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@@ -0,0 +1,10 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
P = (1, 0)
1
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
P = (cos(θ), sin(θ))
4

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docs/images/snippets/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.ascii Normal file
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@@ -0,0 +1,24 @@
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
3k + 4sin(θ)) - 3k · cos(θ)= 8sin│ ─ │
╰ 2 ╯
╭ θ ╮
3k - 3k · cos(θ)= 8sin│ ─ │ - 4sin(θ)
╰ 2 ╯
╭ ╭ θ ╮ ╮
3k (1 - cos(θ))= 4 │ 2sin│ ─ │ - sin(θ) │
╰ ╰ 2 ╯ ╯
θ
2sin(─) - sin(θ)
2
3k= 4 · ────────────────
1 - cos(θ)
╭ θ ╮
2sin│ ─ │ - sin(θ)
4 ╰ 2 ╯
k= ─ · ──────────────────
3 1 - cos(θ)

18
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="2021-04-19T18:35:47+00:00" />
<meta property="og:updated_time" content="2021-06-05T23:23:15+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -8789,7 +8789,7 @@ for p = 1 to points.length-3 (inclusive):
P = (1, 0)
1
P = (1, c)
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
@@ -8798,7 +8798,7 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
width="208px"
height="85px"
loading="lazy"
@@ -8806,9 +8806,9 @@ for p = 1 to points.length-3 (inclusive):
<p>
Only P<sub>3</sub> isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P<sub>4</sub>,
P<sub>3</sub>) is a right angled triangle, with the distance between the origin and P<sub>4</sub> being 1 (because we're working with a
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being _c , so that we can represent P<sub>3</sub> as "The point
P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>c</em>".
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being <em>k</em>, so that we can represent P<sub>3</sub> as "The
point P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>k</em>".
</p>
<p>
With that, we can determine the <em>y</em>-coordinates for A, B, e<sub>1</sub>, and e<sub>2</sub>, after which we have all the information
@@ -8866,7 +8866,7 @@ for p = 1 to points.length-3 (inclusive):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
@@ -8891,8 +8891,8 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
width="356px"
src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
width="357px"
height="263px"
loading="lazy"
/>

18
docs/ja-JP/index.html
View File

@@ -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="2021-04-19T18:35:47+00:00" />
<meta property="og:updated_time" content="2021-06-05T23:23:15+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -9007,7 +9007,7 @@ for p = 1 to points.length-3 (inclusive):
P = (1, 0)
1
P = (1, c)
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
@@ -9016,7 +9016,7 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
width="208px"
height="85px"
loading="lazy"
@@ -9024,9 +9024,9 @@ for p = 1 to points.length-3 (inclusive):
<p>
Only P<sub>3</sub> isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P<sub>4</sub>,
P<sub>3</sub>) is a right angled triangle, with the distance between the origin and P<sub>4</sub> being 1 (because we're working with a
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being _c , so that we can represent P<sub>3</sub> as "The point
P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>c</em>".
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being <em>k</em>, so that we can represent P<sub>3</sub> as "The
point P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>k</em>".
</p>
<p>
With that, we can determine the <em>y</em>-coordinates for A, B, e<sub>1</sub>, and e<sub>2</sub>, after which we have all the information
@@ -9084,7 +9084,7 @@ for p = 1 to points.length-3 (inclusive):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
@@ -9109,8 +9109,8 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
width="356px"
src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
width="357px"
height="263px"
loading="lazy"
/>

2
docs/news/2020-09-18.html
View File

@@ -34,7 +34,7 @@
<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 Apr 19 2021 18:35:47 +00:00" />
<meta property="og:updated_time" content="Sat Jun 05 2021 23:23:15 +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/2020-11-22.html
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@@ -34,7 +34,7 @@
<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 Apr 19 2021 18:35:47 +00:00" />
<meta property="og:updated_time" content="Sat Jun 05 2021 23:23:15 +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
View File

@@ -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 Apr 19 2021 18:35:47 GMT+0000 (Coordinated Universal Time)" />
<meta property="og:published_time" content="Sat Jun 05 2021 23:23:15 GMT+0000 (Coordinated Universal Time)" />
<meta property="og:updated_time" content="" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />

2
docs/news/rss.xml
View File

@@ -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 Apr 19 2021 18:35:47 +00:00</lastBuildDate>
<lastBuildDate>Sat Jun 05 2021 23:23:15 +00:00</lastBuildDate>
<image>
<url>https://pomax.github.io/bezierinfo/images/og-image.png</url>
<title>A Primer on Bézier Curves</title>

