a r t i c l e i n f o a b s t r a c t 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,… (More)
a r t i c l e i n f o a b s t r a c t Based on cyclic curves/surfaces introduced in Róth 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… (More)
We provide control point based necessary and sufficient conditions for (n, m) Bézier surfaces to have linear isoparametric lines.
We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n ∈ N defined on any compact interval [0, α], where α ∈ (0, π). Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension δ n =… (More)
We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored in a half-edge data structure, at first we produce a local interpolating network of curves by optimizing quadratic… (More)
Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational curves and surfaces. Concerning computer aided geometric design, the unique normalized B-bases of such vector spaces ensure… (More)