Evaluation and Refinement of Generalized B-splines

Evaluation and Refinement of Generalized B-Splines Ian Daniel Henriksen Department of Mathematics, BYU Master of Science In this thesis a method for direct evaluation of Generalized B-splines (GB-splines) via the representation of these curves as piecewise functions is presented. A local structure is introduced that makes the GB-spline curves more amenable to the integration used in constructing bases of higher degree. This basis is used to perform direct computation of piecewise representation of GB-spline bases and curves. Algorithms for refinement using these local structures are also developed.