A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Curvature continuous curves and surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
A geometric investigation of the rational bezier scheme of computer aided design
Computers in Industry
Infinite Control Points-A Method for Representing Surfaces of Revolution Using Boundary Data
IEEE Computer Graphics and Applications
A new local basis for designing with tensioned splines
ACM Transactions on Graphics (TOG)
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Computer Aided Geometric Design - Special issue: Topics in CAGD
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Knot insertion for Beta-spline curves and surfaces
ACM Transactions on Graphics (TOG)
Local Control of Bias and Tension in Beta-splines
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.
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
Manipulating Shape and Producing Geometuic Contnuity in β-Spline Curves
IEEE Computer Graphics and Applications
Knot insertion for Beta-spline curves and surfaces
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
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
Cubic polynomial curves with a shape parameter
ROCOM'06 Proceedings of the 6th WSEAS international conference on Robotics, control and manufacturing technology
Modeling with rational biquadratic splines
Computer-Aided Design
Free-form splines combining NURBS and basic shapes
Graphical Models
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Goodman (Properties of Beta-splines. J. Approx. Theory 44, 2 (June 1985), 132-153) gave an explicit formula for cubic Beta-splines on a uniform knot sequence with varying &bgr;1 and &bgr;2 values at the knots. We establish an alternative explicit formula for cubic Beta-splines on a nonuniform knot sequence with constant &bgr;1 = 1 and varying &bgr;2 values at the knots. This alternative formula can also be used if the knot sequence contains multiple knots, and is useful for knot insertion. We show how to efficiently evaluate a cubic Beta-spline curve at many values using this formula. We introduce rational cubic Beta-spline curves and surfaces that have extra weight parameters for shape control, and show that they satisfy the same geometric continuity conditions and properties as nonrational cubic Beta-spline curves and surfaces.