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2021-08-30 15:13:19 -07:00
parent e763f3b966
commit d257a563f7
32 changed files with 117 additions and 207 deletions
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - start
│ 1
│ C = start + ───────────
╡ 1 t
│ v - end
│ 2
│ C = end + ─────────
╰ 2 1 - t

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t

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@@ -1,7 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3
(1-t)
u(t) = ───────────
cubic 3 3
t + (1-t)

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@@ -1,10 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - start
│ 1
│ C '= start + ───────────
╡ 1 t
│ v - end
│ 2
│ C '= end + ─────────
╰ 2 1 - t

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@@ -1,10 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ A - e
│ 1
│ v = A - ──────
╡ 1 1 - t
│ A - e
│ 2
│ v = A - ──────
╰ 2 t

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@@ -1,4 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
C = u(t) · P + (1-u(t)) · P
start end

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@@ -1,10 +1,10 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t

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@@ -1,5 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
distance(B,C)
ratio(t) = ───────────── = Constant
distance(A,B)

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@@ -1,5 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
C - B B - C
A = B - ──────── = B + ────────
ratio(t) ratio(t)

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@@ -1,7 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3 3
t + (1-t) - 1
ratio(t) = |───────────────|
cubic 3 3
t + (1-t)

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@@ -1,7 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2
(1-t)
u(t) = ───────────
quadratic 2 2
t + (1-t)

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@@ -1,10 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - start
│ 1
│ C '= start + ──────────
╡ 1 t
│ v - end
│ 2
│ C '= end + ────────
╰ 2 1 - t

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@@ -1,10 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ A' - e
│ 1
│ v = A' - ───────
╡ 1 1 - t
│ A' - e
│ 2
│ v = A' - ───────
╰ 2 t

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@@ -1,7 +0,0 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2 2
t + (1-t) - 1
ratio(t) = |───────────────|
quadratic 2 2
t + (1-t)

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@@ -38,7 +38,7 @@
<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="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="2021-08-30T21:59:19+00:00" /> <meta property="og:updated_time" content="2021-08-30T22:10:17+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" />
@@ -6120,28 +6120,28 @@ lli = function(line1, line2):
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" />
<p>And then reverse engineer the curve's control points:</p> <p>And then reverse engineer the curve's control points:</p>
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" />
<p> <p>

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@@ -41,7 +41,7 @@
<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="2021-08-30T21:59:19+00:00" /> <meta property="og:updated_time" content="2021-08-30T22:10:17+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" />
@@ -6235,28 +6235,28 @@ lli = function(line1, line2):
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" />
<p>And then reverse engineer the curve's control points:</p> <p>And then reverse engineer the curve's control points:</p>
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" />
<p> <p>

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@@ -33,8 +33,8 @@
<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 Aug 30 2021 21:59:19 +00:00" /> <meta property="og:updated_time" content="Mon Aug 30 2021 15:10:17 +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" />

4
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@@ -33,8 +33,8 @@
<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 Aug 30 2021 21:59:19 +00:00" /> <meta property="og:updated_time" content="Mon Aug 30 2021 15:10:17 +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" />

2
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@@ -33,7 +33,7 @@
<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 Aug 30 2021 21:59:19 GMT+0000 (Coordinated Universal Time)" /> <meta property="og:published_time" content="Mon Aug 30 2021 15:10:17 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" />

