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2023-07-24 09:18:56 -07:00
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commit edfe2daf50
10 changed files with 2639 additions and 2471 deletions
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<meta property="og:locale" content="ja-JP" /> <meta property="og:locale" content="ja-JP" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" /> <meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2023-06-05T00:41:07+00:00" /> <meta property="og:updated_time" content="2023-07-24T16:16:38+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" /> <meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" /> <meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" /> <meta property="og:tag" content="Bézier Curves" />
@@ -194,7 +194,7 @@
<br style="clear: both;" /> <br style="clear: both;" />
<p>— <a href="https://twitter.com/TheRealPomax">Pomax</a></p> <p>— <a href="https://mastodon.social/@TheRealPomax">Pomax</a></p>
<noscript> <noscript>
<div class="note"> <div class="note">
<header> <header>

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<meta property="og:description" content="Rewriting the tech stack" /> <meta property="og:description" content="Rewriting the tech stack" />
<meta property="og:locale" content="en-GB" /> <meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:published_time" content="Fri Sep 18 2020 00:00:00 +00:00" /> <meta property="og:published_time" content="Thu Sep 17 2020 17:00:00 +00:00" />
<meta property="og:updated_time" content="Mon Jun 05 2023 00:41:07 +00:00" /> <meta property="og:updated_time" content="Mon Jul 24 2023 09:16:38 +00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" /> <meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" /> <meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" /> <meta property="og:tag" content="Bézier Curves" />
@@ -176,15 +176,15 @@
</ul> </ul>
<blockquote> <blockquote>
<!-- <!--
__ n=3 n-k k __ n=3 n-k k
B(t) = ❯ \ P \binomnk(1-t) t B(t) = ❯ \ P \binomnk(1-t) t
cubic ‾‾ k=0 cubic ‾‾ k=0
k k
3 2 2 3 3 2 2 3
= P (1-t) + 3 P (1-t) t + 3P (1-t)t + P t = P (1-t) + 3 P (1-t) t + 3P (1-t)t + P t
0 1 2 3 0 1 2 3
--> -->
<img class="LaTeX SVG" src="./images/news/2020-09-18.html/15225da473048d8c7b5b473b89de0b66.svg" width="401px" height="97px" loading="lazy" /> <img class="LaTeX SVG" src="./images/news/2020-09-18.html/15225da473048d8c7b5b473b89de0b66.svg" width="401px" height="97px" loading="lazy" />
@@ -271,7 +271,7 @@ draw() {
<a href="https://github.com/Pomax/BezierInfo-2/issues">you know where to go</a>. <a href="https://github.com/Pomax/BezierInfo-2/issues">you know where to go</a>.
</p> </p>
<p>See you in the next post!</p> <p>See you in the next post!</p>
<p>— <a href="https://mastodon.social/@TheRealPomaxTheRealPomax">Pomax</a></p> <p>— <a href="https://mastodon.social/@TheRealPomax">Pomax</a></p>
</main> </main>
<hr /> <hr />

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<meta property="og:description" content="Curve-circle intersections" /> <meta property="og:description" content="Curve-circle intersections" />
<meta property="og:locale" content="en-GB" /> <meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:published_time" content="Sun Nov 22 2020 00:00:00 +00:00" /> <meta property="og:published_time" content="Sat Nov 21 2020 16:00:00 +00:00" />
<meta property="og:updated_time" content="Mon Jun 05 2023 00:41:07 +00:00" /> <meta property="og:updated_time" content="Mon Jul 24 2023 09:16:38 +00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" /> <meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" /> <meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" /> <meta property="og:tag" content="Bézier Curves" />

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<meta property="og:description" content="" /> <meta property="og:description" content="" />
<meta property="og:locale" content="en-GB" /> <meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" /> <meta property="og:type" content="article" />
<meta property="og:published_time" content="Mon Jun 05 2023 00:41:07 GMT+0000 (Coordinated Universal Time)" /> <meta property="og:published_time" content="Mon Jul 24 2023 09:16:38 GMT-0700 (Pacific Daylight Time)" />
<meta property="og:updated_time" content="" /> <meta property="og:updated_time" content="" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" /> <meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" /> <meta property="og:section" content="Bézier Curves" />

