Computing projective equivalences of special algebraic varieties

DOI10.1016/j.cam.2019.112438zbMath1436.14096arXiv1806.05827OpenAlexW2973118323MaRDI QIDQ2332748

Michal Bizzarri, Jan Vršek, Miroslav Lávička

Publication date: 5 November 2019

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

Full work available at URL: https://arxiv.org/abs/1806.05827

zbMATH Keywords

symmetryrational curvealgebraic surfaceprojective transformationrational ruled surface

Mathematics Subject Classification ID

Computational aspects of algebraic surfaces (14Q10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computational aspects of algebraic curves (14Q05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (14)

Affine equivalences of surfaces of translation and minimal surfaces, and applications to symmetry detection and design ⋮ Efficient reparametrization into standard form and algorithmic characterization of rational ruled surfaces ⋮ Using \(\mu \)-bases to reduce the degree in the computation of projective equivalences between rational curves in \(n\)-space ⋮ Symmetries of discrete curves and point clouds via trigonometric interpolation ⋮ Computing symmetries of implicit algebraic surfaces ⋮ Detecting similarities of rational plane curves using complex differential invariants ⋮ Affine equivalences, isometries and symmetries of ruled rational surfaces ⋮ Approximate symmetries of planar algebraic curves with inexact input ⋮ Computing projective equivalences of planar curves birationally equivalent to elliptic and hyperelliptic curves ⋮ Projective isomorphisms between rational surfaces ⋮ On curves with affine-congruent arcs in an \(n \)-dimensional affine space ⋮ Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors ⋮ A new method to detect projective equivalences and symmetries of rational \(3 D\) curves ⋮ Detecting affine equivalences between implicit planar algebraic curves

Cites Work

• Detecting symmetries of rational plane and space curves
• Rotations, translations and symmetry detection for complexified curves
• Involutions of polynomially parametrized surfaces
• Testing congruence and symmetry for general 3-dimensional objects.
• Projective and affine symmetries and equivalences of rational curves in arbitrary dimension
• Projective and affine symmetries and equivalences of rational and polynomial surfaces
• Detecting similarity of rational plane curves
• Efficient detection of symmetries of polynomially parametrized curves
• Similarity detection of rational space curves
• Symmetry detection of rational space curves from their curvature and torsion
• Symmetries and similarities of planar algebraic curves using harmonic polynomials
• Computational line geometry
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