diff --git a/docs/index.html b/docs/index.html index fa24d6eb..5b2d0988 100644 --- a/docs/index.html +++ b/docs/index.html @@ -38,7 +38,7 @@ - + diff --git a/docs/ja-JP/index.html b/docs/ja-JP/index.html index ac40deb0..2ee94444 100644 --- a/docs/ja-JP/index.html +++ b/docs/ja-JP/index.html @@ -41,7 +41,7 @@ - + diff --git a/docs/news/2020-09-18.html b/docs/news/2020-09-18.html index 4423a988..612c6637 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 new file mode 100644 index 00000000..c955b352 --- /dev/null +++ b/docs/news/2020-11-22.html @@ -0,0 +1,143 @@ + + + + + + A Primer on Bézier Curves - Curve-circle intersections + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ This page on GitHub + + This page on GitHub + +
+ +
+

Curve-circle intersections

+
Sun, 22 Nov 2020
+
+ +
+ +
+ + + submit to reddit + submit to hacker news + tweet your read + +
+ +

+ While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: + circle/curve intersections. You'd think those were just an extension on the maths used for the other three, but unfortunately, this is not the + case. Rather than using calculus, the only real way to determine where a polynomial curve intersects it is to sample the curve at a resolution + high enough to find you intervals on the curve where there likely is an intersection, then refining that interval until you find actual + intersections. +

+

+ It is, in fact, rather similar to projecting a point onto a bezier curve where + the point is the circle's center, and where the projection distance actually needs to match the circle radius, so: + let's see how to do that! +

+

Pomax

+
+ +
+ + + + diff --git a/docs/news/2020-11-22.md b/docs/news/2020-11-22.md new file mode 100644 index 00000000..a22cb0b1 --- /dev/null +++ b/docs/news/2020-11-22.md @@ -0,0 +1,8 @@ +# Curve-circle intersections + +While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: circle/curve intersections. You'd think those were just an extension on the maths used for the other three, but unfortunately, this is not the case. Rather than using calculus, the only real way to determine where a polynomial curve intersects it is to sample the curve at a resolution high enough to find you intervals on the curve where there likely is an intersection, then refining that interval until you find actual intersections. + +It is, in fact, rather similar to [projecting a point onto a bezier curve](https://pomax.github.io/bezierinfo/#projections) where the point is the circle's center, and where the projection distance actually needs to match the circle radius, so: [let's see how to do that](https://pomax.github.io/bezierinfo/#circleintersection)! + + +— [Pomax](https://twitter.com/TheRealPomax) diff --git a/docs/news/index.html b/docs/news/index.html index b3c6e558..1df6d07a 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -33,7 +33,7 @@ - + @@ -102,6 +102,7 @@ diff --git a/docs/news/rss.xml b/docs/news/rss.xml index 1193cee5..8bc79c85 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 - Sat Nov 21 2020 11:09:32 +00:00 + Sun Nov 22 2020 10:06:08 +00:00 https://pomax.github.io/bezierinfo/images/og-image.png A Primer on Bézier Curves @@ -109,6 +109,18 @@ draw() { Thu Sep 17 2020 17:00:00 +00:00 2020-09-18.html + + Curve-circle intersections + https://pomax.github.io/bezierinfo/news/2020-11-22.html + + +<p>While the primer covered line/line, line/curve, and curve/curve intersections, there was one other obvious intersection conspicuously missing: circle/curve intersections. You'd think those were just an extension on the maths used for the other three, but unfortunately, this is not the case. Rather than using calculus, the only real way to determine where a polynomial curve intersects it is to sample the curve at a resolution high enough to find you intervals on the curve where there likely is an intersection, then refining that interval until you find actual intersections.</p> +<p>It is, in fact, rather similar to <a href="https://pomax.github.io/bezierinfo/#projections">projecting a point onto a bezier curve</a> where the point is the circle's center, and where the projection distance actually needs to match the circle radius, so: <a href="https://pomax.github.io/bezierinfo/#circleintersection">let's see how to do that</a>!</p> +<p>— <a href="https://twitter.com/TheRealPomax">Pomax</a></p> + + + Sat Nov 21 2020 16:00:00 +00:00 + 2020-11-22.html diff --git a/docs/uk-UA/index.html b/docs/uk-UA/index.html index 6fdfe930..d7ffa037 100644 --- a/docs/uk-UA/index.html +++ b/docs/uk-UA/index.html @@ -39,7 +39,7 @@ - + diff --git a/docs/zh-CN/index.html b/docs/zh-CN/index.html index 0647832f..63a0854b 100644 --- a/docs/zh-CN/index.html +++ b/docs/zh-CN/index.html @@ -41,7 +41,7 @@ - +