initial commit

.gitignore

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+.nfs*
+**/auto/*
+target/*
+*~
+.#*
+*.dat
+*.png
+*.svg
+*.dat.gz
+
+# benchmarks
+flamegraph.svg
+perf.data*
+
+# LaTeX
+*.aux
+*.bbl
+*.bcf
+*.blg
+*.fdb_latexmk
+*.fls
+*.glg
+*.glo
+*.gls
+*.ilg
+*.ind
+*.ist
+*.lof
+*.log
+*.lot
+*.out
+*.pdf
+*.ps
+*.run.xml
+*.synctex.gz
+*.toc
+*.xdv

Cargo.lock

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+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 3
+
+[[package]]
+name = "proc-macro2"
+version = "1.0.70"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "39278fbbf5fb4f646ce651690877f89d1c5811a3d4acb27700c1cb3cdb78fd3b"
+dependencies = [
+ "unicode-ident",
+]
+
+[[package]]
+name = "quote"
+version = "1.0.33"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5267fca4496028628a95160fc423a33e8b2e6af8a5302579e322e4b520293cae"
+dependencies = [
+ "proc-macro2",
+]
+
+[[package]]
+name = "serde"
+version = "1.0.193"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "25dd9975e68d0cb5aa1120c288333fc98731bd1dd12f561e468ea4728c042b89"
+dependencies = [
+ "serde_derive",
+]
+
+[[package]]
+name = "serde_derive"
+version = "1.0.193"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "43576ca501357b9b071ac53cdc7da8ef0cbd9493d8df094cd821777ea6e894d3"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "syn"
+version = "2.0.39"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "23e78b90f2fcf45d3e842032ce32e3f2d1545ba6636271dcbf24fa306d87be7a"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "unicode-ident",
+]
+
+[[package]]
+name = "unicode-ident"
+version = "1.0.12"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3354b9ac3fae1ff6755cb6db53683adb661634f67557942dea4facebec0fee4b"
+
+[[package]]
+name = "yz-curvep-exs"
+version = "0.1.0"
+dependencies = [
+ "serde",
+]

Cargo.toml

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+[package]
+name = "yz-curvep-exs"
+description = "examples of curve paramterizations"
+version = "0.1.0"
+edition = "2021"
+license = "Apache-2.0"
+
+[dependencies]
+
+[dependencies.serde]
+version = "1.0"
+features = ["derive"]
+optional = true

src/ex.rs

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+/// explicit parametrizations of some curves
+/// (t is a parameter in [0,1] with f(0) = f(1) periodic)
+
+pub fn circle(t: f64) -> [f64; 2] {
+    // t * τ
+    let tt2pi = t * core::f64::consts::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]
+}
+
+pub fn ellipse(a: f64, b: f64) -> impl Fn(f64) -> [f64; 2] {
+    move |t: f64| {
+        let cdat = circle(t);
+        [a * cdat[0], b * cdat[1]]
+    }
+}
+
+pub fn intersect_eight(t: f64) -> [f64; 2] {
+    //  __  __
+    // /  \/  \
+    // \  /\  /
+    //  ''  ''
+
+    let circle_data = circle(2.0 * t + 0.5);
+    let l = circle_data[0] + 1.0;
+    let l2 = if t >= 0.5 { -1.0 } else { 1.0 };
+    [l * l2, circle_data[1]]
+}
+
+pub fn intersect_8pp(t: f64) -> [f64; 2] {
+    // like `intersec_eight`, but we use 3/4 circles on the outer ends,
+    // and a 90° intersect in the middle
+
+    let sqrt2_16: f64 = 8.0 * (2.0_f64).sqrt();
+    let sqrt2m1: f64 = (2.0_f64).sqrt() - 1.0;
+    let afterh: bool = t >= 0.5;
+
+    // circle1 : 1/16..7/16
+    // circle2 : 9/16..15/16
+    if (t >= 0.0625 && t < 0.4375) || (t >= 0.5625 && t < 0.9375) {
+        let x8p = intersect_eight(t);
+        let newx = x8p[0] + sqrt2m1 * if t >= 0.5 { -1.0 } else { 1.0 };
+        [newx, x8p[1]]
+    } else if (t < 0.0625) || (t >= 0.9375) {
+        // /
+        let tx = sqrt2_16 * if afterh {
+            t - 1.0
+        } else {
+            t
+        };
+        [tx, -tx]
+    } else {
+        // \
+        let tx = sqrt2_16 * (t - 0.5);
+        [-tx, -tx]
+    }
+}
+
+// doesn't work yet...
+pub fn stadion(t: f64, gap: f64) -> [f64; 2] {
+    // circle1 : 1/8..3/8
+    // circle2 : 5/8..7/8
+    todo!();
+    if t < 0.125 {
+        [1.0, t * 4.0 * gap - 1.0]
+    } else if t >= 0.125 && t < 0.375 {
+        circle(2.0 * t - 0.25)
+    } else if t >= 0.375 && t < 0.625 {
+        [-1.0, 1.0 - t * 4.0 * gap]
+    } else if t >= 0.625 && t < 0.875 {
+        let cdat = circle(2.0 * t - 0.75);
+        [cdat[0], cdat[1] - 2.0 * gap]
+    } else {
+        [1.0, (t - 1.0) * 4.0 * gap - 1.0]
+    }
+}
+
+pub fn wobbly(t: f64, wob: u32) -> [f64; 2] {
+    let tt2pi = t * core::f64::consts::TAU;
+    let (ttsin, ttcos) = tt2pi.sin_cos();
+    let (ttxsin, ttxcos) = (tt2pi * (wob as f64)).sin_cos();
+    let wobinv = 1.0 / (wob as f64);
+    [ttcos + wobinv * ttxcos, ttsin + wobinv * ttxsin]
+}
+
+pub fn lemniskate(t: f64, a: f64) -> [f64; 2] {
+    let tt2pi = t * core::f64::consts::TAU;
+    let (ttsin, ttcos) = tt2pi.sin_cos();
+    [a * ttcos, a * ttcos * ttsin]
+}
+
+pub fn cassini_oval(a: f64, c: f64) -> impl Fn(f64) -> [f64; 2] {
+    let c2 = c * c;
+    let c4 = c2 * c2;
+    let a2 = a * a;
+    let a4 = a2 * a2;
+    let cahyp = c.hypot(a);
+    move |t: f64| {
+        let tt2pi = t * core::f64::consts::TAU;
+        let (ttsin, ttcos) = tt2pi.sin_cos();
+        let denom = c2 + a2 * ttsin * ttsin;
+        [
+          (c2 * cahyp * ttcos) / denom,
+          (cahyp * ttsin * (c4 - a4 * ttsin * ttsin).sqrt()) / denom,
+        ]
+    }
+}
+
+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 wobinv = 1.0 / (wob as f64);
+    move |t: f64| {
+        let ttx2pi = t * wobx;
+        let (ttxsin, ttxcos) = (ttx2pi).sin_cos();
+        let cas = cassini(t);
+        [ttxcos.mul_add(wobinv, cas[0]), ttxsin.mul_add(wobinv, cas[1])]
+    }
+}
+
+pub fn astroid_pedal(t: f64, a: f64) -> [f64; 2] {
+    let tt2pi = t * core::f64::consts::TAU;
+    let (ttsin, ttcos) = tt2pi.sin_cos();
+    [a * ttcos * ttsin * ttsin, a * ttcos * ttcos * ttsin]
+}
+
+pub fn cassini_astroid(ca: f64, cc: f64, aa: f64) -> impl Fn(f64) -> [f64; 2] {
+    let cassini = cassini_oval(ca, cc);
+    move |t: f64| {
+        let ap = astroid_pedal(t, aa);
+        let cs = cassini(t);
+        [ap[0] + cs[0], ap[1] + cs[1]]
+    }
+}

