A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Curvature continuous curves and surfaces
Computer Aided Geometric Design
Recursive subdivision without the convex hull property
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue: Topics in CAGD
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On the definition of geometric continuity
Computer-Aided Design
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
Knot insertion for Beta-spline curves and surfaces
ACM Transactions on Graphics (TOG)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
Computer-aided design applications of the rational b-spline approximation form.
Computer-aided design applications of the rational b-spline approximation form.
Polar forms for geometrically continuous spline curves of arbitrary degree
ACM Transactions on Graphics (TOG)
Rational Beta-Splines for Representing Curves and Surfaces
IEEE Computer Graphics and Applications
C2 quadratic trigonometric polynomial curves with local bias
Journal of Computational and Applied Mathematics
Quadratic trigonometric polynomial curves concerning local control
Applied Numerical Mathematics
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)
Quadratic trigonometric polynomial curves concerning local control
Applied Numerical Mathematics
C2 quadratic trigonometric polynomial curves with local bias
Journal of Computational and Applied Mathematics
A class of general quartic spline curves with shape parameters
Computer Aided Geometric Design
Cubic polynomial curves with a shape parameter
ROCOM'06 Proceedings of the 6th WSEAS international conference on Robotics, control and manufacturing technology
Graphical Models
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Quartic Beta-splines have third-degree arc-length or geometric continuity at simple knots and are determined by three &bgr; or shape parameters. We present a general explicit formula for quartic Beta-splines, and determine and illustrate the effects of varying the &bgr; parameters on the shape of a quartic Beta-spline curve. We show that quartic (and higher degree) rational Beta-splines with arc-length continuity satisfy the same continuity conditions as (nonrational) Beta-splines. We also show that the torsion continuous spline curves presented by Boehm ("Smooth Curves and Surfaces.” In Geometric Modeling: Algorithms and New Trends, G. E. Farin, Ed. SIAM, Philadelphia, Pa., 1987, pp. 175-184.) are equivalent to nonrational quartic Beta-spline curves, and determine the relationship between the shape parameters for the two types of curves. Finally, we present an algorithm for inserting a new knot and determining the refined control polygon.