Mathematical methods in computer aided geometric design
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
Shape preserving representations for trigonometric polynomial curves
Computer Aided Geometric Design
Two different forms of C-B-splines
Computer Aided Geometric Design
The NURBS book (2nd ed.)
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
Shape preserving alternatives to the rational Bézier model
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
IEEE Computer Graphics and Applications
From Conics to NURBS: A Tutorial and Survey
IEEE Computer Graphics and Applications
Blending parametric patches with subdivision surfaces
Journal of Computer Science and Technology
Uniform hyperbolic polynomial B-spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
On Convergence of the Control Polygons Series of C-Bézier Curves
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Explicit representations of changeable degree spline basis functions
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric (AHT) Bézier curves and non-uniform algebraic hyperbolic trigonometric (NUAHT) B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., tn-5}, n ≥ 5. The two kinds of curves share most of the properties as those of the Bézier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.