Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
The NURBS book
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
IEEE Computer Graphics and Applications
Journal of Computational and Applied Mathematics
On the singularity of a class of parametric curves
Computer Aided Geometric Design
Piecewise quartic polynomial curves with a local shape parameter
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
A class of algebraic-trigonometric blended splines
Journal of Computational and Applied Mathematics
A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design
Curves and Surfaces Construction Based on New Basis with Exponential Functions
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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The quartic curve of Han [X. Han, Piecewise quartic polynomial curves with shape parameter, Journal of Computational and Applied Mathematics 195 (2006) 34-45] can be considered as the generalization of the cubic B-spline curve incorporating shape parameters into the polynomial basis functions. We show that this curve can be considered as the linear blending of the original cubic B-spline curve and a fixed quartic curve. Moreover, we present the Bezier form of the curve, which is useful in terms of incorporating the curve into existing CAD systems. Geometric effects of the alteration of shape parameters is also discussed, including design oriented computational methods for constrained shape control of the curve.