Fatiamento de malhas triangulares: teoria e experimentos

Abstract

Additive Manufacturing, also known as 3D printing, is a process based on the addition of sucessive layers in order to build a physical object. The data for building this object come from geometric 3D model, usually represented by a triangle mesh. One of the main procedures in this process is to slice the triangle mesh and output a sequence of contours, representing each one of the layers of the object. There are many strategies for slicing meshes, however, most of the current literature is concerned with ad hoc issues such as the quality of the model, specific improvements in the slicing process and memory usage, whereas few of them address the problem from an algorithmic complecity perspective. While current algorithms for this problem ruin in O(n² + k²) or O(n² + nlognk), the proposed algorithm runs in O(nk), for a given input with n triangles, k planes and where k is the average number of slices cutting each triangle in this specific input. This is asymptotically the best that can be achieved under certain fairly common assumptions. The proposed algorithm, called here Slicing by Stabbing (SS), was compared both theoretically and experimentally against known methods in the literature and the results show considerable improvement in execution time.