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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Henriksen, Ian Daniel, "Evaluation and Refinement of Generalized B-splines" (2015). Theses and Dissertations. 5887.
GB-splines, Trigonometric splines, Hyperbolic splines, Exponential splines, Curve Refinement, Knot Insertion, Degree Elevation