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I've been looking around a bit and can't seem to find just what I"m looking for. I've found "canonical formulas," but what's the best way to use these? Do I have to scale every single vertex down? Or is there a better way?
A formula would really help me out, but I'm also looking for an explanation about the near and far z planes relative the viewer's position
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Example(Orthogonal projection onto a line) u · x ) / ( u · u ) is a solution of u T uc = u T x , and hence x L = uc =( u · x ) / ( u · u ) u .
Solution The general formula for the orthogonal projection onto the column space of a matrix A is P = A(AT A)−1AT . Remarks: Since we're projecting onto a one-dimensional space, AT A is just a number and we can write things like P = (AAT )/(AT A).
Here is a reasonable source that derives an orthogonal project matrix:
Consider a few points: First, in eye space, your camera is positioned at the origin and looking directly down the z-axis. And second, you usually want your field of view to extend equally far to the left as it does to the right, and equally far above the z-axis as below. If that is the case, the z-axis passes directly through the center of your view volume, and so you have r = –l and t = –b. In other words, you can forget about r, l, t, and b altogether, and simply define your view volume in terms of a width w, and a height h, along with your other clipping planes f and n. If you make those substitutions into the orthographic projection matrix above, you get this rather simplified version:
All of the above gives you a matrix that looks like this (add rotation and translation as appropriate if you'd like your resulting transformation matrix to treat an arbitrary camera position and orientation).
(source: codeguru.com)
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http://mathworld.wolfram.com/OrthogonalProjection.html
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/mathematics-2/node51.html
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