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Simple 3D collision detection?

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Unfortunately arbitrary mesh to arbitrary mesh collision is the hardest of all. To speed collision detection we usually make assumptions about the shapes involved, eg: they are convex or made up of boxes and spheres. Since you're new to collision detection I'd start with simple shapes first like spheres and axis aligned boxes. These will let you localise collisions betwen objects to specific areas by surrounding your meshes with these simpler objects to approximate their shape. From there on work your way up object aligned boxes and triangles which will let you further refine your collision detection and find collision points. Only when you're confident with these basics and have a good collision library to work off should you consider more general and complex collision schemes. To give yourself a kick start you might want to download a free-ware collision engine like Tokamak and have a play around with their intersection routines to start yourself thinking along the right lines. Have fun

PS: You might want to check out Magic-Software.com for some help with colliding various shapes together

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