From d8fc124a49f62831021e57d82e9f430fbe93aff3 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Wed, 29 May 2024 21:20:22 +1000
Subject: [PATCH 01/23] init

---
 src/lib.rs      |   2 +
 src/triangle.rs | 375 ++++++++++++++++++++++++++++++++++++++++++++++++
 src/vec2.rs     |   3 +
 3 files changed, 380 insertions(+)
 create mode 100644 src/triangle.rs

diff --git a/src/lib.rs b/src/lib.rs
index b5088b4e..676863b3 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -98,6 +98,7 @@ mod insets;
 mod line;
 mod mindist;
 pub mod offset;
+mod triangle;
 mod param_curve;
 mod point;
 mod quadbez;
@@ -123,6 +124,7 @@ pub use crate::ellipse::*;
 pub use crate::fit::*;
 pub use crate::insets::*;
 pub use crate::line::*;
+pub use crate::triangle::*;
 pub use crate::param_curve::*;
 pub use crate::point::*;
 pub use crate::quadbez::*;
diff --git a/src/triangle.rs b/src/triangle.rs
new file mode 100644
index 00000000..a0fe54c6
--- /dev/null
+++ b/src/triangle.rs
@@ -0,0 +1,375 @@
+// Copyright 2024 the Kurbo Authors
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+//! Triangle shape
+use crate::{Ellipse, Insets, PathEl, Rect, Point, RoundedRect, RoundedRectRadii, Shape, Size, Vec2};
+
+use core::ops::{Add, Sub};
+
+/// Triangle
+//     A
+//     *
+//    / \
+//   /   \
+//  *-----*
+//  B     C
+#[derive(Clone, Copy, PartialEq)]
+#[cfg_attr(feature = "schemars", derive(schemars::JsonSchema))]
+#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
+pub struct Triangle {
+    pub a: Point,
+    pub b: Point,
+    pub c: Point,
+}
+
+impl Default for Triangle {
+    fn default() -> Self {
+        Self::IDENTITY
+    }
+}
+
+impl Triangle {
+    /// The empty triangle at the origin
+    pub const ZERO: Self = Self::from_coords((0., 0.), (0., 0.), (0., 0.));
+
+    pub const IDENTITY: Self = Self::from_coords((1.0, 1.0), (0.0, 0.0), (2.0, 0.0));
+
+    /// A new [`Triangle`] from three vertices ([`Points`])
+    #[inline]
+    pub fn new(a: impl Into<Point>, b: impl Into<Point>, c: impl Into<Point>) -> Self {
+        Self { a: a.into(), b: b.into(), c: c.into() }
+    }
+
+    /// A new [`Triangle`] from three float vertex coordinates
+    #[inline]
+    pub const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
+        Self { a: Point::new(a.0, a.1), b: Point::new(b.0, b.1), c: Point::new(c.0, c.1) }
+    }
+
+    /// A new `Triangle` from centroid and sizes
+    #[inline]
+    pub fn from_centroid_sizes(centroid: impl Into<Point>, sizes: [f64; 3]) -> Self {
+        let centroid = centroid.into();
+        Self::new(
+            (centroid.x, centroid.y + sizes[0]),
+            centroid + Vec2::IDENTITY * sizes[1],
+            centroid + Vec2::IDENTITY * sizes[2],
+        )
+    }
+
+    /// A new equilateral [`Triangle`]
+    /// takes the center and a point equidistant to the midpoints of the vertices (radius)
+    #[inline]
+    pub fn from_center_size(center: impl Into<Point>, radius: f64) -> Self {
+        const THETA: f64 = 60.0; // equilateral triangle guarantee
+        let center = center.into().to_vec2();
+
+        let h = (radius/((THETA/2.0).tan()) *radius/((THETA/2.0).tan()) + radius*radius).sqrt();
+        let a = center.y + radius;
+        let b = center + Vec2::IDENTITY * h;
+        let c = center - Vec2::IDENTITY * h;
+
+        Self::new((center.x, a), b.to_point(), c.to_point())
+    }
+
+    /// A new [`Triangle`] moved to `centroid`
+    #[inline]
+    pub fn with_centroid(self, centroid: impl Into<Point>) -> Self {
+        Self::from_centroid_sizes(centroid, self.sizes())
+    }
+
+    /// Creates a new [`Triangle`] with new `sizes`
+    #[inline]
+    pub fn with_sizes(self, sizes: [f64; 3]) -> Self {
+        Self::from_centroid_sizes(self.centroid(), sizes)
+    }
+
+    /// The centroid of the [`Triangle`]
+    #[inline]
+    pub fn centroid(&self) -> Point {
+        Point::new(
+            (self.a.x + self.b.x + self.c.x)/3.0,
+            (self.a.y + self.b.y + self.c.y)/3.0,
+        )
+    }
+
+    /// The distance of each vertex from the centroid
+    #[inline]
+    pub fn sizes(&self) -> [f64; 3] {
+        let centroid = self.centroid();
+
+        [
+            self.a.distance(centroid),
+            self.b.distance(centroid),
+            self.c.distance(centroid)
+        ]
+    }
+
+    /// The area of the [`Triangle`]
+    #[inline]
+    pub fn area(&self) -> f64 {
+        let ab = self.a.distance(self.b);
+        let ac = self.a.distance(self.c);
+        let bc = self.b.distance(self.c);
+
+        // cos rule
+        let theta = ((bc*bc - ab*ab - ac*ac)/-2.0*ab*ac).acos();
+
+        // A = 1/2*a*b*sin(C)
+        (ab*ac*theta.sin())/2.0
+    }
+
+    // TODO: maybe make height functions for right and non right angled triangles
+
+    /// The area of a right angled [`Triangle`]
+    #[inline]
+    pub fn right_angled_area(&self) -> f64 {
+        // A = 1/2*b*h
+        (self.b.distance(self.c)*self.b.midpoint(self.c).distance(self.a))/2.0
+    }
+
+    /// Maximum x-coordinate of the [`Triangle`]'s vertices
+    #[inline]
+    pub fn max_x(&self) -> f64 {
+        self.a.x.max(self.b.x.max(self.c.x))
+    }
+
+    /// Minimum x-coordinate of the [`Triangle`]'s vertices
+    #[inline]
+    pub fn min_x(&self) -> f64 {
+        self.a.x.min(self.b.x.min(self.c.x))
+    }
+
+    /// Mayimum y-coordinate of the [`Triangle`]'s vertices
+    #[inline]
+    pub fn max_y(&self) -> f64 {
+        self.a.y.max(self.b.y.max(self.c.y))
+    }
+
+    /// Minimum y-coordinate of the [`Triangle`]'s vertices
+    #[inline]
+    pub fn min_y(&self) -> f64 {
+        self.a.y.min(self.b.y.min(self.c.y))
+    }
+
+    /// Whether this [`Triangle`] has no (zero) area
+    #[inline]
+    pub fn is_empty(&self) -> bool {
+        self.area() == 0.0
+    }
+
+    /// Whether this right angled [`Triangle`] has no (zero) area
+    #[inline]
+    pub fn is_empty_right_angled(&self) -> bool {
+        self.right_angled_area() == 0.0
+    }
+
