# 4D Triangle collision

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Hi guys. How are you, fine? I hope so. I've got a question about collisions, that old and so reviewed topic... Which method is better for detect triangle collisions a - priori? http://www.usuarios.lycos.es/tripticon/fasttriangle.jpg I've heard about raycasting. May it is possible to raycast one triangle vs the point trajectories of the other. Or you can build a polyhedron from the moving triangle, and find time for collision via separating axis. Keep in mind that both triangles can move linearly and have rotations two. And what about if we have a morphing model, like a earthquake? How we can simulate a mesh vs mesh collision whose models are moving too fast? May this forum can regard us a brand new method for resolve 4D collisions. That would be amazing!

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 Original post by leoptimusHi guys. How are you, fine? I hope so.I've got a question about collisions, that old and so reviewed topic...Which method is better for detect triangle collisions a - priori?http://www.usuarios.lycos.es/tripticon/fasttriangle.jpgI've heard about raycasting. May it is possible to raycast one triangle vs the point trajectories of the other.Or you can build a polyhedron from the moving triangle, and find time for collision via separating axis.

YOu can extend the separation axis theorem to a swept test. linky

press 2 for the triangle - cube demo (and ~ to remove the console). Docs included.

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Thanks Oliii. Great Demo [wow].

Also, in other forum, you've mentioned GJK as a fast algorithm that compute distance and penetration between convex objects.
But the fact is that it is a problematic algorithm due of their tricky math and floating error management. I've got poor results with it , and Kwizatz has gained many grey hairs trying to implement an stable GJK algorithm without success. [grin]

But, dear Oliii, does your demo Cube3D manages 4D collisions?

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 But, dear Oliii, does your demo Cube3D manages 4D collisions?
By 4d do you mean 3d intersection that incorporates the motion of the objects involved? (Some standard terms for this are swept, dynamic, or continuous collision detection.)

If so, then yes, the separating axis method can easily be extended to '4d', and is a good practical solution for a family of objects that includes most polytopes in 2d, and simple polytopes (including triangles and boxes) in 3d. Furthermore, intersection of circles and spheres with each other and with the aforementioned objects is straightforward and fairly easy to implement.

There are other convex objects for which swept tests are more difficult; these would include capsules, ellipses and ellipsoids, cones, cylinders, and complex polytopes in 3d. Here GJK comes into play, as it can perform a swept test between any objects that can be represented fully through a support function.

So in theory at least, swept ('4d') collision detection between convex objects may be a solved problem. However, as you note, GJK is non-trivial to implement.

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