标题： 自由曲面网格表面的分段直纹逼近 显示英文标题

标题： Piecewise Ruled Approximation for Freeform Mesh Surfaces

摘要： 由在三维空间中移动一条直线所形成的形状称为直纹面。 由于其简单的几何形式，直纹面在建筑和工程等多个领域有应用。 过去，已有各种方法被提出，使用可展开表面（具有零高斯曲率的特殊直纹面）来近似目标形状。 然而，使用一般直纹面进行形状近似的方法仍然有限，并且通常要求目标形状以参数化表面表示，或者具有非正高斯曲率。 本文提出一种方法，用于计算近似任意自由形态网格表面的分段直纹面。 我们首先使用组稀疏性公式将给定的网格形状优化为近似分段直纹形式，同时结合一个指示直纹方向的切向量场。 随后，我们利用优化结果提取分离平滑直纹族的接缝，并利用这些接缝构造初始直纹。 最后，我们进一步优化直纹的位置和方向，以提高与输入目标形状的对齐度。 我们将该方法应用于具有不同拓扑和复杂度的多种自由形态形状，证明了其在近似任意形状方面的有效性。 显示英文摘要

摘要： A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been proposed to approximate a target shape using developable surfaces, which are special ruled surfaces with zero Gaussian curvature. However, methods for shape approximation using general ruled surfaces remain limited and often require the target shape to be either represented as parametric surfaces or have non-positive Gaussian curvature. In this paper, we propose a method to compute a piecewise ruled surface that approximates an arbitrary freeform mesh surface. We first use a group-sparsity formulation to optimize the given mesh shape into an approximately piecewise ruled form, in conjunction with a tangent vector field that indicates the ruling directions. Afterward, we utilize the optimization result to extract seams that separate smooth families of rulings, and use the seams to construct the initial rulings. Finally, we further optimize the positions and orientations of the rulings to improve the alignment with the input target shape. We apply our method to a variety of freeform shapes with different topologies and complexity, demonstrating its effectiveness in approximating arbitrary shapes.