diff --git a/docs/chapters/projections/content.en-GB.md b/docs/chapters/projections/content.en-GB.md index b28a0f5f..d909afc8 100644 --- a/docs/chapters/projections/content.en-GB.md +++ b/docs/chapters/projections/content.en-GB.md @@ -15,7 +15,7 @@ for (coordinate, index) in LUT: i = index ``` -After this runs, we know that `LUT[i]` is the coordinate on the curve _in our LUT_ that is closest to the point we want to project, so that's a pretty good initial guess as to what the best projection onto our curve is. To refine it, we note that LUT[i] is a better guess than both LUT[i-1] and LUT[i+1], but there might be an even better projection _somewhere else_ between those two values, so that's what we're going to be testing for, using a variation of the binary search. +After this runs, we know that `LUT[i]` is the coordinate on the curve _in our LUT_ that is closest to the point we want to project, so that's a pretty good initial guess as to what the best projection onto our curve is. To refine it, we note that `LUT[i]` is a better guess than both `LUT[i-1]` and `LUT[i+1]`, but there might be an even better projection _somewhere else_ between those two values, so that's what we're going to be testing for, using a variation of the binary search. 1. we start with our point `p`, and the `t` values `t1=LUT[i-1].t` and `t2=LUT[i+1].t`, which span an interval `v = t2-t1`. 2. we test this interval in five spots: the start, middle, and end (which we already have), and the two points in between the middle and start/end points