On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
Polygonization of implicit surfaces
Computer Aided Geometric Design
Scan line display of algebraic surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Base points, resultants, and the implicit representation of rational surfaces
Base points, resultants, and the implicit representation of rational surfaces
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
Reconstructing surfaces form sparse depth information
SAC '92 Proceedings of the 1992 ACM/SIGAPP Symposium on Applied computing: technological challenges of the 1990's
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Implicitization using moving curves and surfaces
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
Mathematical Methods for Curves and Surfaces
Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Characterization of rational ruled surfaces
Journal of Symbolic Computation
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The tutorial presents some tools for free-form modeling with algebraic surfaces, that is, surfaces that can be defined using an implicit polynomial equation f(x, y, z)=0. Cubic algebraic surfaces (defined by an implicit equation of degree 3) are emphasized. While much of this material applies only to cubic surfaces, some applies to algebraic surfaces of any degree. This area of the tutorial introduces terminology, presents different methods for defining and modeling with cubic surfaces, and examines the power basis representation of algebraic surfaces. Methods of forcing an algebraic surface to interpolate a set of points or a space curve are also discussed. The parametric definition of cubic surfaces by imposing base points is treated, along with the classical result that a cubic surface can be defined as the intersection locus of three two-parameter families of planes. Computer-generated images of algebraic surfaces created using a polygonization algorithm and Movie. BYU software illustrate the concepts presented.