Title :
From conics to NURBS: A tutorial and survey
Author_Institution :
Dept. of Comput. Sci., Arizona State Univ., Tempe, AZ, USA
Abstract :
The main geometric features of the nonuniform rational B-splines (NURBS) curve and surface representations are described. It is shown that most of these features are already exhibited by conics, which are a special case of NURBS. The properties typical of NURBS are discussed without dwelling on properties already present in polynomial curves. Conic sections and their representations using rational Bezier curves are reviewed. Cubic NURB curves, geometrical rational splines, rational and B-spline surfaces, and rational Bezier triangles are discussed.<>
Keywords :
computational geometry; solid modelling; splines (mathematics); geometric features; geometrical rational splines; nonuniform rational B-splines; rational Bezier curves; rational Bezier triangles; surface representations; Application software; CADCAM; Computer aided manufacturing; Computer graphics; Design automation; Polynomials; Spline; Surface reconstruction; Surface topography; Tutorial;
Journal_Title :
Computer Graphics and Applications, IEEE
