Applications of power series in computational geometry
Computer-Aided Design
Curve and surface constructions using rational B-splines
Computer-Aided Design
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Curvature continuity and offsets for piecewise conics
ACM Transactions on Graphics (TOG)
On local implicit approximation and its applications
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Hierarchical segmentations of algebraic curves and some applications
Mathematical methods in computer aided geometric design
Approximate parametrization of algebraic curves
Theory and practice of geometric modeling
Locally controllable conic splines with curvature continuity
ACM Transactions on Graphics (TOG)
Piecewise linear approximations of digitized space curves with applications
Scientific visualization of physical phenomena
Symbolic parametrization of curves
Journal of Symbolic Computation
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Computing real inflection points of cubic algebraic curves
Computer Aided Geometric Design
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Graph Theory With Applications
Graph Theory With Applications
Intrinsic topological representation of real algebraic surfaces
ACM SIGSAM Bulletin
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final approximation keeps many important geometric features of the original curve such as the topology, convexity and sharp points. Our method is implemented and experiments show that it may achieve better approximation bound with less segments than previously known methods. We also extend the method to approximate spatial algebraic curves.