Fast Shape-Preserving Method for Integrating Polygon into Two-and-Half Dimensional Triangulation

Abstract

This paper presents an approach in integrating polygons into a triangulation. The motivation behind this work is to find a way to overcome the lack of appropriate shape-preserving methods for modifying 2.5D triangle meshes. Widely used approaches for constructing Constrained Delone Triangulation (CDT) work in two steps: first constructing pure Delone triangulation, and next inserting the line segments one-by-one into it [1], [2], [3]. The presented method implements an effective mesh data structure and a walking-on-mesh approach allowing for fast polygon traversal looking for the intersected edges of the 2.5D mesh. Instead of reconnecting vertices or re-triangulating the affected mesh area, we introduce new mesh vertices and subdivide the mesh in order to integrate the polygon. The technique also examines and enhances the aspect ratios of the 2.5D triangles that are present in (and near) the partitioned area while maintaining the shape.