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Perspective Projection and 3D world coordinates


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#1 lilroo   Members   -  Reputation: 100

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Posted 13 April 2012 - 07:44 AM

How can I define real world coordinates when I am in perspective mode ? I do not understand how the frustum relates the the coordinates in the 3D world. Where is the camera located ? what is the maximum you can go along any axis ? How does this relate to the frustum ?
I have been stuck on this problem for a good week now, any input would be greatly appreciated.

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#2 Bacterius   Crossbones+   -  Reputation: 8318

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Posted 13 April 2012 - 08:17 AM

World space coordinates are converted to camera space by multiplying them by the view matrix. This has the effect of translating and rotating the world around so that the camera is at the origin and facing along the positive Z axis (by convention). Then you multiply the camera space coordinates by the perspective (projection) matrix which produces a pyramid-shaped space (which means objects further from the camera will be closer to the screen's center when mapped to a 2D screen), and you finally clip off the near and far planes to obtain a frustum.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis





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