Abstract: In this paper we consider an approximation theoretic approach to the computer numerically controlled manufacturing of optical studies. Given the kinematic parameters defining a grinding/polishing tool, we develop an expression for the associated material removal rate. Knowing this, and assuming descriptions of the tool center path and speed, we can then derive a general formula for the amount of material removed at a point on the workpiece by the machine. The final phase of the analysis centers on the determination of strategies for tool center movement so as to achieve a desired pattern of material removal. We discuss two means of formulating such a strategy. The first involves the use of constrained best discrete L$-p$/ approximation problems, which for p $EQ 1,2 can be solved by linear and quadratic programming methods. The second employs the notion of a mollifier or smoothing function and avoids the need for discretization. The results of some computational experiments based on the above methods are included.!22
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