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Projective geometry

$\ldots$ $\grave{\omega} \sigma \tau \epsilon$ $\kappa \alpha \lambda \lambda \iota o \nu$ $\acute{\alpha} \pi o \delta \epsilon \xi \epsilon \sigma \theta \alpha \iota$, $\acute{\iota} \sigma \mu \epsilon \nu$ $\pi o \nu$ $\grave{o} \tau \iota$ $\tau \omega$ $\acute{o} \lambda \omega$ $\kappa \alpha \iota$ $\pi \alpha \nu \tau \iota$ $\delta \iota o \iota \sigma \epsilon \iota$ $\grave{\eta} \mu \mu \epsilon \nu o \zeta$ $\tau \epsilon$ $\gamma \epsilon \omega \mu \epsilon \tau \rho \alpha \iota \zeta$ $\kappa \alpha \iota$ $\mu \eta$

``$\ldots$ experience proves that anyone who has studied geometry is infinitely quicker to grasp difficult subjects than one who has not.''
Plato - The Republic, Book 7, 375 B.C.

The work presented in this text draws a lot on concepts of projective geometry. This chapter and the next one introduce most of the geometric concepts used in the rest of the text. This chapter concentrates on projective geometry and introduces concepts as points, lines, planes, conics and quadrics in two or three dimensions. A lot of attention goes to the stratification of geometry in projective, affine, metric and Euclidean layers. Projective geometry is used for its simplicity in formalism, additional structure and properties can then be introduced were needed through this hierarchy of geometric strata. This section was inspired by the introductions on projective geometry found in Faugeras' book [29], in the book by Mundy and Zisserman (in [91]) and by the book on projective geometry by Semple and Kneebone [132]. A detailed account on the subject can be found in the recent book by Hartley and Zisserman [55].



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Next: Projective geometry Up: Visual 3D Modeling from Previous: Structure of the notes   Contents
Marc Pollefeys 2002-11-22