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Assume a pinhole camera (basically a camera with no lens, just a small hole light must pass though to reach a detector) is looking at an object which has well defined dimensions in 3D (we can describe it for (x,y,z)). This camera can have any orientation we wish (so we, basically, know its orientation). how do i go about calculating the way the image will be formed on the camera image sensor? I already know the two basic equations would be of the form:

$x=\frac{t_{11}X+t_{12}Y+t_{13}}{t_{31}X+t_{32}Y+t_{33}}$ and $y=\frac{t_{21}X+t_{22}Y+t_{23}}{t_{31}X+t_{32}Y+t_{33}}$

yet i can't seem to figure out the values for the $t_{ij}$ coefficients. from what i gather, they'll be somhow connected to the extrinsic rotation matrix $ C =\begin{bmatrix} r_{11} & r_{12} & r_{13} & t_{1} \\ r_{21} & r_{22} & r_{23} & t_{2} \\ r_{31} & r_{32} & r_{33} & t_{3} \end{bmatrix}$

but I'm not sure how.

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    I strongly suggest you read any book on computer graphics (or any online tutorial); you particularly want the section on 3D transformations and the one on "camera transformations". In our book, this material takes about 30-some pages, which is why I'm not repeating it here. :( – 2017-01-17
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    In particular, to get a camera xform, you need a camera specification, and these, too, are nontrivial. Your orientation matrix, for instance, only means something if you tell me the initial position of the camera: is it at the origin? Looking along $x$, $y$, or $z$? In the positive or the negative direction? What's the "up" direction in the film plane? In other words, you need to specify both a starting frame AND an orientation matrix. Also helpful: a center of projection, and two field-of-view angles, not to mention the distance from the pinhole to the "film plane". – 2017-01-17
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    Picked up a book on the topic during the weekend and read through these sections which you're referring to precisely.. Thanks alot! – 2017-01-22
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    Glad it was of some use to you. If you're still having troubles, you can ask a specific question using the established vocabulary (which is about 90% of the content!) and I'm sure someone here can answer it. – 2017-01-22

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