Computer-Aided Design
On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Blending quadric surfaces with quadric and cubic surfaces
SCG '87 Proceedings of the third annual symposium on Computational geometry
On computing the intersection of a pair of algebraic surfaces
Computer Aided Geometric Design
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Blending and offsetting solid models (cad/cam, computational geometry, representations, curves, surfaces, approximation)
Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines)
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
An extension of the potential method to higher-order blendings
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An introduction to constructive shell representations for free-form surfaces and solids
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
A parametric surface blending method for complex engineering objects
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
A family of tangent continuous cubic algebraic splines
ACM Transactions on Graphics (TOG)
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
G2 Blending of Corners with Piecewise Algebraic Surfaces
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Computing all parametric solutions for blending parametric surfaces
Journal of Symbolic Computation
Generalized filleting and blending operations toward functional and decorative applications
Graphical Models - Special issue on SMI 2003
Computer Aided Geometric Design
Blending canal surfaces based on PH curves
Journal of Computer Science and Technology
Basic lines, axes and geometric modeling on implicit algebraic surfaces
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
G2 blending of corners by cubic algebraic splines
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Simultaneous blending of convex polyhedra by S32 algebraic splines
Computer-Aided Design
Functional splines with different degrees of smoothness and their applications
Computer-Aided Design
Computer-Aided Design
Computer Aided Geometric Design
Blends of canal surfaces from polyhedral medial transform representations
Computer-Aided Design
Constructive theory and algorithm for blending several implicit algebraic surfaces
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Blending curves for landing problems by numerical differential equations, I. Mathematical modelling
Mathematical and Computer Modelling: An International Journal
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A new definition of geometric continuity for implicitly defined surfaces is introduced. Under this definition, it is shown that algebraic blending surfaces (surfaces that smoothly join two or more surfaces) have a very specific form. In particular, any polynomial whose zero set blends the zero sets of several other polynomials is always expressible as a simple combination of these polynomials. Using this result, new methods for blending several algebraic surfaces simultaneously are derived.