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  • 65 D 07  (1)
  • 65D05  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Positive, monotone, andS-convexC 1-interpolation on rectangular grids (1992)
    Springer
    Computing 48 (1992), S. 363-371 
    Details
    ISSN: 1436-5057
    Keywords: 65 D 07 ; 41 A 15 ; 41 A 63 ; Shape preservingC 1-interpolation ; special rational biquadratic splines ; construction by a search procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit befaßt sich mit formerhaltenderC 1-Interpolation von Daten auf Rechteckgittern. Bei Verwendung von speziellen rational-biquadratischen Splines werden Bedingungen hergeleitet, welche hinreichend für die Positität, Monotonie undS-Konvexität sind und welche sich darüber hinaus erfüllen lassen, sofern die Rationalitätsparameter hinreichend groß sind.
    Notes: Abstract This paper is concerned with shape preservingC 1-interpolation of data sets given on rectangular grids. Using special rational biquadratic splines, criteria are derived which are sufficient for the positivity, monotonicity, andS-convexity and which, in addition, are satisfied for sufficiently large rationality parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238643
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Powell-Sabin splines in range restricted interpolation of scattered data (1994)
    Springer
    Computing 53 (1994), S. 137-154 
    Details
    ISSN: 1436-5057
    Keywords: 65D05 ; 65D07 ; 41A15 ; Shape preserving interpolation of scattered data ; range restrictions ; Powell-Sabin splines ; minimum norm modification ; thin plate functional
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Behandelt wird die Interpolation unregelmäßig verteilter Daten durch quadratische Powell-Sabin-Splines, wobei stückweise konstante obere und untere Schranken für die Funktionswerte der Interpolierenden vorgegeben sind. Die hergeleiteten hinreichenden Bedingungen für die Einhaltung der zweiseitigen Schranken ergeben ein lösbares lineares Ungleichungssytem für die Gradienten als Parameter, welches bezüglich der Datenpunkte separiert ist. Die Auswahl von visuell gefälligen Interpolierenden erfolgt durch die Minimierung geeigneter Funktionale.
    Notes: Abstract The construction of range restricted bivariateC 1 interpolants to scattered data is considered. In particular, we deal with quadratic spline interpolation on a Powell-Sabin refinement of a triangulation of the data sites subject to piecewise constant lower and upper bounds on the values of the interpolant. The derived sufficient conditions for the fulfillment of the range restrictions result in a solvable system of linear inequalities for the gradients as parameters, which is separated with respect to the data sites. Since there exists an infinite number of spline interpolants meeting the constraints, the selection of a visually pleasant solution is based on the minimum norm modification of a suitable initial interpolant or on the minimization of the thin plate functional. While the first proposal reduces to the solution of independent local quadratic programs, the second proposal results in a global quadratic optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252986
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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