23 citations · 39 across the 14 of their papers we have counts for
19 papers
Dual Gauss--Legendre polynomials
Paweł Woźny
We define and investigate two families of dual polynomials associated with the Gauss--Legendre polynomials, which have recently found interesting applications in computer graphics.…
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…
Linear-time geometric algorithm for evaluating Bézier curves
Filip Chudy, Paweł Woźny
A new algorithm for computing a point on a polynomial or rational curve in Bézier form is proposed. The method has a geometric interpretation and uses only convex combinations of c…
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…
An iterative approximate method of solving boundary value problems using dual Bernstein polynomials
Przemysław Gospodarczyk, Paweł Woźny
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using…
Efficient modified Jacobi-Bernstein basis transformations
Przemysław Gospodarczyk, Paweł Woźny
In the paper, we show that the transformations between modified Jacobi and Bernstein bases of the constrained space of polynomials of degree at most can be performed with the c…
Dual polynomial spline bases
Przemysław Gospodarczyk, Paweł Woźny
In the paper, we give methods of construction of dual bases for the B-spline basis and truncated power basis. Explicit formulas for the dual B-spline basis are obtained using the L…
Degree reduction of composite Bézier curves
Przemysław Gospodarczyk, Stanisław Lewanowicz, Paweł Woźny
This paper deals with the problem of multi-degree reduction of a composite Bézier curve with the parametric continuity constraints at the endpoints of the segments. We present a no…
New properties of a certain method of summation of generalized hypergeometric series
Rafał Nowak, Paweł Woźny
In a recent paper (Appl. Math. Comput. 215, 1622--1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more…
Efficient degree reduction of Bézier curves with box constraints using dual bases
Przemysław Gospodarczyk, Paweł Woźny
In this paper, we give an efficient algorithm of degree reduction of Bézier curves with box constraints. The idea is to combine the previous iterative approach, that has been prese…
Bézier form of dual bivariate Bernstein polynomials
Stanisław Lewanowicz, Paweł Keller, Paweł Woźny
Dual Bernstein polynomials of one or two variables have proved to be very useful in obtaining Bézier form of the -solution of the problem of best polynomial approximation of B…
Constrained approximation of rational triangular Bézier surfaces by polynomial triangular Bézier surfaces
Stanisław Lewanowicz, Paweł Keller, Paweł Woźny
We propose a novel approach to the problem of polynomial approximation of rational Bézier triangular patches with prescribed boundary control points. The method is very efficient t…
Weighted polynomial approximation of rational Bézier curves
Stanisław Lewanowicz, Paweł Woźny, Paweł Keller
We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the Bézier curve. The presented algorithm uses th…
-constrained multi-degree reduction of Bézier curves
Przemysław Gospodarczyk, Stanisław Lewanowicz, Paweł Woźny
We present a new approach to the problem of -constrained () multi-degree reduction of Bézier curves with respect to the least squares norm. First, to minimize…
Merging of Bézier curves with box constraints
Przemysław Gospodarczyk, Paweł Woźny
In this paper, we present a novel approach to the problem of merging of Bézier curves with respect to the -norm. We give illustrative examples to show that the solution of the…
Efficient merging of multiple segments of Bézier curves
Paweł Woźny, Przemysław Gospodarczyk, Stanisław Lewanowicz
This paper deals with the merging problem of segments of a composite Bézier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea o…
Bézier representation of the constrained dual Bernstein polynomials
Stanisław Lewanowicz, Paweł Woźny
Explicit formulae for the Bézier coefficients of the constrained dual Bernstein basis polynomials are derived in terms of the Hahn orthogonal polynomials. Using difference properti…