+    /// `true` if `point` lies within `self`
+    #[inline]
+    pub fn contains(&self, point: Point) -> bool {
+        point.x >= self.min_x() && point.x < self.max_x() && point.y >= self.min_y() && point.y < self.max_y()
+    }
+
+    /// The smallest radius of a circle that is within the [`Triangle`]
+    #[inline]
+    pub fn radius(&self) -> f64 {
+        let ab = self.a.distance(self.b);
+        let bc = self.b.distance(self.c);
+        let ac = self.a.distance(self.c);
+
+        let s = (ab + bc + ac) / 2.0;
+
+        // Heron's formula
+        let area = (s * (s - ab) * (s - bc) * (s - ac)).sqrt();
+
+        area / s
+    }
+
+    /// Expand the triangle by a constant amount (`sizes`) in all directions
+    pub fn inflate(&self, sizes: [f64; 3]) -> Self {
+        Self::new(
+            (self.a.to_vec2() + Vec2::IDENTITY * sizes[0]).to_point(),
+            (self.b.to_vec2() + Vec2::IDENTITY * sizes[1]).to_point(),
+            (self.c.to_vec2() + Vec2::IDENTITY * sizes[2]).to_point()
+        )
+    }
+
+    /// A new [`Triangle`] with each vertecie's ordinates rounded to the nearest integer
+    #[inline]
+    pub fn round(self) -> Self {
+        Self::new(
+            self.a.round(),
+            self.b.round(),
+            self.c.round(),
+        )
+    }
+
+    /// A new [`Triangle`] with each vertecie's ordinates rounded up to the nearest integer
+    #[inline]
+    pub fn ceil(self) -> Self {
+        Self::new(
+            self.a.ceil(),
+            self.b.ceil(),
+            self.c.ceil(),
+        )
+    }
+
+    /// A new [`Triangle`] with each vertecie's ordinates rounded down to the nearest integer
+    #[inline]
+    pub fn floor(self) -> Self {
+        Self::new(
+            self.a.floor(),
+            self.b.floor(),
+            self.c.floor(),
+        )
+    }
+
+    /// A new [`Triangle`],
+    /// with each coordinate value rounded towards the center of the [`Triangle`]
+    /// to the nearest integer, unless they are already an integer.
+    /// That is to say this function will return the biggest possible [`Triangle`]
+    /// with integer coordinates that is a subset of `self`.
+    #[inline]
+    pub fn expand(self) -> Self {
+        Self::new(
+            self.a.expand(),
+            self.b.expand(),
+            self.c.expand(),
+        )
+    }
+
+    /// Returns a new [`Triangle`],
+    /// with each coordinate value rounded towards the center of the [`Triangle`]
+    /// to the nearest integer, unless they are already an integer.
+    /// That is to say this function will return the biggest possible [`Triangle`]
+    /// with integer coordinates that is a subset of `self`.
+    #[inline]
+    pub fn trunc(self) -> Self {
+        Self::new(
+            self.a.trunc(),
+            self.b.trunc(),
+            self.c.trunc()
+        )
+    }
+
+    /// Scales the [`Triangle`] by a `factor`
+    #[inline]
+    pub fn scale(self, factor: f64) -> Self {
+        Self::new(
+            (self.a.to_vec2() * factor).to_point(),
+            (self.b.to_vec2() * factor).to_point(),
+            (self.c.to_vec2() * factor).to_point(),
+        )
+    }
+
+    // TODO: functions: insets, to_ellipse (see ellipse TODO), aspect ratio, finite & nan
+}
+
+impl From<(Point, Point, Point)> for Triangle {
+    fn from(points: (Point, Point, Point)) -> Triangle {
+        Triangle::new(points.0, points.1, points.2)
+    }
+}
+
+impl From<(Point, f64)> for Triangle {
+    fn from(params: (Point, f64)) -> Triangle {
+        Triangle::from_center_size(params.0, params.1)
+    }
+}
+
+impl Add<Vec2> for Triangle {
+    type Output = Triangle;
+
+    #[inline]
+    fn add(self, v: Vec2) -> Triangle {
+        Triangle::new(
+            (self.a.to_vec2() + v).to_point(),
+            (self.b.to_vec2() + v).to_point(),
+            (self.c.to_vec2() + v).to_point(),
+        )
+    }
+}
+
+impl Sub<Vec2> for Triangle {
+    type Output = Triangle;
+
+    #[inline]
+    fn sub(self, v: Vec2) -> Triangle {
+        Triangle::new(
+            (self.a.to_vec2() - v).to_point(),
+            (self.b.to_vec2() - v).to_point(),
+            (self.c.to_vec2() - v).to_point(),
+        )
+    }
+}
+
+// TODO: sub, see insets TODO
+
+// TEMP
+// TODO: implement
+#[doc(hidden)]
+pub struct TrianglePathIter {
+    triangle: Triangle,
+    ix: usize
+}
+
+impl Shape for Triangle {
+    type PathElementsIter<'iter> = TrianglePathIter;
+
+    fn path_elements(&self, _tolerance: f64) -> TrianglePathIter {
+        TrianglePathIter { triangle: *self, ix: 0 }
+    }
+
+    #[inline]
+    fn area(&self) -> f64 {
+        Triangle::area(self)
+    }
+
+    #[inline]
+    fn perimeter(&self, _accuracy: f64) -> f64 {
+        self.a.distance(self.b) +
+            self.b.distance(self.c) +
+            self.c.distance(self.a)
+    }
+
+    #[inline]
+    fn winding(&self, pt: Point) -> i32 {
+        let xmin = self.min_x();
+        let xmax = self.max_x();
+        let ymin = self.min_y();
+        let ymax = self.max_y();
+
+        // TODO: may not be correct
+        if pt.x >= xmin && pt.x < xmax && pt.y >= ymin && pt.y < ymax {
+            if (self.c.x > self.b.x) ^ (self.a.y > self.b.y || self.a.y > self.c.y) {
+                -1
+            } else {
+                1
+            }
+        } else {
+            0
+        }
+    }
+
+    #[inline]
+    fn bounding_box(&self) -> Rect {
+        Rect::new(
+            self.min_x(),
+            self.min_y(),
+            self.max_x(),
+            self.max_y()
+        )
+    }
+
+    #[inline]
+    fn as_rect(&self) -> Option<Rect> {
+        Some(self.bounding_box())
+    }
+
+    #[inline]
+    fn contains(&self, pt: Point) -> bool {
+        self.contains(pt)
+    }
+}
+
+// TODO: tests
diff --git a/src/vec2.rs b/src/vec2.rs
index 8b148d1a..d42f43aa 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -31,6 +31,9 @@ impl Vec2 {
     /// The vector (0, 0).
     pub const ZERO: Vec2 = Vec2::new(0., 0.);
 
