Natural neighbor extrapolation using ghost points

CAD Computer Aided Design

Volumn 41, Issue 5, 2009, Pages 350-365

  Bobach, Tom ^a   Farin, Gerald ^b   Hansford, Dianne ^b   Umlauf, Georg ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Extrapolation; Interpolation; Natural neighbor; Scattered data

Indexed keywords

CONVEX HULLS; EXISTING METHODS; INTERPOLANTS; NATURAL NEIGHBOR; NATURAL NEIGHBOR INTERPOLATIONS; SCATTERED DATA; UNIQUE FEATURES;

EXTRAPOLATION; INTERPOLATION;

APPROXIMATION THEORY;

EID: 67349245193     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2008.08.007     Document Type: Article

References (40)

1. Akima H. A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Transactions on Mathematical Software 4 2 (1978) 148-159. http://doi.acm.org/10.1145/355780.355786 URL http://doi.acm.org/10.1145/355780.355786
2. Akima H. On estimating partial derivatives for bivariate interpolation of scattered data. Rocky Mountain Journal of Mathematics 14 (1984) 41-52
3. Alfeld P. Triangular extrapolation. Technical report. Salt Lake City: University of Utah; 1984
4. Alfeld P. Derivative generation from multivariate scattered data by functional minimization. Computer Aided Geometric Design 2 (1985) 281-296
5. Belikov V.V., Ivanov V.D., Kontorovich V.K., Korytnik S.A., and Semenov A.Y. The non-Sibsonian interpolation: A new method of interpolation of the values of a function on an arbitrary set of points. Computational Mathematics and Mathematical Physics 37 1 (1997) 9-15
6. Brown J.L. Systems of coordinates associated with points scattered in the plane. Computer Aided Geometric Design 14 (1997) 547-559
7. CGAL. CGAL-Computational Geometry Algorithms Library. Available online http://www.cgal.org; 2008
8. Christ N.H., Friedberg R., and Lee T.D. Weights of links and plaquettes in a random lattice. Nuclear Physics B 210 3 (1982) 337-346
9. Clarkson KL. Convex hulls: Some algorithms and applications. In: Presentation at fifth MSI-Stony Brook workshop on computational geometry. 1996. URL http://cm.bell-labs.com/who/clarkson/hulltalk.html
10. Cueto E., Calvo B., and Doblaré M. Modelling three-dimensional piece-wise homogeneous domains using the α-shape-based natural element method. International Journal of Numerical Methods in Engineering 54 (2002) 871-897
11. Cueto E., Doblaré M., and Gracia L. Imposing essential boundary conditions in the natural element method by means of density-scaled α-shapes. International Journal of Numerical Methods in Engineering 49 (2000) 519-546
12. Duchon J. Splines minimizing rotation-invariant semi-norms in sobolev spaces. Constructive Theory of Functions of Several Variables (1977) 85-100
13. EMS-i. Watershed modeling system (wms) v8.0. http://www.ems-i.com/wmshelp/Scattered_Data/Interpolation/Natural_Neighbor_Interpolation.htm. 1204 W. South Jordan Parkway, Suite B South Jordan (UT). 84095-4612; 2008
14. Farin G. Surfaces over Dirichlet tessellations. Computer Aided Geometric Design 7 (1990) 281-292
15. Flötotto J. A coordinate system associated to a point cloud issued from a manifold: Definition, properties and applications. Ph.D. thesis. Université de Nice-Sophia Antipolis. http://www.inria.fr/rrrt/tu-0805.html; Sep 2003
16. Franke R. A critical comparison of some methods for interpolation of scattered data. Technical report. Naval Postgraduate School. Available from NTIS, #AD-A081 688/4; 1979
17. Franke R. Scattered data interpolation: Tests of some methods. Mathematics of Computation 38 157 (1982) 181-200
18. Franke R., and Nielson G. Smooth interpolation of large sets of scattered data. International Journal of Numerical Methods in Engineering 15 11 (1980) 1691-1704
19. Franke R., and Nielson G. Scattered data interpolation and applications: A tutorial and survey (1991), Springer p. 131-60 (chapter 9)
20. Gonzáles D, Cueto E, Doblaré M. Higher-order natural element methods: Towards an isogeometric mehsless method. International Journal of Numerical Methods in Engineering
21. Hardy R.L. Multiquadric equation of topography and other irregular surfaces. Journal of Geophysical Research 76 (1971) 1905-1915
22. Hiyoshi H. Stable computation of natural neighbor interpolation. In: Proceedings of the 2nd international symposium on Voronoi diagrams in science and engineering. 2005
23. Hiyoshi H, Sugihara K. Voronoi-based interpolation with higher continuity. In: Symposium on computational geometry. 2000
24. Hiyoshi H, Sugihara K. Improving the global continuity of the natural neighbor interpolation. In: International conference on computational science and its applications (3); 2004
25. Lasser D., and Stüttgen T. Boundary improvement of piecewise linear interpolation defined over delaunay triangulations. Computers and Mathematics with Applications 32 10 (1996) 43-58
26. McCain W, Spivey J. Extrapolation of laboratory measured black oil and solution gas fluid properties for variable bubblepoint simulation. In: SPE annual technical conference and exhibition. Volume Sigma: Reservoir engineering; 1999
27. Miller J., Turner M., Stanley E., Smithwick E., and Dent L. Spatial extrapolation: The science of predicting ecological patterns and processes. Bioscience 54 (2004) 310-320
28. Nielson G. A method for interpolation of scattered data based upon a minimum norm network. Mathematics of Computation 40 (1983) 253-271
29. Okabe A., Boots B., Sugihara K., and Chiu S.N. Spatial tessellations: Concepts and applications of Voronoi diagrams. Wiley series in probability and statistics (2000), John Wiley & Sons Ltd.
30. Owen SJ. Subsurface characterization with three-dimensional natural neighbor interpolation. Master's thesis. 1993. URL http://www.andrew.cmu.edu/user/sowen/natneigh/index.htm
31. Piper BR. Properties of local coordinates based on Dirichlet tesselations. In: Geometric modelling. 1992
32. Shepard D. A two dimensional interpolation function for irregularly spaced data. In: Proceedings of the 23rd ACM national conference. 1968
33. Sibson R. A vector identity for the Dirichlet tessellation. Mathematical Proceedings of Cambridge Philosophical Society 87 (1980) 151-155
34. Sibson R. A brief description of natural neighbor interpolation. Interpreting Multivariate Data (1981) 21-36
35. Stead S. Estimation of gradients from scattered data. Rocky Mountain Journal of Mathematics 14 (1984) 265-279
36. Sugihara K. Surface interpolation based on new local coordinates. Computer Aided Design 13 1 (1999) 51-58
37. Sugihara K. Handbook of computer aided geometric design (2002), Elsevier p. 429-50 (chapter 18)
38. Wendland H. Scattered data approximation. Cambridge monographs on appl. and comp. math. vol. 17 (2004), Cambridge University Press
39. Zeilfelder F., and Seidel H. Handbook of computer aided geometric design (2002), Elsevier p. 701-22 (chapter 28)
40. Zoraster S. Extrapolation in oil exploration. Private communication. 2004