Efficient topology construction from triangle soup

Triangular mesh is one of the most popular shape representations in computer graphics and the CAD/CAM/ CAE area. In this paper we present a memory and time efficient topology construction algorithm from triangle soup, which is a set of triangles without connectivity information. The proposed algorithm consists of the following steps: (1) vertex merging, (2) internal edge linking, (3) multi-disk vertex splitting, and (4) boundary gap stitching. Typical triangle soup comes in the form of an STL file, and topology construction work encounters non-manifold cases for various causes, which should be converted to 2-manifold models for many downstream processes such as rapid prototyping and tool path generation. The proposed algorithm uses a light-weight vertex-based data structure (adapted from a 'corner table' structure), and does not need to construct a full non-manifold topology information. The efficiency of the proposed algorithm is shown by empirical tests on practical examples.

1. Introduction

Among various representations of geometric models, the triangular mesh (T-mesh for short) model has been, mainly due to its simplicity, increasingly used in many fields such as graphics, CAD/CAM/CAE, RE (Reverse Engineering), and RP (Rapid Prototyping) [2], [3], [5], [11]. STL is the most popular format for exchanging triangular mesh models and is supported by many commercial geometric modeling applications. However, STL format contains only a set of unstructured triangles (vertex positions and optional face normal vectors) without their adjacency information [10], which is often called triangle soup. F or the efficient processing of aT-mesh, topology construction is essential to many downstream applications such as mesh simplification, mesh compression, multi-resolution mesh hierarchy creation, subdivision surface generation, tool path generation, collision checking, etc [7], [10], [12], [11], [16].