Scattered data fitting with simplex splines in two and three dimensional spaces

Visual Computer

Volumn 13, Issue 7, 1997, Pages 295-314

  Zhou, Jingfang ^a,b   Patrikalakis, Nicholas M ^a,c   Tuohy, Seamus T ^a,d   Ye, Xiuzi ^a,e  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b SCHLUMBERGER   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d CHARLES STARK DRAPER LABORATORY   (United States)

^e SolidWorks Corporation   (United States)

Author keywords

Fitting; Simplex spline; hull

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER AIDED DESIGN; COMPUTER AIDED MANUFACTURING; COMPUTER VISION; DATA STRUCTURES; DATABASE SYSTEMS; IMAGE SEGMENTATION; INTERPOLATION;

SCATTERED DATA FITTING; SIMPLEX SPLINE;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 0030677382     PISSN: 01782789     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003710050105     Document Type: Article

References (50)

1. Auerbach S, Gmelig Meyling RHR, Neamtu M, and Schaeben H (1991) Approximation and geometric modeling with simplex B-spline associated with irregular triangles. Comput Aided Geom Des 8:67-87
2. Barnhill RE (1977) Representation and approximation of surfaces. In: Rice JR (ed) Mathematical software III, Academic Press, Madison, Wis, pp 69-120
3. Catmull E, Clark J (1978) Recursively generated B-spline surfaces on arbitrary topological meshes. Comput Aided Des 10:350-355
4. Celniker G, Gossard DC (1991) Deformable curve and surface finite elements for free-form shape design. Comput Graph 25:257-266
5. Cho W, Maekawa T, Patrikalakis NM (1996) Topologically reliable approximation of composite Bézier curves. Comput Aided Geom Des 13:497-520
6. Clough RW, Tocher JL (1965) Finite element stiffness matrices for the analysis of plate bending. In: Przemieniecki JS (ed) Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics. US Department of Commerce, Washington, pp 515-545
7. Grain GP, Bhattachary BK (1967) Treatment of non-equispaced two-dimensional data with a digital computer. Geoexploration 5:173-194
8. Cressman GP (1959) An operational objective analysis system. Monthly Weather Review 87:367-374
9. Dahmen W, Micchelli CA (1982) On the linear independence of multivariate B-splines, Part I. Triangulations of simploids. SIAM J Numer Anal 19:993-1012
10. Dahmen W, Micchelli CA, Seidel HP (1992) Blossoming begets B-spline bases built better by B-patches. Math Comp 59:97-115
11. Delingette H, Hebert M, Ikeuchi K (1991) Energy functions for regularization algorithms. In: Vemuri BC (ed) Geometric methods in computer vision 1570, SPIE, San Diego, pp 104-115
12. Dierckx P (1981) An algorithm for surface-fitting with spline functions. IMA J Numer Anal 1:267-283
13. Edelsbrunner H, Kirkpartick DG, Seidel R (1983) On the shape of a set of points in the plane. IEEE Trans Inf Theor 29:551-559
14. Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. ACM Trans Graph 13:43-72
15. Fang L, Gossard DC (1992) Reconstruction of smooth parametric surfaces from unorganized data points. In: Warren JD (edc) Proceedings of Curves and Surfaces in Computer Vision and Graphics III, 1830, SPIE, Bellingham, pp 226-236
16. Farin G (1986) Triangular Bernstein-Bézier patches. Comput Aided Geom Des 3:83-128
17. Farin G (1993) Curves and surfaces for computer aided geometric design: a practical guide, 3rd edn. Academic Press, San Diego
18. Holey TA, Hagen H, Nielson GM (1993) Visualizing and modeling unstructured data. Visual Comput 9:439-449
19. Fong P, Seidel HP (1991) Control points for multivariate B-spline surfaces over arbitrary triangulations. Comput Graph Forum 10:309-317
20. Fong P, Seidel HP (1993) An implementation of triangular B-spline surfaces over arbitrary triangulations. Comput Aided Geom Des 10:267-275
21. Franke R (1982) Scattered data interpolation: tests of some methods. Math Comp 38:181-200
22. Grandine TA (1987) The computational costs of simplex spline functions. SIAM J Numer Anal 24:887-890
23. Greiner G and Seidel HP (1993) Modeling with triangular B-splines. In: Rossignac J, Turner J, and Allen G (eds) Proceedings of the 2nd Symposium on Solid Modeling and Applications, Montreal, Canada, May 1993. ACM SIGGRAPH in cooperation with the IEEE Computer Society, pp 211-220
24. Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophysical Res 76:1905-1915
