Efficient topology determination of implicitly defined algebraic plane curves
References (20)
- et al.
Algebraic decomposition of regular curves
J. Symbolic Comput.
(1988) - et al.
A polynomial time algorithm for the topological type of a real algebraic curve
J. Symbolic Comput.
(1988) - et al.
Tracing surface intersections
Computer Aided Geometric Design
(1988) - et al.
An improved upper complexity bound for the topology computation of a real algebraic plane curve
J. Complexity
(1996) An efficient method for analyzing the topology of plane real algebraic curves
Math. Comput. Simulation
(1996)- et al.
Efficient and exact manipulation of algebraic points and curves
Computer-Aided Design
(2000) - et al.
Efficient and accurate b-rep generation of low degree sculptured solids using exact arithmetic: I—representations
Computer Aided Geometric Design
(1999) - et al.
Efficient and accurate b-rep generation of low degree sculptured solids using exact arithmetic: II—computation
Computer Aided Geometric Design
(1999) - et al.
New structure theorem for subresultants
J. Symbolic Comput.
(2000) - et al.
Algorithms for the shape of semialgebraic sets: a new approach
Cited by (118)
An improved complexity bound for computing the topology of a real algebraic space curve
2024, Journal of Symbolic ComputationGlobally certified G<sup>1</sup> approximation of planar algebraic curves
2024, Journal of Computational and Applied MathematicsComputing the topology of the image of a parametric planar curve under a birational transformation
2023, Computer Aided Geometric DesignDetermining the asymptotic family of an implicit curve
2022, Computer Aided Geometric DesignTools for analyzing the intersection curve between two quadrics through projection and lifting
2021, Journal of Computational and Applied MathematicsCitation Excerpt :In this section, we study the cutcurve of the two quadrics whose intersection curve is to be computed; this is achieved by computing its topology. The usual method of computing the topology of a real algebraic plane curve defined implicitly requires computing its critical points (those that are singular or with a vertical tangent), regular points sharing the same projection as one of the critical points and the number of branches connecting all these points (connecting branches and points will be particularly easy in our case, because we are working with a very special quartic): for details see [33,34] and Section 4.7 (especially Fig. 3). In our case, because we are working with the cutcurve, we need to restrict our attention to the admissible region; this is why we will also pay special attention to the intersection points between the cutcurve and the silhouette curves.
Computing the topology of a plane or space hyperelliptic curve
2020, Computer Aided Geometric Design
- 1
Partially supported by DGES PB98-0713-C02-02 and by FEDER project 1FD-97-0409.