基于最佳圆弧样条逼近的快速距离曲面计算

距离曲面是一种常用的隐式曲面，它在几何造型和计算机动画中具有重要的应用价值，但以往往在对距离曲面进行多边形化时速较慢，为了提高点到曲线最近距离计算的效率，提出了一种基于最佳圆弧样条逼近的快速线骨架距离曲面计算方法，该算法对于一条任意的二维NURBS曲线，在用户给定的误差范围内，先用最少量的圆弧样条来逼近给定的曲线，从而把点到NURBS曲线最近距离的计算问题转化为点到圆弧样条最近距离的计算问题，由于在对曲面进行多边形化时，需要大量的点到曲线最近距离的计算，而该处可以将点到圆弧样条最近距离很少的计算量来解析求得，故该算法效率很高，该实验表明，算法简单实用，具有很大的应用价值。

Fast Distance Surface Computation Based on Optimized Arc Spline Approximation

Implicit surfaces can be used to generate complex topology objects and offer special effects for animators and graphic designers, and they are finding extensive use in a growing number of graphics applications. In contrast to traditional parametric surfaces, implicit surfaces can describe smooth and topology evolving shapes conveniently. Distance surfaces are defined by distance to skeletal elements such as points, curves, surfaces and volumes. In this paper we propose a new fast distance surface computation approach based on optimized arc spline approximation for 2D curve skeletons. For an arbitrary 2D NURBS curve, we first fit it using fewest arc splines within the specified tolerance, and the nearest point to the curve problem is then transferred into the nearest point to an arc spline curve. As a huge times of nearest point computation are involved in the polygonization of distance surfaces, our algorithm is very efficient as the nearest distance from a point to an arc spline curve can be obtained analytically within little computation. Experiments show our algorithm is both simple and useful, and it is of high potential value in practice.