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We have a camera that is looking towards a sphere. We would like

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to calculate the ideal distance so that the camera's view frustrum grazes our

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sphere. We shall first define the radius of the sphere as 'r'.

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We shall now place our camera and begin defining its

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frustrum. In this 2D simplification, the camera frustrum can be

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thought of as an isosceles triangle with the apex angle

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being our field of view, that we will name 'f'.

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We will now bisect our frustrum. One may be tempted to then

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simply use the camera right vector and solve for the camera distance

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x by using trigonometry, this however is incorrect, and will lead to

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our frustrum intersecting the sphere. As you can see this doesn't work

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the way we want it to, let's try something different.

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The correct approach is to use a vector orthogonal to the frustrum

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instead of using the camera's right vector. We can then use trigonometry

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to find X, which in this case will just be the hypotenuse.