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.