IMPROVING ROSENBROCK ALGORITHM TO FIND THE SMALLEST CIRCLE CONTAINING A POLYGON

The problem of finding the smallest circle that contains a given plane polygon comes from the research fields of machine hardware machining and computer graphics. A method applying Rosenbrock algorithm to find the smallest circle that contains a given plane polygon is put forward in this paper. For the smallest circle problem, the success or failure of searching extreme point by Rosenbrock algorithm depends on the choice of the initial point. This paper analyses the goal function condition near the initial point at which Rosenbrock algorithm failed to search the extreme point, and puts forward an improvement to Rosenbrock algorithm. That is to say, if searches by Rosenbrock algorithm along the directions of the initial standard orthogonal vectors at the initial point have no progress, let's rotate the initial standard orthogonal vectors to get new standard orthogonal vectors, and continue searching along the new standard orthogonal vectors at the initial point. Simulation experimental results verify that the improved Rosenbrock algorithm has better search effects.