How about we display the Extents Algorithm?

Oh wise and knowledgeable coding community, I come seeking your expertise...

I am working with the three.js library and facing a challenge in implementing a 'show extents' button. This button should adjust the camera position so that all objects in the scene are visible within the camera view (assuming they are not obstructed).

I have been able to determine the bounding box of all objects in the world, represented by coordinates w0x, w0y, w0z and w1x, w1y, w1z.

Could you advise me on how to position the camera based on these bounds to ensure a clear view of the box edges? It is essential to choose a viewing angle for this purpose. Despite my attempts to search for an algorithm online, I have yet to find a suitable solution. Any help would be greatly appreciated!

javascriptalgorithmgraphicsrenderingthree.js

Answer №1

Imagine you have chosen a specific face and are now selecting a camera position where the camera's line of sight runs parallel to one of the axes.

Assume that the face has a width of "w" and the camera has a horizontal field of view of "a". Your goal is to determine the distance, "d", from the center of the face that the camera should be placed in order to capture the entire width.

If you visualize it, you'll see that you essentially have an isosceles triangle with a base length of w and the angle a at the peak.

In addition, the angle bisector of the apex forms two identical right triangles, and the length (to the base) represents the required distance we need to find out.

Trigonometry teaches us that the tangent of an angle is the ratio of the opposite and adjacent sides of the triangle. Therefore,

tan(a/2) = (w/2) / d

simplifies to:

d = w / 2*tan(a/2)

So, if you position the camera at a certain axis-aligned distance from one of your bounding box faces, simply move d units along the selected axis.

Keep in mind to use radians for the trigonometric functions in JavaScript. You may also need to calculate this again for the height of the face and vertical field of view of the camera, choosing the greater distance if the face is not square.

To encompass the bounding box from any angle, apply the same concepts - starting by determining the aligned bounding box of the scene projected onto a plane perpendicular to the camera's line of sight.

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