3d Camera Position given some points

Question

Heyo,

I'm currently working on a project where I need to place the camera such that the full motion of a character would be viewable without moving the camera. I have the position where the character starts, as well as the maximum distance that the character will travel in all three directions (X,Y, & Z). I also have the field of view (which is 90 degrees).

Is there an equation that'll figure out where I need to place the camera so it won't have to move to see the full motion?

Note: this is using OpenGL.

Clarification: The camera should be "in front" of the character that's in the motion, not above.

It'll also be moving along a ground plane.

Answer 1

If you make a bounding sphere of the points, all you need to do is keep the camera at a distance greater than or equal to the radius of the bounding sphere / sin(FOV/2).

For example, if you have a bounding sphere with radius Radius, and a specified Field of View FOV, your camera just needs to be at a point "Dist" away, pointing towards the center of the bounding sphere.

The equation for calculating the distance is: Dist = Radius / sin( FOV/2 );

This will work in 3D, for a camera at any orientation.