+    // The vector (1, 1)
+    pub const IDENTITY: Vec2 = Vec2::new(1., 1.);
+
     /// Create a new vector.
     #[inline]
     pub const fn new(x: f64, y: f64) -> Vec2 {

From 0878d6097280bcdc0f0a6909ebfcd856813e23ec Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Wed, 29 May 2024 21:26:26 +1000
Subject: [PATCH 02/23] chore: format

---
 src/lib.rs      |  4 +--
 src/triangle.rs | 86 ++++++++++++++++++++++---------------------------
 2 files changed, 40 insertions(+), 50 deletions(-)

diff --git a/src/lib.rs b/src/lib.rs
index 676863b3..38e52022 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -98,7 +98,6 @@ mod insets;
 mod line;
 mod mindist;
 pub mod offset;
-mod triangle;
 mod param_curve;
 mod point;
 mod quadbez;
@@ -113,6 +112,7 @@ mod stroke;
 #[cfg(feature = "std")]
 mod svg;
 mod translate_scale;
+mod triangle;
 mod vec2;
 
 pub use crate::affine::*;
@@ -124,7 +124,6 @@ pub use crate::ellipse::*;
 pub use crate::fit::*;
 pub use crate::insets::*;
 pub use crate::line::*;
-pub use crate::triangle::*;
 pub use crate::param_curve::*;
 pub use crate::point::*;
 pub use crate::quadbez::*;
@@ -138,4 +137,5 @@ pub use crate::stroke::*;
 #[cfg(feature = "std")]
 pub use crate::svg::*;
 pub use crate::translate_scale::*;
+pub use crate::triangle::*;
 pub use crate::vec2::*;
diff --git a/src/triangle.rs b/src/triangle.rs
index a0fe54c6..206a85f5 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,7 +2,9 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{Ellipse, Insets, PathEl, Rect, Point, RoundedRect, RoundedRectRadii, Shape, Size, Vec2};
+use crate::{
+    Ellipse, Insets, PathEl, Point, Rect, RoundedRect, RoundedRectRadii, Shape, Size, Vec2,
+};
 
 use core::ops::{Add, Sub};
 
@@ -37,13 +39,21 @@ impl Triangle {
     /// A new [`Triangle`] from three vertices ([`Points`])
     #[inline]
     pub fn new(a: impl Into<Point>, b: impl Into<Point>, c: impl Into<Point>) -> Self {
-        Self { a: a.into(), b: b.into(), c: c.into() }
+        Self {
+            a: a.into(),
+            b: b.into(),
+            c: c.into(),
+        }
     }
 
     /// A new [`Triangle`] from three float vertex coordinates
     #[inline]
     pub const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
-        Self { a: Point::new(a.0, a.1), b: Point::new(b.0, b.1), c: Point::new(c.0, c.1) }
+        Self {
+            a: Point::new(a.0, a.1),
+            b: Point::new(b.0, b.1),
+            c: Point::new(c.0, c.1),
+        }
     }
 
     /// A new `Triangle` from centroid and sizes
@@ -64,7 +74,8 @@ impl Triangle {
         const THETA: f64 = 60.0; // equilateral triangle guarantee
         let center = center.into().to_vec2();
 
-        let h = (radius/((THETA/2.0).tan()) *radius/((THETA/2.0).tan()) + radius*radius).sqrt();
+        let h = (radius / ((THETA / 2.0).tan()) * radius / ((THETA / 2.0).tan()) + radius * radius)
+            .sqrt();
         let a = center.y + radius;
         let b = center + Vec2::IDENTITY * h;
         let c = center - Vec2::IDENTITY * h;
@@ -88,8 +99,8 @@ impl Triangle {
     #[inline]
     pub fn centroid(&self) -> Point {
         Point::new(
-            (self.a.x + self.b.x + self.c.x)/3.0,
-            (self.a.y + self.b.y + self.c.y)/3.0,
+            (self.a.x + self.b.x + self.c.x) / 3.0,
+            (self.a.y + self.b.y + self.c.y) / 3.0,
         )
     }
 
@@ -101,7 +112,7 @@ impl Triangle {
         [
             self.a.distance(centroid),
             self.b.distance(centroid),
-            self.c.distance(centroid)
+            self.c.distance(centroid),
         ]
     }
 
@@ -113,10 +124,10 @@ impl Triangle {
         let bc = self.b.distance(self.c);
 
         // cos rule
-        let theta = ((bc*bc - ab*ab - ac*ac)/-2.0*ab*ac).acos();
+        let theta = ((bc * bc - ab * ab - ac * ac) / -2.0 * ab * ac).acos();
 
         // A = 1/2*a*b*sin(C)
-        (ab*ac*theta.sin())/2.0
+        (ab * ac * theta.sin()) / 2.0
     }
 
     // TODO: maybe make height functions for right and non right angled triangles
@@ -125,7 +136,7 @@ impl Triangle {
     #[inline]
     pub fn right_angled_area(&self) -> f64 {
         // A = 1/2*b*h
-        (self.b.distance(self.c)*self.b.midpoint(self.c).distance(self.a))/2.0
+        (self.b.distance(self.c) * self.b.midpoint(self.c).distance(self.a)) / 2.0
     }
 
     /// Maximum x-coordinate of the [`Triangle`]'s vertices
@@ -167,7 +178,10 @@ impl Triangle {
     /// `true` if `point` lies within `self`
     #[inline]
     pub fn contains(&self, point: Point) -> bool {
-        point.x >= self.min_x() && point.x < self.max_x() && point.y >= self.min_y() && point.y < self.max_y()
+        point.x >= self.min_x()
+            && point.x < self.max_x()
+            && point.y >= self.min_y()
+            && point.y < self.max_y()
     }
 
     /// The smallest radius of a circle that is within the [`Triangle`]
@@ -190,38 +204,26 @@ impl Triangle {
         Self::new(
             (self.a.to_vec2() + Vec2::IDENTITY * sizes[0]).to_point(),
             (self.b.to_vec2() + Vec2::IDENTITY * sizes[1]).to_point(),
-            (self.c.to_vec2() + Vec2::IDENTITY * sizes[2]).to_point()
+            (self.c.to_vec2() + Vec2::IDENTITY * sizes[2]).to_point(),
         )
     }
 
     /// A new [`Triangle`] with each vertecie's ordinates rounded to the nearest integer
     #[inline]
     pub fn round(self) -> Self {
-        Self::new(
-            self.a.round(),
-            self.b.round(),
-            self.c.round(),
-        )
+        Self::new(self.a.round(), self.b.round(), self.c.round())
     }
 
     /// A new [`Triangle`] with each vertecie's ordinates rounded up to the nearest integer
     #[inline]
     pub fn ceil(self) -> Self {
-        Self::new(
-            self.a.ceil(),
-            self.b.ceil(),
-            self.c.ceil(),
-        )
+        Self::new(self.a.ceil(), self.b.ceil(), self.c.ceil())
     }
 
     /// A new [`Triangle`] with each vertecie's ordinates rounded down to the nearest integer
     #[inline]
     pub fn floor(self) -> Self {
-        Self::new(
-            self.a.floor(),
-            self.b.floor(),
-            self.c.floor(),
-        )
+        Self::new(self.a.floor(), self.b.floor(), self.c.floor())
     }
 
     /// A new [`Triangle`],
@@ -231,11 +233,7 @@ impl Triangle {
     /// with integer coordinates that is a subset of `self`.
     #[inline]
     pub fn expand(self) -> Self {
-        Self::new(
-            self.a.expand(),
-            self.b.expand(),
-            self.c.expand(),
-        )
+        Self::new(self.a.expand(), self.b.expand(), self.c.expand())
     }
 
     /// Returns a new [`Triangle`],
@@ -245,11 +243,7 @@ impl Triangle {
     /// with integer coordinates that is a subset of `self`.
     #[inline]
     pub fn trunc(self) -> Self {
-        Self::new(
-            self.a.trunc(),
-            self.b.trunc(),
-            self.c.trunc()
-        )
+        Self::new(self.a.trunc(), self.b.trunc(), self.c.trunc())
     }
 
     /// Scales the [`Triangle`] by a `factor`
@@ -310,14 +304,17 @@ impl Sub<Vec2> for Triangle {
 #[doc(hidden)]
 pub struct TrianglePathIter {
     triangle: Triangle,
-    ix: usize
+    ix: usize,
 }
 
 impl Shape for Triangle {
     type PathElementsIter<'iter> = TrianglePathIter;
 
     fn path_elements(&self, _tolerance: f64) -> TrianglePathIter {
-        TrianglePathIter { triangle: *self, ix: 0 }
+        TrianglePathIter {
+            triangle: *self,
+            ix: 0,
+        }
     }
 
