PROFILE TOLERANCE EVALUATION OF PARAMETRIC CURVES AND SURFACES

The profile error evaluation of complex curves and surfaces expressed in parametric form is considered. The linear error model is established on the base of two hypotheses firstly. Then the profile error evaluation is converted into one of these optimal formulations:MINIMAX, MAXMIN and MINIDEX problems, which are easier to be solved than the initial form. To each one of them, geometric condition and algebraic condition are presented to arbitrate whether the ideal element reaches to the optimal position. Exchange algorithm is proven highly effective in searching for solutions to these optimization problems. At last some key problems in tolerance evaluation of freeform surfaces and curves in B spline method are discussed.