Projectively invariant classes of geometric continuity for CAGD

DOI10.1016/0167-8396(89)90031-9zbMath0684.65011OpenAlexW2002355661MaRDI QIDQ1825583

Helmut Pottmann

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0167-8396(89)90031-9

zbMATH Keywords

algorithmssplinesBézier curvesgeometric continuitycomputer aided geometric designprojective invariance

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Algorithms for approximation of functions (65D15) Curves in Euclidean and related spaces (53A04) Projective differential geometry (53A20) Affine differential geometry (53A15) Descriptive geometry (51N05)

Related Items (13)

Geometric continuity between adjacent Bézier patches and their constructions ⋮ Theories of contact specified by connection matrices ⋮ New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree ⋮ Geometric construction of spline curves with tension properties ⋮ Geometric continuity of ruled surfaces ⋮ Interpolation with developable Bézier patches ⋮ Developable rational Bézier and B-spline surfaces ⋮ B-spline-Bézier representation of geometric spline curves: Quartics and quintics ⋮ Some remarks on geometric continuity of rational surface patches ⋮ Geometric continuity of arbitrary order between tensor product Bézier surfaces ⋮ A class of general quartic spline curves with shape parameters ⋮ Geometric continuity ⋮ Geometric contact for curves and surfaces

Cites Work

• \(C^ 1\) splines for interpolation of rapidly varying data
• Properties of \(\beta\)-splines
• Geometric spline curves
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• Rational geometric splines
• Piecewise polynomial spaces and geometric continuity of curves
• Curvature continuous curves and surfaces
• Local control of interval tension using weighted splines
• Some remarks on Bézier curves
• Visual continuity
• Letter to the editor: On the definition of geometric continuity
• Verallgemeinerte Regelflächen
• Smooth curves under tension
• Interpolation with interval and point tension controls using cubic weighted v -splines
• Continuity conditions for spline curves
• Deriving the beta-constraints for geometric continuity of parametric curves
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