From 43973e9bb33ff693dfdc7a254a05a40d9e7d5deb Mon Sep 17 00:00:00 2001 From: Steve Nicholson Date: Wed, 18 Nov 2020 07:50:57 -0800 Subject: [PATCH] Fix typos (#282) --- docs/chapters/tracing/content.en-GB.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/chapters/tracing/content.en-GB.md b/docs/chapters/tracing/content.en-GB.md index 1c502746..18833ed2 100644 --- a/docs/chapters/tracing/content.en-GB.md +++ b/docs/chapters/tracing/content.en-GB.md @@ -4,9 +4,9 @@ Say you want to draw a curve with a dashed line, rather than a solid line, or yo Now you have a problem. -The reason you have a problem is that Bézier curves are parametric functions with non-linear behaviour, whereas moving a train along a track is about as close to a practical example of linear behaviour as you can get. The problem we're faced with is that we can't just pick `t` values at some fixed interval and expect the Bézier functions to generate points that are spaced a fixed distance apart. In fact, let's look at the relation between "distance long a curve" and "`t` value", by plotting them against one another. +The reason you have a problem is that Bézier curves are parametric functions with non-linear behaviour, whereas moving a train along a track is about as close to a practical example of linear behaviour as you can get. The problem we're faced with is that we can't just pick `t` values at some fixed interval and expect the Bézier functions to generate points that are spaced a fixed distance apart. In fact, let's look at the relation between "distance along a curve" and "`t` value", by plotting them against one another. -The following graphic shows a particularly illustrative curve, and it's distance-for-t plot. For linear traversal, this line needs to be straight, running from (0,0) to (length,1). That is, it's safe to say, not what we'll see: we'll see something very wobbly, instead. To make matters even worse, the distance-for-t function is also of a much higher order than our curve is: while the curve we're using for this exercise is a cubic curve, which can switch concave/convex form twice at best, the distance function is our old friend the arc length function, which can have more inflection points. +The following graphic shows a particularly illustrative curve, and its distance-for-t plot. For linear traversal, this line needs to be straight, running from (0,0) to (length,1). That is, it's safe to say, not what we'll see: we'll see something very wobbly, instead. To make matters even worse, the distance-for-t function is also of a much higher order than our curve is: while the curve we're using for this exercise is a cubic curve, which can switch concave/convex form twice at best, the distance function is our old friend the arc length function, which can have more inflection points.