Abstract
In this chapter, we review methods for storing, modeling and visualizing 3D data. We focus in particular on representations for raw 3D data, surface-based and solid-based models. We describe and compare the various data structures available for representing triangular meshes and formats for mesh storage. We also provide details on three different subdivision schemes and explain how differential surface properties can be computed from different surface representations. In the context of data compression, we describe in detail the Quadric Error Metric algorithm for mesh simplification. Finally, we suggest areas for future work in this area and provide some concluding remarks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alliez, P., Gotsman, C.: Recent advances in compression of 3d meshes. In: Dodgson, N., Floater, M., Sabin, M. (eds.) Advances in Multiresolution for Geometric Modeling, pp. 3–26. Springer, Berlin (2005)
Asberg, B., Blanco, G., Bose, P., Garcia-Lopez, J., Overmars, M., Toussaint, G., Wilfong, G., Zhu, B.: Feasibility of design in stereolithography. Algorithmica 19(1–2), 61–83 (1997)
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer, Berlin (1997)
Biggs, N.: Algebraic Graph Theory. Cambridge University Press, Cambridge (1993)
Blanz, V., Vetter, T.: A morphable model for the synthesis of 3D faces. In: Proc. SIGGRAPH, pp. 187–194 (1999)
Bloomenthal, J.: Polygonization of implicit surfaces. Comput. Aided Geom. Des. 5(4), 341–355 (1988)
Bloomenthal, J., Bajaj, C., Blinn, J., Cani-Gascuel, M.P., Rockwood, A., Wyvill, B., Wyvill, G. (eds.): Introduction to Implicit Surfaces. Morgan Kaufmann, San Mateo (1997)
Bloomenthal, J., Wyvill, B.: Interactive techniques for implicit modeling. In: Proc. Symposium on Interactive 3D Computer Graphics (1990)
Botsch, M., Kobbelt, L., Pauly, M., Alliez, P., Levy, B.: Polygon Mesh Processing. AK Peters/CRC Press, Wellesley/Boca Raton (2011)
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. SIGGRAPH, pp. 67–76 (2001)
Catmull, E., Clark, J.: Recursively generated b-spline surfaces on arbitrary topological meshes. Comput. Aided Des. 10(6), 350–355 (1978)
Doo, D., Sabin, M.: Behavior of recursive division surfaces near extraordinary points. Comput. Aided Des. 10(6), 356–360 (1978)
Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann, San Mateo (2002)
Foley, J.D., van Dam, A., Feiner, S.K., Hughes, J.F.: Computer Graphics. Addison Wesley, Reading (1995)
Fuchs, H., Kedem, Z.M., Naylor, B.F.: On visible surface generation by a priori tree structures. ACM Comput. Graph., 124–133 (1980)
Garland, M.: Quadric-based polygonal surface simplification. Ph.D. thesis, Computer Science Department, Carnegie Mellon University (1999)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proc. SIGGRAPH, pp. 209–216 (1997)
Gomes, A.J.P., Voiculescu, I., Jorge, J., Wyvill, B., Galbraith, C.: Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms. Springer, Berlin (2009)
Gu, X., Gortler, S., Hoppe, H.: Geometry images. ACM Trans. Graph. 21(3) (2002) (Proceedings of SIGGRAPH)
Hart, J.C.: Ray tracing implicit surfaces. In: SIGGRAPH Course Notes (1993)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)
Heckbert, P.S.: Survey of texture mapping. IEEE Comput. Graph. Appl. 6(11), 56–67 (1986)
Hoppe, H.: Efficient implementation of progressive meshes. Comput. Graph. 22(1), 27–36 (1998)
Jin, S., Lewis, R.R., West, D.: A comparison of algorithms for vertex normal computations. Vis. Comput. 21(1–2), 71–82 (2005)