25. Höllig K (1982) Multivariate splines. SIAM J Numer Anal 19:1013-1013
26. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. Comput Graph (Proceedings of SIGGRAPH '92) 26:71-78
27. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1993) Mesh optimization. Technical Report 93-01-01. Department of Computer Science and Engineering, University of Washington, Seattle
28. Hoppe H, DeRose T, Duchamp T, Jin H, McDonald J, Stuetzle W (1994) Piecewise smooth surface reconstruction. Technical Report 94-01-01, Department of Computer Science and Engineering, University of Washington, Seattle
29. Limeburner R, Beardsley RC (1989) CTD observations off Northern California during the shelf mixed layer experiment, SMILE, November 1988. Technical Report WHOI-89-25, Woods Hole Oceanographic Institution, Falmouth
30. Loop C (1987) Smooth subdivision surfaces based on triangles. Master's Thesis, Department of Mathematics, University of Utah, Salt Lake City
31. Loop C, DeRose TD (1990) Generalized B-spline surfaces of arbitrary topology. IEEE Comput Graph Appl 24:347-356
32. Melissaratos EA (1993) Mesh generation and geometric optimization. PhD Thesis, Department of Mathematics, Rutgers University, New Brunswick, NJ
33. Nielson GM (1983) A method for interpolating scattered data based upon a minimum norm network. Math Compu 40:199-205
34. Nielson GM, Brunet P, Gross M, Hagen H, Klimenko SK (1994) Research issues in data modeling for scientific visualization. IEEE Comput Graph Appl 14:70-73
35. NAG (1990) NAG Fortran library manual, Mark 14, Numerical Algorithms Group, Oxford
36. Peters J (1990) Fitting smooth parametric surfaces to 3D data. PhD Thesis, Department of Mathematics, University of Wisconsin, Madison, Wis
37. Pfeifle R, Seidel HS (1995) Fitting triangular B-splines to functional scattered data. In: Proceedings of Graphics/Vision Interface '95, Quebec City, Canadian Information Processing Society, Toronto, pp 26-33
38. Powell MJ, Sabin MA (1977) Piecewise quadratic approximations on triangles. ACM Trans Math Softw 3:316-325
39. Qin H, Terzopoulos D (1995) Dynamic manipulation of triangular B-splines. In: Hoffmann C, Rossignac J (eds) Proceedings of the 3rd ACM Solid Modelling Symposium, Salt Lake City, ACM, New York, pp 351-360
40. Schumaker LL (1976) Fitting surfaces to scattered data. In: Lorentz GG, Chui CK, Schumaker LL (eds) Approximation theory II, University of Texas, Austin, pp 203-269
41. Seidel HP, Vermeulen AH (1991) Simplex splines support surprisingly strong symmetric structure and subdivision. In: Laurent PJ, Le Méhauté A, Schumaker LL (eds) Curves and surfaces II, AK Peters, Boston, pp 1-13
42. Shepard D (1968) A two-dimensional interpolation function for irregular spaced data. In: Proceedings of 23rd ACM National Conference, Las Vegas, ACM, New York, pp 517-524
43. Terzopoulos D, Qin H (1994) Dynamic NURBS with geometric constraints for interactive sculpting. ACM Trans Graph 13:103-136
44. Terzopoulos D, Vasilescu M (1991) Sampling and reconstruction with adaptive meshes. In: Negahdaripour S (ed) Proceedings of the 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society Press, Los Alamitos, pp 70-75
45. Traas CR (1990) Practice of bivariate quadratic simplicial splines. In: Dahmen W (ed) Computation of curves and surfaces, Kluwer Academic, Dordrecht, pp 383-422
46. Tuohy ST, Yoon JW, Patrikalakis NM (1995a) Reliable interrogation of 3-D non-linear geophysical databases. In: Vince JA, Earnshaw RA (eds) Computer graphics: developments in virtual environments, Proceedings of CGI '95, Leeds, Academic Press, London, pp 327-341
47. Tuohy ST, Yoon JW, Patrikalakis NM (1995b) Trivariate parametric B-splines for visualization of ocean data. In: Proceedings of Oceans '95: challenges of our changing global environment 3, MTS/IEEE Oceanic Oceanic Engineering Society, pp 1601-1608
48. Ye X (1994) Construction and verification of smooth free-form surfaces generated by compatible interpolation of arbitrary meshes. Verlag Dr. Köster, Berlin
49. Zhou J (1995) Interval simplex splines for scientific databases. PhD Thesis, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, Mass
50. Zhou J, Abrams SL, Hu CY, Tuohy ST, Patrikalakis NM (1995) Marching simplices: interrogation of implicit surfaces in irregular domains. Design Laboratory Memorandum 95-7, MIT, Department of Ocean Engineering, Cambridge, Mass