Search results for "subdivision"

showing 10 items of 52 documents

Surface Reconstruction Based on a Descriptive Approach

2000

The design of complex surfaces is generally hard to achieve. A natural method consists in the subdivision of the global surface into basic surface elements. The different elements are independently designed and then assembled together to represent the final surface. This method requires a classification and a formal description of the basic elements. This chapter presents a general framework for surface description, based on a constructive tree approach. In this tree the leaves are surface primitives and the nodes are constructive operators.

Bézier surfaceSurface (mathematics)Tree (data structure)Theoretical computer sciencebusiness.industryComputer scienceDescriptive researchbusinessConstructiveSurface reconstructionFormal descriptionComputingMethodologies_COMPUTERGRAPHICSSubdivision
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Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

2013

We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].

AlgebraDiscrete mathematicsComputational MathematicsOperator (computer programming)Relation (database)business.industryHermite interpolationApplied MathematicsbusinessConvexityMathematicsSubdivisionApplied Mathematics and Computation
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Curvilinear constraints for free form deformations on subdivision surfaces

2010

This paper presents a method to deform a subdivision surface with curvilinear constraints. It combines an intuitive free form deformation with a Loop subdivision algorithm. The main advantage of this method of deformation is that it uses only vertices of an object and satisfies the geometrical constraints provided by the user. It permits us to control the final shape of the deformed object, defining the range (i.e. the impact) of the deformation before applying it. The deformation takes into account the Loop properties to follow the subdivision scheme, allowing the user to fix some curvilinear constraints at the subdivision level he works on and to render the final object at the level he wa…

Surface (mathematics)ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION020101 civil engineering02 engineering and technologyDeformation (meteorology)Topology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]0201 civil engineeringModelling and Simulation0202 electrical engineering electronic engineering information engineeringSubdivision surfaceComputingMilieux_MISCELLANEOUSComputingMethodologies_COMPUTERGRAPHICSMathematicsSubdivisionCurvilinear coordinatesbusiness.industry020207 software engineering[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]Object (computer science)[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]Computer Science ApplicationsRange (mathematics)Modeling and Simulation[ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG]Free-form deformationbusinessMathematical and Computer Modelling
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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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On the use of generalized harmonic means in image processing using multiresolution algorithms

2019

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new famil...

business.industryApplied MathematicsHarmonic meanStability (learning theory)Image processing010103 numerical & computational mathematics01 natural sciencesNonlinear predictionComputer Science Applications010101 applied mathematicsComputational Theory and Mathematics0101 mathematicsbusinessAlgorithmNonlinear operatorsSubdivisionMathematicsInternational Journal of Computer Mathematics
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Representation of NURBS surfaces by Controlled Iterated Functions System automata

2019

Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…

Computer scienceBasis functionBézier curve02 engineering and technology[INFO] Computer Science [cs]Computer Science::Computational Geometry01 natural scienceslcsh:QA75.5-76.95Iterated function system0202 electrical engineering electronic engineering information engineeringSubdivision surface[INFO]Computer Science [cs]0101 mathematicsComputingMilieux_MISCELLANEOUSSubdivisionFinite-state machinebusiness.industry010102 general mathematicsGeneral Engineering020207 software engineeringComputer Graphics and Computer-Aided Design[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]AutomatonHuman-Computer InteractionAlgebraComputer Science::GraphicsIterated functionlcsh:Electronic computers. Computer sciencebusinessComputers & Graphics: X
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Revisited mixed-value method via symmetric BEM in the substructuring approach

2012

Abstract Within the Symmetric Boundary Element Method, the mixed-value analysis is re-formulated. This analysis method contemplates the subdivision of the body into substructures having interface kinematical and mechanical quantities. For each substructure an elasticity equation, connecting weighted displacements and tractions to nodal displacements and forces of the same interface boundary and to external action vector, is introduced. The assembly of the substructures is performed through both the strong and weak regularity conditions of the displacements and tractions. We obtain the solving equations where the compatibility and the equilibrium are guaranteed in the domain Ω for the use of…

business.industryApplied MathematicsLinear elasticityMathematical analysisGeneral EngineeringGeometrySymmetric GalerkinBEMMacro-element Substructuring Displacement approach Mixed-value approachDisplacement methodComputational MathematicsCompatibility (mechanics)Fundamental solutionSubstructureSettore ICAR/08 - Scienza Delle CostruzionibusinessBoundary element methodAnalysisMathematicsEquation solvingSubdivisionEngineering Analysis with Boundary Elements
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A nonlinear Chaikin-based binary subdivision scheme

2019

Abstract In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear 3-cell subdivision scheme. Our scheme seeks to improve the lack of convergence in the uniform metric of the nonlinear scheme proposed in Amat et al. (2012), where the authors define a cell-average version of the PPH subdivision scheme (Amat et al., 2006). The properties of the new scheme are analyzed and its performance is illustrated through numerical examples.

Nonlinear subdivisionScheme (programming language)business.industryApplied MathematicsMathematicsofComputing_NUMERICALANALYSISBinary numberComputer Science::Computational GeometryComputational MathematicsNonlinear systemMetric (mathematics)Convergence (routing)Applied mathematicsbusinesscomputerComputingMethodologies_COMPUTERGRAPHICSMathematicsSubdivisioncomputer.programming_languageJournal of Computational and Applied Mathematics
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Ositusmetodit reaaliaikaisessa renderöinnissä

2017

Tietokonegrafiikka ja siihen liittyvät menetelmät ovat nopeasti kehittyvä tutkimuksen ala. Tämän tutkimuksen tavoitteena on pohtia eri ositusmenetelmien toimintaa reaaliaikaisessa käytössä sekä vertailla näitä menetelmiä. Nykyaikaiselle käytölle tehokkaimmaksi osoittautui kolmesta tutkitusta menetelmästä tuorein (Brainerd ym. 2016). Tulevassa tutkimuksessa laitteistointegraatioon keskittyminen voisi tuoda ositusmenetelmät nopeammin kuluttajien saataville. Computergraphicsanditsmethodsarearapidlydevelopingfieldinresearch.The purpose of this study is to discuss and compare the functionality of several subdivision methods in real-time use. The latest of the three studied methods turned out to be…

subdivision surfacestietokonegrafiikkacomputer graphicsosa-aluepinnatrenderingrenderöinti
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Multiresolution Analysis for Irregular Meshes

2003

International audience; The concept of multiresolution analysis applied to irregular meshes has become more and more important. Previous contributions proposed a variety of methods using simplification and/or subdivision algorithms to build a mesh pyramid. In this paper, we propose a multiresolution analysis framework for irregular meshes with attributes. Our framework is based on simplification and subdivision algorithms to build a mesh pyramid. We introduce a surface relaxation operator that allows to build a non-uniform subdivision for a low computational cost. Furthermore, we generalize the relaxationoperator to attributes such as color, texture, temperature, etc. The attribute analysis…

Surface (mathematics)Theoretical computer scienceMultiresolution analysisNoise reductionComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR]02 engineering and technology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesmultiresolution analysisIrregular mesh010309 opticsOperator (computer programming)[INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]0103 physical sciences0202 electrical engineering electronic engineering information engineeringPolygon meshPyramid (image processing)SubdivisionMathematicsComputingMethodologies_COMPUTERGRAPHICSbusiness.industrysurface attributes[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]020207 software engineeringsurface relaxation[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]Computer Science::Graphics[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]Computer Science::Computer Vision and Pattern RecognitionRelaxation (approximation)businessAlgorithm
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