to produce quad meshes with better quality and simpler structure. We provide a comprehensive evaluation of our framework using different input parameters on a number of representative planar quad meshes with various boundary configurations. To demonstrate the advantages of our method, we compare it with a few existing frameworks. Our comparison shows that our simplification framework usually produces simpler structure with faster computation than the state-of-the-art methods.