From 8989cee2c600d37b9d43e58fb58f34472d3ac2a6 Mon Sep 17 00:00:00 2001 From: Simon Cozens Date: Tue, 11 Jun 2019 01:05:37 +0100 Subject: [PATCH] Edits to de Casteljau section. (#182) * Edits to de Casteljau section. * Update content.en-GB.md --- components/sections/decasteljau/content.en-GB.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/components/sections/decasteljau/content.en-GB.md b/components/sections/decasteljau/content.en-GB.md index 04f87bae..fd1dc75f 100644 --- a/components/sections/decasteljau/content.en-GB.md +++ b/components/sections/decasteljau/content.en-GB.md @@ -1,6 +1,6 @@ # de Casteljau's algorithm -If we want to draw Bézier curves we can run through all values of `t` from 0 to 1 and then compute the weighted basis function, getting the `x/y` values we need to plot, but the more complex the curve gets, the more expensive this becomes. Instead, we can use "de Casteljau's algorithm" to draw curves, which is a geometric approach to drawing curves, and really easy to implement. So easy, in fact, you can do it by hand with a pencil and ruler. +If we want to draw Bézier curves, we can run through all values of `t` from 0 to 1 and then compute the weighted basis function at each value, getting the `x/y` values we need to plot. Unfortunately, the more complex the curve gets, the more expensive this computation becomes. Instead, we can use *de Casteljau's algorithm* to draw curves. This is a geometric approach to curve drawing, and it's really easy to implement. So easy, in fact, you can do it by hand with a pencil and ruler. Rather than using our calculus function to find `x/y` values for `t`, let's do this instead: @@ -10,8 +10,8 @@ Rather than using our calculus function to find `x/y` values for `t`, let's do t - Now form lines between `those` points. This gives `n-1` lines. - Place markers along each of these line at distance `t`. - Form lines between `those` points. This'll be `n-2` lines. -- place markers, form lines, place markers, etc. -- repeat this until you have only one line left. The point `t` on that line coincides with the original curve point at `t`. +- Place markers, form lines, place markers, etc. +- Repeat this until you have only one line left. The point `t` on that line coincides with the original curve point at `t`.