7 papers
Evaluation of Gauss-Legendre curves
Filip Chudy, Paweł Woźny
We present new representations of Gauss--Legendre polynomials and their derivatives in the shifted power basis and in bases related to symmetric orthogonal Jacobi polynomials. Usin…
Fast subdivision of Bézier curves
Paweł Woźny, Filip Chudy
It is well-known that a -dimensional polynomial Bézier curve of degree can be subdivided into two segments using the famous de Casteljau algorithm in time. Can thi…
Efficient evaluation of Bernstein-Bézier coefficients of B-spline basis functions over one knot span
Filip Chudy, Paweł Woźny
New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-Bézier coefficients of B-spline ba…
Fast evaluation of derivatives of Bézier curves
Filip Chudy, Paweł Woźny
New geometric methods for fast evaluation of derivatives of polynomial and rational Bézier curves are proposed. They apply an algorithm for evaluating polynomial or rational Bézier…
Linear-time algorithm for computing the Bernstein-Bézier coefficients of B-spline basis functions
Filip Chudy, Paweł Woźny
A new differential-recurrence relation for the B-spline functions of the same degree is proved. From this relation, a recursive method of computing the coefficients of B-spline fun…
Fast and accurate evaluation of dual Bernstein polynomials
Filip Chudy, Paweł Woźny
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one o…
Differential-recurrence properties of dual Bernstein polynomials
Filip Chudy, Paweł Woźny
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using…