Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Faculty Publications
A survey of some techniques that may have potential for free-form modeling with algebraic surfaces is continued. Classical results as well as several recent innovations are included. Specific attention is paid to cubic algebraic surfaces, although many of the ideas presented have application to algebraic surfaces of any degree. Topics addressed include piecewise constructions, interpolation to points and space curves, and parameterization.
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Faculty Publications
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 …