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Edits to arcapproximation section (#195)

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* Fix capitalization. Sentence with too many colons - use more interesting punctuation.

* Update content.en-GB.md

https://www.youtube.com/watch?v=M94ii6MVilw
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Simon Cozens
2019-06-11 01:45:24 +01:00
committed by Pomax
parent cab6924b4c
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components/sections/arcapproximation/content.en-GB.md
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@@ -46,4 +46,4 @@ With that in place, all that's left now is to "restart" the procedure by treatin
<Graphic title="Arc approximation of a Bézier curve" setup={this.setupCubic} draw={this.drawArcs} onKeyDown={this.props.onKeyDown} />
So... what is this good for? Obviously, If you're working with technologies that can't do curves, but can do lines and circles, then the answer is pretty straight-forward, but what else? There are some reasons why you might need this technique: using circular arcs means you can determine whether a coordinate lies "on" your curve really easily: simply compute the distance to each circular arc center, and if any of those are close to the arc radii, at an angle between the arc start and end: bingo, this point can be treated as lying "on the curve". Another benefit is that this approximation is "linear": you can almost trivially travel along the arcs at fixed speed. You can also trivially compute the arc length of the approximated curve (it's a bit like curve flattening). The only thing to bear in mind is that this is a lossy equivalence: things that you compute based on the approximation are guaranteed "off" by some small value, and depending on how much precision you need, arc approximation is either going to be super useful, or completely useless. It's up to you to decide which, based on your application!
So... what is this good for? Obviously, if you're working with technologies that can't do curves, but can do lines and circles, then the answer is pretty straightforward, but what else? There are some reasons why you might need this technique: using circular arcs means you can determine whether a coordinate lies "on" your curve really easily (simply compute the distance to each circular arc center, and if any of those are close to the arc radii, at an angle between the arc start and end, bingo, this point can be treated as lying "on the curve"). Another benefit is that this approximation is "linear": you can almost trivially travel along the arcs at fixed speed. You can also trivially compute the arc length of the approximated curve (it's a bit like curve flattening). The only thing to bear in mind is that this is a lossy equivalence: things that you compute based on the approximation are guaranteed "off" by some small value, and depending on how much precision you need, arc approximation is either going to be super useful, or completely useless. It's up to you to decide which, based on your application!