Coordinate representation of order types requires exponential storage
Jacob Eli Goodman, Richard M. Pollack, Bernd Sturmfels · 1989
We give doubly exponential upper and lower bounds on the size of the smallest grid on which we can embed every planar configuration of n points in general position up to order type. The lower bound is achieved by the construction of a widely dispersed “rigid” configuration which is then modified to one in general position by recent techniques of Sturmfels and White, while the upper bound uses recent results of Grigor'ev and Vorobjou on the solution of simultaneous inequalities. This provides a sharp answer to a question first posed by Chazelle.