Interpolation

MESHING
RESEARCH
CORNER

Alauzet, Frederic, Adrien Loseille, Alain Dervieux, and Pascal Frey

"Multi-Dimensional Continuous Metric for Mesh Adaptation", Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.191-214, September 17-20 2006
keywords:


continuous metric	metric tensor
mesh adaptation	anisotropy
interpolation error	order of convergence

Abstract
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"Derivative Generation From Multivariate Scattered Data by Functional Minimization", Computer Aided Geometric Design, Elsevier Science Publishers (North-Holland), Num 2, pp.281-296, 1985
keywords:


gradient estimation	interpolation
n-dimensional	scattered data

"Scattered Data Interpolation in Three or More Variables", Mathematical Methods in Computer Aided Geometric Design (Tom Lyche and Larry L. Schumaker eds.), Academic Press, pp.1-33, 1989
keywords:


n-dimensional	natural neighbor interpolation
scattered data	three-dimensional

"Pointerless Implementation of Hierarchical Simplicial Meshes and Efficient Neighbor Finding In Arbitrary Dimensions", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.15-26, September 19-22 2004
keywords:


data structures	pointerless data structures
neighbor finding	hierarchical meshes
simplicial meshes	interpolation.

Abstract
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"Interpolation from a cloud of points", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.55-63, Sept 2003
keywords:


interpolation	least squares estimation
point clouds	solution projection
surface reconstruction

Abstract
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"Interpolating Scattered Multivariate Data as a Function of Time", Computer Aided Geometric Deisgn, Elsevier Science Publishers, Num 9, pp.337-348, 1992
keywords:


interpolation	n-dimensional
scattered data

"Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive generating isolines algorithm", Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross., B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp.277-286, July 1998
keywords:


interpolation	natural neighbor
non-Sibsonian interpolation	Sibsonian interpolation

Abstract

"Vertex based data dependent triangulations", Computer Aided Geometric Design, North-Holland, Vol 8, pp.239-251, 1997
keywords:


data dependent triangulation	triangulation
interpolation

Abstract

"Systems of Coordinates Associated With Points Scattered in the Plane"
keywords:


natural neighbor interpolation

"Anisotropic Surface Mesh Generation", INRIA Report No. 2672, INRIA, pp.31, October 1995
keywords:


anisotropy	surface meshing
surface interpolation	triangles

Abstract

"On Optimal Interpolation Triangle Incidences", SIAM, Society for Industrial and Applied Mathematics, Vol 6, Num 10, pp.1063-1075, November 1989
keywords:


Delaunay triangulation	interpolation
triangulation	two-dimensional

"Mesh Generation Methods Over Plane and Curved Surfaces", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.397-407, October 1998
keywords:


quadrilateral	triangle
surface meshing	advancing front
transfinite interpolation	multiblock
structured	ruled surface
quadric surface	revolution surface

Abstract
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"Natural surface approximation by constrained stochastic interpolation", Computer Aided Design, Vol 3, Num 22, April 1990
keywords:


interpolation	stochastic interpolation
terrain modeling

"Scattered data interpolation and approximation with error bounds", Computer Aided Geometric Design, Elsevier, Num 3, pp.163-177, 1986
keywords:


error bounds	Hermite
interpolation	least-squares
three-dimensional

"Efficient, Fair Interpolation using Catmull-Clark Surfaces", Computer Graphics, ACM, pp.35-44
keywords:


interpolation	surface patches
surface reconstruction

"Mesh Association: Formulation and Algorithms", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.75-82, October 1999
keywords:


computational geometry	point association
data transfer	search
interpolation	geometry management
data structures

Abstract
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"Geoscientific Modeling with TINs", Geobyte, pp.44-49, August 1992
keywords:


contouring	interpolation
scattered data	subsurface characterization
TINS	two-dimensional

"Plume Characterization with Natural Neighbor Interpolation", Geoenvironment 2000, Proceedings of a Specialty Conference Sponsored by the Geotechnical Engineering and Environmental Engineering Divisions/ASCE Held February 24-26, 1995, New Orleans, Louisiana, ASCE, pp.331-345
keywords:


interpolation	inverse distance weighted
kriging	natural neighbor

Abstract

"Improving Clough-Tocher Interpolants", Computer Aided Geometric Design, Elsevier, Vol 13, pp.629-651, 1996
keywords:


clough-tocher	interpolation
scattered data

Abstract

"Optimal Mesh for P1 Interpolation in H1 Seminorm", Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.259-270, September 17-20 2006
keywords:


interpolation	hessian
adaptivity	optimal mesh

Abstract
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"Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials", Computer Aided Geometric Design, Elsevier, Vol 13, pp.81-88, 1996
keywords:


interpolation

Abstract

"Software for C1 Surface Interpolation", Mathematical Software III, J. Rice ed., Academic Press, New York, pp.161-194, 1977
keywords:


Delaunay	interpolation
triangulation	two-dimensional

Abstract

"Surface Gridding from Discrete Data", Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.29-44, October 1995
keywords:


advancing front	interpolation
scattered data	surface mesh
surface reconstruction	terrain modeling

