由控制线生成可展B样条曲面
Developable B-spline surface generation from control rulings
摘要：
提出了一种由一系列表示曲面形状的直线段生成直纹B样条可展曲面的直观设计方法。第一条和最后一条线段被强制为结果曲面的头部和尾部划线，而内部线被要求尽可能地近似结果曲面上的划线。这种可展曲面设计的方式在概念上类似于CAD社区中自由形式曲线和曲面设计的流行方式，观察到可展直纹曲面是单参数直线族。这种新的可展曲面设计模式也比目前广泛采用的从曲面的两条边界曲线设计可展曲面的方法提供了更大的灵活性。该问题是由数值优化方法，其中一个特定的距离误差水平是允许的。因此，我们提供了一个有效的工具，用于创建具有高度的可展性的曲面时，输入控制规则不在于精确的可展曲面。我们认为这种能力的优越性分析方法，它可以处理任意的设计输入，并找到实际有用的结果。
英文摘要：
An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.
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