| The global optimization strategy of Simulated Annealing is applied to the optimization of weight and knot parameters of NURBS for curve fitting and surface fitting; the objective being the reduction of fitting error to obtain smooth curves and surfaces with the least cumulative error possible.; For weight optimization, a uniform knot vector and a fixed number of control points are calculated using the least squares technique, while the sum of squared errors is taken as the objective function. In knot optimization, the weight vector is set to unity. The number of elements of the weight vector is taken the same as the number of control points. A good initial solution of knot vector is taken. New knot vectors are calculated using the neighborhood function of the Simulated Annealing Algorithm.; Finally, results obtained from optimization of weights and knots of NURBS for both curves and surfaces indicate that weight optimization is a better option than knot optimization because knot optimization requires a good initial location of knot vector. |
