Before revision:  In this work, we propose a novel approximation scheme of the Laplace--Beltrami operator on point clouds and utilize it for developing a free-boundary conformal parameterization method for disk-type point clouds  .
After revision:  In this work, we propose a novel approximation scheme of the Laplace--Beltrami operator on point clouds and utilize it for developing a free-boundary conformal parameterization method for disk-type point clouds , which involves a novel approximation scheme of the point cloud Laplacian with accumulated cotangent weights together with a special treatment at the boundary points .