论文标题
可开发的B型载体表面产生从控制裁定
Developable B-spline surface generation from control rulings
论文作者
论文摘要
提出了一种直观的设计方法，用于从一系列直线片段中生成可开发的统治B-Spline表面，指示表面形状。第一和最后一行的段被强制为所得表面的头部和尾部统治线，而内部线需要尽可能近似于所得表面的裁定。这种可开发的表面设计的方式在概念上与CAD社区中自由形曲线和表面设计的流行方式相似，观察到可开发的统治表面是单个直线的单个参数家族。与从表面的两个边界曲线中使用广泛使用的可开发表面设计的方式相比，这种可开发表面的新设计模式也提供了更大的灵活性。该问题通过数值优化方法处理，允许使用特定级别的距离误差。因此，当输入控制裁决不在确切的开发表面时，我们提供了一种具有高度可开发性的表面的有效工具。我们将这种能力视为优于分析方法的优势，因为它可以处理任意设计输入并找到实际有用的结果。
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.