Abstract
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"Cubic precision Clough-Tocher interpolation", Computer Aided Geometric Design, Elsevier, Vol 16, pp.85-55, 1999
keywords:


Clough-Tocher	interpolation
scattered data

Abstract

"Smooth Interpolation to Scattered Data by Bivariate Piecewise Polynomials of Odd Degree", Computer Aided Geometric Design, Elsevier Science Publishers (North-Holland), Num 7, pp.439-458, 1990
keywords:


interpolation	polynomial interpolation
scattered data	two-dimensional

"Interpolation on a Triangulated 3D Surface", Journal of Computational Physics, Academic Press, Num 80, pp.331-343, 1989
keywords:


interpolation

"Non-Simplicial Unstructured Mesh Generation", Dissertation, Department of Civil and Environmental Engineering, Carnegie Mellon University, April 1999
keywords:


boundary constrained	overview
classification	hexahedra
quadrilateral	Q-Morph
H-Morph	boundary recovery
edge recovery	face recovery
element sizing	natural neighbor interpolation
data structure	pyramid
cleanup	smoothing
tetrahedral transformations

Abstract
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"An Implementation of Natural Neighbor Interpolation in Three Dimensions", Master's Thesis, Brigham Young University, pp.118, 1992
keywords:


Delaunay triangulation	interpolation comparison
interpolation	natural neighbor
polytope	Voronoi

Abstract

"Surface Mesh Sizing Control", International Journal for Numerical Methods in Engineering, Wiley, Vol 1, Num 47, pp.289-312, 2000
keywords:


mesh generation	surface mesh sizing
natural neighbor interpolation	surface curvature
boundary layer	anisotropy
background mesh	interpolation
size control

Abstract

"Neighborhood-Based Element Sizing Control for Finite Element Surface Meshing", Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.143-154, October 1997
keywords:


background mesh	boundary layer
CFD	curvature
natural neighbor interpolation	size control
surface meshing

Abstract
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"A Comprehensive Modeling Environment for the Simulation of Groundwater Flow and Transport", Engineering With Computers, Springer-Verlag, Vol 12, pp.235-242, December 1996
keywords:


Delaunay	finite elements
GMS	groundwater
iso-surface	kriging
MODFLOW	natural neighbor interpolation
paving	relaxation
site characterization	three-dimensional
TINS	triangulation
two-dimensional

Abstract

"Remeshing in analysis of large plastic deformations", Computers and Structures, Pergammon, Vol 67, pp.279-288, 1998
keywords:


remeshing	large deformations
interpolation	rezoning

Abstract

"Equilibrium and Interpolation Solutions Using Wavelet Bases", ?, pp.507-524
keywords:


interpolation

wavelets

Abstract

"Curvature Continuous Spline Surfaces Over Irregular Meshes", Computer Aided Geometric Design, Vol 13, pp.101-131, 1996
keywords:


blending	geometric continuity
interpolation	parametric surfaces
quadrilateral	surface mesh
surface reconstruction

Abstract

"Discretization of 3D Surfaces Reconstructed by Interpolating Subdivision", Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.679-688, September 2000
keywords:


advancing front technique	Butterfly scheme
discrete surface	discretization formula
interpolation	subdivision
triangular

Abstract

"A Brief Description of Natural Neighbor Interpolation", Interpreting Multivariate Data, V. Barnett ed., John Wiley & Sons, New York, pp.21-36
keywords:


interpolation

natural neighbor interpolation

"Surface Interpolation Based on New Local Coordinates", Computer-Aided Design, Elsevier Science, Num 31, pp.51-58, 1999
keywords:


Voronoi diagram	Delaunay diagram
interpolation	natural neighbor interpolation
local coordinates

Abstract

"Current experience with transfinite interpolation", Computer Aided Geometric Design, Elsevier, Vol 16, pp.77-83, 1999
keywords:


transfinite interpolation	derivative
surface	Gordon method

Abstract

"A Refinement of Inverse Distance Weighted Interpolation", Geo-Processing, Elsevier Science Publishers, Num 2, pp.315-327
keywords:


gradient estimation	interpolation
inverse distance interpolation	natural neighbors

"Triangle Based Interpolation", Mathematical Geology, Plenum publishing, Vol 8, Num 16, pp.779-795, 1984
keywords:


contouring	Delaunay triangulation
gradient	interpolation
linear interpolation	scattered data
triangulation	Voronoi

"Neighbor-Based Interpolation", Geobyte, Vol 2, Num 2, pp.12-16, 1987
keywords:


gradient estimation	interpolation
natural neighbor interpolation	two-dimensional

"The Surface Grid Generation Using Wavelet Modeling", Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.779-786, September 2000
keywords:


DLG scheme	linear interpolation
recursive subdivision	surface grid generation
wavelets

Abstract

"Interpolation schemes for rigid body motions", Computer-Aided Design, Elsevier, Vol 30, Num 3, pp.179-189, 1998
keywords:


motion interpolation	Euclidean group
Riemannian geometry	animation
quaternions

Abstract

"A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 45, Num 10, pp.1509 - 1526, August 1999
keywords:


consistent point-searching algorithm	solution interpolation
unstructured

Abstract