Abstract
This paper reviews some basic ideas concerning the relationship between free-form surface design and high-quality, i. e. photorealistic, rendering techniques. In particular, the possibilities of closing the present gap between both tasks by employing the same mathematical representation of geometry are investigated.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Appel, A.: Some techniques for shading machine rendering of solids, AFIPS 1968 Spring Joint Computer Conference, 37–45.
Arvo, J., Kirk, D.: Fast ray-tracing by ray classification, it Computer Graphics, bf 21 (1987), 55–64.
Barr, A. H.: Superquadrics and angle preserving transformations, it IEEE Computer Graphics and Applications, bf 1 (1) (1981), 11–23.
Bajaj, C.: Geometric modeling with algebraic surfaces, in: D. Handscomb, editor, it The Mathematics of Surfaces Ill, Oxford University Press, 1988, 3–48.
Bajaj, C.: Automatic parametrization of rational curves and surfaces II: cubics and cubicoids, it Computer Aided Design, bf 19 (9) (1987), 499–502.
Bajaj, C., Ihm, I.: Algebraic surface design with Hermite interpolation, it ACM Transaction on Graphics, bf 19 (1992), 61–91.
Bajaj, C., Ihm, I.: Smoothing polyhedra using implicit algebraic splines, it Computer Graphics, bf 26 (1992), 79–88.
Bajaj, C.L., Chen, J., Xu, G.: It Interactive Modeling with A-Patches, Technical Report CSD-TR-93–002, CAPO Report CER-93–02, Department of Computer Sciences, Purdue University, 1993.
Blinn, J. F.: Notes on geometric modeling, SIGGRAPH 1980, Tutorial.
Cohen, M.F., Greenberg, D.P.: The Hemi-Cube: A radiosity solution for complex environments, it Computer Graphics, 24 (1985), 31–40.
Cohen, M.F., Wallace, J.R.: it Radiosity and Realistic Image Synthesis, Academic Press, 1993.
Dahmen, W.: Smooth piecewise quadric surfaces, in: T. Lynche and L. L. Schumaker, editors, it Mathematical Methods in Computer Aided Geometric Design, Academic Press, 1989, 181–193.
Dahmen, W., Thamm, T.-M.: Cubicoids: Modeling and Visualization, it Computer Aided Geometric Design, bf 10 (1993) 89–108.
Duff, T.: The soid and roid manual, New York Institute of Technology, 1980.
Farin, G.: it Curves and Surfaces for Computer Aided Geometric Design, Second Edition, Academic Press, 1990.
Hoschek, J., Lasser, D.: it Grundlagen der geometrischen Datenverarbeitung, Teubner, Germany, Stuttgart, 1989.
Hanrahan, P.: Ray tracing algebraic surfaces, it Computer Graphics, bf 17 (1983), 83–90.
Ihm, I.: it Surface design with implicit algebraic surfaces, PhD thesis, Purdue University, August 1991.
Lorensen, W., Cline, H.: Marching cubes: a high resolution 3D surface construction algorithm, it Computer Graphics, bf 21 (1987), 163–169.
Herken, R., Hödicke, R., Thamm-Schaar, T.-M., Yost, J. and Borac, S.: High Quality Visualization of CAD Data, it Freeform Tools in CAD Systems — A Comparison -, Hoschek, H., (Ed.), B.G. Teubner Stuttgart Germany, 1991, 173–194.
Moore, D., Warren, J.: Approximation of dense scattered data using algebraic surfaces, it in: Proc. of the 24th Hawaii Intl. Conference in Systems Science, Kauai, Hawaii, 1991, 681–690.
Nielson, G.: Transfinite visually continous triangular interpolant, in: G. Farin, editor, it Geometric Modeling Application and New Trends, SIAM, 1986.
Peters J.: Local cubic and bicubic Cl surface interpolation with linearly varying boundary normal, it Computer Aided Geometric Design, bf 7 (1990), 499–516.
Peters, J.: Smooth interpolation of a mesh of curves, it Constructive Approximation, bf 7 (1991), 221–246.
Patrikalakis, N.: Kriezis, G., Representation of piecewise continous algebraic surfaces in terms of B-splines, it The Visual Computer, bf 5 (6) (1989), 360–374.
Powell, M.J.D., Smbin, M.: Piecewise quadric approximations on triangles, it ACM Trans. on Math. Software, bf 3 (1977)’ 310–325.
Sederberg, T.: Piecewise algebraic surface patches, it Computer Aided Geometric Design, bf 2 (1989) 23–32.
Whined, T.: An Improved Illumination model for shaded display, it Communication of the ACM, bf 23 (6) 1980. 343–349.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Dahmen, W., Raabe, B., Thamm, TM. (1999). Optimal Geometry Representations for High-Quality Visualization. In: Dress, A., Jäger, G. (eds) Visualisierung in Mathematik, Technik und Kunst. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-07748-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-663-07748-0_2
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-06912-4
Online ISBN: 978-3-663-07748-0
eBook Packages: Springer Book Archive