     #[inline]
@@ -327,9 +324,7 @@ impl Shape for Triangle {
 
     #[inline]
     fn perimeter(&self, _accuracy: f64) -> f64 {
-        self.a.distance(self.b) +
-            self.b.distance(self.c) +
-            self.c.distance(self.a)
+        self.a.distance(self.b) + self.b.distance(self.c) + self.c.distance(self.a)
     }
 
     #[inline]
@@ -353,12 +348,7 @@ impl Shape for Triangle {
 
     #[inline]
     fn bounding_box(&self) -> Rect {
-        Rect::new(
-            self.min_x(),
-            self.min_y(),
-            self.max_x(),
-            self.max_y()
-        )
+        Rect::new(self.min_x(), self.min_y(), self.max_x(), self.max_y())
     }
 
     #[inline]

From c5b255e7bf35c3ddb31e3f641d1c5cdb6d738568 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Thu, 30 May 2024 17:34:18 +1000
Subject: [PATCH 03/23] path iterator

---
 src/triangle.rs | 23 ++++++++++++++++++++---
 1 file changed, 20 insertions(+), 3 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 206a85f5..969458e9 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -7,6 +7,7 @@ use crate::{
 };
 
 use core::ops::{Add, Sub};
+use core::f64::consts::FRAC_PI_3;
 
 /// Triangle
 //     A
@@ -71,7 +72,7 @@ impl Triangle {
     /// takes the center and a point equidistant to the midpoints of the vertices (radius)
     #[inline]
     pub fn from_center_size(center: impl Into<Point>, radius: f64) -> Self {
-        const THETA: f64 = 60.0; // equilateral triangle guarantee
+        const THETA: f64 = FRAC_PI_3; // equilateral triangle guarantee
         let center = center.into().to_vec2();
 
         let h = (radius / ((THETA / 2.0).tan()) * radius / ((THETA / 2.0).tan()) + radius * radius)
@@ -299,8 +300,6 @@ impl Sub<Vec2> for Triangle {
 
 // TODO: sub, see insets TODO
 
-// TEMP
-// TODO: implement
 #[doc(hidden)]
 pub struct TrianglePathIter {
     triangle: Triangle,
@@ -362,4 +361,22 @@ impl Shape for Triangle {
     }
 }
 
+// Anticlockwise direction from vertices a, b, c
+// NOTE: vertices a, b and c are not garunteed to be in order as described in the struct comments
+//       (i.e. vertex a is topmost, vertex b is leftmost, and vertex c is rightmost)
+impl Iterator for TrianglePathIter {
+    type Item = PathEl;
+
+    fn next(&mut self) -> Option<PathEl> {
+        self.ix += 1;
+        match self.ix {
+            1 => Some(PathEl::MoveTo(self.triangle.a)),
+            2 => Some(PathEl::LineTo(self.triangle.b)),
+            3 => Some(PathEl::LineTo(self.triangle.c)),
+            4 => Some(PathEl::ClosePath),
+            _ => None,
+        }
+    }
+}
+
 // TODO: tests

From 8bfd8f45599b56226ddd36b9e5d9d45c2bbc45f7 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Thu, 30 May 2024 18:34:28 +1000
Subject: [PATCH 04/23] extend api

fix TODOS is_nan is_finite ellipses
---
 src/ellipse.rs  | 20 +++++++++++++++++++-
 src/triangle.rs | 36 ++++++++++++++++++++++++++----------
 src/vec2.rs     |  2 +-
 3 files changed, 46 insertions(+), 12 deletions(-)

diff --git a/src/ellipse.rs b/src/ellipse.rs
index af1c11e6..c6217f52 100644
--- a/src/ellipse.rs
+++ b/src/ellipse.rs
@@ -9,7 +9,7 @@ use core::{
     ops::{Add, Mul, Sub},
 };
 
-use crate::{Affine, Arc, ArcAppendIter, Circle, PathEl, Point, Rect, Shape, Size, Vec2};
+use crate::{Affine, Arc, ArcAppendIter, Circle, PathEl, Point, Rect, Shape, Size, Triangle, Vec2};
 
 #[cfg(not(feature = "std"))]
 use crate::common::FloatFuncs;
@@ -58,6 +58,24 @@ impl Ellipse {
         Ellipse::private_new(center, width, height, 0.0)
     }
 
+    // TODO: this returns the largest circle not ellipse
+    /// Returns the largest ellipse that can be bounded by this [`Triangle`].
+    ///
+    /// This ellipse is always axis-aligned; to apply rotation you can call
+    /// [`with_rotation`] with the result.
+    ///
+    /// [`with_rotation`]: Ellipse::with_rotation
+    #[inline]
+    pub fn from_triangle(triangle: Triangle) -> Self {
+        let radius = triangle.radius();
+        Ellipse::private_new(
+            triangle.centroid().to_vec2(),
+            radius / 2.0,
+            radius / 2.0,
+            0.0,
+        )
+    }
+
     /// Create an ellipse from an affine transformation of the unit circle.
     #[inline]
     pub fn from_affine(affine: Affine) -> Self {
diff --git a/src/triangle.rs b/src/triangle.rs
index 969458e9..02857481 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,12 +2,10 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{
-    Ellipse, Insets, PathEl, Point, Rect, RoundedRect, RoundedRectRadii, Shape, Size, Vec2,
-};
+use crate::{Ellipse, PathEl, Point, Rect, Shape, Vec2};
 
-use core::ops::{Add, Sub};
 use core::f64::consts::FRAC_PI_3;
+use core::ops::{Add, Sub};
 
 /// Triangle
 //     A
@@ -20,8 +18,11 @@ use core::f64::consts::FRAC_PI_3;
 #[cfg_attr(feature = "schemars", derive(schemars::JsonSchema))]
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
 pub struct Triangle {
+    /// vertex a
     pub a: Point,
+    /// vertex b
     pub b: Point,
+    /// vertex c
     pub c: Point,
 }
 
@@ -35,7 +36,8 @@ impl Triangle {
     /// The empty triangle at the origin
     pub const ZERO: Self = Self::from_coords((0., 0.), (0., 0.), (0., 0.));
 
-    pub const IDENTITY: Self = Self::from_coords((1.0, 1.0), (0.0, 0.0), (2.0, 0.0));
+    /// Triangle identity
+    pub const IDENTITY: Self = Self::from_coords((3.0, 6.0), (0.0, 0.0), (6.0, 0.0));
 
     /// A new [`Triangle`] from three vertices ([`Points`])
     #[inline]
@@ -185,7 +187,7 @@ impl Triangle {
             && point.y < self.max_y()
     }
 
-    /// The smallest radius of a circle that is within the [`Triangle`]
+    /// The greatest radius of a circle that is within the [`Triangle`]
     #[inline]
     pub fn radius(&self) -> f64 {
         let ab = self.a.distance(self.b);
@@ -257,7 +259,23 @@ impl Triangle {
         )
     }
 
-    // TODO: functions: insets, to_ellipse (see ellipse TODO), aspect ratio, finite & nan
+    /// Returns the [`Ellipse`] that is bounded by this [`Triangle`].
+    #[inline]
+    pub fn to_ellipse(self) -> Ellipse {
+        Ellipse::from_triangle(self)
+    }
+
+    /// Is this [`Triangle`] finite?
+    #[inline]
+    pub fn is_finite(&self) -> bool {
+        self.a.is_finite() && self.b.is_finite() && self.c.is_finite()
+    }
+
+    /// Is this [`Triangle`] NaN?
+    #[inline]
+    pub fn is_nan(&self) -> bool {
+        self.a.is_nan() || self.b.is_nan() || self.c.is_nan()
+    }
 }
 
 impl From<(Point, Point, Point)> for Triangle {
@@ -298,8 +316,6 @@ impl Sub<Vec2> for Triangle {
     }
 }
 
