Abstract: 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.
Key words: Parametric
form Profile tolerance Linear error model Exchange algorithm
*
This
project is supported by National Natural Science Foundation of China
(No. 59990470). Received May 29, 2001; received in revised form October
16, 2001; accepted October 22, 2001
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