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7-animation/1-bezier-curve/article.md

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Bezier curves are used in computer graphics to draw shapes, for CSS animation and in many other places.
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They are actually a very simple thing, worth to study once and then feel comfortable in the world of vector graphics and advanced animations.
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They are a very simple thing, worth to study once and then feel comfortable in the world of vector graphics and advanced animations.
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## Control points
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[iframe src="demo.svg?p=0,0,1,1,0,1,1,0&animate=1" height=370]
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```online
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If there's anything unclear in the algorithm description, then live examples above show how
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If there's something unclear in the algorithm description, please look at the live examples above to see how
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the curve is built.
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```
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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.
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```smart header="How to draw a curve *through* given points?"
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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.
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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.
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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.
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We saw two definitions of Bezier curves:
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1. Using a mathematical formulas.
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2. Using a drawing process: De Casteljau's algorithm
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1. Using a drawing process: De Casteljau's algorithm.
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2. Using a mathematical formulas.
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Good properties of Bezier curves:
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- We can draw smooth lines with a mouse by moving around control points.
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- We can draw smooth lines with a mouse by moving control points.
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- Complex shapes can be made of several Bezier curves.
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Usage:

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