-// TODO: sub, see insets TODO
-
 #[doc(hidden)]
 pub struct TrianglePathIter {
     triangle: Triangle,
@@ -363,7 +379,7 @@ impl Shape for Triangle {
 
 // Anticlockwise direction from vertices a, b, c
 // NOTE: vertices a, b and c are not garunteed to be in order as described in the struct comments
-//       (i.e. vertex a is topmost, vertex b is leftmost, and vertex c is rightmost)
+//       (i.e. as "vertex a is topmost, vertex b is leftmost, and vertex c is rightmost")
 impl Iterator for TrianglePathIter {
     type Item = PathEl;
 
diff --git a/src/vec2.rs b/src/vec2.rs
index d42f43aa..c160db92 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -31,7 +31,7 @@ impl Vec2 {
     /// The vector (0, 0).
     pub const ZERO: Vec2 = Vec2::new(0., 0.);
 
-    // The vector (1, 1)
+    /// The vector (1, 1)
     pub const IDENTITY: Vec2 = Vec2::new(1., 1.);
 
     /// Create a new vector.

From 84039504e0884ed87c9a5a6b857b1f36fa3e1e6a Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Thu, 30 May 2024 18:37:05 +1000
Subject: [PATCH 05/23] fix ci

---
 src/triangle.rs | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/src/triangle.rs b/src/triangle.rs
index 02857481..ffcf9db7 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -7,6 +7,9 @@ use crate::{Ellipse, PathEl, Point, Rect, Shape, Vec2};
 use core::f64::consts::FRAC_PI_3;
 use core::ops::{Add, Sub};
 
+#[cfg(not(feature = "std"))]
+use crate::common::FloatFuncs;
+
 /// Triangle
 //     A
 //     *

From a8360f0d4e11e568bc1af0c1014e4cd605fc9c98 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sat, 1 Jun 2024 13:11:56 +1000
Subject: [PATCH 06/23] TODO completion progress

more functions & start testing
---
 src/size.rs     |  10 +++
 src/triangle.rs | 174 ++++++++++++++++++++++++++++++++++++++++++------
 src/vec2.rs     |  10 ++-
 3 files changed, 174 insertions(+), 20 deletions(-)

diff --git a/src/size.rs b/src/size.rs
index 009d612a..a352659d 100644
--- a/src/size.rs
+++ b/src/size.rs
@@ -336,6 +336,16 @@ impl SubAssign<Size> for Size {
     }
 }
 
+impl From<f64> for Size {
+    #[inline]
+    fn from(s: f64) -> Size {
+        Size {
+            width: s,
+            height: s,
+        }
+    }
+}
+
 impl From<(f64, f64)> for Size {
     #[inline]
     fn from(v: (f64, f64)) -> Size {
diff --git a/src/triangle.rs b/src/triangle.rs
index ffcf9db7..e2e4a124 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,10 +2,11 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{Ellipse, PathEl, Point, Rect, Shape, Vec2};
+use crate::{Ellipse, PathEl, Point, Rect, Shape, Size, Vec2};
 
 use core::f64::consts::FRAC_PI_3;
 use core::ops::{Add, Sub};
+use std::cmp::*;
 
 #[cfg(not(feature = "std"))]
 use crate::common::FloatFuncs;
@@ -17,7 +18,7 @@ use crate::common::FloatFuncs;
 //   /   \
 //  *-----*
 //  B     C
-#[derive(Clone, Copy, PartialEq)]
+#[derive(Clone, Copy, PartialEq, Debug)]
 #[cfg_attr(feature = "schemars", derive(schemars::JsonSchema))]
 #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
 pub struct Triangle {
@@ -62,29 +63,45 @@ impl Triangle {
         }
     }
 
-    /// A new `Triangle` from centroid and sizes
+    /// A new [`Triangle`] from centroid and sizes ([`Size`]) - offset of each vertex from the centroid
     #[inline]
-    pub fn from_centroid_sizes(centroid: impl Into<Point>, sizes: [f64; 3]) -> Self {
+    pub fn from_centroid_sizes(centroid: impl Into<Point>, sizes: [impl Into<Size>; 3]) -> Self {
         let centroid = centroid.into();
+
+        let mut points: [Point; 3] = Default::default();
+        for (i, size) in sizes.into_iter().enumerate() {
+            points[i] = centroid + size.into().to_vec2();
+        }
+
+        Self::new(points[0], points[1], points[2])
+    }
+
+    /// A new [`Triangle`] with vertex distances of `distances` from the `centroid`
+    ///
+    /// NOTE: the new [`Triangle`] does not keep `centroid`
+    #[inline]
+    pub fn from_centroid_distances(centroid: impl Into<Point>, distances: [f64; 3]) -> Self {
+        let centroid = centroid.into();
+
         Self::new(
-            (centroid.x, centroid.y + sizes[0]),
-            centroid + Vec2::IDENTITY * sizes[1],
-            centroid + Vec2::IDENTITY * sizes[2],
+            centroid + (0.0, distances[0]),
+            centroid - Vec2::ONE * distances[1] / 2.0,
+            centroid + Vec2::ONE * distances[2] / 2.0,
         )
     }
 
     /// A new equilateral [`Triangle`]
     /// takes the center and a point equidistant to the midpoints of the vertices (radius)
     #[inline]
-    pub fn from_center_size(center: impl Into<Point>, radius: f64) -> Self {
+    pub fn from_center_radius(center: impl Into<Point>, radius: f64) -> Self {
         const THETA: f64 = FRAC_PI_3; // equilateral triangle guarantee
         let center = center.into().to_vec2();
 
         let h = (radius / ((THETA / 2.0).tan()) * radius / ((THETA / 2.0).tan()) + radius * radius)
             .sqrt();
         let a = center.y + radius;
-        let b = center + Vec2::IDENTITY * h;
-        let c = center - Vec2::IDENTITY * h;
+        let b = center + Vec2::ONE * h;
+        let c = center - Vec2::ONE * h;
 
         Self::new((center.x, a), b.to_point(), c.to_point())
     }
@@ -95,12 +112,18 @@ impl Triangle {
         Self::from_centroid_sizes(centroid, self.sizes())
     }
 
-    /// Creates a new [`Triangle`] with new `sizes`
+    /// Creates a new [`Triangle`] with `sizes`
     #[inline]
-    pub fn with_sizes(self, sizes: [f64; 3]) -> Self {
+    pub fn with_sizes(self, sizes: [impl Into<Size>; 3]) -> Self {
         Self::from_centroid_sizes(self.centroid(), sizes)
     }
 
+    /// Creates a new [`Triangle`] with each vertice's `distances` offset from centroid
+    #[inline]
+    pub fn with_distances(self, distances: [f64; 3]) -> Self {
+        Self::from_centroid_distances(self.centroid(), distances)
+    }
+
     /// The centroid of the [`Triangle`]
     #[inline]
     pub fn centroid(&self) -> Point {
@@ -110,9 +133,9 @@ impl Triangle {
         )
     }
 
-    /// The distance of each vertex from the centroid
+    /// The euclidean distance of each vertex from the centroid
     #[inline]
-    pub fn sizes(&self) -> [f64; 3] {
+    pub fn distance(&self) -> [f64; 3] {
         let centroid = self.centroid();
 
