Article

Radial Hermite Operators for Scattered Point Cloud Data with Normal Vectors and Applications to Implicitizing Polygon Mesh Surfaces for Generalized CSG Operations and Smoothing

Author:

Gregory M. NielsonAuthors Info & Claims

VIS '04: Proceedings of the conference on Visualization '04

Pages 203 - 210

https://doi.org/10.1109/VISUAL.2004.87

Published: 10 October 2004 Publication History

Abstract

We describe a new technique for fitting scattered point cloud data. Given a scattered point cloud of 3D data points and associated normal vectors, our new method produces an implicit volume model whose zero level isosurface interpolates the given points and associated normal vectors. In this paper, we concentrate on certain application of these new volume modeling techniques. We take existing polygon mesh surfaces and use the present methods to construct implicit volume models for these surfaces. Implicit models allow for the application of Boolean operations on these surfaces through the techniques of constructive solid geometry. Also, standard wavelet and filter operators can be applied to the implicit volume model leading to effective smoothing and filtering algorithms which are simple to implement.

References

[1]

{1} J. Algorri and E. Shmitt. Surface reconstruction from unstructured 3D data, Computer Graphics Forum, 19:69-81, 2000.

[2]

{2} A. Barr. Global and local deformations of solid primitives, Proceedings of SIGGRAPH 1884, pages 21-30, ACM Press, 1984.

Digital Library

[3]

{3} F. Bernardini, C. Silva, J. Mittleman, H. Rushmeier and G. Taubin. The ball-pivoting algorithm for surface reconstruction, ACM Transactions on Graphics, 3:266-286, 1999.

[4]

{4} M. Bertram. Fairing scalar fields by vaiational modelling of contours, Proceedings of Visualization 2003, pages 387-396, IEEE CS Press, 2003.

Digital Library

[5]

{5} G. Bonneau, S. Hahmann and G. M. Nielson. BlaC-Wavelets: A multiresolution analysis with non-nested spaces, Proceedings of Visualization '96, pages 43-48. ACM Press, 1996.

Digital Library

[6]

{6} J. Carr, R. Beatson, J. Cherrie, T. Mitchell, W, Fright, B. McCallum and T. Evans. Reconstruction and representation of 3D objects with radial basis functions, Proceedings of SIGGRAPH 2001, pages 67- 76, ACM Press, 2001.

Digital Library

[7]

{7} B. Curless and M. Levoy. A volumetric method for building complex models from range images, Proceedings of SIGGRAPH 1996, pages 303-312, ACM Press, 1996.

Digital Library

[8]

{8} H. Edelsbrunner and E. Mücke. Three-dimensional alpha shapes, ACM Transactions on Graphics, 13:43-72. 1994

Digital Library

[9]

{9} M. Floater. Parameterization of trianguations and unorganized points, In Tutorials on Multiresolution in Geometric Modelling, I. Aske, E. Quak and M. S. Floater, eds., pages 287-316. Springer, 2002.

[10]

{10} R. Franke and G. M. Nielson. Smooth interpolation to large sets of data, International Journal Num. Meth. Engn., 15:1691-1704. 1980.

[11]

{11} R. Franke and G. M. Nielson. Scattered data interpolation and applications: A tutorial and survey, In Geometric Modelling: Methods and Applications, H. Hagen & D. Roller, eds., pages 131- 160. Springer, 1990.

[12]

{12} B. Guo. Surface reconstruction: From points to splines, CAGD, 29:269-277, 1997.

[13]

{13} I. Hotz. Isometric embedding by surface reconstruction from distances, Proceedings Visualization 2002, pages 251-258, IEEE CS Press, 2002.

Digital Library

[14]

{14} H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle. Surface reconstruction from unorganized points, Proceedings of SIGGRAPH 1992, pages 71-78, ACM Press, 1992.

Digital Library

[15]

{15} N. Max. Weights for computing vertex normals from facet normals, Journal of Graphics Tools, 4:1-6, 1999.

