Fast Distance Surface Computation Based on Optimized Arc Spline Approximation
基于最佳圆弧样条逼近的快速距离曲面计算

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.