Metric first reconstruction for interactive curvature-aware modeling

Abstract

We present a novel curvature-aware modeling technique for interactively designing shapes. The basic principle we used is that an intrinsic metric of a mesh determines the Euclidean edge lengths and the angles, thereby defining the Laplacian matrix. Hence central to our approach is a metric first algorithm that interactively reconstructs a shape for matching the prescribed curvatures. Given Gaussian curvature, the Calabi flow, which implies a conformal deformation, is first used to compute the desired intrinsic metric. We accelerate the convergence of the Calabi flow using a progressive strategy. Then we reconstruct a shape by solving a new unconstrained problem to match the target Euclidean edge lengths defined by the computed metric and the input mean curvature computed by the Laplacian matrix. Since the obtained metric makes the target edge lengths and the Laplacian matrix fixed during the optimization, we can easily apply a local–global solver capable of interactively reconstructing shapes. Based on this reconstruction tool, we develop three curvature-aware modeling operations. A large number of experiments demonstrate the capability and feasibility of our method for interactively modeling complex shapes.