Abstract
Applications in computer graphics and geometric modeling generally require the integration of a variety of curve and surface types into a single system. Object-oriented design offers the opportunity to use the inherent hierarchical structure of curves and surfaces to solve this problem. This paper presents a top down approach to the design of an object-oriented framework for curves and surfaces together with its C++ implementation. We start from an abstract class of general differentiate curves and surfaces and in turn refine this design to various parametric representations of curves and surfaces. This design includes all of the standard curve and surface types and provides a powerful and uniform interface for applications. Examples from differential geometry, blending, and scattered data interpolation illustrate the approach.
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References
R.H. Bartels, J.C. Beatty, and B.A. Barsky. An Introduction to Splines for Use in Computer Graphics and Geometric Modelling. Morgan Kaufman, 1987.
J. Beck, R. Farouki, and J. Hinds. Surface Analysis Methods. Computer Graphics & Applications, 6 (12): 18 – 38, December 1986.
J. Bloomenthal. Polygonization for implicit surfaces. Computer Aided Geometric Design, 5: 341 – 355, 1988.
M. P. do Carmo. Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, N.J., 1976.
Margaret A. Ellis and Bjarne Stroustrup. The Annotated C++ Reference Manual. Addison Wesley, 1991.
Gerald E. Farin. Triangular Bernstein-Bùzier patches. Computer Aided Geometric Design, 3:pp. 83 – 127, 1986.
Gerald E. Farin . Curves and Surfaces in Computer Aided Geometric Design. Academic Press, 1988.
R. T. Farouki . Graphical Methods for Surface Differential Geometry. In R. R. Martin, ed¬itor, The Mathematics of Surfaces II, pages 363 – 385. Oxford Science Publications, Oxford, 1987.
Philip Fong and Hans-Peter Seidel. Control Points for Multivariate B-spline Surfaces over Arbitrary Triangulations. Computer Graphics Forum, 10: 309 – 317, 1991.
A. R. Forrest. Interactive Interpolation and Approximation by Bezier Polynomials. The Computer Journal, 15:pp. 71 – 79, 1972.
S. Fortune . Voronoi Diagrams and Delaunay Triangulations. In D. Z. Du and F. Hwang, editors, Computing in Euclidean Geometry, pages 193–223. World Scientific Publ., 1992.
R. Franke and G. Nielson. Scattered Data Interpolation: A Tutorial and Survey. In H. Hagen and D. Roller, editors, Geometric Modelling: Methods and Applications, pages 131–160, New York, 1991. Springer-Verlag.
Priamos N. Georgiades and Donald P. Greenberg. Locally Manipulating the Geometry of Curved Surfaces. IEEE Computer Graphics & Applications, 12 (l): 54 - 64, January 1992.
G. Greiner . Blending Techniques Based on Variational Principles. In J. Warren, editor, urves and Surfaces in Computer Vision and Graphics III, Proc. SPIE 1830, pages 174–184. SPIE, 1992.
G. Greiner . Surface Contructions Based on Variational Principles. In P.-J. Laurent, A. Le Méhauté, and L. L. Schumaker, editors, Curves and Surfaces II, Chamonix, 1993.
G. Greiner and H.-P. Seidel. Curvature Continuous Blend Surfaces. In B. Falcidieno and T. L. Kunii, editors, Modelling in Computer Graphics, pages 309–317. Springer-Verlag, 1993.
M. Kallay . Constrained optimization in surface design. In B. Falcidieno and T. L. Kunii, editors, Modeling in Computer Graphics, pages 85–94. Springer-Verlag, 1993.
R. Klass. Correction of Local Surface Irregularities Using Reflection Lines. Computer Aided Design, 12 (2): 73 – 76, February 1980.
R. Klein and Ph. Slusallek. An Object-Oriented Framework for Curves and Surfaces. In J. Warren, editor, Curves and Surfaces in Computer Vision and Graphics III, Proc. SPIE 1830, pages 284–295. SPIE, 1992.
Andreas Kolb. Interpolating Scattered Data with C2 surfaces. Technical report, Universität Erlangen, 1993.
M. Lounsbery, S. Mann, and S. and T. deRose. Parametric Surface Interpolation. Com¬puter Graphics & Applications, 9: 97 – 115, 1992.
H. P. Moreton and C. H. Séquin. Functional Optimization for Fair Surface Design. In E. E. Catmull, editor, Computer Graphics, pages 167 – 176. ACM Siggraph, ACM Press, 1992.
Paul S. Strauss and Rikk Carey. An Object-Oriented 3D Graphics Toolkit. Computer Graphics, 26 (l): 341 – 352, July 1992.
Bjarne Stroustrup. The C++ Programming Language. Addison Wesley, 2. edition, 1991.
Allan H. Vermeulen and Richard H. Bartels. C++ Spline Classes for Prototyping. In Curves and Surfaces in Computer Graphics II pages 121–131. SPIE, 1991.
William Welch and Andrew Witkin. Variational Surface Modeling. In Edwin E Catmull, editor, Computer Graphics, pages 157 – 166. ACM Siggraph, ACM Press, 1992.
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© 1996 EUROGRAPHICS The European Association for Computer Graphics
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Slusallek, P., Klein, R., Kolb, A., Greiner, G. (1996). An Object-Oriented Approach to Curves and Surfaces. In: Wisskirchen, P. (eds) Object-Oriented and Mixed Programming Paradigms. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61062-2_4
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DOI: https://doi.org/10.1007/978-3-642-61062-2_4
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