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POCalculating point relative to another point in 3D space
 

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  1. POCalculating point relative to another point in 3D space
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    <p>This is going to be a rather complicated explanation so bear with me. In 3D space, a player has 2 rotation values for looking around them, the rotation about the x and y axis. Given a view distance, I have calculated the point in the center of the players view port which is the view distance away (as show below).</p> <p><img src="https://i.stack.imgur.com/oJcjS.png" alt="enter image description here"></p> <ul> <li>'vd' is the view distance</li> <li>'c' is a value holder</li> <li>'(x,y,z)' is the point to be calculated</li> <li>'rot.x' and 'rot.y' are the rotations about the x and y axis, respectively.</li> </ul> <p>Given this point (x,y,z), I need to calculate four points relative to this position (as shown below)</p> <p><img src="https://i.stack.imgur.com/Tbf0X.png" alt="enter image description here"></p> <ul> <li>'(x2,y2,z2)', '(x3,y3,z3)', etc. are the points I need to calculate.</li> <li>The width and height of the green plane is known. Let's call each one 'w' and 'h' respectively.</li> </ul> <p>Now given I still have access to all the values in the first graph (such as rotations, etc), how can I calculate the each of the four points?</p> <p>A little background.. I am doing this for a culling method called frustum culling. I am trying to do this with LWJGL in order to speed up rendering and reduce the toll on the GPU. I haven't been able to figure out the trigonometry for this calculation, and I have been trying for the past few hours. Any help is appreciated. If any more explanation/clarification is needed, just let me know. Thanks.</p> <p>EDIT: Also, the points have to be on the same plane and rotate about the x and y axis with the point (x,y,z). </p>
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    1. COWouldn't this be trivial to calculate with matrix math by forming position as a a matrix and then multiplying that with your projection matrix? Or is your question actually how to forma a projection matrix? So in this case just make rotation matrices and position matrix and multiply them together with your projection matrix.
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    2. COI don't have any experience with matrices. I have managed to get around using them so far. So an answer without having to extract the perspective matrix or anything to calculate the points would be preferable.
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    3. COThing is the exact point of using matrices would be to actually eliminate the need to understand the math altogether. The matrices are just that trigonometry nicely packaged into a matrix form. Since the matrices can be multipled together to form one entity that does the entire thing in one go. This eliminates the need to do all the steps together as you can only ever design any one sub step at a time. In fact the furstrum culling can be espressed as a matrix form as if point is outside of the furstrum space -1 to 1. Saving you a lot of calculation.
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