Approximate pyramidal shape decomposition

Author:

Hu Ruizhen1,Li Honghua2,Zhang Hao2,Cohen-Or Daniel3

Affiliation:

1. Simon Fraser University and Zhejiang University

2. Simon Fraser University

3. Tel Aviv University

Abstract

A shape is pyramidal if it has a flat base with the remaining boundary forming a height function over the base. Pyramidal shapes are optimal for molding, casting, and layered 3D printing. However, many common objects are not pyramidal. We introduce an algorithm for approximate pyramidal shape decomposition . The general exact pyramidal decomposition problem is NP-hard. We turn this problem into an NP-complete problem which admits a practical solution. Specifically, we link pyramidal decomposition to the Exact Cover Problem (ECP). Given an input shape S , we develop clustering schemes to derive a set of building blocks for approximate pyramidal parts of S . The building blocks are then combined to yield a set of candidate pyramidal parts. Finally, we employ Knuth's Algorithm X over the candidate parts to obtain solutions to ECP as pyramidal shape decompositions. Our solution is equally applicable to 2D or 3D shapes, and to shapes with polygonal or smooth boundaries, with or without holes. We demonstrate our algorithm on numerous shapes and evaluate its performance.

Funder

Natural Sciences and Engineering Research Council of Canada

China Scholarship Council

Israeli Ministry of Science

Israel Science Foundation

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design

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