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Ru ru (#292)
* ru-RU introduction Translation of introduction to Russian * ru-RU whatis Translation of chapter 2 to Russian * (fixup) ru-RU intro fixed missing translations * ru-RU index.html Translated header, meta, title and link names for existing chapter's traslations. (will be updated with every new commit) * . * locale fixup * build chapters 1,2 * npm start Co-authored-by: Mammoth <echo@mammothnotes.com>
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>A Primer on Bézier Curves - Curve-circle intersections</title>
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<title>A Primer on Bézier Curves - Curve-circle intersections</title>
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font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;
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<meta property="og:title" content="Curve-circle intersections" />
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<meta property="og:published_time" content="Sun Nov 22 2020 00:00:00 +00:00" />
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<meta property="og:updated_time" content="Fri Dec 25 2020 19:54:14 +00:00" />
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<meta property="og:author" content="Mike 'Pomax' Kamermans" />
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<link rel="stylesheet" href="style.css" />
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<!--
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<meta name="description" content="Curve-circle intersections" />
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<!-- opengraph information -->
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<meta property="og:title" content="Curve-circle intersections" />
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<meta property="og:image" content="https://pomax.github.io/bezierinfo/images/og-image.png" />
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<meta property="og:type" content="text" />
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<meta property="og:url" content="https://pomax.github.io/bezierinfo/news/2020-11-22.html" />
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<meta property="og:description" content="Curve-circle intersections" />
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<meta property="og:locale" content="en-GB" />
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<meta property="og:type" content="article" />
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<meta property="og:published_time" content="Sat Nov 21 2020 16:00:00 +00:00" />
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<meta property="og:updated_time" content="Fri Dec 25 2020 12:00:11 +00:00" />
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<meta property="og:author" content="Mike 'Pomax' Kamermans" />
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<meta property="og:section" content="Bézier Curves" />
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<meta property="og:tag" content="Bézier Curves" />
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<script src="./js/site/referrer.js" type="module" async></script>
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The part that makes interactive graphics work: an HTML5 <graphics-element> custom element.
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Note that we're not defering this: we just want it to kick in as soon as possible, and
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given how much HTML there is, that means this can, and thus should, kick in before the
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DEV PREVIEW ONLY
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(function () {
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DEV PREVIEW ONLY
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e.removeAttribute("style");
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</div>
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<div class="github">
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<img src="images/ribbon.png" alt="This page on GitHub" style="border: none;" usemap="#githubmap" width="200" height="149" />
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<area shape="poly" coords="30,0, 200,0, 200,114" href="http://github.com/pomax/BezierInfo-2" alt="This page on GitHub" />
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<img src="images/ribbon.png" alt="This page on GitHub" style="border:none;" useMap="#githubmap" width="200" height="149" />
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<header>
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<h1>Curve-circle intersections</h1>
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<h5 class="post-date">Sun, 22 Nov 2020</h5>
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<header>
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<h1>Curve-circle intersections</h1>
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<h5 class="post-date">Sun, 22 Nov 2020</h5>
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<p>
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While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing:
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circle/curve intersections. You'd think those were just an extension on the maths used for the other three, but unfortunately, this is not the
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case. Rather than using calculus, the only real way to determine where a polynomial curve intersects it is to sample the curve at a resolution
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high enough to find you intervals on the curve where there likely is an intersection, then refining that interval until you find actual
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intersections.
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</p>
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<p>
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It is, in fact, rather similar to <a href="https://pomax.github.io/bezierinfo/#projections">projecting a point onto a bezier curve</a> where
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the point is the circle's center, and where the projection distance actually needs to match the circle radius, so:
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<a href="https://pomax.github.io/bezierinfo/#circleintersection">let's see how to do that</a>!
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</p>
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<p>— <a href="https://twitter.com/TheRealPomax">Pomax</a></p>
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</main>
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<footer class="copyright">This post is a news entry for the <a href="https://pomax.github.io/bezierinfo/">Primer on Bézier Curves</a></footer>
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<p>While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: circle/curve intersections. You'd think those were just an extension on the maths used for the other three, but unfortunately, this is not the case. Rather than using calculus, the only real way to determine where a polynomial curve intersects it is to sample the curve at a resolution high enough to find you intervals on the curve where there likely is an intersection, then refining that interval until you find actual intersections.</p>
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<p>It is, in fact, rather similar to <a href="https://pomax.github.io/bezierinfo/#projections">projecting a point onto a bezier curve</a> where the point is the circle's center, and where the projection distance actually needs to match the circle radius, so: <a href="https://pomax.github.io/bezierinfo/#circleintersection">let's see how to do that</a>!</p>
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<p>— <a href="https://twitter.com/TheRealPomax">Pomax</a></p>
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</main>
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<hr>
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<footer class="copyright">
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This post is a news entry for the <a href="https://pomax.github.io/bezierinfo/">Primer on Bézier Curves</a>
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</footer>
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</body>
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</html>
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