ABSTRACT
Projection is the basic operation of both real and virtual cameras. Therefore, from the point of view of the four universes paradigm, projective geometry plays an important role in the search for a virtual camera model:
From the projective geometry point of view, the most generic projection possible is given by a projective transformation T : RP3 → RP2 which, in homogeneous coordinates, can be represented using matrices:
⎛⎝y1y2 y3
⎞⎠ = ⎛⎝a11 a12 a13 a14a21 a22 a23 a24 a31 a32 a33 a34
⎞⎠ ⎛⎜⎜⎝ x1 x2 x3 x4
⎞⎟⎟⎠ . We therefore have 11 degrees of freedom to define a virtual camera model using this transformation. In this model, several types of cameras are possible, including perspective (using the conical projection), affine, weak-perspective, and orthographic, among others. In this chapter we will study a camera model based on the conical projection, which is adapted for image synthesis.