6
docs/news/rss.xml
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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 Aug 30 2021 21:59:19 +00:00</lastBuildDate> <lastBuildDate>Mon Aug 30 2021 15:10:17 +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>
@@ -23,7 +23,7 @@
&lt;p&gt;— &lt;a href=&quot;https://twitter.com/TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt; &lt;p&gt;— &lt;a href=&quot;https://twitter.com/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>
@@ -119,7 +119,7 @@ draw() {
&lt;p&gt;— &lt;a href=&quot;https://twitter.com/TheRealPomax&quot;&gt;Pomax&lt;/a&gt;&lt;/p&gt; &lt;p&gt;— &lt;a href=&quot;https://twitter.com/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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@@ -34,7 +34,7 @@
<meta property="og:locale" content="ru-RU" /> <meta property="og:locale" content="ru-RU" />
<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="2021-08-30T21:59:19+00:00" /> <meta property="og:updated_time" content="2021-08-30T22:10:17+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" />
@@ -6392,28 +6392,28 @@ lli = function(line1, line2):
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" />
<p>And then reverse engineer the curve's control points:</p> <p>And then reverse engineer the curve's control points:</p>
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" />
<p> <p>

34
docs/uk-UA/index.html generated
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@@ -39,7 +39,7 @@
<meta property="og:locale" content="uk-UA" /> <meta property="og:locale" content="uk-UA" />
<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="2021-08-30T21:59:19+00:00" /> <meta property="og:updated_time" content="2021-08-30T22:10:17+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" />
@@ -6368,28 +6368,28 @@ lli = function(line1, line2):
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" />
<p>And then reverse engineer the curve's control points:</p> <p>And then reverse engineer the curve's control points:</p>
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" />
<p> <p>

34
docs/zh-CN/index.html generated
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@@ -41,7 +41,7 @@
<meta property="og:locale" content="zh-CN" /> <meta property="og:locale" content="zh-CN" />
<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="2021-08-30T21:59:19+00:00" /> <meta property="og:updated_time" content="2021-08-30T22:10:17+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" />
@@ -6211,28 +6211,28 @@ lli = function(line1, line2):
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ e - t · A ╭ e - t · A
│ 1 │ 1
╭ e = (1-t) · v + t · A │ v = ─────────── ╭ e = (1-t) · v + t · A │ v = ───────────
╡ 1 1 \Rightarrow ╡ 1 1-t ╡ 1 1 ==> ╡ 1 1-t
│ e = (1-t) · A + t · v │ e - (1-t) · A │ e = (1-t) · A + t · v │ e - (1-t) · A
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ v = ─────────────── │ v = ───────────────
╰ 2 t ╰ 2 t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/3166afa345aec1abda432c39b68d39a0.svg" width="339px" height="73px" loading="lazy" />
<p>And then reverse engineer the curve's control points:</p> <p>And then reverse engineer the curve's control points:</p>
<!-- <!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math \setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ v - (1-t) · start ╭ v - (1-t) · start
│ 1 │ 1
╭ v = (1-t) · start + t · C │ C = ──────────────────── ╭ v = (1-t) · start + t · C │ C = ────────────────────
╡ 1 1 \Rightarrow ╡ 1 t ╡ 1 1 ==> ╡ 1 t
│ v = (1-t) · C + t · end │ v - t · end │ v = (1-t) · C + t · end │ v - t · end
╰ 2 2 │ 2 ╰ 2 2 │ 2
│ C = ────────────── │ C = ──────────────
╰ 2 1-t ╰ 2 1-t
--> -->
<img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" /> <img class="LaTeX SVG" src="./images/chapters/abc/8bd3e6fed5bf8d871d30221ae400fd93.svg" width="383px" height="75px" loading="lazy" />
<p> <p>

6
src/tex2utf/tex2utf.pl vendored
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@@ -2134,6 +2134,12 @@ $contents{"\\rightarrow"}=" ──> ";
$type{"\\leftarrow"}="string"; $type{"\\leftarrow"}="string";
$contents{"\\leftarrow"}=" <── "; $contents{"\\leftarrow"}=" <── ";
$type{"\\Rightarrow"}="string";
$contents{"\\Rightarrow"}=" ==> ";
$type{"\\Leftarrow"}="string";
$contents{"\\Leftarrow"}=" <== ";
$type{"\\mapsto"}="string"; $type{"\\mapsto"}="string";
$contents{"\\mapsto"}=" ├──> "; $contents{"\\mapsto"}=" ├──> ";