src/lib.rs

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+#![forbid(unsafe_code)]
+
+pub mod ex;
+
+#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+#[cfg_attr(feature = "serde", serde(rename_all = "kebab-case", tag = "type"))]
+pub enum SelectExample {
+    AstroidPedal { a: f64 },
+
+    CassiniOval { a: f64, c: f64 },
+
+    CassiniAstroid { ca: f64, cc: f64, aa: f64 },
+    CassiniAstroidTsq { ca: f64, cc: f64, aa: f64 },
+
+    Ellipse { a: f64, b: f64 },
+
+    Lemniskate { a: f64 },
+
+    Circle,
+    Intersect8,
+    Intersect8pp,
+}
+
+impl SelectExample {
+    pub fn add_offset(&mut self, l: f64) {
+        match self {
+            Self::AstroidPedal { a } => *a += l,
+            Self::CassiniOval { a, c } => {
+                *a += l;
+                *c += l;
+            }
+            Self::CassiniAstroid { ca, cc, aa } | Self::CassiniAstroidTsq { ca, cc, aa } => {
+                *ca += l;
+                *cc += l;
+                *aa += l;
+            }
+            Self::Ellipse { a, b } => {
+                *a /= 1.0 + l;
+                *b *= 1.0 + l;
+            }
+            Self::Lemniskate { a } => {
+                *a += l;
+            }
+            Self::Circle | Self::Intersect8 | Self::Intersect8pp => {
+                panic!("offsetting not supported for this example")
+            }
+        }
+    }
+
+    pub fn instantiate(self) -> Box<dyn Fn(f64) -> [f64; 2]> {
+        match self {
+            Self::AstroidPedal { a } => Box::new(move |t: f64| ex::astroid_pedal(t, a)),
+            Self::CassiniOval { a, c } => Box::new(ex::cassini_oval(a, c)),
+            Self::CassiniAstroid { ca, cc, aa } => Box::new(ex::cassini_astroid(ca, cc, aa)),
+            Self::CassiniAstroidTsq { ca, cc, aa } => {
+                let x = ex::cassini_astroid(ca, cc, aa);
+                Box::new(move |t: f64| x(t * t))
+            },
+            Self::Ellipse { a, b } => Box::new(ex::ellipse(a, b)),
+            Self::Lemniskate { a } => Box::new(move |t: f64| ex::lemniskate(t, a)),
+            Self::Circle => Box::new(ex::circle),
+            Self::Intersect8 => Box::new(ex::intersect_eight),
+            Self::Intersect8pp => Box::new(ex::intersect_8pp),
+        }
+    }
+}