18
docs/ru-RU/index.html
View File

@@ -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="2021-04-19T18:35:47+00:00" />
<meta property="og:updated_time" content="2021-06-05T23:23:15+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -9164,7 +9164,7 @@ for p = 1 to points.length-3 (inclusive):
P = (1, 0)
1
P = (1, c)
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
@@ -9173,7 +9173,7 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
width="208px"
height="85px"
loading="lazy"
@@ -9181,9 +9181,9 @@ for p = 1 to points.length-3 (inclusive):
<p>
Only P<sub>3</sub> isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P<sub>4</sub>,
P<sub>3</sub>) is a right angled triangle, with the distance between the origin and P<sub>4</sub> being 1 (because we're working with a
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being _c , so that we can represent P<sub>3</sub> as "The point
P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>c</em>".
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being <em>k</em>, so that we can represent P<sub>3</sub> as "The
point P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>k</em>".
</p>
<p>
With that, we can determine the <em>y</em>-coordinates for A, B, e<sub>1</sub>, and e<sub>2</sub>, after which we have all the information
@@ -9241,7 +9241,7 @@ for p = 1 to points.length-3 (inclusive):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
@@ -9266,8 +9266,8 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
width="356px"
src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
width="357px"
height="263px"
loading="lazy"
/>

18
docs/uk-UA/index.html
View File

@@ -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="2021-04-19T18:35:47+00:00" />
<meta property="og:updated_time" content="2021-06-05T23:23:15+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -9138,7 +9138,7 @@ for p = 1 to points.length-3 (inclusive):
P = (1, 0)
1
P = (1, c)
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
@@ -9147,7 +9147,7 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
width="208px"
height="85px"
loading="lazy"
@@ -9155,9 +9155,9 @@ for p = 1 to points.length-3 (inclusive):
<p>
Only P<sub>3</sub> isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P<sub>4</sub>,
P<sub>3</sub>) is a right angled triangle, with the distance between the origin and P<sub>4</sub> being 1 (because we're working with a
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being _c , so that we can represent P<sub>3</sub> as "The point
P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>c</em>".
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being <em>k</em>, so that we can represent P<sub>3</sub> as "The
point P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>k</em>".
</p>
<p>
With that, we can determine the <em>y</em>-coordinates for A, B, e<sub>1</sub>, and e<sub>2</sub>, after which we have all the information
@@ -9215,7 +9215,7 @@ for p = 1 to points.length-3 (inclusive):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
@@ -9240,8 +9240,8 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
width="356px"
src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
width="357px"
height="263px"
loading="lazy"
/>

18
docs/zh-CN/index.html
View File

@@ -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="2021-04-19T18:35:47+00:00" />
<meta property="og:updated_time" content="2021-06-05T23:23:15+00:00" />
<meta property="og:author" content="Mike 'Pomax' Kamermans" />
<meta property="og:section" content="Bézier Curves" />
<meta property="og:tag" content="Bézier Curves" />
@@ -8983,7 +8983,7 @@ for p = 1 to points.length-3 (inclusive):
P = (1, 0)
1
P = (1, c)
P = (1, k)
2
P = P + k · (sin(θ), -cos(θ))
3 4
@@ -8992,7 +8992,7 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
width="208px"
height="85px"
loading="lazy"
@@ -9000,9 +9000,9 @@ for p = 1 to points.length-3 (inclusive):
<p>
Only P<sub>3</sub> isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P<sub>4</sub>,
P<sub>3</sub>) is a right angled triangle, with the distance between the origin and P<sub>4</sub> being 1 (because we're working with a
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being _c , so that we can represent P<sub>3</sub> as "The point
P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>c</em>".
unit circle), and the distance between P<sub>4</sub> and P<sub>3</sub> being <em>k</em>, so that we can represent P<sub>3</sub> as "The
point P<sub>4</sub> plus the vector from the origin to P<sub>4</sub> but then rotated a quarter circle, counter-clockwise, and scaled by
<em>k</em>".
</p>
<p>
With that, we can determine the <em>y</em>-coordinates for A, B, e<sub>1</sub>, and e<sub>2</sub>, after which we have all the information
@@ -9060,7 +9060,7 @@ for p = 1 to points.length-3 (inclusive):
<!--
\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
3k + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
@@ -9085,8 +9085,8 @@ for p = 1 to points.length-3 (inclusive):
-->
<img
class="LaTeX SVG"
src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
width="356px"
src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
width="357px"
height="263px"
loading="lazy"
/>