Multi-boundary Mesh Parameterization With A Virtual Boundary

Mesh parameterization has various applications in computer graphics, such as texture mapping, remeshing and smooth surface fitting. However, all the parameterizations (non-developable surface) will inevitably produce certain deformations, such as area distortion, angle distortion and stretch distortion. To decrease the area distortion and stretch distortion, we propose a multi-boundary mesh parameterization with a virtual boundary.Firstly, we present a new parameterization with a virtual boundary by adding a local stretch to each inner vertex of the mesh. One disadvantage of previous virtual boundary parameterization is the inability to deal with multi-boundary cases. We overcome the disadvantage by transforming the multi-boundary mesh into one-boundary mesh by using barycenter method and adaptive method. In the end of the paper, we have performed some experiments on the multi-boundary beetle model, face model and hat model and then compared the results of three classic methods:Least squares conformal maps, Linear angle-based flattening and As rigid as possible. Numerical experiments demonstrate that our method has less distortion and performs better on texture mapping than other three classical parameterization methods.