Fast and symmetry-aware quadrangulation

A variety of methods have been developed to produce quad meshes of high quality; however, there are still limitations in those state-of-the-art algorithms. First, there is little consideration in the symmetry of a mesh shape, which is important for further use of the quad mesh, such as UV layout. Second, most of current methods are time consuming for large models. To address these problems, we propose a new quadrangulation method to preserve shape symmetry. A hierarchical approach is also presented to accelerate the whole process. Our method achieves the symmetry of the final quad mesh by controlling the positions of singular points. After an initial construction of a cross field, we detect the symmetric relations among singularities and refine their positions to make them better reflect symmetries of the model. By taking the singularities as constraints, a cross field is then recomputed as the guided direction field for a global parameterization. To reduce the time spent on quadrangulation of a large model, we first simplify it while preserving its most significant geometric features. A coarse quadrangulation is then performed on the simplified mesh, and the final one is obtained by improving the coarse one in terms of the original mesh.