We present a method for the generation of a pure quad mesh approximating a discrete manifold of arbitrary topology that preserves the patch layout characterizing the intrinsic object structure. A three-step procedure constitutes the core of our approach which first extracts the patch layout of the object by a topological partitioning of the digital shape, then computes the minimal surface given by the boundaries of the patch layout (basic quad layout) and then evolves it towards the object boundaries. The Lagrangian evolution of the initial surface (basic quad layout) in the direction of the gradient of the signed distance function is smoothed by a mean curvature term. The direct control over the global quality of the generated quad mesh is provided by two types of tangential redistributions: area-based, to equally distribute the size of the quads, and angle-based, to preserve quad corner angles. Experimental results showed that the proposed method generates pure quad meshes of arbitrary topology objects, composed of well-shaped evenly distributed elements with few extraordinary vertices.

我们提出了一种生成纯四边形网格的方法，该方法近似于任意拓扑的离散流形，保留了表征固有对象结构的面片布局。三个步骤构成了我们方法的核心，该方法首先通过数字形状的拓扑划分来提取对象的斑块布局，然后计算出斑块布局（基本四边形布局）的边界给出的最小表面，然后进行演化它朝向对象边界。初始表面（基本四边形布局）在有符号距离函数的梯度方向上的拉格朗日演化通过平均曲率项进行平滑处理。可以通过两种类型的切向重分布来直接控制生成的四边形网格的整体质量：基于面积的，均匀分布四边形的尺寸 和基于角度的角度，以保留四角角度。实验结果表明，该方法能够生成任意拓扑对象的纯四边形网格，该网格由形状良好，分布均匀的元素组成，几乎没有异常顶点。