[simplify] Tweaks to simplification blog post

Author: raphlinus

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

@@ -87,9 +87,9 @@ This state of affairs is not acceptable in most applications. It is evidence tha
 
 ![Figure 9.2 from the thesis: Two circle approximations with equal distance error](/assets/simplify-distance-error.png)
 
-Given that aggressively optimizing Fréchet may undesirable results, what is to be done? The most systematic approach would be to design an error metric that takes both distance and angle into account, and calibrate it to correlate strongly with perception. That is perhaps a tall order, requiring research to properly establish tuning parameters, and likely with complexity and runtime performance implications to evaluate. Even so, I think it should be pursued.
+Given that aggressively optimizing Fréchet may give undesirable results, what is to be done? The most systematic approach would be to design an error metric that takes both distance and angle into account, and calibrate it to correlate strongly with perception. That is perhaps a tall order, requiring research to properly establish tuning parameters, and likely with complexity and runtime performance implications to evaluate. Even so, I think it should be pursued.
 
-A simpler approach, implemented in the current code, is to recognize that these bumpy cubic Béziers can be recognized by their parameters; when the distance from the endpoints to the control points roughly equal to the distance between endpoints, then curves can have cusps or nearly so. These are the δ values from the core quartic-based curve fitting solver; a simple approach would be to simply exclude curves with δ values greater than some threshold (0.85 works well), and this also improves performance by decreasing the number of error evaluations needed, but a more sophisticated approach is to multiply the error by a penalty factor for larger δ. One advantage of the latter approach is that it is still possible to fit every actual exact Bézier input. 
+A simpler approach, implemented in the current code, is to recognize that these bumpy cubic Béziers can be recognized by their parameters; when the distance from the endpoints to the control points roughly equal to the chord length, then curves can have cusps or nearly so. These are the δ values from the core quartic-based curve fitting solver; a simple approach would be to simply exclude curves with δ values greater than some threshold (0.85 works well), and this also improves performance by decreasing the number of error evaluations needed, but a more sophisticated approach is to multiply the error by a penalty factor for larger δ. One advantage of the latter approach is that it is still possible to fit every actual exact Bézier input.
 
 Applying this tweak gives a much smoother result, though it does require one more segment (44 rather than 43 previously).