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> For example the distance function of two objects moving in a linear fashion is (IIRC) a squared parabola This is only true for points. It’s demonstrably untr
by layoutIfNeeded 7y ago
> For example the distance function of two objects moving in a linear fashion is (IIRC) a squared parabola
This is only true for points. It’s demonstrably untrue for arbitrary shapes.
- heavenlyblue 7y agoWell, actually it's also true for spheres. Then you can approximate any shape with spheres and use that as an optimisation before actually calculating the more costly distance functions.
- progval 7y agoApproximating a (solid) object with spheres means the spheres are in constant distance and angles with each other. So their trajectories are no longer linear if there is any kind of rotation.
- lonelappde 7y agoWhat is a linear rotation? If one sphere is in linear rotation, why can't two?
- wtallis 7y agoThe point isn't to approximate a solid object as several spheres, but to approximate it with one enclosing sphere. If two objects aren't close enough for their bounding spheres to touch, then you don't need to do a collision detection using the more complicated geometry.
- progval 7y agoOh, right. Thanks for the clarification.