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computer algebra based 2d soldat-style game

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hey. I was going to post this in the game design forum but figured that the people here might have a better idea about what im suggesting: Is it feasible to write a 2-D game which would be based on a computer algebra system? Specifically, one like soldat. As in, objects in the game could all be defined in terms of equations. Then you would be able to use curves, etc in the game, and arbitrarily complicated shapes(polynomials up to order 4, ovals, circles, etc. Soldat just uses triangles). Collision detection could be done by solving equations, etc, differentiation for finding normals and integration for torques and so on. Is this theoretically do-able? It just came to me one day and it sounded like a neat idea.

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