优化B样条曲面的可展性和镶嵌建筑自由曲面
Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces
摘要：
受建筑和设计中的应用的启发，我们提出了一种新的方法来增加B样条曲面的可展性。我们使用的属性，高斯图像的可展曲面是1维的，可以局部很好地近似圆。这是投到一个算法细化的高斯图像，通过增加适当的邻域的高斯图像的平面性。主要方法的变型允许我们解决用可展面板对自由形式的建筑表面进行镶板的问题，特别是强制执行旋转圆柱形、旋转圆锥形和平面面板，由于降低了制造成本，这些面板是建筑中可展面板的主要优选类型。
英文摘要：
Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing.
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