On automatic tuning of basis functions in Bezier method

International Conference on Information Technologies in Business and Industry 2016

计算机科学;经济学;工业技术

Reizlin, V.I.^1 ; Demin, A.Y.^1 ; Rybushkina, S.V.^1 ; Sultanguzin, M.F.^1

Tomsk Polytechnic University, 30, Lenina ave., Tomsk

634050, Russia^1

关键词: Analytical description;    Automatic tuning;    Basis functions;    Curves and surfaces;    Geometric objects;    Geometric problems;    Non-uniform rational B-splines;    Parameter vectors;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/803/1/012126/pdf
DOI  :  10.1088/1742-6596/803/1/012126

来源: IOP

【 摘 要 】

A transition from the fixed basis in Bezier's method to some class of base functions is proposed. A parameter vector of a basis function is introduced as additional information. This achieves a more universal form of presentation and analytical description of geometric objects as compared to the non-uniform rational B-splines (NURBS). This enables control of basis function parameters including control points, their weights and node vectors. This approach can be useful at the final stage of constructing and especially local modification of compound curves and surfaces with required differential and shape properties; it also simplifies solution of geometric problems. In particular, a simple elimination of discontinuities along local spline curves due to automatic tuning of basis functions is demonstrated.