diff --git a/docs/images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg b/docs/images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg new file mode 100644 index 00000000..ad4f7cf0 --- /dev/null +++ b/docs/images/chapters/circles_cubic/9054528132317434ae2c0be27572d86b.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/docs/images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg b/docs/images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg new file mode 100644 index 00000000..00f95bd3 --- /dev/null +++ b/docs/images/chapters/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/docs/images/snippets/circles_cubic/9054528132317434ae2c0be27572d86b.ascii b/docs/images/snippets/circles_cubic/9054528132317434ae2c0be27572d86b.ascii new file mode 100644 index 00000000..563547cf --- /dev/null +++ b/docs/images/snippets/circles_cubic/9054528132317434ae2c0be27572d86b.ascii @@ -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 diff --git a/docs/images/snippets/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.ascii b/docs/images/snippets/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.ascii new file mode 100644 index 00000000..4fba34b6 --- /dev/null +++ b/docs/images/snippets/circles_cubic/cb6686f1aff26d9f47ed4c695109fd5f.ascii @@ -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) diff --git a/docs/index.html b/docs/index.html index 8525b1c1..ecc8e873 100644 --- a/docs/index.html +++ b/docs/index.html @@ -38,7 +38,7 @@ - + @@ -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): --> Only P3 isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P4, P3) is a right angled triangle, with the distance between the origin and P4 being 1 (because we're working with a - unit circle), and the distance between P4 and P3 being _c , so that we can represent P3 as "The point - P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by - c". + unit circle), and the distance between P4 and P3 being k, so that we can represent P3 as "The + point P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by + k".

With that, we can determine the y-coordinates for A, B, e1, and e2, after which we have all the information @@ -8866,7 +8866,7 @@ for p = 1 to points.length-3 (inclusive): diff --git a/docs/ja-JP/index.html b/docs/ja-JP/index.html index 73144735..cfcae011 100644 --- a/docs/ja-JP/index.html +++ b/docs/ja-JP/index.html @@ -41,7 +41,7 @@ - + @@ -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): --> Only P3 isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P4, P3) is a right angled triangle, with the distance between the origin and P4 being 1 (because we're working with a - unit circle), and the distance between P4 and P3 being _c , so that we can represent P3 as "The point - P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by - c". + unit circle), and the distance between P4 and P3 being k, so that we can represent P3 as "The + point P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by + k".

With that, we can determine the y-coordinates for A, B, e1, and e2, after which we have all the information @@ -9084,7 +9084,7 @@ for p = 1 to points.length-3 (inclusive): diff --git a/docs/news/2020-09-18.html b/docs/news/2020-09-18.html index ac979fb4..4dc411f5 100644 --- a/docs/news/2020-09-18.html +++ b/docs/news/2020-09-18.html @@ -34,7 +34,7 @@ - + diff --git a/docs/news/2020-11-22.html b/docs/news/2020-11-22.html index 6c87701c..3eda705f 100644 --- a/docs/news/2020-11-22.html +++ b/docs/news/2020-11-22.html @@ -34,7 +34,7 @@ - + diff --git a/docs/news/index.html b/docs/news/index.html index 9f548e31..9982e13a 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -33,7 +33,7 @@ - + diff --git a/docs/news/rss.xml b/docs/news/rss.xml index 49b21d6d..6db19b96 100644 --- a/docs/news/rss.xml +++ b/docs/news/rss.xml @@ -6,7 +6,7 @@ News updates for the primer on Bézier Curves by Pomax en-GB - Mon Apr 19 2021 18:35:47 +00:00 + Sat Jun 05 2021 23:23:15 +00:00 https://pomax.github.io/bezierinfo/images/og-image.png A Primer on Bézier Curves diff --git a/docs/ru-RU/index.html b/docs/ru-RU/index.html index f369a017..bf102fc0 100644 --- a/docs/ru-RU/index.html +++ b/docs/ru-RU/index.html @@ -34,7 +34,7 @@ - + @@ -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): --> Only P3 isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P4, P3) is a right angled triangle, with the distance between the origin and P4 being 1 (because we're working with a - unit circle), and the distance between P4 and P3 being _c , so that we can represent P3 as "The point - P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by - c". + unit circle), and the distance between P4 and P3 being k, so that we can represent P3 as "The + point P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by + k".

With that, we can determine the y-coordinates for A, B, e1, and e2, after which we have all the information @@ -9241,7 +9241,7 @@ for p = 1 to points.length-3 (inclusive): diff --git a/docs/uk-UA/index.html b/docs/uk-UA/index.html index 8ff5f10f..606a37f8 100644 --- a/docs/uk-UA/index.html +++ b/docs/uk-UA/index.html @@ -39,7 +39,7 @@ - + @@ -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): --> Only P3 isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P4, P3) is a right angled triangle, with the distance between the origin and P4 being 1 (because we're working with a - unit circle), and the distance between P4 and P3 being _c , so that we can represent P3 as "The point - P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by - c". + unit circle), and the distance between P4 and P3 being k, so that we can represent P3 as "The + point P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by + k".

With that, we can determine the y-coordinates for A, B, e1, and e2, after which we have all the information @@ -9215,7 +9215,7 @@ for p = 1 to points.length-3 (inclusive): diff --git a/docs/zh-CN/index.html b/docs/zh-CN/index.html index 9933cd9b..cc71ebd3 100644 --- a/docs/zh-CN/index.html +++ b/docs/zh-CN/index.html @@ -41,7 +41,7 @@ - + @@ -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): --> Only P3 isn't quite straight-forward here, and its description is based on the fact that the triangle (origin, P4, P3) is a right angled triangle, with the distance between the origin and P4 being 1 (because we're working with a - unit circle), and the distance between P4 and P3 being _c , so that we can represent P3 as "The point - P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by - c". + unit circle), and the distance between P4 and P3 being k, so that we can represent P3 as "The + point P4 plus the vector from the origin to P4 but then rotated a quarter circle, counter-clockwise, and scaled by + k".

With that, we can determine the y-coordinates for A, B, e1, and e2, after which we have all the information @@ -9060,7 +9060,7 @@ for p = 1 to points.length-3 (inclusive):