Eurographics Symposium on Geometry Processing 2014

Figure 1: (Left) Quadrangulations of N-sided patches using our algorithm, where 2 ≤ N ≤ 6. Our algorithm is guaranteed to successfully quadrangulate N-sided patches with arbitrary numbers of edge subdivisions specified at the patch boundary. (Right) Integration of our algorithm into the UI framework of Takayama et al. [TPSHSH13b] to efficiently retopologize triangle meshes. We propose an algorithm to quadrangulate an N-sided patch (2 ≤ N ≤ 6) with prescribed numbers of edge subdivisions at its boundary. Our algorithm is guaranteed to succeed for arbitrary valid input, which is proved using a canonical simplification of the input and a small set of topological patterns that are sufficient for supporting all possible cases. Our algorithm produces solutions with minimal number of irregular vertices by default, but it also allows the user to choose other feasible solutions by solving a set of small integer linear programs. We demonstrate the effectiveness of our algorithm by integrating it into a sketch-based quad remeshing system. A reference C++ implementation of our algorithm is provided as a supplementary material