I am trying to determine whether two frusta intersect in 3D space and to quantify this intersection as a percentage of one frustum volume (eg. 100% intersection meaning that the two frusta occupy the same exact space, 0% the two frusta don't touch).

I have all the possible data about each frustum, the six planes and their position and so on but I can't figure out what's a reliable method to get what I want.

I had a look at the Separating Axis Algorithm for collision detection but I don't understand if it's what I need.

Can anyone direct me towards the right path?


  • $\begingroup$ A method (though probably not a great one) would be to represent one of the frusta as a 6 sided polyhedron and then do a 3D clip of it with the other's planes. There are probably free libraries out there to do the clipping/intersection....but I haven't looked. $\endgroup$ – Simon F Jan 28 at 16:40
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    $\begingroup$ Thank you very much @SimonF I'm relatively new to this, would you happen to have any suggestion to what keywords to look for in a library? is this computational geometry? $\endgroup$ – Francesco Jan 30 at 14:06
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    $\begingroup$ @SimonF I really appreciate your help $\endgroup$ – Francesco Jan 30 at 14:29
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    $\begingroup$ Thanks everyone for the help, it's pretty clear to me how this is out of my reach with my current geometry and math knowledge. @lightxbulb isn't the montecarlo simulation very computationally expensive? I think I am approaching the problem from the wrong angle: I need to calculate an image overlap without using feature matching, but using the viewing frusta of the images. I assumed that the intersection of the two frusta would be proportional to the image overlap, but I might try to use the canvas planes and project one onto the other, instead of going the intersecting frusta way $\endgroup$ – Francesco Jan 31 at 14:35
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    $\begingroup$ For future users: we have clarified that the problem is so vague since it is a definition from a paper that was not explained in details, as it stands it's not clear what exactly the 'correct' formulation should be. $\endgroup$ – lightxbulb Jan 31 at 15:54

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