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updated curve fitting 'revisiting' forumula

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Pomax
2021-07-11 09:50:12 -07:00
parent 30a62f93fa
commit 8ebd0d0d45
13 changed files with 3559 additions and 55 deletions
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6
docs/chapters/curvefitting/content.en-GB.md
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@@ -46,9 +46,9 @@ With that arrangement, we can easily decompose this as a matrix multiplication:
\begin{bmatrix}1 & t & t^2 \end{bmatrix}
\cdot
\begin{bmatrix}
a & 0 & 0 \\
-2a & 2b & 0 \\
a &-2b & c
a &+& 0 &+& 0 \\
-2a &+& 2b &+& 0 \\
a &+&-2b &+& c
\end{bmatrix}
=
\begin{bmatrix}1 & t & t^2 \end{bmatrix}

1
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docs/images/snippets/curvefitting/db85a7a46b869c892662c26b6aea15a1.ascii Normal file
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@@ -0,0 +1,5 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘

12
docs/index.html
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@@ -38,7 +38,7 @@
<meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2021-06-07T15:25:25+00:00" />
<meta property="og:updated_time" content="2021-07-11T16:48:57+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -6887,14 +6887,14 @@ findClosest(start, p, r, LUT):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
-->
<img
class="LaTeX SVG"
src="./images/chapters/curvefitting/134baa1043d0849f31a1943d6d5bc607.svg"
width="565px"
src="./images/chapters/curvefitting/db85a7a46b869c892662c26b6aea15a1.svg"
width="616px"
height="53px"
loading="lazy"
/>

12
docs/ja-JP/index.html
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@@ -41,7 +41,7 @@
<meta property="og:locale" content="ja-JP" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2021-06-07T15:25:25+00:00" />
<meta property="og:updated_time" content="2021-07-11T16:48:57+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -7053,14 +7053,14 @@ findClosest(start, p, r, LUT):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
-->
<img
class="LaTeX SVG"
src="./images/chapters/curvefitting/134baa1043d0849f31a1943d6d5bc607.svg"
width="565px"
src="./images/chapters/curvefitting/db85a7a46b869c892662c26b6aea15a1.svg"
width="616px"
height="53px"
loading="lazy"
/>

4
docs/news/2020-09-18.html
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@@ -33,8 +33,8 @@
<meta property="og:description" content="Rewriting the tech stack" />
<meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="Fri Sep 18 2020 00:00:00 +00:00" />
<meta property="og:updated_time" content="Mon Jun 07 2021 15:25:25 +00:00" />
<meta property="og:published_time" content="Thu Sep 17 2020 17:00:00 +00:00" />
<meta property="og:updated_time" content="Sun Jul 11 2021 09:48:57 +00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />

4
docs/news/2020-11-22.html
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@@ -33,8 +33,8 @@
<meta property="og:description" content="Curve-circle intersections" />
<meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="Sun Nov 22 2020 00:00:00 +00:00" />
<meta property="og:updated_time" content="Mon Jun 07 2021 15:25:25 +00:00" />
<meta property="og:published_time" content="Sat Nov 21 2020 16:00:00 +00:00" />
<meta property="og:updated_time" content="Sun Jul 11 2021 09:48:57 +00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />

2
docs/news/index.html
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@@ -33,7 +33,7 @@
<meta property="og:description" content="" />
<meta property="og:locale" content="en-GB" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="Mon Jun 07 2021 15:25:25 GMT+0000 (Coordinated Universal Time)" />
<meta property="og:published_time" content="Sun Jul 11 2021 09:48:57 GMT-0700 (Pacific Daylight Time)" />
<meta property="og:updated_time" content="" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<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>
<description>News updates for the <a href="https://pomax.github.io/bezierinfo">primer on Bézier Curves</a> by Pomax</description>
<language>en-GB</language>
<lastBuildDate>Mon Jun 07 2021 15:25:25 +00:00</lastBuildDate>
<lastBuildDate>Sun Jul 11 2021 09:48:57 +00:00</lastBuildDate>
<image>
<url>https://pomax.github.io/bezierinfo/images/og-image.png</url>
<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;
</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>
</item><item>
<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;
</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>
</item>
</channel>

12
docs/ru-RU/index.html
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@@ -34,7 +34,7 @@
<meta property="og:locale" content="ru-RU" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2021-06-07T15:25:25+00:00" />
<meta property="og:updated_time" content="2021-07-11T16:48:57+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -7210,14 +7210,14 @@ findClosest(start, p, r, LUT):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
-->
<img
class="LaTeX SVG"
src="./images/chapters/curvefitting/134baa1043d0849f31a1943d6d5bc607.svg"
width="565px"
src="./images/chapters/curvefitting/db85a7a46b869c892662c26b6aea15a1.svg"
width="616px"
height="53px"
loading="lazy"
/>

12
docs/uk-UA/index.html
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@@ -39,7 +39,7 @@
<meta property="og:locale" content="uk-UA" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2021-06-07T15:25:25+00:00" />
<meta property="og:updated_time" content="2021-07-11T16:48:57+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -7184,14 +7184,14 @@ findClosest(start, p, r, LUT):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
-->
<img
class="LaTeX SVG"
src="./images/chapters/curvefitting/134baa1043d0849f31a1943d6d5bc607.svg"
width="565px"
src="./images/chapters/curvefitting/db85a7a46b869c892662c26b6aea15a1.svg"
width="616px"
height="53px"
loading="lazy"
/>

12
docs/zh-CN/index.html
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@@ -41,7 +41,7 @@
<meta property="og:locale" content="zh-CN" />
<meta property="og:type" content="article" />
<meta property="og:published_time" content="2013-06-13T12:00:00+00:00" />
<meta property="og:updated_time" content="2021-06-07T15:25:25+00:00" />
<meta property="og:updated_time" content="2021-07-11T16:48:57+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -7029,14 +7029,14 @@ findClosest(start, p, r, LUT):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌ a 0 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a 2b 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a -2b c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
┌ a + 0 + 0 ┐ ┌ 1 0 0 ┐ ┌ a ┐
B = T · M · C = ┌ 2 ┐ · │ -2a + 2b + 0 │ = ┌ 2 ┐ · │ -2 2 0 │ · │ b │
quadratic └ 1 t t ┘ └ a + -2b + c ┘ └ 1 t t ┘ └ 1 -2 1 ┘ └ c ┘
-->
<img
class="LaTeX SVG"
src="./images/chapters/curvefitting/134baa1043d0849f31a1943d6d5bc607.svg"
width="565px"
src="./images/chapters/curvefitting/db85a7a46b869c892662c26b6aea15a1.svg"
width="616px"
height="53px"
loading="lazy"
/>

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