+SingularPetalRose

src/ex.rs

@@ -1,15 +1,15 @@
 /// explicit parametrizations of some curves
 /// (t is a parameter in [0,1] with f(0) = f(1) periodic)
+use core::f64::consts::TAU;
 
 pub fn circle(t: f64) -> [f64; 2] {
     // t * τ
-    let tt2pi = t * core::f64::consts::TAU;
+    let tt2pi = t * TAU;
     let (ttsin, ttcos) = tt2pi.sin_cos();
     [ttcos, ttsin]
 }
 
 pub fn circle_deriv(t: f64) -> [f64; 2] {
-    use core::f64::consts::TAU;
     let tt2pi = t * TAU;
     let (ttsin, ttcos) = tt2pi.sin_cos();
     [-TAU * ttsin, TAU * ttcos]
@@ -93,7 +93,7 @@ pub fn square(t: f64) -> [f64; 2] {
 }
 
 pub fn wobbly(t: f64, wob: u32) -> [f64; 2] {
-    let tt2pi = t * core::f64::consts::TAU;
+    let tt2pi = t * TAU;
     let (ttsin, ttcos) = tt2pi.sin_cos();
     let (ttxsin, ttxcos) = (tt2pi * (wob as f64)).sin_cos();
     let wobinv = 1.0 / (wob as f64);
@@ -101,7 +101,7 @@ pub fn wobbly(t: f64, wob: u32) -> [f64; 2] {
 }
 
 pub fn lemniskate(t: f64, a: f64) -> [f64; 2] {
-    let tt2pi = t * core::f64::consts::TAU;
+    let tt2pi = t * TAU;
     let (ttsin, ttcos) = tt2pi.sin_cos();
     [a * ttcos, a * ttcos * ttsin]
 }
@@ -113,7 +113,7 @@ pub fn cassini_oval(a: f64, c: f64) -> impl Fn(f64) -> [f64; 2] {
     let a4 = a2 * a2;
     let cahyp = c.hypot(a);
     move |t: f64| {
-        let tt2pi = t * core::f64::consts::TAU;
+        let tt2pi = t * TAU;
         let (ttsin, ttcos) = tt2pi.sin_cos();
         let denom = c2 + a2 * ttsin * ttsin;
         [
@@ -125,7 +125,7 @@ pub fn cassini_oval(a: f64, c: f64) -> impl Fn(f64) -> [f64; 2] {
 
 pub fn cassini_wobbly(a: f64, c: f64, wob: u32) -> impl Fn(f64) -> [f64; 2] {
     let cassini = cassini_oval(a, c);
-    let wobx = (wob as f64) * core::f64::consts::TAU;
+    let wobx = (wob as f64) * TAU;
     let wobinv = 1.0 / (wob as f64);
     move |t: f64| {
         let ttx2pi = t * wobx;
@@ -139,7 +139,7 @@ pub fn cassini_wobbly(a: f64, c: f64, wob: u32) -> impl Fn(f64) -> [f64; 2] {
 }
 
 pub fn astroid_pedal(t: f64, a: f64) -> [f64; 2] {
-    let tt2pi = t * core::f64::consts::TAU;
+    let tt2pi = t * TAU;
     let (ttsin, ttcos) = tt2pi.sin_cos();
     [a * ttcos * ttsin * ttsin, a * ttcos * ttcos * ttsin]
 }
@@ -163,9 +163,9 @@ pub fn cassini_anti_astroid(ca: f64, cc: f64, aa: f64) -> impl Fn(f64) -> [f64;
 }
 
 pub fn spiral(k: u32) -> impl Fn(f64) -> [f64; 2] {
-    let x2pi = (k as f64) * core::f64::consts::TAU;
+    let x2pi = (k as f64) * TAU;
     move |t: f64| {
-        let ttcos = (t * core::f64::consts::TAU).cos();
+        let ttcos = (t * TAU).cos();
         let (ttxsin, ttxcos) = (t * x2pi).sin_cos();
         [ttcos * ttxcos, ttcos * ttxsin]
     }
@@ -173,10 +173,21 @@ pub fn spiral(k: u32) -> impl Fn(f64) -> [f64; 2] {
 
 pub fn spiral_1d(k: u32) -> impl Fn(f64) -> [f64; 2] {
     let k = k as f64;
-    let x2pi = k * core::f64::consts::TAU;
+    let x2pi = k * TAU;
     move |t: f64| {
-        let ttcos = k * (t * core::f64::consts::TAU).cos();
+        let ttcos = k * (t * TAU).cos();
         let ttxsin = (t * x2pi).sin();
         [ttcos, ttxsin]
     }
 }
+
+// see also: https://commons.wikimedia.org/wiki/File:3_Petal_rose.svg
+pub fn singular_petal_rose(k: u32) -> impl Fn(f64) -> [f64; 2] {
+    let k = k as f64;
+    let x2pi = k * TAU;
+    move |t: f64| {
+        let (txs, txc) = (t * x2pi).sin_cos();
+        let (ts, tc) = (t * TAU).sin_cos();
+        [txs + tc, ts + txc]
+    }
+}

src/lib.rs

@@ -20,6 +20,7 @@ pub enum SelectExample {
 
     Spiral { k: u32 },
     Spiral1D { k: u32 },
+    SingularPetalRose { k: u32 },
 
     Circle,
     Square,
@@ -51,6 +52,7 @@ impl SelectExample {
             }
             Self::Spiral { .. }
             | Self::Spiral1D { .. }
+            | Self::SingularPetalRose { .. }
             | Self::Circle
             | Self::Square
             | Self::Intersect8
@@ -76,6 +78,7 @@ impl SelectExample {
             Self::Lemniskate { a } => Box::new(move |t: f64| ex::lemniskate(t, a)),
             Self::Spiral { k } => Box::new(ex::spiral(k)),
             Self::Spiral1D { k } => Box::new(ex::spiral_1d(k)),
+            Self::SingularPetalRose { k } => Box::new(ex::singular_petal_rose(k)),
             Self::Circle => Box::new(ex::circle),
             Self::Square => Box::new(ex::square),
             Self::Intersect8 => Box::new(ex::intersect_eight),