Amy's Final Project
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Optimized Toolpath Generation
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After many daytrips down adjacent paths, this project finds a toolpath given a 2D shape described as vertices of a polyshape.
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At the heart of the project, I convert an ".svg" (Scalar Vector Graphics) polyshape to a set of inequalities.  Chained together, they are used for tool collision detection.  
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Evaluate real-time calc window by figuring out feed speed of machine and instr speed of micro.
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Given a 3-D surface and assumptions about tool speed and size, and acceptable variation from desired surface topology, what is the optimal path a ball-end tool should take to minimize machining time?
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<i>an aside</i> If can get active feedback from bit, want machine to dynamically recalculate toolpath to make final object more precise.
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Previous work (by others)
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Sarma, S., "The Crossing Function and its Application to Zig-Zag Tool Paths," Computer-Aided Design 31 (14), 881-890, 2000.
<p><i>This paper basically says that minimizing the number of switchbacks contributes significantly to shortening machining time.  The parameter to minimize was machining time.</i>
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Kim, T. and Sarma, S. E., "Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths," Computer Aided Design 34 (6), 453-468, May 2002. 
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<i>This paper basically utilizes material removed quantity as the minimized parameter.
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Formulating the problem:
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Problem statement: given a piece and given a desired output geometry...  generate a "smart" toolpath to generate output geometry
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Problem statement (in math): something like 
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<ul>f(x) = starting block 
<br>y(x) = desired geometry
<br>g = cost functions - say, number of direction changes
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Goodness measurement: time (also, toolpath length incl. z direction)
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Constraints: maximum depth of cut into material, x/y/z motion of tool, surface quality (?)
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Assumptions: single tool (no tool changes), "2.5D" machining (x,y,z motion only, tool axis does not change), constant tool movement speed in all axes
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