Construction of exponential tension B-splines of arbitrary order
Curves and surfaces
The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
C-curves: an extension of cubic curves
Computer Aided Geometric Design
Two different forms of C-B-splines
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Unified and extended form of three types of splines
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
AHT Bézier curves and NUAHT B-spline curves
Journal of Computer Science and Technology
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
A class of algebraic-trigonometric blended splines
Journal of Computational and Applied Mathematics
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
| Hi-index | 0.00 |
In this paper, the trigonometric basis {sin t, cos t, t, 1} and the hyperbolic basis {sinh t, cosh t, t, 1} are unified by a shape parameter C (0 ≤ C C2 continuity, and can represent elliptic and hyperbolic arcs exactly. They are adjustable, and each control point bi can have its unique shape parameter Ci. As Ci increases from 0 to ∞, the corresponding breakpoint of bi on the curve is moved to the location of bi, and the curvature of this breakpoint is increased from 0 to ∞ too. For a set of control points and their shape parameters, SB-spline and FB-spline have the same position, tangent, and curvature on each breakpoint. If two adjacent control points in the set have identical parameters, their SB-spline and FB-spline segments overlap. However, in general cases, FB-splines have no simple subdivision equation, and SB-splines have no common evaluation function. Furthermore, FB-splines and SB-splines can generate shape adjustable surfaces. They can represent the quadric surfaces precisely for engineering applications. However, the exact proof of C2 continuity for the general SB-spline surfaces has not been obtained yet.