What are the best practices for evaluating the accuracy of computational geometry libraries and tools?

1 Error sources

When evaluating the accuracy of computational geometry libraries and tools, one of the first steps is to identify the possible sources of errors that can affect their performance and output. These sources can include numerical errors, such as rounding, overflow, underflow, and truncation; algorithmic errors resulting from bugs, logical flaws, incorrect assumptions, or limitations of the chosen methods; and input errors stemming from the quality, format, or validity of the input data. These errors can cause significant deviations from expected results, incorrect or incomplete solutions, or unexpected behaviors or exceptions.

2 Error measures

When evaluating the accuracy of computational geometry libraries and tools, it is important to define and apply appropriate error measures to quantify and compare the performance and output of the software. Absolute error, for example, is the difference between the exact or expected value and the computed or observed value, and can be used to measure the accuracy of a single result or output. Relative error is the ratio of the absolute error to the exact or expected value, and can be used to measure accuracy relative to magnitude or scale. Root mean square error (RMSE) is the square root of the average of the squared absolute errors, and can be used to measure accuracy of a set of results or outputs. Lastly, Hausdorff distance is the maximum distance between two sets of points, such as two curves or two surfaces, which can be used to measure accuracy of a shape or region.

3 Error analysis

The final step in evaluating the accuracy of computational geometry libraries and tools is to perform an error analysis that can reveal the causes, effects, and patterns of the errors observed in the software. To do this, testing, debugging, and benchmarking are all necessary methods. Testing involves applying the libraries and tools to a set of input data and verifying the correctness and reliability of the output data. Debugging is used to identify and fix errors that occur during development or testing. Benchmarking compares the performance and output of the libraries and tools to other software or standards. By using these best practices, you can evaluate the accuracy of computational geometry libraries and tools, ensuring you choose the most suitable and reliable software for your problem domain and application.

4 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?