Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Multivariate trigonometric B-splines
Journal of Approximation Theory
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
A rational cubic spline with tension
Computer Aided Geometric Design
The NURBS book
Trigonometric Be´zier and Stancu polynomials over intervals and triangles
Computer Aided Geometric Design
Shape preserving representations for trigonometric polynomial curves
Computer Aided Geometric Design
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
Quadratic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design
Piecewise quadratic trigonometric polynomial curves
Mathematics of Computation
Cubic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design
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Quadratic trigonometric polynomial curves with local bias are presented in this paper. The quadratic trigonometric polynomial curves have C^2 continuity with a non-uniform knot vector and any value of the bias, while the quadratic B-spline curves have C^1 continuity. The changes of a local bias parameter will only affect two curve segments. With the bias parameters, the quadratic trigonometric polynomial curves can move locally toward or against a control vertex. A quadratic trigonometric Bezier curve is also introduced as special case of the given trigonometric polynomial curves.