Manifoldness preserving contraction

Abstract

The contraction operation is a common manipulating operation in simplicial complexes. A prominent application of them is incremental mesh simplification, a processing task that reduces the size a mesh while does not alter the shape of the surface it models too much. An ordinary contraction may change a complex from manifold to non-manifold. In applications such as mesh processing, the existence of non-manifolds adds the complexity of algorithm design and drags down program performance. In this dissertation, a new contraction operation is proposed. The proposed contraction operation guarantees manifold output when the input is a 2-dimensional manifold. Its possible generalization in 3-dimensional input is explored. A C++ program is implemented to replace the ordinary contraction with manifoldness preserving contraction in mesh simplification, which has shown superior results.

Date of Award	2020
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology