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@@ -38,7 +38,7 @@
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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="2013-06-13T12:00:00+00:00" />
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<meta property="og:updated_time" content="2021-04-19T18:35:47+00:00" />
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<meta property="og:updated_time" content="2021-06-05T23:23:15+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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@@ -8789,7 +8789,7 @@ for p = 1 to points.length-3 (inclusive):
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P = (1, 0)
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1
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P = (1, c)
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P = (1, k)
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2
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P = P + k · (sin(θ), -cos(θ))
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3 4
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@@ -8798,7 +8798,7 @@ for p = 1 to points.length-3 (inclusive):
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-->
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<img
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class="LaTeX SVG"
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src="./images/chapters/circles_cubic/fe6cc524978eaa4f35d8de32c3b9ad94.svg"
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src="./images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg"
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width="208px"
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height="85px"
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loading="lazy"
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@@ -8806,9 +8806,9 @@ for p = 1 to points.length-3 (inclusive):
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<p>
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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>,
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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
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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
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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
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<em>c</em>".
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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
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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
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<em>k</em>".
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</p>
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<p>
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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
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@@ -8866,7 +8866,7 @@ for p = 1 to points.length-3 (inclusive):
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<!--
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
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3c + 4sin(θ)) - 3k · cos(θ) θ
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3k + 4sin(θ)) - 3k · cos(θ) θ
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────────────────────────────= sin(─)
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8 2
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╭ θ ╮
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@@ -8891,8 +8891,8 @@ for p = 1 to points.length-3 (inclusive):
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-->
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<img
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class="LaTeX SVG"
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src="./images/chapters/circles_cubic/b985384d01cb32d422f5d1123707ebc8.svg"
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width="356px"
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src="./images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg"
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width="357px"
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height="263px"
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loading="lazy"
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/>
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