Digital Library

[16]

{16} B. Morse, T. Yoo, P. Rheingans, D. Chen and K. Subramanian. Interpolating Implicit Surfaces from Scattered Surface Data Using Compactly Supported Radial Basis Functions. Proceedings of International Conference on Shape Modeling and Applications '01, pages 89-98, IEEE CS Press, 2001.

Digital Library

[17]

{17} H. Müller. Surface reconstruction - An introduction, In Scientific Visualization, H. Hagen, G. Nielson, F. Post, eds., pages 239-242, IEEE CS Press, 1999.

Digital Library

[18]

{18} G. M. Nielson. Scattered data modelling, Computer Graphics and Applications, 13: 60-7,1, IEEE Press, 1993.

Digital Library

[19]

{19} G. M. Nielson. Tools for triangulations and tetrahedrizations, In Scientific Visualization: Overviews, Methodologies, Techniques, G. Nielson, H. Hagen & H. Mueller, eds., IEEE CS Press, pages 429- 526. 1997.

Digital Library

[20]

{20} G. M. Nielson. Volume modeling, In Volume Graphics, M. Chen, A. E. Kaufman and R. Yagel, eds., pages 29-48, Springer, 2000.

[21]

{21} G. M. Nielson. On marching cubes, Transactions on Visualization and Computer Graphics, 9:283-297. 2003

Digital Library

[22]

{22} G. M. Nielson. Dual marching cubes, Proceedings of Visualization 2004, this volume, IEEE CS Press, 2004.

Digital Library

[23]

{23} G. M. Nielson and J. Tvedt. Comparing methods of interpolation for scattered volumetric data, In State of the Art in Computer Graphics - Aspects of Visualization, D. Rogers and R. A. Earnshaw, eds., pages 67-86, Springer, 1994.

Digital Library

[24]

{24} G. M. Nielson and A. Huang. Approximating normals for marching cubes applied to locally supported isosurfaces, Proceedings of Visualization 2002, pages 459-466. IEEE CS Press, 2002.

Digital Library

[25]

{25} G. M. Nielson, H. Hagen and K. Lee. Split 'N Fit: Adaptive least squares fitting of triangular mesh surfaces to scattered point cloud data, In Scientific Data Visualization, Bonneau, Ertl & Nielson, eds., pages 19-43, Springer, 2004.

[26]

{26} V. Savchenko, A. Pasko, O. Okunev and T. Kunii. Function representation of solids reconstructed from scattered surface points and contours, Computer Graphics Forum, 14:181-188. 1995.

[27]

{27} L. Schumaker. Scattered data approximation, In Approximation Theory II, pages 123-145. Academic Press, 1976.

[28]

{28} T. Sederberg and S. Parry. Free-from deformations of solid geometric models, Proceedings of SIGGRAPH 1986, pages 151-160. ACM Press, 1986.

Digital Library

[29]

{29} C. Sigg, R. Peikert and M. Gross. Signed distance transformation using graphics hardware, Proceedings of Visualization 2003, pages 83-90. IEEE CS Press, 2003.

Digital Library

[30]

{30} T. Tasdizen, R. Whitaker, Burchard and S. Osher. Geometric surface smoothing via ansistropic diffusion of normals, Proceedings of Visualization 2002, pages 125-132. IEEE CS Press, 2002.

Digital Library

[31]

{31} G. Turk and J. O'Brien. Shape transformation using variational implicit functions, Proceedings of SIGGRAPH 1999, pages 335-342, ACM Press, 1991.

Digital Library

[32]

{32} B. Wyvill, A. Guy and E. Galin. Extending the CSG tree warping, blending and Boolean operations in an implicit surface modelling system, Proceedings of Implicit Surfaces 1998. pages 123-456. IEEE CS Press, 1998.

[33]

{33} H. Xie, J. Wang, J. Hua, J. Qin, A. Kaufman. Piecewise C1 continuous surface reconstruction of noisy point clouds via local implicit quadric regression, Proceedings of IEEE Visualization 2003, pages 91-98. IEEE CS Press, 2003.

