Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Algebraic decomposition of regular curves
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Polygonization of implicit surfaces
Computer Aided Geometric Design
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Simplicial pivoting for mesh generation of implicitly defined surfaces
Computer Aided Geometric Design
Graphics Gems III
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
Numeric-symbolic algorithms for evaluating one-dimensional algebraic sets
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
Journal of Symbolic Computation
MAPC: a library for efficient and exact manipulation of algebraic points and curves
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Reliable two-dimensional graphing methods for mathematical formulae with two free variables
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Converting Discrete Images to Partitioning Trees
IEEE Transactions on Visualization and Computer Graphics
A Tracking Algorithm for Implicitly Defined Curves
IEEE Computer Graphics and Applications
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Robust Adaptive Approximation of Implicit Curves
SIBGRAPI '01 Proceedings of the 14th Brazilian Symposium on Computer Graphics and Image Processing
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Visualisation of Implicit Algebraic Curves
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
New bounds for the Descartes method
Journal of Symbolic Computation
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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Mathematical systems (e.g., Mathematica, Maple, Matlab, and DPGraph) easily plot planar algebraic curves implicitly defined by polynomial functions. However, these systems, and most algorithms found in the literature, cannot draw many implicit curves correctly; in particular, those with singularities (self-intersections, cusps, and isolated points). They do not detect sign-invariant components either, because they use numerical methods based on the Bolzano corollary, that is, they assume that the curve-describing function f flips sign somewhere in a line segment &ABhorbar; that crosses the curve, or f(A)·f(B) Generalized False Position (GFP) method. It allows us to sample an implicit curve against the Binary Space Partitioning (BSP), say bisection lines, of a rectangular region of R2. Interestingly, the GFP method can also be used to determine isolated points of the curve. The result is a general algorithm for sampling and rendering planar implicit curves with topological guarantees.