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@@ -6,7 +6,7 @@
<atom:link href="https://pomax.github.io/bezierinfo" rel="self"></atom:link> <atom:link href="https://pomax.github.io/bezierinfo" rel="self"></atom:link>
<description>News updates for the <a href="https://pomax.github.io/bezierinfo">primer on Bézier Curves</a> by Pomax</description> <description>News updates for the <a href="https://pomax.github.io/bezierinfo">primer on Bézier Curves</a> by Pomax</description>
<language>en-GB</language> <language>en-GB</language>
<lastBuildDate>Mon Jun 05 2023 00:41:07 +00:00</lastBuildDate> <lastBuildDate>Mon Jul 24 2023 09:16:38 +00:00</lastBuildDate>
<image> <image>
<url>https://pomax.github.io/bezierinfo/images/og-image.png</url> <url>https://pomax.github.io/bezierinfo/images/og-image.png</url>
<title>A Primer on Bézier Curves</title> <title>A Primer on Bézier Curves</title>
@@ -17,19 +17,19 @@
<title>Curve-circle intersections</title> <title>Curve-circle intersections</title>
<link>https://pomax.github.io/bezierinfo/news/2020-11-22.html</link> <link>https://pomax.github.io/bezierinfo/news/2020-11-22.html</link>
<description> <description>
&lt;p&gt;While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: circle/curve intersections. You&#39;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.&lt;/p&gt; &lt;p&gt;While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: circle/curve intersections. You&#39;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.&lt;/p&gt;
&lt;p&gt;It is, in fact, rather similar to &lt;a href=&quot;https://pomax.github.io/bezierinfo/#projections&quot;&gt;projecting a point onto a bezier curve&lt;/a&gt; where the point is the circle&#39;s center, and where the projection distance actually needs to match the circle radius, so: &lt;a href=&quot;https://pomax.github.io/bezierinfo/#circleintersection&quot;&gt;let&#39;s see how to do that&lt;/a&gt;!&lt;/p&gt; &lt;p&gt;It is, in fact, rather similar to &lt;a href=&quot;https://pomax.github.io/bezierinfo/#projections&quot;&gt;projecting a point onto a bezier curve&lt;/a&gt; where the point is the circle&#39;s center, and where the projection distance actually needs to match the circle radius, so: &lt;a href=&quot;https://pomax.github.io/bezierinfo/#circleintersection&quot;&gt;let&#39;s see how to do that&lt;/a&gt;!&lt;/p&gt;
&lt;p&gt;— &lt;a href=&quot;https://mastodon.social/@TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt; &lt;p&gt;— &lt;a href=&quot;https://mastodon.social/@TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt;
</description> </description>
<pubDate>Sun Nov 22 2020 00:00:00 +00:00</pubDate> <pubDate>Sat Nov 21 2020 16:00:00 +00:00</pubDate>
<guid>2020-11-22.html</guid> <guid>2020-11-22.html</guid>
</item><item> </item><item>
<title>Rewriting the tech stack</title> <title>Rewriting the tech stack</title>
<link>https://pomax.github.io/bezierinfo/news/2020-09-18.html</link> <link>https://pomax.github.io/bezierinfo/news/2020-09-18.html</link>
<description> <description>
&lt;p&gt;Once upon a time, I needed to draw some Bezier curves because I was trying to create a Japanese kanji composition system that turned strokes into outlines, and that required knowing how to offset Bezier curves and... at the time (2011, time flies) there was no good single source of information for Bezier curves on the web. So I made one. Sure it started small, but it turns out that if you just keep adding bits to something, several years later you have quite the monster, and a single HTML file becomes intractible.&lt;/p&gt; &lt;p&gt;Once upon a time, I needed to draw some Bezier curves because I was trying to create a Japanese kanji composition system that turned strokes into outlines, and that required knowing how to offset Bezier curves and... at the time (2011, time flies) there was no good single source of information for Bezier curves on the web. So I made one. Sure it started small, but it turns out that if you just keep adding bits to something, several years later you have quite the monster, and a single HTML file becomes intractible.&lt;/p&gt;
