Two different forms of C-B-splines
Computer Aided Geometric Design
Practical Computer-Aided Lens Design
Practical Computer-Aided Lens Design
Uniform hyperbolic polynomial B-spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Computer Aided Geometric Design
Technical Section: User-guided inverse reflector design
Computers and Graphics
A cyclic basis for closed curve and surface modeling
Computer Aided Geometric Design
C-curves: An extension of cubic curves
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Optimal properties of the uniform algebraic trigonometric B-splines
Computer Aided Geometric Design
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Based on cyclic curves/surfaces introduced in Roth et al. (2009), we specify control point configurations that result an exact description of those closed curves and surfaces the coordinate functions of which are (separable) trigonometric polynomials of finite degree. This class of curves/surfaces comprises several famous closed curves like ellipses, epi- and hypocycloids, Lissajous curves, torus knots, foliums; and surfaces such as sphere, torus and other surfaces of revolution, and even special surfaces like the non-orientable Roman surface of Steiner. Moreover, we show that higher order (mixed partial) derivatives of cyclic curves/surfaces are also cyclic curves/surfaces, and we describe the connection between the cyclic and Fourier bases of the vector space of trigonometric polynomials of finite degree.