Computation of singularities and intersections of offsets of planar curves

DOI10.1016/0167-8396(93)90020-4zbMath0792.65006OpenAlexW2066253548MaRDI QIDQ1315816

Takashi Maekawa, Nicholas M. Patrikalakis

Publication date: 31 July 1994

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-8396(93)90020-4

zbMATH Keywords

singularitiesnumerical examplessystems of polynomial equationsintersectionspolynomial curverounded interval arithmeticoffsets of planar curves

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (14)

An algebraic framework for computing the topology of offsets to rational curves ⋮ NUMERICAL AND GEOMETRIC PROPERTIES OF INTERVAL B-SPLINES ⋮ Efficient computation of dual space and directional multiplicity of an isolated point ⋮ Topologically reliable approximation of composite Bézier curves ⋮ Umbilics and lines of curvature for shape interrogation ⋮ Solving interval constraints by linearization in computer-aided design ⋮ Approximation of circular arcs and offset curves by Bézier curves of high degree ⋮ The square-freeness of the offset equation to a rational planar curve, computed via resultants ⋮ Self-intersections of offsets of quadratic surfaces. I: Explicit surfaces ⋮ Automated exploration of envelopes and offsets with networking of technologies ⋮ A new method to compute the singularities of offsets to rational plane curves ⋮ Conformal mapping in linear time ⋮ IGB-offset for plane curves -- loop removal by scanning of interval sequences ⋮ Analysis and applications of pipe surfaces

Cites Work

• A dimensionality paradigm for surface interrogations
• Method for intersecting algebraic surfaces with rational polynomial patches
• Algebraic properties of plane offset curves
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Offsetting operations in solid modelling
• Decompostition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems
• On the computational geometry of pocket machining
• Algorithm for algebraic curve intersection
• Computation of the solutions of nonlinear polynomial systems
• Analytic properties of plane offset curves
• Computational techniques for processing parametric surfaces
• Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
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