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From Ancient Greeks to Pixels Read chapter Read first chapter

2021 | OriginalPaper | Chapter

2. Geometric Shapes

Author : Alexei Sourin

Published in: Making Images with Mathematics

Publisher: Springer International Publishing

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Abstract

This chapter presents the mathematical foundations of shape modeling. Curves, surfaces, and solid objects are considered as set of points, which are obtained by sampling various types of mathematical functions. Using the concept of sweeping, many varieties of shapes are defined based on only a few simple foundation principles.

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Literature
1.
Pasko A, Adzhiev V, Sourin A, Savchenko V. Function representation in geometric modeling: concepts, implementation and applications. The Visual Computer, Springer, 11(8): 429–446, 1995
2.
V.L. Rvachev, “On the analytical description of some geometric objects”, Reports of Ukrainian Academy of Sciences, vol. 153, no. 4, 1963, pp. 765–767 (in Russian).
3.
V. Shapiro, Semi-analytic geometry with R-Functions, Acta Numerica, Cambridge University Press, 2007, 16: 239–303
4.
J. Blinn. A Generalization of Algebraic Surface Drawing., ACM Transactions on Graphics. 1982.
5.
G. Wyvill, C. McPheeters, B. Wyvill. Data Structure for soft objects. Visual Computer. 1986
6.
G. Wyvill, C. McPheeters, B. Wyvill. Animating soft objects. Visual Computer. 1986
7.
S. Muraki. Volumetric Shape Description of Range Data using “Blobby Model”. ACM SIGGRAPH. 1991.
Metadata
Title
Geometric Shapes
Author
Alexei Sourin
Copyright Year
2021
Book
Making Images with Mathematics

Print ISBN: 978-3-030-69834-8

Electronic ISBN: 978-3-030-69835-5

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-69835-5_2