By P. & M. Bridgeford ; edited by Hu. Berry ; illustrations, M. Bridgeford.
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Extra resources for Cape Cross : Past and Present
Vision systems satisfying the single viewpoint constraint are called central projection systems. The perspective camera is an example of a central projection system. The mapping of points in the scene into points in the image is linear in homogeneous coordinates, and can be described by a 3 × 4 projection matrix P (pin-hole model). Perspective projection can be modeled by intersecting a plane with a pencil of lines going through the scene points and the projection center O. There are central projection systems whose geometry can not be described using the conventional pin-hole model.
Mt is composed of two lines m and l lying on the projective plane ℘2 . In this case the conic is said to be degenerate, the 3 ×3 symmetric matrix Ω is rank 2, and Equation (15) becomes ⎤ ⎡ 1 0 0 0 0 0 ⎢0 2 0 0 0 0⎥ ⎥ ⎢ ⎢0 0 1 0 0 0⎥ t t ⎥. Γ(m, l) ⎢ Ω = ml + lm −→ ω = ⎢ (16) ⎥ ⎢0 0 0 2 0 0⎥ ⎣0 0 0 0 2 0⎦ 0 0 0 0 0 1 e D In a similar way a conic locus can be composed of a single line n = (nx , ny , nz )t . x = 0. Point x is on the line if, and only if, its lifted coordinates n are orthogonal to the homogeneous vector n (nt x = 0).
This can be diﬃcult CATADIOPTRIC NON-CENTRAL SENSORS 43 to handle with, especially when we extend the problem to three dimension curves where r is root of a quadratic equation. Bearing in mind the advantages and weaknesses of the Jacobian method, we present here another technique to compute the caustic curve, where only local mathematical properties of M are taken into account. The caustic of a curve M , is function of the source light S. The basic idea is to consider a conic where S is placed on one of its foci.