Piecewise polynomial spaces and geometric continuity of curves

DOI10.1007/BF01396765zbMath0638.65010MaRDI QIDQ1099576

N. Richter-Dyn, Charles A. Micchelli

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133321

zbMATH Keywords

computer-aided geometric designFrenet framesurfacestotal positivityspline functionsparametric representationcurvaturespiecewise polynomialsvariation diminishingarc-length continuitybeta-splines and nu-splinesfree form curvesshape preservations

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15) Curves in Euclidean and related spaces (53A04)

Related Items (36)

Totally positive bases for shape preserving curve design and optimality of \(B\)-splines ⋮ Constructing totally positive piecewise Chebyshevian B-spline bases ⋮ Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices ⋮ Theories of contact specified by connection matrices ⋮ A generalization of the variation diminishing property ⋮ New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree ⋮ Inflections on curves in two and three dimensions ⋮ Affine arc length polylines and curvature continuous uniform B-splines ⋮ Pseudoaffinity, de Boor algorithm, and blossoms ⋮ de Boor-fix dual functionals and algorithms for Tchebycheffian B-spline curves ⋮ Properties of functions in an auxiliary spline space ⋮ Geometric continuity of ruled surfaces ⋮ Design or not design? A numerical characterisation for piecewise Chebyshevian splines ⋮ An \(O(h^{2n})\) Hermite approximation for conic sections ⋮ Spaces with Almost Strictly Totally Positive Bases ⋮ Geometrically continuous piecewise Chebyshevian NU(R)BS ⋮ Polynomial splines as examples of Chebyshevian splines ⋮ How to build all Chebyshevian spline spaces good for geometric design? ⋮ Constructing piecewise rational curves with Frenet frame continuity ⋮ Identities for piecewise polynomial spaces determined by connection matrices ⋮ Piecewise extended Chebyshev spaces: a numerical test for design ⋮ Joining rational curves smoothly ⋮ Totally positive bases for shape preserving curve design and optimality of B-splines ⋮ Extending B-spline tools and algorithms to geometrically continuous splines: A study of similarities and differences ⋮ Piecewise Chebyshevian splines: interpolation versus design ⋮ On multi-degree splines ⋮ Computing ECT-B-splines recursively ⋮ Cardinal ECT-splines ⋮ One sided Hermite interpolation by piecewise different generalized polynomials ⋮ Towards existence of piecewise Chebyshevian B-spline bases ⋮ B-spline bases and osculating flats: One result of H.-P. Seidel revisited ⋮ Projectively invariant classes of geometric continuity for CAGD ⋮ A practical method for computing with piecewise Chebyshevian splines ⋮ Two chain rules for divided differences and Faà di Bruno’s formula ⋮ ECT-B-splines defined by generalized divided differences ⋮ Geometric contact for curves and surfaces

Cites Work

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• Properties of \(\beta\)-splines
• Geometric spline curves
• The Wilson-Fowler spline is a v-spline
• A survey of curve and surface methods in CAGD
• On Polya Frequency Function. III. The Positivity of Translation Determinants With an Application to the Interpolation Problem by Spline Curves

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