Specified–Precision Computation of Curve/Curve Bisectors

DOI10.1142/S0218195998000291zbMath1026.65010MaRDI QIDQ4513229

Rajesh Ramamurthy, Rida T. Farouki

Publication date: 7 November 2000

Published in: International Journal of Computational Geometry & Applications (Search for Journal in Brave)

zbMATH Keywords

error boundsVoronoi diagramdistance functionsmedial axisskeletoncurve-curve bisectorsgeometric Hermite interpolants

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (12)

Efficient Voronoi diagram construction for planar freeform spiral curves ⋮ Algebro-geometric analysis of bisectors of two algebraic plane curves ⋮ Exploiting curvatures to compute the medial axis for domains with smooth boundary ⋮ Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries ⋮ Automatic piloting in progressive dies using medial axis transform ⋮ PRECISE VORONOI CELL EXTRACTION OF FREE-FORM PLANAR PIECEWISE C¹-CONTINUOUS CLOSED RATIONAL CURVES ⋮ Approximations of 2D and 3D generalized Voronoi diagrams ⋮ COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS ⋮ Two-dimensional offsets and medial axis transform ⋮ Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. II: Detailed algorithm description ⋮ Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. I: Theoretical foundations ⋮ Voronoi diagrams on the sphere

Cites Work

• High accurate rational approximation of parametric curves
• An O(n log n) algorithm for the Voronoi diagram of a set of simple curve segments
• On the numerical condition of polynomials in Bernstein form
• High accuracy geometric Hermite interpolation
• Algorithms for polynomials in Bernstein form
• Bounds on a polynomial
• An automatic coarse and fine surface mesh generation scheme based on medial axis transform. I: Algorithms
• Shape description using weighted symmetric axis features
• The bisector of a point and a plane parametric curve
• Optimal parameterizations
• Mathematical theory of medial axis transform
• Representing the Voronoï diagram of a simple polygon using rational quadratic Bézier curves
• Continuous skeleton computation by Voronoi diagram
• Symmetry sets
• Local Symmetry of Plane Curves
• 2D finite element mesh generation by medial axis subdivision
• Shape Recognition, Prairie Fires, Convex Deficiencies and Skeletons

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