+dumbbell

src/ex.rs

@@ -34,6 +34,29 @@ pub fn circle_sin_chain1(w: f64) -> impl Fn(f64) -> [f64; 2] {
     }
 }
 
+// source: https://mathworld.wolfram.com/DumbbellCurve.html
+pub fn dumbbell(a: f64) -> impl Fn(f64) -> [f64; 2] {
+    move |t: f64| {
+        if t <= 0.25 {
+            let tm4 = t * 4.0;
+            let t2 = tm4 * tm4;
+            [a * tm4, a * t2 * (1.0 - t2).sqrt()]
+        } else if t <= 0.5 {
+            let tm4 = 1.0 - (t - 0.25) * 4.0;
+            let t2 = tm4.powi(2);
+            [a * tm4, -a * t2 * (1.0 - t2).sqrt()]
+        } else if t <= 0.75 {
+            let tm4 = (t - 0.5) * 4.0;
+            let t2 = tm4.powi(2);
+            [-a * tm4, a * t2 * (1.0 - t2).sqrt()]
+        } else {
+            let tm4 = 1.0 - (t - 0.75) * 4.0;
+            let t2 = tm4.powi(2);
+            [-a * tm4, -a * t2 * (1.0 - t2).sqrt()]
+        }
+    }
+}
+
 pub fn ellipse(a: f64, b: f64) -> impl Fn(f64) -> [f64; 2] {
     move |t: f64| {
         let cdat = circle(t);

src/lib.rs

@@ -12,6 +12,7 @@ pub enum SelectExample {
     CassiniAntiAstroid { ca: f64, cc: f64, aa: f64 },
     CassiniAstroidTsq { ca: f64, cc: f64, aa: f64 },
 
+    Dumbbell { a: f64 },
     Ellipse { a: f64, b: f64 },
     Lemniskate { a: f64 },
     CirclePow { k: f64 },
@@ -42,6 +43,9 @@ impl SelectExample {
                 *cc += l;
                 *aa += l;
             }
+            Self::Dumbbell { a } => {
+                *a += l;
+            }
             Self::Ellipse { a, b } => {
                 *a /= 1.0 + l;
                 *b *= 1.0 + l;
@@ -79,6 +83,7 @@ impl SelectExample {
                 let x = ex::cassini_astroid(ca, cc, aa);
                 Box::new(move |t: f64| x(t * t))
             }
+            Self::Dumbbell { a } => Box::new(ex::dumbbell(a)),
             Self::Ellipse { a, b } => Box::new(ex::ellipse(a, b)),
             Self::Lemniskate { a } => Box::new(move |t: f64| ex::lemniskate(t, a)),
             Self::CirclePow { k } => Box::new(ex::circle_pow(k)),