A new body recovery algorithm based on support function measurements is proposed. The proposed algorithm represents a linear or quadratic programming problem in Gardner-Kiderlen form with smaller number of constraints. The reduction of constraint number is based on a new method that allows one to eliminate a part of initial constraints as redundant. A new approach of body recovery based on shadow contours is proposed. It allows one to reuse body recovery methods based on support function measurements. The implementation of the algorithm is described and some results of its testing on real industrial contours are discussed. The proposed method ensures the reduction of constraint number by 80% in the discussed example and also enables to speedup the initial Gardner-Kiderlen algorithm by an order of magnitude.

Keywords: support function, geometric bodies recovery, linear programming, quadratic programming, shadow contour, duality transformation.

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