Curvature continuous curves and surfaces
Computer Aided Geometric Design
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
Curve and surface constructions using rational B-splines
Computer-Aided Design
Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Constructing piecewise rational curves with Frenet frame continuity
Computer Aided Geometric Design
Mathematical methods in computer aided geometric design
An explicit derivation of discretely shaped Beta-spline basis functions of arbitrary order
Mathematical methods in computer aided geometric design II
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
A Symbolic Derivation of Beta-splines of Arbitrary Order
A Symbolic Derivation of Beta-splines of Arbitrary Order
Beta Continuity and Its Application to Rational Beta-splines
Beta Continuity and Its Application to Rational Beta-splines
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
Partial shape-preserving splines
Computer-Aided Design
Modeling with rational biquadratic splines
Computer-Aided Design
Free-form splines combining NURBS and basic shapes
Graphical Models
| Hi-index | 0.00 |
The rational Beta-spline representation, which offers the features of the rational form as well as those of the Beta-spline, is discussed. The rational form provides a unified representation for conventional free-form curves and surfaces along with conic sections and quadratic surfaces, is invariant under projective transformation, and possesses weights, which can be used to control shape in a manner similar to shape parameters. Shape parameters are an inherent property of the Beta-spline and provide intuitive and natural control over shape. The Beta-spline is based on geometric continuity, which provides an appropriate measure of smoothness in computer-aided geometric design. The Beta-spline has local control with respect to vertex movement, is affine invariant, and satisfies the convex hull property. The rational Beta-spline enjoys the benefit of all these attributes. The result is a general, flexible representation, which is amenable to implementation in modern geometric modeling systems.