Smoothing polyhedra using implicit algebraic splines
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Modeling arbitrary smooth objects with algebraic surfaces
Modeling arbitrary smooth objects with algebraic surfaces
Constructive shell representations for free-form surfaces and solids
Constructive shell representations for free-form surfaces and solids
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Cubicoids: Modeling and visualization
Computer Aided Geometric Design
More Powerful Solid Modeling Through Ray Representations
IEEE Computer Graphics and Applications
Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
More Powerful Solid Modeling Through Ray Representations
IEEE Computer Graphics and Applications
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Quartic supercyclides for geometric design
From geometric modeling to shape modeling
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We usually model freeform surfaces (mathematically, 2D r-sets embedded in 3D Euclidean space E/sup 3/) as a finite union of patches represented in the traditional parametric or the recently developed algebraic forms. The article introduces a new representation scheme for freeform surfaces called constructive shell representation (CSR), that draws on recent research on algebraic patches. CSRs of surfaces that constitute boundaries of solids are very useful for solid modeling. They represent thick shells derived from freeform surfaces and provide a means to compute exact CSG representations of freeform solids.