An intriguing if rather bizarre problem. :wacko: So, to rephrase, you have a predetermined orbit center (C) and radius (cd) and you want to find the possible camera location(s) such that the line segment AB subtends a predetermined angle from the camera’s point of view?

Assuming I’ve correctly understood your problem, I don’t have a full solution, but here’s another way of looking at it. You have two constraints (camera’s radius from C and the angle between A and :). You can thus think of the point you want to find as the intersection of two curves. One curve would be a circle around C of radius cd, i.e. all the points that satisfy the radius constraint. The second curve would be all the points that satisfy the angle constraint. The shape of this second curve isn’t obvious; a quick sketch suggests it’s kind of like a cardioid, but with two cusps, one each at A and B. But perhaps with a bit of work you can find the equation of this curve, and then algebraically intersect it with the circle.

EDIT: One way to construct the latter curve might be as follows: imagine two lines, one through A and one through B; the absolute angles of the two lines differ by the desired AB angle. Their intersection point is thus one point on the curve we wish to find. As you rotate the two lines around their respective points, in lockstep so that their relative angle remains constant, their intersection point should sweep out that double-cardioid curve.

Hello!

A bit of a math question here, hopefully someone finds this interesting, or better yet, a possible solution. :)

I’ve drawn this up on a diagram, but I’ll explain it here for further illustration.

I’ve got a camera that orbits around a point. It has a set radius away from it’s orbit point, and an object it ‘looks at’.

Here’s where things start to get interesting. The object it’s looking at can have a target, somewhere else in the world. I’d like to constrain the camera to orbit such that it keeps a set number of degrees between the target and the object it’s looking at.

Is there any mathematical way of getting the precise location(s) of the new camera resting point? Ideally one that isn’t too computationally expensive, and ideally one I can understand? :)

Here’s a diagram where I’ve tried to illustrate the issues, as well as the knowns and unknowns.

After doing some research, I’m thinking I can solve this using a combination of cosine law and tan law, substituting when necessary, but I’m not entirely confident and it’ll take a while to build the equations and plug it in. In the meantime, I’d love to have other people’s opinions or ideas.

Cheers,

-e-