Applications of b-spline approximation to geometric problems of computer-aided design.
Applications of b-spline approximation to geometric problems of computer-aided design.
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
Urn models, recursive curve schemes, and computer aided geometric design
Urn models, recursive curve schemes, and computer aided geometric design
On the parameterization of Catmull-Rom curves
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Representation of facial features by Catmull-Rom splines
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Parameterization and applications of Catmull-Rom curves
Computer-Aided Design
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It is known that certain Catmull-Rom splines [7] interpolate their control vertices and share many properties such as affine invariance, global smoothness, and local control with B-spline curves; they are therefore of possible interest to computer aided design. It is shown here that another property a class of Catmull-Rom splines shares with B-spline curves is that both schemes possess a simple recursive evaluation algorithm. The Catmull-Rom evaluation algorithm is constructed by combining the de Boor algorithm for evaluating B-spline curves with Neville's algorithm for evaluating Lagrange polynomials. The recursive evaluation algorithm for Catmull-Rom curves allows rapid evaluation of these curves by pipelining with specially designed hardware. Furthermore it facilitates the development of new, related curve schemes which may have useful shape parameters for altering the shape of the curve without moving the control vertices. It may also be used for constructing transformations to Bézier and B-spline form.