An efficient approximation of arbitrary curves and surfaces using intersecting polylines and meshes

This paper presents an efficient method for approximating curves and surfaces. An idea is introduced using a circle, where an arc-intersecting polyline is used instead of the traditional inner-arc polyline. The approach is then generalized to arbitrary 2D curves. The method is extended into 3D, where the approximation of spherical surface is developed based on surface-intersecting facets. Finally, a method is described for approximating the general curved surface. Theoretical analysis and the experimental results showed that the new algorithm requires considerably less geometric data at the same approximation error than the traditional one.