Free-Boundary Conformal Parameterization of Point Clouds

With the advancement in 3D scanning technology, there has been a surge of interest use point clouds science and engineering. To facilitate computations analyses clouds, prior works have considered parameterizing them onto some simple planar domains with fixed boundary shape such as unit circle or rectangle. However, geometry may lead to undesirable distortion parameterization. It is therefore more natural consider free-boundary conformal parameterizations which minimize local geometric mapping without constraining overall shape. In this work, we develop parameterization method for disk-type involves novel approximation scheme cloud Laplacian accumulated cotangent weights together special treatment at points. aid parameterization, high-quality meshing can be easily achieved. Furthermore, show that using idea welding complex analysis, computed divide-and-conquer manner. Experimental results are presented demonstrate effectiveness proposed method.