Geometric modeling
The characterization of parametric surface sections
Computer Vision, Graphics, and Image Processing
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
A triangulation algorithm from arbitrary shaped multiple planar contours
ACM Transactions on Graphics (TOG)
Mathematical methods in computer aided geometric design II
Computer Graphics and Geometric Modeling for Engineers
Computer Graphics and Geometric Modeling for Engineers
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
A New Artificial Intelligence Paradigm for Computer-Aided Geometric Design
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems - Special issue: Computer graphics and geometric modeling
Functional networks for B-spline surface reconstruction
Future Generation Computer Systems
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Information Sciences: an International Journal
Information Sciences: an International Journal
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
| Hi-index | 0.00 |
In this article functional equations are used to characterize some families of surfaces. First, the most general surfaces in implicit form f(x, y, z) = 0, such that any arbitrary intersection with the planes z = z0, y = y0, and x = x0 are linear combinations of sets of functions of the other two variables, are characterized. It is shown that only linear combinations of tensor products of univariate functions are possible for fx, y, z). Second, we obtain the most general families of surfaces in explicit form such that their intersections with planes parallel to the planes y = 0 and x = 0 belong to two, not necessarily equal, parametric families of curves. Finally, functional equations are used to analyze the uniqueness of representation of Gordon-Coon surfaces. Some practical examples are used to illustrate the theoretical results.