I have drawn diagram after diagram of how to calculate the bounding points of the viewing frustum in a three-dimensional space. To start, I have a two sets of data containing three values each: the xyz coordinates of the camera and the rotation around the x, y, and z axis. Given a certain view distance, it should be possible to calculate the bounding points of each of the 6 planes. I have been using these equations to calculate the width and height of the far plane:
hfar = 2 * tan(45/2) * view_distance
wfar = hfar * ratio
hfar being the height of the far plane, wfar being the width, and ratio being the ratio of the view port width divided by the height. I have been using the following diagram to try and figure it out:
I need to find the points annotated by (?,?,?). I have been trying to calculate these values for a few days now but to no avail. Any help would be appreciated.
Also, some nice sources providing information on the topic can be found here and here.
EDIT: Another image I whipped up shows a single slice through the y axis looking down on the x axis. It shows the same information as the image above, but it also shows my issue: I can't calculate the proper z axis values for each of the bounding points of the far plane.
Keep in mind, the same cut could be made through the x axis to show the same process but with the angle at which the player is looking up or down.
Compute the center points of the near and far planes:
vec3 nearCenter = camPos - camForward * nearDistance;
vec3 farCenter = camPos - camForward * farDistance;
Compute the widths and heights of the near and far planes:
real nearHeight = 2 * tan(fovRadians/ 2) * nearDistance;
real farHeight = 2 * tan(fovRadians / 2) * farDistance;
real nearWidth = nearHeight * viewRatio;
real farWidth = farHeight * viewRatio;
Compute the corner points from the near and far planes:
vec3 farTopLeft = farCenter + camUp * (farHeight*0.5) - camRight * (farWidth*0.5);
vec3 farTopRight = farCenter + camUp * (farHeight*0.5) + camRight * (farWidth*0.5);
vec3 farBottomLeft = farCenter - camUp * (farHeight*0.5) - camRight * (farWidth*0.5);
vec3 farBottomRight = farCenter - camUp * (farHeight*0.5) + camRight * (farWidth*0.5);
vec3 nearTopLeft = nearCenter + camY * (nearHeight*0.5) - camX * (nearWidth*0.5);
vec3 nearTopRight = nearCenter + camY * (nearHeight*0.5) + camX * (nearWidth*0.5);
vec3 nearBottomLeft = nearCenter - camY * (nearHeight*0.5) - camX * (nearWidth*0.5);
vec3 nearBottomRight = nearCenter - camY * (nearHeight*0.5) + camX * (nearWidth*0.5);
Compute each plane from any three corners of the plane, wound CW or CCW to point inward (depending on coordinate system).
vec3 p0, p1, p2;
p0 = nearBottomLeft; p1 = farBottomLeft; p2 = farTopLeft;
vec3 leftPlaneNormal = Normalize(Cross(p1-p0, p2-p1));
vec3 leftPlaneOffset = Dot(leftPlaneNormal, p0);
p0 = nearTopLeft; p1 = farTopLeft; p2 = farTopRight;
vec3 topPlaneNormal = Normalize(Cross(p1-p0, p2-p1));
vec3 topPlaneNormal = Dot(topPlaneNormal , p0);
p0 = nearTopRight; p1 = farTopRight; p2 = farBottomRight;
vec3 rightPlaneNormal = Normalize(Cross(p1-p0, p2-p1));
vec3 rightPlaneNormal = Dot(rightPlaneNormal , p0);
p0 = nearBottomRight; p1 = farBottomRight; p2 = farBottomLeft;
vec3 bottomPlaneNormal = Normalize(Cross(p1-p0, p2-p1));
vec3 bottomPlaneNormal = Dot(bottomPlaneNormal , p0);