         [
@@ -122,6 +145,18 @@ impl Triangle {
         ]
     }
 
+    /// The offset of each vertex from the centroid
+    #[inline]
+    pub fn sizes(&self) -> [Size; 3] {
+        let centroid = self.centroid().to_vec2();
+
+        [
+            (centroid - self.a.to_vec2()).to_size(),
+            (centroid - self.b.to_vec2()).to_size(),
+            (centroid - self.c.to_vec2()).to_size(),
+        ]
+    }
+
     /// The area of the [`Triangle`]
     #[inline]
     pub fn area(&self) -> f64 {
@@ -145,6 +180,65 @@ impl Triangle {
         (self.b.distance(self.c) * self.b.midpoint(self.c).distance(self.a)) / 2.0
     }
 
+    /// Updates [`Triangle`]'s vertice positions
+    /// such that [`Triangle::a`] is topmost, [`Triangle::b`] is leftmost, and [`Triangle::c`] is rightmost
+    #[inline]
+    pub fn organise(self) -> Self {
+        Self::new(self.topmost(), self.leftmost(), self.rightmost())
+    }
+
+    /// Vertex coordinate ([`Point`]) of [`Triangle`] with `x` ordinate
+    #[inline]
+    pub fn vertex_from_x(&self, x: f64) -> Option<Point> {
+        self.as_array().iter().find(|&v| v.x == x).copied()
+    }
+
+    /// Vertex coordinate ([`Point`]) of [`Triangle`] with `y` ordinate
+    #[inline]
+    pub fn vertex_from_y(&self, y: f64) -> Option<Point> {
+        self.as_array().iter().find(|&v| v.y == y).copied()
+    }
+
+    /// The topmost vertex of `self` as a [`Point`]
+    #[inline]
+    pub fn topmost(&self) -> Point {
+        *self
+            .as_array()
+            .iter()
+            .max_by(|x, y| x.y.total_cmp(&y.y))
+            .unwrap()
+    }
+
+    /// The bottommost vertex of `self` as a [`Point`]
+    #[inline]
+    pub fn bottommost(&self) -> Point {
+        *self
+            .as_array()
+            .iter()
+            .max_by(|x, y| y.y.total_cmp(&x.y))
+            .unwrap()
+    }
+
+    /// The rightmost vertex of `self` as a [`Point`]
+    #[inline]
+    pub fn rightmost(&self) -> Point {
+        *self
+            .as_array()
+            .iter()
+            .max_by(|x, y| x.x.total_cmp(&y.x))
+            .unwrap()
+    }
+
+    /// The leftmost vertex of `self` as a [`Point`]
+    #[inline]
+    pub fn leftmost(&self) -> Point {
+        *self
+            .as_array()
+            .iter()
+            .max_by(|x, y| y.x.total_cmp(&x.x))
+            .unwrap()
+    }
+
     /// Maximum x-coordinate of the [`Triangle`]'s vertices
     #[inline]
     pub fn max_x(&self) -> f64 {
@@ -208,9 +302,9 @@ impl Triangle {
     /// Expand the triangle by a constant amount (`sizes`) in all directions
     pub fn inflate(&self, sizes: [f64; 3]) -> Self {
         Self::new(
-            (self.a.to_vec2() + Vec2::IDENTITY * sizes[0]).to_point(),
-            (self.b.to_vec2() + Vec2::IDENTITY * sizes[1]).to_point(),
-            (self.c.to_vec2() + Vec2::IDENTITY * sizes[2]).to_point(),
+            (self.a.to_vec2() + Vec2::ONE * sizes[0]).to_point(),
+            (self.b.to_vec2() + Vec2::ONE * sizes[1]).to_point(),
+            (self.c.to_vec2() + Vec2::ONE * sizes[2]).to_point(),
         )
     }
 
@@ -279,6 +373,12 @@ impl Triangle {
     pub fn is_nan(&self) -> bool {
         self.a.is_nan() || self.b.is_nan() || self.c.is_nan()
     }
+
+    /// [`Triangle`]'s vertices as an array of Points
+    #[inline]
+    pub fn as_array(&self) -> [Point; 3] {
+        [self.a, self.b, self.c]
+    }
 }
 
 impl From<(Point, Point, Point)> for Triangle {
@@ -289,7 +389,7 @@ impl From<(Point, Point, Point)> for Triangle {
 
 impl From<(Point, f64)> for Triangle {
     fn from(params: (Point, f64)) -> Triangle {
-        Triangle::from_center_size(params.0, params.1)
+        Triangle::from_center_radius(params.0, params.1)
     }
 }
 
@@ -398,4 +498,40 @@ impl Iterator for TrianglePathIter {
     }
 }
 
-// TODO: tests
+#[cfg(test)]
+mod tests {
+    use crate::{Point, Triangle};
+
+    #[test]
+    fn from_centroid_distances() {
+        let test = Triangle::from_centroid_distances((0.6, 12.2), [11.9, 1.2, 12.3]);
+        let expected = Triangle::new((0.0, 0.0), (0.1882, 4.3293), (0.8494, 18.1853));
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn from_center_radius() {
+        let test = Triangle::from_center_radius((0.2, 3.3), 10.1);
+        let expected = Triangle::new((20.4, 3.3), (-9.9, 20.779), (-9.9, -14.179));
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn centroid() {
+        let test = Triangle::new((-90.02, 3.5), (7.2, -9.3), (8.0, 9.1)).centroid();
+        let expected = Point::new(-24.939999999999998, 1.0999999999999996);
+
+        assert_eq!(test, expected);
+    }
+
+    // should only need one out of Triangle:: topmost, rightmost, leftmost, bottommost
+    #[test]
+    fn topmost() {
+        let test = Triangle::new((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).topmost();
+        let expected = Point::new(12.3, 12.3);
+
+        assert_eq!(test, expected);
+    }
+}
diff --git a/src/vec2.rs b/src/vec2.rs
index c160db92..3fa8be56 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -32,7 +32,7 @@ impl Vec2 {
     pub const ZERO: Vec2 = Vec2::new(0., 0.);
 
     /// The vector (1, 1)
-    pub const IDENTITY: Vec2 = Vec2::new(1., 1.);
+    pub const ONE: Vec2 = Vec2::new(1., 1.);
 
     /// Create a new vector.
     #[inline]
@@ -142,6 +142,14 @@ impl Vec2 {
         }
     }
 
+    /// A vector with magnitude `magnitude` with components in `direction` direction
+    ///
+    /// see [`Self::from_angle`] to get a unit vector from an angle
+    ///
+    /// NOTE: direction should be a unit vector, it is not normalized in this function
+    // #[inline]
+    // pub fn from_magnitude(magnitude: f64, direction: Vec2) -> Vec2 {}
+
     /// Linearly interpolate between two vectors.
     #[inline]
     pub fn lerp(self, other: Vec2, t: f64) -> Vec2 {

From be6ed8d8792555e55d8baf1f9c15b9fcdee31e25 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sat, 1 Jun 2024 15:59:09 +1000
Subject: [PATCH 07/23] tests

add all necessary tests
---
 src/point.rs    |  25 ++++++++
 src/triangle.rs | 150 +++++++++++++++++++++++++++++++++++-------------
 src/vec2.rs     |   8 ++-
 3 files changed, 139 insertions(+), 44 deletions(-)

diff --git a/src/point.rs b/src/point.rs
index cd4909b4..8f17af9e 100644
--- a/src/point.rs
+++ b/src/point.rs
@@ -3,6 +3,7 @@
 
 //! A 2D point.
 
