Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Extended free-form deformation: a sculpturing tool for 3D geometric modeling
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Direct manipulation of free-form deformations
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
An optimal algorithm for expanding the composition of polynomials
ACM Transactions on Graphics (TOG)
The symmetric analogue of the polynomial power basis
ACM Transactions on Graphics (TOG)
Applications of the polynomial s-power basis in geometry processing
ACM Transactions on Graphics (TOG)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A framework for geometric warps and deformations
ACM Transactions on Graphics (TOG)
Inversion approximations for functions via s-power series
Computer Aided Geometric Design
NURBS-Based Free-Form Deformations
IEEE Computer Graphics and Applications
Accurate B-spline free-form deformation of polygonal objects
Journal of Graphics Tools
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Free-form deformation with weighted T-spline
The Visual Computer: International Journal of Computer Graphics
Inside Rhinoceros 4
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Real-time haptic incision simulation using FEM-based discontinuous free-form deformation
Computer-Aided Design
A survey of spatial deformation from a user-centered perspective
ACM Transactions on Graphics (TOG)
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
Composition of parametrizations, using the paired algebras of forms and sites
Computer Aided Geometric Design
Technical Section: Real-time B-spline Free-Form Deformation via GPU acceleration
Computers and Graphics
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Free-Form Deformation Techniques (FFD) are commonly used to generate animations, where a polygonal approximation of the final object suffices for visualization purposes. However, for some CAD/CAM applications, we need an explicit expression of the object, rather than a collection of sampled points. If both object and deformation are polynomial, their composition yields a result that is also polynomial, albeit very high degree, something undesirable in real applications. To solve this problem, we transform each curve or surface composing the object, usually expressed in the Bernstein basis, to a modified Newton form. In this representation, the two-point analogue of Taylor expansions, the composition admits a simple expression in terms of discrete convolutions, and degree reduction corresponding to Hermite approximation is trivial by dropping high-degree coefficients. Furthermore, degree-reduction can be incorporated into the composition. Finally, the deformed curve or surface is converted back to the Bernstein form. This method extends to general non-polynomial deformation, such as bending and twisting, by computing a polynomial approximant of the deformation.