Curvature continuous curves and surfaces
Computer Aided Geometric Design
Making the Oslo algorithm more efficient
SIAM Journal on Numerical Analysis
A new local basis for designing with tensioned splines
ACM Transactions on Graphics (TOG)
Recursive subdivision without the convex hull property
Computer Aided Geometric Design
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
Multiple-knot and rational cubic beta-splines
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)
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Discrete Beta-splines arise when a Beta-spline curve is subdivided; that is, extra knots are inserted so that the curve is expressed in terms of a larger number of control vertices and Beta-splines. Their properties and an algorithm for their computation are given in “Discrete Beta-Splines” by Joe (Computer Graphics, vol. 21, pp. 137-144). We prove a stronger version of one of these properties, from which a new algorithm for computing discrete Beta-splines is obtained. This algorithm can also be used to compute discrete B-splines. We give a comparison of operation counts for this algorithm versus other algorithms, and for two methods to compute the new control vertices of Beta-spline and B-spline curves and surfaces.