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Contents
Index
5. Intersection Problems
Subsections
- 5.1 Overview of intersection problems
- 5.2 Intersection problem classification
- 5.2.1 Classification by dimension
- 5.2.2 Classification by type of geometry
- 5.2.3 Classification by number system
- 5.3 Point/point intersection
- 5.4 Point/curve intersection
- 5.4.1 Point/implicit algebraic curve intersection
- 5.4.2 Point/rational polynomial parametric curve intersection
- 5.4.2.1 Elementary method
- 5.4.2.2 Bounding box and subdivision followed by minimization method
- 5.4.2.3 Distance function method
- 5.4.2.4 Implicitization
- 5.4.3 Point/procedural parametric curve intersection
- 5.5 Point/surface intersection
- 5.5.1 Point/implicit algebraic surface intersection
- 5.5.2 Point/rational polynomial parametric surface intersection
- 5.5.2.1 Implicitization
- 5.5.2.2 Newton's method
- 5.5.2.3 Bounding box and subdivision followed by minimization method
- 5.5.2.4 Distance function method
- 5.5.3 Point/procedural parametric surface intersection
- 5.6 Curve/curve intersection
- 5.6.1 Rational polynomial parametric/implicit algebraic curve intersection (Case D3)
- 5.6.1.1 2-D planar case
- 5.6.1.2 3-D space curve
- 5.6.2 Rational polynomial parametric/rational polynomial parametric curve intersection (Case D1)
- 5.6.3 Rational polynomial parametric/procedural parametric and
procedural parametric/procedural parametric curve intersections (Cases
D2 and D5)
- 5.6.4 Procedural parametric/implicit algebraic curve intersection (Case D6)
- 5.6.5 Implicit algebraic/implicit algebraic curve intersection (Case D8)
- 5.6.5.1 Implicitization
- 5.6.5.2 Newton's method
- 5.6.5.3 Interval Projected Polyhedron solver
- 5.7 Curve/surface intersection
- 5.7.1 Rational polynomial parametric curve/implicit algebraic surface intersection (Case E3)
- 5.7.2 Rational polynomial parametric curve/rational polynomial parametric surface intersection (Case E1)
- 5.7.2.1 Implicitization
- 5.7.2.2 Bounding box and subdivision followed by minimization method
- 5.7.2.3 Interval Projected Polyhedron solver
- 5.7.3 Rational polynomial parametric/procedural parametric and procedural parametric/procedural parametric curve/surface intersections (Cases E2/E6)
- 5.7.4 Procedural parametric curve/implicit algebraic surface intersection (Case E7)
- 5.7.5 Implicit algebraic curve/implicit algebraic surface intersection (Case E11)
- 5.7.6 Implicit algebraic curve/rational polynomial parametric surface intersection (Case E9)
- 5.8 Surface/surface intersections
- 5.8.1 Rational polynomial parametric/implicit algebraic surface intersection (Case F3)
- 5.8.1.1 Formulation
- 5.8.1.2 Tracing method
- 5.8.1.3 Characteristic points
- 5.8.1.4 Analysis of singular points
- 5.8.1.5 Computing starting points for all branches
- 5.8.2 Rational polynomial parametric/rational polynomial parametric surface intersection (Case F1)
- 5.8.2.1 Lattice methods
- 5.8.2.2 Subdivision methods
- 5.8.2.3 Marching methods
- 5.8.3 Implicit algebraic/implicit algebraic surface intersection (Case F8)
- 5.9 Overlapping of curves and surfaces
- 5.10 Self-intersection of curves and surfaces
- 5.11 Summary
December 2009