Johnson, A., Spin-images: A representation for 3-d surface matching. Ph.D. thesis, Robotics Institute, Carnegie Mellon University (1997)
Karni, Z., Gotsman, C.: Spectral compression of mesh geometry. In: Proc. SIGGRAPH, pp. 279–286 (2000)
Kazhdan, M.: Reconstruction of solid models from oriented point sets. In: Proc. Eurographics Symposium on Geometry Processing (2005)
Keller, P.R., Keller, M.M.: Visual Cues: Practical Data Visualization. IEEE Comput. Soc., Los Alamitos (1993)
Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. Proc. Natl. Acad. Sci. 95(15), 8431–8435 (1998)
Kobbelt, L.: Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Comput. Graph. Forum 15(3), 409–420 (1996)
Koenderink, J.J., van Doorn, A.J.: Surface shape and curvature scales. Image Vis. Comput. 10(8), 557–565 (1992)
Kutulakos, K.N., Seitz, S.M.: A theory of shape by space carving. Int. J. Comput. Vis. 38(3), 199–218 (2000)
Laidlaw, D.H., Trumbore, W.B., Hughes, J.F.: Constructive solid geometry for polyhedral objects. In: Proc. SIGGRAPH, pp. 161–170 (1986)
Lebeck, A.O.: Principles and Design of Mechanical Face Seals. Wiley-Interscience, New York (1991)
Leotta, M.J., Mundy, J.L.: Predicting high resolution image edges with a generic, adaptive, 3-d vehicle model. In: Proc. CVPR, pp. 1311–1318 (2009)
Levoy, M.: Display of surfaces from volume data. IEEE Comput. Graph. Appl. 8(3), 29–37 (1988)
Litke, N., Levin, A., Schröder, P.: Fitting subdivision surfaces. In: Proc. Conference on Visualization (2001)
Loop, C.: Smooth subdivision surfaces based on triangles. Master’s thesis, University of Utah (1987)
Lorensen, W.E., Cline, H.E.: Arching cubes: a high resolution 3d surface construction algorithm. Comput. Graph. 21(4) (1987)
Max, N.: Weights for computing vertex normals from facet normals. J. Graph. Tools 4(2), 1–6 (1999)
Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Vis. Math. 3(7), 35–57 (2002)
Muller, D.E., Preparata, F.P.: Finding the intersection of two convex polyhedra. Theor. Comput. Sci. 7, 217–236 (1978)
Murali, T.M., Funkhouser, T.A.: Consistent solid and boundary representations from arbitrary polygonal data. In: Proc. Symposium on Interactive 3D Graphics (1997)
Nehab, D., Rusinkiewicz, S., Davis, J.E., Ramamoorthi, R.: Efficiently combining positions and normals for precise 3D geometry. ACM Trans. Graph. 24(3), 536–543 (2005) (Proceedings of SIGGRAPH)
Nielson, G.M., Hagen, H., Müller, H.: Scientific Visualization: Overviews, Methodologies, and Techniques. IEEE Computer Society Press, New York (1997)
Pajarola, R., Rossignac, J.: Compressed progressive meshes. IEEE Trans. Vis. Comput. Graph. 6(1), 79–93 (2000)
Paysan, P., Knothe, R., Amberg, B., Romdhani, S., Vetter, T.: A 3D face model for pose and illumination invariant face recognition. In: Proc. IEEE Intl. Conf. on Advanced Video and Signal based Surveillance (2009)
Peng, J., Kim, C.S., Kuo, C.C.J.: Technologies for 3d mesh compression: a survey. J. Vis. Commun. Image Represent. 16(6), 688–733 (2005)
Peters, J., Reif, U.: Subdivision Surfaces. Springer, New York (2008)
Pharr, M., Humphreys, G.: Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann, San Mateo (2010)
Phillips, P.J., Flynn, P.J., Scruggs, T., Bowyer, K.W., Chang, J., Hoffman, K., Marques, J., Jaesik, M., Worek, W.: Overview of the face recognition grand challenge. In: Proc. CVPR, pp. 947–954 (2005)
Piegl, L., Tiller, W.: The NURBS Book. Springer, Berlin (1996)
Post, F.H., Nielson, G.M., Bonneau, G.P. (eds.): Data Visualization: The State of the Art. Springer, Berlin (2002)
