Minor wording improvement

Author: raphlinus

_posts/2023-04-18-bezpath-simplify.md

@@ -61,7 +61,7 @@ An extremely common approach is adaptive subdivision. Compute an approximation,
 
 Fancier techniques try to optimize the subdivision points to reduce the number of segments. That is equivalent to dividing the source curve into ranges such that each range is just barely below the threshold; ironically, it basically amounts to *maximizing* the error metric right up to the constraint.
 
-One technique is given in section 9.6.4 in my [thesis]. Basically you start on one end and for each segment find a subdivision point from the last point to one that's just barely under the error threshold. Under the assumption that errors are monotonic (which is not always going to be the case), this finds the global minimum number of segments needed. The last segment will have an error well below the threshold. Then, another search finds the minimum error for which this process yields the same number of segments. Again, if error is monotonic, the result is the Fréchet distance of all segments being equal, which is (at least roughly) equivalent to the overall Fréchet distance being minimized.
+One technique is given in section 9.6.4 of my [thesis]. Basically you start on one end and for each segment find a subdivision point from the last point to one that's just barely under the error threshold. Under the assumption that errors are monotonic (which is not always going to be the case), this finds the global minimum number of segments needed. The last segment will have an error well below the threshold. Then, another search finds the minimum error for which this process yields the same number of segments. Again, if error is monotonic, the result is the Fréchet distance of all segments being equal, which is (at least roughly) equivalent to the overall Fréchet distance being minimized.
 
 For smooth source curves, monotonic error is a reasonable assumption. Even so, the above technique seems to work fairly robustly, producing fewer segments than simple adaptive subdivision, though it is somewhere around 50x slower.