Overview
Mathematical operations on points, vectors and matrices are needed for processing information related to geometrical objects. Even in the modelling of a simple three-dimensional scene, vectors and matrices play an important role in specifying an object’s position, orientation and transformations. Methods for lighting, intersection testing, projections, etc., use a series of vector operations. This chapter gives an overview of computations using geometrical primitives and shapes that form the basis for several algorithms presented in subsequent chapters of the book.
Parametric representations are often used in methods involving geometrical primitives. This chapter deals with analytical equations of lines, planes and curves, and their applications in geometrical computations. Properties of three-dimensional transformations are discussed using their matrix representations. The chapter also introduces concepts such as signed area and distance, affine combinations of points and barycentric coordinates.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agoston, M. K. (2005). Computer graphics and geometric modeling. London: Springer.
Angel, E. (2008). Interactive computer graphics: A top-down approach using OpenGL (5th ed.). Boston/London: Pearson Addison-Wesley.
Buss, S. R. (2003). 3-D computer graphics: A mathematical introduction with OpenGL. New York: Cambridge University Press.
Comninos, P. (2006). Mathematical and computer programming techniques for computer graphics. London: Springer.
Dunn, F., & Parberry, I. (2002). 3D math primer for graphics and game development. Plano: Jones & Bartlett Publishers.
Farin, G. E., & Hansford, D. (2005). Practical linear algebra: A geometry toolbox. Wellesley: A K Peters.
Goldman, R. (1990). Intersection of three planes. In A. S. Glassner (Ed.), Graphics gems (Vol. I, p. 305). San Diego: Academic Press.
Hill, F. S., & Kelley, S. M. (2007). Computer graphics: Using OpenGL (3rd ed.). Upper Saddle River: Pearson Prentice Hall.
Lengyel, E. (2004). Mathematics for 3D game programming and computer graphics (2nd ed.). Hingham/London: Charles River Media/Transatlantic.
McConnell, J. J. (2006). Computer graphics: Theory into practice. Boston/London: Jones and Bartlett Publishers.
Schneider, P. J., & Eberly, D. H. (2003). Geometric tools for computer graphics. Amsterdam/ London: Morgan Kaufmann.
Vince, J. (2001). Essential mathematics for computer graphics fast. London: Springer.
Vince, J., & Vince, J. E. (2006). Mathematics for computer graphics (2nd ed.). London: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Mukundan, R. (2012). Mathematical Preliminaries. In: Advanced Methods in Computer Graphics. Springer, London. https://doi.org/10.1007/978-1-4471-2340-8_2
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2340-8_2
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2339-2
Online ISBN: 978-1-4471-2340-8
eBook Packages: Computer ScienceComputer Science (R0)