+use core::cmp::Ordering;
 use core::fmt;
 use core::ops::{Add, AddAssign, Sub, SubAssign};
 
@@ -185,6 +186,30 @@ impl Point {
     pub fn is_nan(self) -> bool {
         self.x.is_nan() || self.y.is_nan()
     }
+
+    /// The topmost [`Point`]
+    #[inline]
+    pub fn topmost(&self, other: &Self) -> Ordering {
+        self.y.total_cmp(&other.y)
+    }
+
+    /// The bottommost [`Point`]
+    #[inline]
+    pub fn bottommost(&self, other: &Self) -> Ordering {
+        other.y.total_cmp(&self.y)
+    }
+
+    /// The rightmost [`Point`]
+    #[inline]
+    pub fn rightmost(&self, other: &Self) -> Ordering {
+        self.x.total_cmp(&other.x)
+    }
+
+    /// The leftmost [`Point`]
+    #[inline]
+    pub fn leftmost(&self, other: &Self) -> Ordering {
+        other.x.total_cmp(&self.x)
+    }
 }
 
 impl From<(f32, f32)> for Point {
diff --git a/src/triangle.rs b/src/triangle.rs
index e2e4a124..d676bdbf 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -4,9 +4,9 @@
 //! Triangle shape
 use crate::{Ellipse, PathEl, Point, Rect, Shape, Size, Vec2};
 
+use core::cmp::*;
 use core::f64::consts::FRAC_PI_3;
 use core::ops::{Add, Sub};
-use std::cmp::*;
 
 #[cfg(not(feature = "std"))]
 use crate::common::FloatFuncs;
@@ -32,16 +32,25 @@ pub struct Triangle {
 
 impl Default for Triangle {
     fn default() -> Self {
-        Self::IDENTITY
+        Self::EQUILATERAL
     }
 }
 
+macro_rules! most_ordering {
+    ($x: ident, $by: block) => {
+        *$x.as_array().iter().max_by($by).unwrap()
+    };
+}
+
 impl Triangle {
-    /// The empty triangle at the origin
+    /// The empty [`Triangle`] at the origin
     pub const ZERO: Self = Self::from_coords((0., 0.), (0., 0.), (0., 0.));
 
-    /// Triangle identity
-    pub const IDENTITY: Self = Self::from_coords((3.0, 6.0), (0.0, 0.0), (6.0, 0.0));
+    /// empty [`Triangle`] at (1.0, 1.0)
+    pub const ONE: Self = Self::from_coords((1.0, 1.0), (1.0, 1.0), (1.0, 1.0));
+
+    /// equilateral [`Triangle`] identity
+    pub const EQUILATERAL: Self = Self::from_coords((3.0, 6.0), (0.0, 0.0), (6.0, 0.0));
 
     /// A new [`Triangle`] from three vertices ([`Points`])
     #[inline]
@@ -151,12 +160,18 @@ impl Triangle {
         let centroid = self.centroid().to_vec2();
 
         [
-            (centroid - self.a.to_vec2()).to_size(),
-            (centroid - self.b.to_vec2()).to_size(),
-            (centroid - self.c.to_vec2()).to_size(),
+            (self.a.to_vec2() - centroid).to_size(),
+            (self.b.to_vec2() - centroid).to_size(),
+            (self.c.to_vec2() - centroid).to_size(),
         ]
     }
 
+    /// The perimeter of the [`Triangle`]
+    #[inline]
+    fn perimeter(&self) -> f64 {
+        self.a.distance(self.b) + self.b.distance(self.c) + self.c.distance(self.a)
+    }
+
     /// The area of the [`Triangle`]
     #[inline]
     pub fn area(&self) -> f64 {
@@ -165,7 +180,7 @@ impl Triangle {
         let bc = self.b.distance(self.c);
 
         // cos rule
-        let theta = ((bc * bc - ab * ab - ac * ac) / -2.0 * ab * ac).acos();
+        let theta = ((bc * bc - ab * ab - ac * ac) / (-2.0 * ab * ac)).acos();
 
         // A = 1/2*a*b*sin(C)
         (ab * ac * theta.sin()) / 2.0
@@ -174,17 +189,21 @@ impl Triangle {
     // TODO: maybe make height functions for right and non right angled triangles
 
     /// The area of a right angled [`Triangle`]
+    ///
+    /// NOTE: assumed [`Triangle::organise`]d positions
     #[inline]
     pub fn right_angled_area(&self) -> f64 {
         // A = 1/2*b*h
-        (self.b.distance(self.c) * self.b.midpoint(self.c).distance(self.a)) / 2.0
+        (self.b.distance(self.c) * (self.a.y - self.b.y)) / 2.0
     }
 
     /// Updates [`Triangle`]'s vertice positions
     /// such that [`Triangle::a`] is topmost, [`Triangle::b`] is leftmost, and [`Triangle::c`] is rightmost
     #[inline]
     pub fn organise(self) -> Self {
-        Self::new(self.topmost(), self.leftmost(), self.rightmost())
+        let t = Self::new(self.topmost(), self.leftmost(), self.rightmost());
+
+        t
     }
 
     /// Vertex coordinate ([`Point`]) of [`Triangle`] with `x` ordinate
@@ -202,41 +221,25 @@ impl Triangle {
     /// The topmost vertex of `self` as a [`Point`]
     #[inline]
     pub fn topmost(&self) -> Point {
-        *self
-            .as_array()
-            .iter()
-            .max_by(|x, y| x.y.total_cmp(&y.y))
-            .unwrap()
+        most_ordering!(self, { |x, y| x.topmost(y) })
     }
 
     /// The bottommost vertex of `self` as a [`Point`]
     #[inline]
     pub fn bottommost(&self) -> Point {
-        *self
-            .as_array()
-            .iter()
-            .max_by(|x, y| y.y.total_cmp(&x.y))
-            .unwrap()
+        most_ordering!(self, { |x, y| x.bottommost(y) })
     }
 
     /// The rightmost vertex of `self` as a [`Point`]
     #[inline]
     pub fn rightmost(&self) -> Point {
-        *self
-            .as_array()
-            .iter()
-            .max_by(|x, y| x.x.total_cmp(&y.x))
-            .unwrap()
+        most_ordering!(self, { |x, y| x.x.total_cmp(&y.x) })
     }
 
     /// The leftmost vertex of `self` as a [`Point`]
     #[inline]
     pub fn leftmost(&self) -> Point {
-        *self
-            .as_array()
-            .iter()
-            .max_by(|x, y| y.x.total_cmp(&x.x))
-            .unwrap()
+        most_ordering!(self, { |x, y| y.x.total_cmp(&x.x) })
     }
 
     /// Maximum x-coordinate of the [`Triangle`]'s vertices
@@ -300,11 +303,13 @@ impl Triangle {
     }
 
     /// Expand the triangle by a constant amount (`sizes`) in all directions
-    pub fn inflate(&self, sizes: [f64; 3]) -> Self {
+    pub fn inflate(&self, size: impl Into<Size>) -> Self {
+        let size = size.into();
+
         Self::new(
-            (self.a.to_vec2() + Vec2::ONE * sizes[0]).to_point(),
-            (self.b.to_vec2() + Vec2::ONE * sizes[1]).to_point(),
-            (self.c.to_vec2() + Vec2::ONE * sizes[2]).to_point(),
+            (self.a.to_vec2() + size.to_vec2()).to_point(),
+            (self.b.to_vec2() + size.to_vec2()).to_point(),
+            (self.c.to_vec2() + size.to_vec2()).to_point(),
         )
     }
 