Reddy, D., Agrawal, A., Chellappa, R.: Enforcing integrability by error correction using ℓ 1-minimization. In: Proc. CVPR (2009)
Rogers, D.F.: An Introduction to NURBS with Historical Perspective. Morgan Kaufmann, San Mateo (2001)
Rusinkiewicz, S., Levoy, M.: Qsplat: a multiresolution point rendering system for large meshes. In: Proc. SIGGRAPH, pp. 343–352 (2000)
Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comput. Vis. 47(1–3), 7–42 (2002)
Sheffer, A., Praun, E., Rose, K.: Mesh parameterization methods and their applications. Found. Trends Comput. Graph. Vis. 2(2), 105–171 (2006)
Shen, C., O’Brien, J.F., Shewchuk, J.R.: Interpolating and approximating implicit surfaces from polygon soup. In: Proc. SIGGRAPH, pp. 896–904 (2004)
Smith, C.: On vertex-vertex systems and their use in geometric and biological modeling. Ph.D. thesis, University of Calgary (2006)
Smith, N.B., Webb, A.: Introduction to Medical Imaging: Physics, Engineering and Clinical Applications. Cambridge University Press, Cambridge (2010)
Smith, R.C., Cheeseman, P.: On the representation and estimation of spatial uncertainty. Int. J. Robot. Res. 5(4), 56–68 (1986)
Stam, J.: Exact evaluation of Catmull–Clark subdivision surfaces at arbitrary parameter values. In: Proc. SIGGRAPH, pp. 395–404 (1998)
Stroud, I.: Boundary Representation Modeling Techniques. Springer, Berlin (2006)
Suetens, P.: Fundamentals of Medical Imaging. Cambridge University Press, Cambridge (2009)
Takeuchi, S., Kanai, T., Suzuki, H., Shimada, K., Kimura, F.: Subdivision surface fitting with QEM-based mesh simplification and reconstruction of approximated b-spline surfaces. In: Proc. Pacific Conference on Computer Graphics and Applications, pp. 202–212 (2000)
Taubin, G.: A signal processing approach to fair surface design. In: Proc. SIGGRAPH, pp. 351–358 (1995)
Taubin, G., Rossignac, J.: Geometric compression through topological surgery. ACM Trans. Graph. 17(2), 84–115 (1998)
Thürmer, G., Wüthrich, C.A.: Computing vertex normals from polygonal facets. J. Graph. Tools 3(1), 43–46 (1998)
Unwin, A., Theus, M., Hofmann, H.: Graphics of Large Datasets: Visualizing a Million. Springer, Berlin (2006)
Vince, J.A.: Mathematics for Computer Graphics. Springer, Berlin (2010)
Watt, A.: 3D Computer Graphics. Addison Wesley, Reading (1999)
Wikipedia: http://en.wikipedia.org/wiki/Catmull-Clark_subdivision_surface. Accessed 23rd January 2012
Wikipedia: http://en.wikipedia.org/wiki/Constructive_solid_geometry. Accessed 23rd January 2012
Wikipedia: http://en.wikipedia.org/wiki/K-d_tree. Accessed 23rd January 2012
Wikipedia: http://en.wikipedia.org/wiki/Loop_subdivision_surface. Accessed 23rd January 2012
Weiler, K.: Edge-based data structures for solid modeling in a curved surface environment. IEEE Comput. Graph. Appl. 5(1), 21–40 (1985)
Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z.: The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann, Stoneham (2005)
Zorin, D., Schröder, P., Sweldens, W.: Interpolating subdivision for meshes with arbitrary topology. In: Proc. SIGGRAPH, pp. 189–192 (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London
About this chapter
Cite this chapter
Smith, W.A.P. (2012). Representing, Storing and Visualizing 3D Data. In: Pears, N., Liu, Y., Bunting, P. (eds) 3D Imaging, Analysis and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-4063-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4063-4_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4062-7
Online ISBN: 978-1-4471-4063-4
eBook Packages: Computer ScienceComputer Science (R0)