Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves (ResearchIndex)

Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves (2002) (Make Corrections)
João Batista Oliveira

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Abstract: Most methods for computing offsets, bisectors, and medial axes of parametric curves in the plane are based on a local formulation of the distance to a curve. As a consequence, the computed objects may contain spurious parts and components, and have to be trimmed. We approach these problems as global optimization problems, and solve them using interval arithmetic, thus generating robust approximations that need not be trimmed. (Update)

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BibTeX entry: (Update)

@misc{ oliveira-robust,
  author = "João Batista Oliveira",
  title = "Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves",
  url = "citeseer.nj.nec.com/batistaoliveira02robust.html" }

Citations (may not include all citations):
534 The Design and Analysis of Spatial Data Structures (context) - Samet - 1990
312 Interval Analysis (context) - Moore - 1966
207 Global Optimization using Interval Analysis (context) - Hansen - 1992
163 Applications of Spatial Data Structures: Computer Graphics (context) - Samet - 1990
66 Interval analysis for computer graphics - Snyder - 1992
52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
25 On Ray Tracing Parametric Surfaces (context) - Toth - 1985
22 Interval methods in computer graphics (context) - Suffern, Fackerell - 1991
21 Robust Ray Intersection with Interval Arithmetic (context) - Mitchell - 1990
19 Curve reconstruction: connecting dots with good reason - Dey, Mehlhorn et al. - 2000
19 Generative Modeling for Computer Graphics and CAD (context) - Snyder - 1992
18 Interval Methods for Processing Geometric Objects (context) - Mudur, Koparkar - 1984
14 Shape offsets via level sets (context) - Kimmel, Bruckstein - 1993
13 Affine arithmetic and its applications to computer graphics - Comba - 1993
13 Ray-Tracing Procedural Displacement Shaders - Heidrich, Seidel - 1998
12 Algebraic properties of plane offset curves (context) - Farouki, Neff - 1990
10 Sampling procedural shaders using affine arithmetic - Heidrich, Slusallik et al. - 1998
9 Analytic properties of plane offset curves (context) - Farouki, Neff - 1990
9 An interval refinement technique for surface intersection (context) - Gleicher, Kass - 1992
8 Adaptive enumeration of implicit surfaces with affine arithm.. - de Figueiredo, Stolfi - 1996
8 The bisector of a point and a plane parametric curve (context) - Farouki, Johnstone - 1994
7 Ray Tracing General Parametric Surfaces Using Interval Arith.. (context) - Barth, Lieger et al. - 1994
7 Curve reconstruction from unorganized points - Lee - 2000
6 How to compute offsets without self-intersection (context) - Chiang, Hoffmann - 1991
6 Surface intersection using affine arithmetic - de Figueiredo - 1996
5 Interval methods for ray casting implicit surfaces with affi.. - Jr, de Figueiredo et al. - 1999
4 Comparing Offset Curve Approximation Methods - Elber, Lee et al. - 1997
4 Offset curves and surfaces: a brief survey (context) - Pham - 1992
3 An overview of offset curves and surfaces (context) - Maekawa - 1999
2 Data reduction of polygonal curves using B-splines (context) - Saux, Daniel - 1999
http://cs.utep.edu/interval-comp/

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