Detecting symmetries of rational plane and space curves

DOI10.1016/j.cagd.2014.02.004zbMath1293.65023arXiv1207.4047OpenAlexW2950183434MaRDI QIDQ396195

Juan Gerardo Alcázar, Georg Muntingh, Carlos Hermoso Ortíz

Publication date: 8 August 2014

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

Full work available at URL: https://arxiv.org/abs/1207.4047

zbMATH Keywords

reflectionsrotation symmetrysymmetry detectioncurve shapeplane rational curvesspace rational curves

Mathematics Subject Classification ID

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

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Uses Software

• SageMath

Cites Work

• Unnamed Item
• Computing the shapes arising in a family of space rational curves depending on one parameter
• Topology of 2D and 3D rational curves
• Rotations, translations and symmetry detection for complexified curves
• Affine invariant fitting of algebraic curves using Fourier descriptors
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• Rational algebraic curves. A computer algebra approach
• Testing congruence and symmetry for general 3-dimensional objects.
• Congruence, similarity, and symmetries of geometric objects
• Numerically invariant signature curves
• Detection of rotational and involutional symmetries and congruity of polyhedra
• Efficient detection of symmetries of polynomially parametrized curves
• Improving the stability of algebraic curves for applications
• Rethinking Quaternions