- F. Preparata, M. Shamos, D. Stieren, R. Veale, Joonsoo Choi. 2007. 8 Practical Considerations in Our Approach 7 Testing Software. Abstract: Navy coordinate measuring machines: a study of needs. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. A review of current geometric tolerancing theories and inspection data analysis algorithms. 9 CONCLUSION 13 error from data rounding and coding error remains. But as we noted, imperfect input data is not a problem of the algorithm but calls for algorithms diierent than those designed for \perfect data". As for coding error, we suggest that testing correctness of code is orders of magnitude easier with our exact algorithms than with traditional xed-precision algorithms. 9 Conclusion We propose to implement non-heuristic algorithms motivated by CG, using exact computational techniques. Most of the sources of uncertainty in current metrology will be abolished by our approach. No other approaches in the quest for reference softwares comes close to this guarantee. We also note that exact CG algorithms will also be useful in the larger picture of software testing. To highlight the problems of oating-point computation, recall the running example of computing the minimum annulus for a set of input points. It would seem that the closer the input points are to being co-circular (perfect form), the more devastating an error can be expected in a oating-point computation! We conclude with a parable 3 on the economic value of dimensional metrology. In the manufacture of the tops of aluminium soda cans, it is empirically established that their thickness must be at least 0.03 inch (otherwise, the cans might spontaneously explode) but no more than 0.07 inch (in order for the pop-top mechanism to work). Since the metrological uncertainty in measuring this thickness is 0.01 inch, these can tops are speciied to have a nominal thickness of 0.04 inch. Now, if we could reduce the metrological uncertainty by a further 0.001 inch, leading to a nominal thickness of 0.039 inch, the material savings would be $73 million per year. We call this a parable because the basic message does not depend on the literalness of these numbers. Acknowledgements We are greatly indebted to discussions with Vijay Srinivasan, Ted Hopp and Herb Voelcker, who inform us about the eld of tolerancing and metrology; to J urgen Sellen for his comments and feedback on this paper. 3 We are indebted to Ted Hopp as our source for this. 8 PRACTICAL CONSIDERATIONS IN OUR APPROACH 12 in manufactured discs), we can devise G to generate points taken …
