Search results for "Subdivision schemes"

showing 3 items of 3 documents

The PCHIP subdivision scheme

2016

In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741

Scheme (programming language)Generalized JacobianStability (learning theory)MathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematics01 natural sciencesConvergence (routing)ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0101 mathematicsMATLABMathematicscomputer.programming_languageSubdivisionNonlinear subdivision schemesbusiness.industryApplied MathematicsProcess (computing)Approximation order010101 applied mathematicsComputational MathematicsThird orderbusinessConvergencecomputerAlgorithmStability
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Study and construction of the quasi-linear subdivision schemes over bi-regular meshs

2012

Subdivision schemes are commonly used to generate a smooth shape from a much more coarseone. The reverse subdivision is designed to describe a high resolution mesh from a coarse one. Bothof these tools are used in numerous graphical modelisation domains. In this thesis, we focused ontwo distinct aspects: on one hand the construction of quasi-linear subdivision schemes and on theother hand the construction of reverse quad/triangle subdivision schemes. The work, presented inthe context of the subdivision, describes the construction of a new type of subdivision schemes, andtheirs applications to solve some problems coming from the application of linear subdivision schemes.The work presented in…

Polynomial generationPolynomial reproduction[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][INFO.INFO-OH]Computer Science [cs]/Other [cs.OH]Subdivision quad/triangle[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Génération des polynômesInterpolation[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]QuasiinterpolationReverse subdivision[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM][ INFO.INFO-OH ] Computer Science [cs]/Other [cs.OH]Schémas de subdivisionQuad/triangle subdivisionSubdivision schemesReproduction des polynômesSchémas de subdivision inverseApproximation
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Error bounds for a convexity-preserving interpolation and its limit function

2008

AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.

Mathematical optimizationNonlinear subdivision schemesbusiness.industryApplied MathematicsNumerical analysisMathematicsofComputing_NUMERICALANALYSISStairstep interpolationComputer Science::Computational GeometryConvexityMultivariate interpolationComputational MathematicsError boundsComputer Science::GraphicsNearest-neighbor interpolationTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematicsComputer Science::Symbolic ComputationConvexity preservingbusinessSpline interpolationSubdivisionInterpolationMathematicsComputingMethodologies_COMPUTERGRAPHICSJournal of Computational and Applied Mathematics
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