diff --git a/7-animation/1-bezier-curve/article.md b/7-animation/1-bezier-curve/article.md index 6166f25c..4a806514 100644 --- a/7-animation/1-bezier-curve/article.md +++ b/7-animation/1-bezier-curve/article.md @@ -2,7 +2,7 @@ Bezier curves are used in computer graphics to draw shapes, for CSS animation and in many other places. -They are actually a very simple thing, worth to study once and then feel comfortable in the world of vector graphics and advanced animations. +They are a very simple thing, worth to study once and then feel comfortable in the world of vector graphics and advanced animations. ## Control points @@ -130,14 +130,14 @@ A non-smooth Bezier curve (yeah, that's possible too): [iframe src="demo.svg?p=0,0,1,1,0,1,1,0&animate=1" height=370] ```online -If there's anything unclear in the algorithm description, then live examples above show how +If there's something unclear in the algorithm description, please look at the live examples above to see how the curve is built. ``` As the algorithm is recursive, we can build Bezier curves of any order, that is: using 5, 6 or more control points. But in practice many points are less useful. Usually we take 2-3 points, and for complex lines glue several curves together. That's simpler to develop and calculate. ```smart header="How to draw a curve *through* given points?" -We use control points for a Bezier curve. As we can see, they are not on the curve, except the first and the last ones. +To specify a Bezier curve, control points are used. As we can see, they are not on the curve, except the first and the last ones. Sometimes we have another task: to draw a curve *through several points*, so that all of them are on a single smooth curve. That task is called [interpolation](https://en.wikipedia.org/wiki/Interpolation), and here we don't cover it. @@ -186,12 +186,12 @@ Bezier curves are defined by their control points. We saw two definitions of Bezier curves: -1. Using a mathematical formulas. -2. Using a drawing process: De Casteljau's algorithm +1. Using a drawing process: De Casteljau's algorithm. +2. Using a mathematical formulas. Good properties of Bezier curves: -- We can draw smooth lines with a mouse by moving around control points. +- We can draw smooth lines with a mouse by moving control points. - Complex shapes can be made of several Bezier curves. Usage: