Algorithms for Graphics and Imag
Algorithms for Graphics and Imag
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Cylindrical Algebraic Decomposition by Quantifier Elimination
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Algorithms for the geometry of semi-algebraic sets
Algorithms for the geometry of semi-algebraic sets
Automatic analysis of real algebraic curves
ACM SIGSAM Bulletin
Algebraic decomposition of regular curves
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
Algorithm 671: FARB-E-2D: fill area with bicubics on rectangles—a contour plot program
ACM Transactions on Mathematical Software (TOMS)
Scan line display of algebraic surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
A parallel implementation of the cylindrical algebraic decomposition algorithm
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Contour tracing by piecewise linear approximations
ACM Transactions on Graphics (TOG)
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
An accurate algorithm for rasterizing algebraic curves
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Numeric-symbolic algorithms for evaluating one-dimensional algebraic sets
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
User interfaces for three-dimensional geometric modelling
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
Reliable two-dimensional graphing methods for mathematical formulae with two free variables
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A Tracking Algorithm for Implicitly Defined Curves
IEEE Computer Graphics and Applications
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Journal of Computational and Applied Mathematics
Computing exact aspect graphs of curved objects: parametric surfaces
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 2
| Hi-index | 0.00 |
An algebraic curve is a set of points in the plane satisfying an equation F(x,y) &equil; 0, where F(x,y) is a polynomial in x and y with rational number coefficients. The topological structure of an algebraic curve can be complicated. It may, for example, have multiple components, isolated points, or intricate self-crossings. In the field of Computer Algebra (Symbolic Mathematical Computation), algorithms for exact computations on polynomials with rational number coefficients have been developed. In particular, the cylindrical algebraic decomposition (cad) algorithm of Computer Algebra determines the topological structure of an algebraic curve, given F(x,y) as input. We describe methods for algebraic curve display which, by making use of the cad algorithm, correctly portray the topological structure of the curve. The running times of our algorithms consist almost entirely of the time required for the cad algorithm, which varies from seconds to hours depending on the particular F(x,y).