Comment 4 for bug 1421392

    There is an analytical explanation for the round-off error. If we monitor the usage of the routine sp_svg_write_path, in svg-path.cpp, which is responsible for writing data to XML, then we see that the routine is called four times during the creation of a single Bezier path. The first two calls produce data in units of px and the second two produce data in units of mm. Each of these calls involves truncation of the data to the precision specified in the preference value for SVG Output Numeric Precision, normally 8. The problem with this truncation is that it uses the total number of digits both before and after the decimal point, and the number of digits before the decimal point may be different (less) after the unit conversion from px to mm has occurred. Therefore the level of precision required in the converted number (in mm) may be higher than the precision required in the original data (in px). This leads to two classes of data, those which have the same number of leading digits before and after conversion, where we do not anticipate any round-off error problems, and those which have fewer digits before the decimal point after unit conversion, where we have a significant statistical likelihood of encountering round-off error.
    This is illustrated in the attached diagram. The green areas are areas where the unit conversion does not change the number of leading digits. The red areas are areas where a change occurs in both x and y. Snapping a line randomly between and within the green areas does not lead to round-off error, while snapping a line randomly within the red area leads to a high probability of error. In the red area the probability of success, namely that a particular x value or y value will not have error, can be predicted to be s/10, where s is the conversion factor from mm to px, namely 96/25.4. This leads to a probability of success = 38% in the red areas.
    The way to avoid this problem would be to prevent the writing, and truncation, of the original px data to XML, however I don't know how to do that.