Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Conversion from Be´zier rectangles to Be´zier triangles
Computer-Aided Design
Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
Knot insertion from a blossoming point of view
Computer Aided Geometric Design
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Creating multisided rational Bézier surfaces using base points
ACM Transactions on Graphics (TOG)
An optimal algorithm for expanding the composition of polynomials
ACM Transactions on Graphics (TOG)
Applications of the polynomial s-power basis in geometry processing
ACM Transactions on Graphics (TOG)
Sketch- and constraint-based design of B-spline surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Bounding the Hausdorff distance between implicitly defined and/or parametric curves
Mathematical Methods for Curves and Surfaces
Surface construction by fitting unorganized curves
Graphical Models
Accurate B-spline free-form deformation of polygonal objects
Journal of Graphics Tools
Composition of parametrizations, using the paired algebras of forms and sites
Computer Aided Geometric Design
Constraint-based design of B-spline surfaces from curves
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Sliding windows algorithm for B-spline multiplication
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Approximate computation of curves on B-spline surfaces
Computer-Aided Design
Triangular subpatches of rectangular Bézier surfaces
Computers & Mathematics with Applications
Simploidals sets: Definitions, operations and comparison with simplicial sets
Discrete Applied Mathematics
A vertex-first parametric algorithm for polyhedron blending
Computer-Aided Design
Composition of parametrizations, using the paired algebras of forms and sites
Computer Aided Geometric Design
Trimming Bézier surfaces on Bézier surfaces via blossoming
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Algorithm for orthogonal projection of parametric curves onto B-spline surfaces
Computer-Aided Design
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
Approximate reachability computation for polynomial systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Some geometrical aspects of control points for toric patches
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Hermite approximation for free-form deformation of curves and surfaces
Computer-Aided Design
SMI 2012: Full Medial design of blades for hydroelectric turbines and ship propellers
Computers and Graphics
G1 continuous approximate curves on NURBS surfaces
Computer-Aided Design
Technical note: Modeling by composition
Computer-Aided Design
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In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions F and G, compute a representation of the function H = F o G. We examine this problem in detail for the case when F and G are given in either Be´zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.