Digital Library

[34]

{34} H. Zhao, S. Osher and F. Fedkiw. Fast surface reconstruction using the level set method, Proceedings 8th International Conference on Computer Vision (ICCV), Vancouver, Canada, pages 194-202. IEEE Press, 2001.

Digital Library

Cited By

Du XZhou QCarr NJu T(2021)Boundary-sampled halfspacesACM Transactions on Graphics10.1145/3450626.345987040:4(1-15)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1145/3450626.3459870
Jin JGarland MRamos EHaines EMcGuire MAliaga DOliveira M(2009)MLS-based scalar fields over triangle meshes and their application in mesh processingProceedings of the 2009 symposium on Interactive 3D graphics and games10.1145/1507149.1507173(145-153)Online publication date: 27-Feb-2009
https://dl.acm.org/doi/10.1145/1507149.1507173
Chen YCohen JKrolik J(2007)Similarity-Guided Streamline Placement with Error EvaluationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2007.7059513:6(1448-1455)Online publication date: 1-Nov-2007
https://dl.acm.org/doi/10.1109/TVCG.2007.70595
Show More Cited By

Radial Hermite Operators for Scattered Point Cloud Data with Normal Vectors and Applications to Implicitizing Polygon Mesh Surfaces for Generalized CSG Operations and Smoothing
1. Computing methodologies
  1. Computer graphics
2. Theory of computation
  1. Randomness, geometry and discrete structures

Recommendations

Technical Section: Mesh reconstruction by meshless denoising and parameterization

We present a new approach to simultaneously denoise and parameterize unorganized point cloud data. This is achieved by minimizing an appropriate energy function defined on the point cloud and its parameterization. An iterative algorithm to minimize the ...
Implicit fitting of point cloud data using radial hermite basis functions
Special issue on Geometric Modeling (Dagstuhl 2005)

We describe a new technique for fitting noisy scattered point cloud data. The fitting surface is determined as zero level isosurface of a trivariate model which is an implicit least squares fit of the data based upon Radial Hermite Operators (RHO). We ...
Point-normal subdivision curves and surfaces
Abstract
This paper proposes to generalize linear subdivision schemes to nonlinear subdivision schemes for curve and surface modeling by refining vertex positions together with refinement of unit control normals at the vertices. For each round ...
Graphical abstract
Highlights
- We generalize linear subdivision schemes to nonlinear subdivision schemes by refining control points and control normals.

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

VIS '04: Proceedings of the conference on Visualization '04

October 2004

667 pages

ISBN:0780387880

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

IEEE Computer Society

United States

Publication History

Published: 10 October 2004

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
11
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Du XZhou QCarr NJu T(2021)Boundary-sampled halfspacesACM Transactions on Graphics10.1145/3450626.345987040:4(1-15)Online publication date: 19-Jul-2021
https://dl.acm.org/doi/10.1145/3450626.3459870
Jin JGarland MRamos EHaines EMcGuire MAliaga DOliveira M(2009)MLS-based scalar fields over triangle meshes and their application in mesh processingProceedings of the 2009 symposium on Interactive 3D graphics and games10.1145/1507149.1507173(145-153)Online publication date: 27-Feb-2009
https://dl.acm.org/doi/10.1145/1507149.1507173
Chen YCohen JKrolik J(2007)Similarity-Guided Streamline Placement with Error EvaluationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2007.7059513:6(1448-1455)Online publication date: 1-Nov-2007
https://dl.acm.org/doi/10.1109/TVCG.2007.70595
Miao YFeng JXiao CLi HPeng Q(2006)Detail-Preserving local editing for point-sampled geometryProceedings of the 24th international conference on Advances in Computer Graphics10.1007/11784203_65(673-681)Online publication date: 26-Jun-2006
https://dl.acm.org/doi/10.1007/11784203_65

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents