Merge pull request #95 from raphlinus/simplify

Simplifying Bézier paths

Author: raphlinus

.gitignore

@@ -1,3 +1,5 @@
 _site
 .sass-cache
 .jekyll-metadata
+target/
+

_figures/simplify_figs/Cargo.lock

@@ -0,0 +1,8 @@
+[package]
+name = "simplify_figs"
+license = "Apache-2.0"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+kurbo = "0.9.2"

_figures/simplify_figs/Cargo.toml

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+// Copyright 2022 the raphlinus.github.io Authors
+// SPDX-License-Identifier: Apache-2.0
+
+//! Program to generate figures for "Simplifying Bézier paths" blog. Run with
+//! figure type ("th" or "arc"), generates svg file as stdout.
+
+use kurbo::{CubicBez, ParamCurve, ParamCurveArclen, ParamCurveDeriv, Point, Shape, Vec2};
+use kurbo::common::solve_cubic;
+
+fn intersect(c: CubicBez, p: Point, tangent: Vec2) -> Vec<f64> {
+    let p1 = 3.0 * (c.p1 - c.p0);
+    let p2 = 3.0 * c.p2.to_vec2() - 6.0 * c.p1.to_vec2() + 3.0 * c.p0.to_vec2();
+    let p3 = (c.p3 - c.p0) - 3.0 * (c.p2 - c.p1);
+    let c0 = (c.p0 - p).dot(tangent);
+    let c1 = p1.dot(tangent);
+    let c2 = p2.dot(tangent);
+    let c3 = p3.dot(tangent);
+    solve_cubic(c0, c1, c2, c3)
+        .into_iter()
+        .filter(|t| (0.0..=1.0).contains(t))
+        .collect()
+}
+
+
+fn main() {
+    let fig = std::env::args().skip(1).next().expect("need figure type");
+    let c1 = CubicBez::new((10., 150.), (300., 150.), (310., 150.), (310., 450.));
+    let a: f64 = if fig == "arc2" { 40. } else { 400. };
+    let c2 = CubicBez::new((10., 150.), (300. + a, 150.), (310., 150. - a), (310., 450.));
+    let arclen = c1.arclen(1e-9);
+    let arclen2 = c2.arclen(1e-9);
+    println!("<svg width='450' height='480' xmlns='http://www.w3.org/2000/svg'>");
+    println!("  <!-- figure generated by simplify_figs program in _figures subdir -->");
+    println!("  <path d='{}' stroke='#000' fill='none'/>", c1.into_path(1e-9).to_svg());
+    println!("  <path d='{}' stroke='#000' fill='none'/>", c2.into_path(1e-9).to_svg());
+    const N: usize = 11;
+    for i in 1..N {
+        let s = (i as f64 / N as f64) * arclen;
+        let t = c1.inv_arclen(s, 1e-9);
+        let p = c1.eval(t);
+        println!("  <circle cx='{}' cy='{}' r='2' fill='#008'/>", p.x, p.y);
+        let t2;
+        if fig == "th" {
+            let d = c1.deriv().eval(t);
+            let t2s = intersect(c2, p, d.to_vec2());
+            t2 = t2s[0];
+        } else {
+            let s2 = (i as f64 / N as f64) * arclen2;
+            t2 = c2.inv_arclen(s2, 1e-9);
+        }
+        let p2 = c2.eval(t2);
+        if fig != "th" {
+            println!("  <circle cx='{}' cy='{}' r='2' fill='#008'/>", p2.x, p2.y);
+        }
+        println!("  <line x1='{}' y1='{}' x2='{}' y2='{}' stroke='#000'/>",
+            p.x, p.y, p2.x, p2.y);
+    }
+    println!("</svg>");
+}