Real-time shape editing using radial basis functions

Computer Graphics Forum

Volumn 24, Issue 3, 2005, Pages 611-621

  Botsch, Mario ^a   Kobbelt, Leif ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; OPTIMIZATION; PROBLEM SOLVING; RADIAL BASIS FUNCTION NETWORKS; REAL TIME SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); THREE DIMENSIONAL COMPUTER GRAPHICS;

DEFORMATION BASIS FUNCTIONS; SHAPE EDITING; SPACE DEFORMATION; VARIATIONAL OPTIMIZATION;

COMPUTER GRAPHICS;

EID: 33745318653     PISSN: 01677055     EISSN: 14678659     Source Type: Journal    
DOI: 10.1111/j.1467-8659.2005.00886.x     Document Type: Article

References (38)

1. [BBK05] BOTSCH M., BOMMES D., KOBBELT L.: Efficient linear system solvers for mesh processing. In Proc. of IMA conference on Mathematics of Surfaces (2005).
2. [BK01] BOTSCH M., KOBBELT L.: A robust procedure to eliminate degenerate faces from triangle meshes. In Proc. of Vision, Modeling, and Visualization 01 (2001), pp. 283-289.
3. [BK03a] BENDELS G. H., KLEIN R.: Mesh forging: editing of 3D-meshes using implicitly defined occluders. In Proc. of the Eurographics/ACM SIGGRAPH symposium on Geometry processing (2003), Eurographics Association, pp. 207-217.
4. [BK03b] BOTSCH M., KOBBELT L.: High-quality point-based rendering on modern GPUs. In Proc. of Pacific Graphics 03 (2003), pp. 335-343.
5. [BK04a] BOTSCH M., KOBBELT L.: An intuitive framework for real-time freeform modeling. In Proc. of ACM SIGGRAPH 04 (2004), pp. 630-634.
6. [BK04b] BOTSCH M., KOBBELT L.: A remeshing approach to multiresolution modeling. In Proc. of Eurographics symposium on Geometry Processing 04 (2004), pp. 189-196.
7. [BR94] BORREL P., RAPPOPORT A.: Simple constrained deformations for geometric modeling and interactive design. ACM Transactions on Graphics 13, 2 (1994), 137-155.
8. [CBC*01] CARR J. C., BEATSON R. K., CHERRIE J. B., MITCHELL T. J., FRIGHT W. R., MCCALLUM B. C., EVANS T. R.: Reconstruction and representation of 3D objects with radial basis functions. In Proc. of ACM SIGGRAPH 01 (2001), pp. 67-76.
9. [Coq90] COQUILLART S.: Extended free-form deformation: a sculpturing tool for 3D geometric modeling. In Proc. of ACM SIGGRAPH 90 (1990), ACM, pp. 187-196.
10. [CRT04] CLARENZ U., RUMPF M., TELEA A.: Finite elements on point based surfaces. In Proc. of symposium on Point-Based Graphics 04 (2004), pp. 201-211.
11. [Duc77] DUCHON J.: Spline minimizing rotation-invariant semi-norms in Sobolev spaces. In Constructive Theory of Functions of Several Variables, Schempp W., Zeller K., (Eds.), no. 571 in Lecture Notes in Mathematics. Springer Verlag, 1977, pp. 85-100.
12. [GL89] GOLUB G. H., LOAN C. F. V.: Matrix Computations. Johns Hopkins University Press, Baltimore, 1989.
13. [HHK92] HSU W. M., HUGHES J. F., KAUFMAN H.: Direct manipulation of free-form deformations. In Proc. of ACM SIGGRAPH 92 (1992), pp. 177-184.
14. [Hop99] HOPPE H.: Optimization of mesh locality for transparent vertex caching. In Proc. of ACM SIGGRAPH 99 (1999), pp. 269-276.
15. [KB04] KOBBELT L., BOTSCH M.: A survey of pointbased techniques in computer graphics. Computers & Graphics 28, 6 (2004), 801-814.
16. [KCVS98] KOBBELT L., CAMPAGNA S., VORSATZ J., SEIDEL H.-P.: Interactive multi-resolution modeling on arbitrary meshes. In Proc. of ACM SIGGRAPH 98 (1998), pp. 105-114.
17. [KSSH02] KOJEKINE N., SAVCHENKO V., SENIN M., HAGIWARA I.: Real-time 3D deformations by means of compactly supported radial basis functions. In Eurographics Short Presentations 02 (2002).
