Combining two or more Unity colliders using Boolean algebra for the physics system

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I have an object representing an old-fashioned cubic dice. These are approximately cuboidal, but with rounded corners and circular facets. I may need to roll a lot of these, and I don't want any ending up balanced on their corner, so the best way to accomplish this (to my mind) is by combining a Box collider with a Sphere collider.

Normally when you do this in Unity, a collision would be detected when either the box or the sphere touches something else, but I need it to happen when both the box and the sphere touch something else. This should be much faster than using a mesh, but I'm not sure how to accomplish it.

Any ideas?

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