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Asked: 2026-06-15T18:18:12+00:00

This is going to be a rather complicated explanation so bear with me. In

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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).

enter image description here

  • ‘vd’ is the view distance
  • ‘c’ is a value holder
  • ‘(x,y,z)’ is the point to be calculated
  • ‘rot.x’ and ‘rot.y’ are the rotations about the x and y axis, respectively.

Given this point (x,y,z), I need to calculate four points relative to this position (as shown below)

enter image description here

  • ‘(x2,y2,z2)’, ‘(x3,y3,z3)’, etc. are the points I need to calculate.
  • The width and height of the green plane is known. Let’s call each one ‘w’ and ‘h’ respectively.

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?

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.

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).

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1 Answer

  1. Editorial Team

    Assuming rotation order is X first then Y rotation then the matrix calculation would be:

    V*Ry*Rx

    Since the V vector was established being.

    V = [view_distance, tan(22.5)*view_distance, tan(22.5)*view_distance*(WIDTH/HEIGHT)]

    Then that means:

    X2 = cos(rot.Y) * view_distance - 
     (tan(22.5) * WIDTH * view_distance * sin(rot.Y))/HEIGHT
Y2 = tan(22.5) * cos(rot.X) * view_distance + 
     (tan(22.5) * WIDTH * cos(rot.Y) * view_distance * sin(rot.X))/HEIGHT +
      view_distance * sin(rot.X) * sin(rot.Y)
Z2 = (tan(22.5) * WIDTH * cos(rot.X) * cos(rot.Y) * view_distance)/HEIGHT - 
     tan(22.5) * view_distance * sin(rot.X) +
     cos(rot.X) * view_distance * sin(rot.Y)

    The expressions could be simplified a bit more, since for example view distance can be factored out of all the expressions. Since calculating this was a bit pointless and error prone id prefer to use the matrix functions with numeric values as its much easier stuff.

    PS: The matrix notation is much easier on your eyes and your programming experience.

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