18. [LKG*03] LLAMAS I., KIM B., G ARGUS J., ROSSIGNAC J., SHAW C. D.: Twister: a space-warp operator for the two-handed editing of 3D shapes. In Proc. of ACM SIGGRAPH 03 (2003), pp. 663-668.
19. [LSCO*04] LIPMAN Y., SORKINE O., COHEN-OR D., RÖSSL C., SEIDEL H.-P.: Differential coordinates for interactive mesh editing. In Proc. of Shape Modeling International 04 (2004), pp. 181-190.
20. [MBK05] MARINOV M., BOTSCH M., KOBBELT L.: Hardware accelerated real-time rendering of multiresolution deformations. Submitted, 2005.
21. [Mic86] MICCHELLI C. A.: Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation 2 (1986), 11-22.
22. [MJ96] MACCRACKEN R., JOY K. I.: Free-form deformations with lattices of arbitrary topology. In Proc. of ACM SIGGRAPH 95 (1996), pp. 181-188.
23. [MS92] MORETON H. P., SÉQUIN C. H.: Functional optimization for fair surface design. In Proc. of ACM SIGGRAPH 92 (1992), pp. 167-176.
24. [MYC*01] MORSE B. S., YOO T. S., CHEN D. T., RHEINGANS P., SUBRAMANIAN K. R.: Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In Proc. of Shape Modeling & Applications 01 (2001), pp. 89-98.
25. [OBS03] OHTAKE Y., BELYAEV A., SEIDEL H.-P.: A multiscale approach to 3D scattered data interpolation with compactly supported basis fuctions. In Proc. of Shape Modeling International 03 (2003), pp. 153-161.
26. [OBS04] OHTAKE Y., BELYAEV A., SEIDEL H.-P.: 3D scattered data approximation with adaptive compactly supported radial basis functions. In Proc. of Shape Modeling International 04 (2004).
27. [PKKG03] PAULY M., KEISER R., KOBBELT L., GROSS M.: Shape modeling with point-sampled geometry. In Proc. of ACM SIGGRAPH 03 (2003), pp. 641-650.
28. [RTSD03] REUTER P., TOBOR I., SCHLICK C., DEDIEU S.: Point-based modelling and rendering using radial basis functions. In Proc. of GRAPHITE 03 (2003), pp. 111-118.
29. [Sap94] SAPIDIS N. S.: Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design. SIAM, 1994.
30. [SCOL*04] SORKINE O., COHEN-OR D., LIPMAN Y., ALEXA M., RÖSSL C., SEIDEL H.-P.: Laplacian surface editing. In Proc. of Eurographics symposium on Geometry Processing 04 (2004), pp. 179-188.
31. [SF98] SINGH K., FlUME E.: Wires: A geometric deformation technique. In Proc. of ACM SIGGRAPH 98 (1998), ACM Press/ACM SIGGRAPH, pp. 405-414.
32. [SP86] SEDERBERG T. W., PARRY S. R.: Free-form deformation of solid geometric models. In Proc. of ACM SIGGRAPH 86 (1986), pp. 151-159.
33. [SPOK95] SAVCHENKO V. V., PASKO A. A., OKUNEV O. G., KUNII T. L.: Function representation of solids reconstructed from scattered surface points and contours. Computer Graphics Forum 14, 4 (1995), 181-188.
34. [TO02] TURK G., O'BRIEN J. F.: Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics 21, 4 (2002), 855-873.
35. [TRS04] TOBOR I., REUTER P., SCHLICK C.: Reconstruction of implicit surfaces with attributes from large unorganized point sets. In Proc. of Shape Modeling International 04 (2004), pp. 19-30.
36. [WW92] WELCH W., WITKIN A.: Variational surface modeling. In Proc. of ACM SIGGRAPH 92 (1992), pp. 157-166.
37. [YZX*04] YU Y., ZHOU K., XU D., SHI X., BAO H., GUO B., SHUM H.-Y.: Mesh editing with Poisson-based gradient field manipulation. In Proc. of ACM SIGGRAPH 04 (2004), pp. 644-651.
38. [ZPvBG01] ZWICKER M., PFISTER H., VAN BAAR J., GROSS M.: Surface splatting. In Proc. of ACM SIGGRAPH 01 (2001), pp. 371-378.