I am not sure if this is the correct SE to ask this question. However, lets say I have been given 3D models of several enclosed spaces.

I want to populate spaces with, lets say, planes flying through them, taking the optimum route from A to B. Since there are many of them, I want to write an algorithm that does this; I already have the 3D models of the planes.

I am looking for resources I can use to learn how to do define the boundary conditions for the opimization algorithm given the 3D model.

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    $\begingroup$ I'm assuming by "planes" you mean aeroplanes (as I originally interpreted 'planes' in the mathematical/graphics sense :-) ). Seriously though, when you say "lets say I have been given 3D models of several enclosed spaces." do you mean they are a set of objects the aircraft must avoid (e..g like the stereotypical "spaceship in an asteroid field" ) or do you mean, given an arbitrary one of these enclosed volumes, allow the aircraft to fly around inside it (and not crash)? $\endgroup$ – Simon F Feb 7 at 9:22
  • $\begingroup$ @Simon F Hmm, I am interested in learning both, but for this question I'll restrict it to enclosed volumes if the methods are fundamentally different. $\endgroup$ – Avatrin Feb 7 at 14:45
  • $\begingroup$ Look into winding numbers $\endgroup$ – Makogan Feb 14 at 20:31

As no one else seems to want to suggest something, given that you said you wanted to navigate within an arbitrary enclosed volume, perhaps you could use an approach similar to that of the 1995 game Descent.

IIRC the world model of the 'mine' the spacecraft and enemy robots navigated was made up of "cuboid" units/voxels that pieced seamlessly together, some of which had solid walls that then formed the boundaries of the enclosing volume. The source code is freely available online e.g. here .

If, in the likely scenario you can't force the enclosing volume to have quadrilateral facets, you might want to consider "tetrahedral" volumes.

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