Algorithms for computing the approximation of offsets of toric Bezier curves

Algorithms for curve offsetting are of great importance in computer-aided design, computer-aided manufacture, and numerical control of machines. Toric surfaces, a kind of rational parametric surfaces, have been proposed for use in these areas. When the parameter domain is one dimensional, they are called toric curves, and it has been proved that such curves have many desirable properties for applications in geometric design, such as the construction of blending surfaces. This paper investigates algorithms for constructing offset curves of toric curves, including algorithms based on control polygons or on degree elevation, as well as approximate offsetting algorithms. These algorithms are able to deal with curves exhibiting self-intersections and cusps. Examples of constructing non-self-intersecting offset curves and comparison with other methods are proposed. Some illustrative examples are presented.

Automated summary

This paper investigates algorithms for constructing offset curves of toric curves, including algorithms based on control polygons or on degree elevation, as well as approximate offsetting algorithms. These algorithms are able to deal with curves exhibiting self-intersections and cusps. Examples of constructing non-self-intersecting offset curves and comparison with other methods are proposed.