Computer Aided Geometric Design
Second-order surface analysis using hybrid symbolic and numeric operators
ACM Transactions on Graphics (TOG)
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Free form surface analysis using a hybrid of symbolic and numeric computation
Free form surface analysis using a hybrid of symbolic and numeric computation
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Multiplication as a general operation for splines
Proceedings of the international conference on Curves and surfaces in geometric design
Computing a chain of blossoms, with application to products of splines
Computer Aided Geometric Design
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Curves and surfaces in geometric modeling: theory and algorithms
Curves and surfaces in geometric modeling: theory and algorithms
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Perspective silhouette of a general swept volume
The Visual Computer: International Journal of Computer Graphics
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Technical note: Modeling by composition
Computer-Aided Design
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B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines, is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. We present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for B-spline multiplication that addresses the difficulties mentioned heretofore.