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.

我们提出了一种新颖的曲率感知建模技术，用于交互式设计形状。我们使用的基本原理是，网格的固有度量确定欧几里得边的长度和角度，从而定义拉普拉斯矩阵。因此，我们方法的核心是度量优先算法，该算法以交互方式重建形状以匹配指定的曲率。在给定高斯曲率的情况下，首先使用暗示变形的卡拉比流来计算所需的固有度量。我们使用渐进策略来加速Calabi流的收敛。然后，我们通过解决一个新的无约束问题来重构形状，以匹配由计算量度定义的目标欧几里得边长度和由Laplacian矩阵计算出的输入平均曲率。由于获得的度量使目标边缘长度和拉普拉斯矩阵在优化期间固定不变，因此我们可以轻松地应用能够交互式重构形状的局部全局求解器。基于此重建工具，我们开发了三种曲率感知建模操作。大量实验证明了我们的方法对复杂形状进行交互式建模的能力和可行性。