Totally positive bases for shape preserving curve design and optimality of B-splines
Computer Aided Geometric Design
C-curves: an extension of cubic curves
Computer Aided Geometric Design
Low-harmonic rational Be´zier curves for trajectory generation of high-speed machinery
Computer Aided Geometric Design
Shape preserving representations for trigonometric polynomial curves
Computer Aided Geometric Design
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
Journal of Symbolic Computation
Harmonic rational Bézier curves, p-Be´zier curves and trigonometric polynomials
Computer Aided Geometric Design
Corner cutting algorithms associated with optimal shape preserving representations
Computer Aided Geometric Design
A closed algebraic interpolation curve
Computer Aided Geometric Design
Shape preserving alternatives to the rational Bézier model
Computer Aided Geometric Design
Control point based exact description of a class of closed curves and surfaces
Computer Aided Geometric Design
Constrained surface interpolation by means of a genetic algorithm
Computer-Aided Design
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We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from n to n+r, r=1 and prove that the control polygon of the degree elevated curve converges to the curve itself if r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of closed curves and surfaces with C^~ continuity at all of their points.