OpenGL: Fit scene to screen

Question

I have a 3D scene with a perspective projection.

I want to fit the scene to the screen based on a bounding box ( min and max ).

I have centered my scene like this:

glm::vec3 center = (min + max) / 2.0f;
rootNode->translate(-center.x, -center.y, -center.z);

Now I need a scale factor to scale my rootNode to fit the screen. How do I do this?

(this: 8.070 How can I automatically calculate a view that displays my entire model? (I know the bounding sphere and up vector.) does not help because its based on a orthogonal projection)

Answer 1

The reason this question is harder with a perspective projection than it is with an orthogonal projection is that the min and max you need are not constant with a perspective projection.

With a perspective projection the distance between either edge of the visible region increases as you move away from the camera.

With a perspective projection you typically have a field of view angle, theta , a camera position, and a "looking at" vector, v . At any distance, d from the camera's position (in the direction of v ) you can imagine a plane whose normal is v . The region of this plane that your camera can "see" has width:

2 * d * tan(theta / 2).

In a simple fixed camera setup you might have your camera at the origin and looking down the z-axis, and then the distance d for any point will just be the point's z coordinate.

Note also that you may have different horizontal and vertical field of view angles. If you have set a vertical field of view angle "fovy" and an aspect ratio (viewport width / viewport height) then your horizontal field of view angle is your vertical field of view angle times the aspect ratio.