基于圆填充的离散建筑曲面自由造型设计
Free-form Design of Discrete Architectural Surfaces by use of Circle Packing
摘要：
本文提出了一种有效的方法，用于概念设计的建筑表面，这是由三角形面板。在离散建筑表面的自由形式设计中，高斯曲率不仅在美学上而且在刚度和可构造性方面都起着重要作用。然而，手动设计具有特定高斯曲率的曲面可能是一项耗时的任务。我们提出了一种方法来找到一个三角化的表面与用户指定的高斯曲率（不限于常数高斯曲率）和边界顶点位置。此外，可以指定最终设计的保形类;也就是说，用户可以控制每个三角形面板的形状（角）。可以鼓励面板形成规则的镶嵌，或者保持接近初始设计的镶嵌。保形类的可控性抑制了面板的可能变形，从而获得更高的结构性能和美观性。我们的方法依赖于计算保形几何中的概念，称为圆填充。在这条研究线中，离散Ricci流已被广泛用于表面建模。然而，它不是微不足道的，包括约束，如边界位置和凸性的跨越表面，这是必不可少的建筑应用。我们提出了一个扰动的离散Ricci能量，并开发了一个基于最小二乘的优化方案，以解决这些问题与一个开源的实现在线。
英文摘要：
This paper presents an efficient approach for the conceptual design of architectural surfaces which are composed of triangular panels. In the free-form design of discrete architectural surfaces, the Gaussian curvature plays an important role not only aesthetically but also in terms of stiffness and constructability. However, designing a surface manually with specific Gaussian curvatures can be a time-consuming task. We propose a method to find a triangulated surface with user-specified Gaussian curvatures (not limited to constant Gaussian curvatures) and boundary vertex positions. In addition, the conformal class of the final design can be specified; that is, the user has control over the shape (the corner angles) of each triangular panel. The panels could be encouraged to form a regular tessellation or kept close to those of the initial design. The controllability of the conformal class suppresses possible distortion of the panels, resulting in higher structural performance and aesthetics. Our method relies on the idea in computational conformal geometry called circle packing. In this line of research, the discrete Ricci flow has been widely used for surface modelling. However, it is not trivial to incorporate constraints such as boundary locations and convexity of the spanned surface, which are essential to architectural applications. We propose a perturbation of the discrete Ricci energy and develop a least-squares-based optimisation scheme to address these problems with an open-source implementation available online.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
