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 w...[ Read more ]

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.