Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. I: Theoretical foundations

DOI10.1016/S0377-0427(98)00211-8zbMath0939.65018MaRDI QIDQ1300788

Rida T. Farouki, Rajesh Ramamurthy

Publication date: 19 June 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmVoronoi diagrammedial axisfree-form curves

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (13)

Exploiting curvatures to compute the medial axis for domains with smooth boundary ⋮ PRECISE VORONOI CELL EXTRACTION OF FREE-FORM PLANAR PIECEWISE C¹-CONTINUOUS CLOSED RATIONAL CURVES ⋮ Computation of medial axis and offset curves of curved boundaries in planar domains based on the Cesáro's approach ⋮ Text region extraction in a document image based on the Delaunay tessellation ⋮ COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS ⋮ Exact Voronoi diagram of smooth convex pseudo-circles: general predicates, and implementation for ellipses ⋮ COMPUTATIONAL AND STRUCTURAL ADVANTAGES OF CIRCULAR BOUNDARY REPRESENTATION ⋮ Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions ⋮ Optimal slicing of free-form surfaces ⋮ An Entropy Satisfying Boundary Layer Surface Mesh Generation ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces ⋮ Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. II: Detailed algorithm description ⋮ Voronoi diagrams on the sphere

Cites Work

• An O(n log n) algorithm for the Voronoi diagram of a set of simple curve segments
• Degenerate point/curve and curve/curve bisectors arising in medial axis computations for planar domains with curved boundaries
• An automatic coarse and fine surface mesh generation scheme based on medial axis transform. I: Algorithms
• On the computational geometry of pocket machining
• Shape description using weighted symmetric axis features
• Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. II: Detailed algorithm description
• The bisector of a point and a plane parametric curve
• 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
• Medial Axis Transformation of a Planar Shape
• Automated interrogation and adaptive subdivision of shape using medial axis transform
• 2D finite element mesh generation by medial axis subdivision
• Specified–Precision Computation of Curve/Curve Bisectors
• Shape Recognition, Prairie Fires, Convex Deficiencies and Skeletons
• Continuous Skeletons from Digitized Images
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Voronoi diagram and medial axis algorithm for planar domains with curved boundaries. I: Theoretical foundations