Abstract
Texture mapping is an efficient and effective tool in computer graphics and animation. While computationally very cost-effective, texture mapping may produce non-realistic appearances of shapes in 3D environment, especially when viewing closely. To improve the realism of 3D modeling, bump mapping technique is developed to add details with the 3D models on top of texture mapping. Bump mapping, however, offers only simple and visual enhancement. Displacement mapping technique can further improve the localized detail of geometry. In this paper, Monge mapping technique is developed for detail and local shape modification of NURBS represented geometry in a 3D environment. Based on multiresolution and refinement schemes, Hierarchical NURBS (H-NURBS) is first investigated to design a mechanism for the purpose of carrying localized geometric information. Monge mapping on H-NURBS patch can be easily performed via simple cut-and-paste operation. Parametric control of the local shapes is developed to facilitate easier and better 3D local modeling.
Similar content being viewed by others
References
Catmull, E.: A subdivision algorithm for computer display of curved surfaces. The University of Utah, 83 (1974)
Heckbert, P.: Fundamentals of Texture Mapping and Image Warping. University of California at Berkeley, Berkeley (1989)
Blinn, J.: Simulation of wrinkled surfaces. SIGGRAPH Comput. Graph. 12(3), 286–292 (1978)
Cook, R.: Shade trees. ACM SIGGRAPH Comput. Graph. 18(3), 223–231 (1984)
Cook, R., Carpenter, L., Catmull, E.: The Reyes image rendering architecture. ACM SIGGRAPH Comput. Graph. 21(4), 95–102 (1987)
Piegl, L., Tiller, W.: The NURBS Book. Springer, New York (1997)
Blinn, J., Newell, M.: Texture and reflection in computer generated images. Commun. ACM 19(10), 542–547 (1976)
Geoffrey, Y.: Visual simulation of clouds. In: Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, ACM (1985)
Miller, G., Hoffman, C.: Illumination and reflection maps: Simulated objects in simulated and real environments. In: Course Notes for Advanced Computer Graphics Animation, SIGGRAPH 84 (1984)
Fournier, A.: Normal distribution functions and multiple surfaces. In: Graphics Interface ’92 Workshop on Local Illumination, pp. 45–52 (1992)
Wang, L., Wang, X., Tong, X., Lin, S., Hu, S., Guo, B., Shum, H.: View-dependent displacement mapping. ACM Trans. Graph. (TOG) 22(3), 334–339 (2003)
Oliveira, M., Bishop, G., McAllister, D.: Relief texture mapping. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques. ACM Press/Addison-Wesley, New York (2000)
Williams, L.: Pyramidal parametrics. ACM SIGGRAPH Comput. Graph. 17(3), 1–11 (1983)
Bartels, R., Beatty, J., Barsky, B.: An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann, Los Altos (1987)
Cohen, E., Lyche, T., Riesenfeld, R.: Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics. Comput. Graph. Image Process. 14(2), 87–111 (1980)
Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. Academic Press, New York (1996)
Lane, J., Riesenfeld, R.: Theoretical development for the computer-generation and display of piecewise polynomial surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 2(1), 35–46 (1980)
Forsey, D., Bartels, R.: Hierarchical B-spline refinement. Comput. Graph. 22(4), 205–212 (1988)
Olsen, L., Samavati, F., Bartels, R.: Multiresolution B-splines based on wavelet constraints. In: Poster Presentation at the Third Eurographics Symposium on Geometry Processing (2005)
Olsen, L., Samavati, F., Bartels, R.: Multiresolution for curves and surfaces based on constraining wavelets. Comput. Graph. 31(3), 449–462 (2007)
Samavati, F., Bartels, R., Olsen, L.: Local B-spline multiresolution with examples in iris synthesis and volumetric rendering. In: Image Pattern Recognition: Synthesis and Analysis in Biometrics. Series in Machine Perception and Artificial Intelligence, pp. 65–102. World Scientific, Singapore (2007)
Forsey, D., Bartels, R.: Surface fitting with hierarchical splines. ACM Trans. Graph. 14(2), 134–161 (1995)
Gonzalez-Ochoa, C., Peters, J.: Localized-hierarchy surface splines (LeSS). In: Proceedings of the 1999 Symposium on Interactive 3D Graphics, pp. 7–15 (1999)
Yvart, A., Hahmann, S., Bonneau, G.: Hierarchical triangular splines. ACM Trans. Graph. 24(4), 1374–1391 (2005)
Yvart, A., Hahmann, S., Bonneau, G.: Smooth adaptive fitting of 3D models using hierarchical triangular splines. In: International Conference on Shape Modeling and Applications, pp. 13–22. IEEE Computer Society Press, Los Alamitos (2005)
Chen, W., Cai, Y., Zheng, J.: Generalized hierarchical NURBS for interactive shape modification. In: Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry, ACM (2008)
Mørken, K.: Some identities for products and degree raising of splines. Constr. Approx. 7(1), 195–208 (1991)
Strøm, K.: Products of B-patches. Numer. Algorithms 4(3), 323–337 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, W., Zheng, J. & Cai, Y. Monge mapping using hierarchical NURBS. Vis Comput 26, 779–789 (2010). https://doi.org/10.1007/s00371-010-0475-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-010-0475-5