&lt;p&gt;So, in 2016, when &lt;a href=&quot;https://reactjs.org/&quot;&gt;React.js&lt;/a&gt; exploded onto the scene, I rewrote the primer as a React app, and it became a lot easier to maintain. Like, &lt;em&gt;a lot&lt;/em&gt; a lot. However, there was a downside: no JS meant no content. Sure, server-side rendering sort of existed, but not really, and because the Primer is hosted through github, there was no &quot;server&quot; to run. Plus, trying to rehydrate an app the size of the Primer from a giant HTML file had truly &lt;em&gt;dire&lt;/em&gt; performance.&lt;/p&gt; &lt;p&gt;So, in 2016, when &lt;a href=&quot;https://reactjs.org/&quot;&gt;React.js&lt;/a&gt; exploded onto the scene, I rewrote the primer as a React app, and it became a lot easier to maintain. Like, &lt;em&gt;a lot&lt;/em&gt; a lot. However, there was a downside: no JS meant no content. Sure, server-side rendering sort of existed, but not really, and because the Primer is hosted through github, there was no &quot;server&quot; to run. Plus, trying to rehydrate an app the size of the Primer from a giant HTML file had truly &lt;em&gt;dire&lt;/em&gt; performance.&lt;/p&gt;
&lt;p&gt;So I left it a regular React app, and every time I thought &quot;wouldn&#39;t it be nice if it was just... a web page again?&quot; the browser landscape just hadn&#39;t caught up. Finally, in 2020, things are different: with a global pandemic, and some vacation time, and something random causing me to look up the state of HTML custom elements, everything was pointing at it being time to finally, &lt;em&gt;finally&lt;/em&gt;, turn the Primer back into a normal web page.&lt;/p&gt; &lt;p&gt;So I left it a regular React app, and every time I thought &quot;wouldn&#39;t it be nice if it was just... a web page again?&quot; the browser landscape just hadn&#39;t caught up. Finally, in 2020, things are different: with a global pandemic, and some vacation time, and something random causing me to look up the state of HTML custom elements, everything was pointing at it being time to finally, &lt;em&gt;finally&lt;/em&gt;, turn the Primer back into a normal web page.&lt;/p&gt;
@@ -57,15 +57,15 @@
&lt;/ul&gt; &lt;/ul&gt;
&lt;blockquote&gt; &lt;blockquote&gt;
&lt;!-- &lt;!--
__ n=3 n-k k __ n=3 n-k k
B(t) = ❯ \ P \binomnk(1-t) t B(t) = ❯ \ P \binomnk(1-t) t
cubic ‾‾ k=0 cubic ‾‾ k=0
k k
3 2 2 3 3 2 2 3
= P (1-t) + 3 P (1-t) t + 3P (1-t)t + P t = P (1-t) + 3 P (1-t) t + 3P (1-t)t + P t
0 1 2 3 0 1 2 3
--&gt; --&gt;
&lt;img class=&quot;LaTeX SVG&quot; src=&quot;./images/news/2020-09-18.html/15225da473048d8c7b5b473b89de0b66.svg&quot; width=&quot;401px&quot; height=&quot;97px&quot; loading=&quot;lazy&quot;&gt; &lt;img class=&quot;LaTeX SVG&quot; src=&quot;./images/news/2020-09-18.html/15225da473048d8c7b5b473b89de0b66.svg&quot; width=&quot;401px&quot; height=&quot;97px&quot; loading=&quot;lazy&quot;&gt;
@@ -105,7 +105,7 @@ draw() {
&lt;tr&gt;&lt;td&gt;11&lt;/td&gt;&lt;/tr&gt; &lt;tr&gt;&lt;td&gt;11&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;12&lt;/td&gt;&lt;/tr&gt; &lt;tr&gt;&lt;td&gt;12&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td&gt;13&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt; &lt;tr&gt;&lt;td&gt;13&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
&lt;ul&gt; &lt;ul&gt;
&lt;li&gt;Responsive CSS, so the content intelligently reflows where possible.&lt;/li&gt; &lt;li&gt;Responsive CSS, so the content intelligently reflows where possible.&lt;/li&gt;
&lt;li&gt;A &quot;Live build&quot; setup for working on the content and code.&lt;/li&gt; &lt;li&gt;A &quot;Live build&quot; setup for working on the content and code.&lt;/li&gt;
@@ -118,7 +118,7 @@ draw() {
&lt;p&gt;— &lt;a href=&quot;https://mastodon.social/@TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt; &lt;p&gt;— &lt;a href=&quot;https://mastodon.social/@TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt;
</description> </description>
<pubDate>Fri Sep 18 2020 00:00:00 +00:00</pubDate> <pubDate>Thu Sep 17 2020 17:00:00 +00:00</pubDate>
<guid>2020-09-18.html</guid> <guid>2020-09-18.html</guid>
</item> </item>
</channel> </channel>

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