@@ -442,7 +447,7 @@ impl Shape for Triangle {
 
     #[inline]
     fn perimeter(&self, _accuracy: f64) -> f64 {
-        self.a.distance(self.b) + self.b.distance(self.c) + self.c.distance(self.a)
+        self.perimeter()
     }
 
     #[inline]
@@ -500,7 +505,7 @@ impl Iterator for TrianglePathIter {
 
 #[cfg(test)]
 mod tests {
-    use crate::{Point, Triangle};
+    use crate::{Point, Size, Triangle};
 
     #[test]
     fn from_centroid_distances() {
@@ -526,11 +531,74 @@ mod tests {
         assert_eq!(test, expected);
     }
 
-    // should only need one out of Triangle:: topmost, rightmost, leftmost, bottommost
     #[test]
-    fn topmost() {
-        let test = Triangle::new((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).topmost();
-        let expected = Point::new(12.3, 12.3);
+    fn sizes() {
+        let test = Triangle::new((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).sizes();
+        let expected = [
+            Size::new(-110.39999999999999, 86.8),
+            Size::new(-89.19999999999999, -93.39999999999999),
+            Size::new(199.60000000000002, 6.6000000000000085),
+        ];
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn perimeter() {
+        let test = Triangle::new(
+            (781239.273894, 789234.234789),
+            (234897.823471, 378902.234789),
+            (789241.789234, 789234.234897),
+        )
+        .perimeter();
+        let expected = 1380963.0638877784;
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn area() {
+        let test = Triangle::new(
+            (12123.423, 2382.7834),
+            (7892.729, 238.459),
+            (7820.2, 712.23),
+        )
+        .area();
+        let expected = 1079952.91574081;
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn right_angled_area() {
+        let test = Triangle::new((1.2, 5.3), (1.2, 1.6), (10.0, 1.6)).right_angled_area();
+        let expected = 16.28;
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn vertex_from_x() {
+        let test = Triangle::new((1.0, 3.2), (63.8, 30.2), (2.0, 2.0))
+            .vertex_from_x(63.8)
+            .unwrap();
+        let expected = Point::new(63.8, 30.2);
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn organise() {
+        let test = Triangle::new((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).organise();
+        let expected = Triangle::new((12.3, 12.3), (-20.1, 3.2), (9.2, -100.8));
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn radius() {
+        let test = Triangle::EQUILATERAL.radius();
+        let expected = 1.8541019662496845;
 
         assert_eq!(test, expected);
     }
diff --git a/src/vec2.rs b/src/vec2.rs
index 3fa8be56..c6a3b937 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -142,13 +142,15 @@ impl Vec2 {
         }
     }
 
-    /// A vector with magnitude `magnitude` with components in `direction` direction
+    /// A [`Vec2`] with magnitude `magnitude` with components in `direction` direction
     ///
     /// see [`Self::from_angle`] to get a unit vector from an angle
     ///
-    /// NOTE: direction should be a unit vector, it is not normalized in this function
+    /// NOTE: direction should be a unit vector because it is not [`Self::normalize`]d in this function
     // #[inline]
-    // pub fn from_magnitude(magnitude: f64, direction: Vec2) -> Vec2 {}
+    pub fn from_magnitude(magnitude: f64, direction: Vec2) -> Vec2 {
+        todo!()
+    }
 
     /// Linearly interpolate between two vectors.
     #[inline]

From a2527bc698fa5f10f7b97fda97ad5bbc2a5b3a40 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sat, 1 Jun 2024 19:28:19 +1000
Subject: [PATCH 08/23] bug fixes

---
 src/triangle.rs | 90 ++++++++++++++++++++++++++++++++++++-------------
 src/vec2.rs     | 10 ------
 2 files changed, 66 insertions(+), 34 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index d676bdbf..8f78c078 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -5,7 +5,7 @@
 use crate::{Ellipse, PathEl, Point, Rect, Shape, Size, Vec2};
 
 use core::cmp::*;
-use core::f64::consts::FRAC_PI_3;
+use core::f64::consts::FRAC_PI_4;
 use core::ops::{Add, Sub};
 
 #[cfg(not(feature = "std"))]
@@ -94,30 +94,41 @@ impl Triangle {
 
         Self::new(
             centroid + (0.0, distances[0]),
-            centroid - Vec2::ONE * distances[1] / 2.0,
-            centroid + Vec2::ONE * distances[2] / 2.0,
+            centroid + distances[1] * Vec2::from_angle(5.0 * FRAC_PI_4),
+            centroid + distances[2] * Vec2::from_angle(7.0 * FRAC_PI_4),
         )
     }
 
     /// A new equilateral [`Triangle`]
     /// takes the center and a point equidistant to the midpoints of the vertices (radius)
     #[inline]
-    pub fn from_center_radius(center: impl Into<Point>, radius: f64) -> Self {
-        const THETA: f64 = FRAC_PI_3; // equilateral triangle guarantee
-        let center = center.into().to_vec2();
+    pub fn from_radius(radius: f64) -> Self {
+        // sqrt(3) (until https://github.com/rust-lang/rust/issues/103883)
+        pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
 
-        let h = (radius / ((THETA / 2.0).tan()) * radius / ((THETA / 2.0).tan()) + radius * radius)
-            .sqrt();
-        let a = center.y + radius;
-        let b = center + Vec2::ONE * h;
-        let c = center - Vec2::ONE * h;
+        let center = Point::new(0.0, 0.0); // self.centroid().to_vec2();
 
-        Self::new((center.x, a), b.to_point(), c.to_point())
+        let length = 2.0 * SQRT_3 * radius;
+        let height = length * SQRT_3 / 2.0;
+        let distance = height / 3.0;
+
+        let sizes: [Size; 3] = [
+            (0.0, 2.0 * distance).into(),
+            (-length / 2.0, -height / 3.0).into(),
+            (length / 2.0, -height / 3.0).into(),
+        ];
+
+        // let a = (center.x, center.y + 2.0 * distance);
+        // let b = (center + Vec2::ONE * h;
+        // let c = center - Vec2::ONE * h;
+
+        // Self::new(a, b.to_point(), c.to_point())
+        Self::from_centroid_sizes(center, sizes)
     }
 
     /// A new [`Triangle`] moved to `centroid`
     #[inline]
-    pub fn with_centroid(self, centroid: impl Into<Point>) -> Self {
+    pub fn with_centroid(&self, centroid: impl Into<Point>) -> Self {
         Self::from_centroid_sizes(centroid, self.sizes())
     }
 
@@ -294,6 +305,7 @@ impl Triangle {
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
+        // semi perimeter
         let s = (ab + bc + ac) / 2.0;
 
         // Heron's formula
@@ -394,7 +406,7 @@ impl From<(Point, Point, Point)> for Triangle {
 
 impl From<(Point, f64)> for Triangle {
     fn from(params: (Point, f64)) -> Triangle {
-        Triangle::from_center_radius(params.0, params.1)
+        Triangle::from_radius(params.1).with_centroid(params.0)
     }
 }
 
@@ -424,6 +436,8 @@ impl Sub<Vec2> for Triangle {
     }
 }
 
+// TODO: Insets
+
 #[doc(hidden)]
 pub struct TrianglePathIter {
     triangle: Triangle,
@@ -507,25 +521,53 @@ impl Iterator for TrianglePathIter {
 mod tests {
     use crate::{Point, Size, Triangle};
 
+    #[test]
+    fn from_centroid_sizes() {
+        let test = Triangle::from_centroid_distances((0.06, 12.2), [11.9, 1.2, 12.3]);
+        let expected = Triangle::from_coords(
+            (0.06, 24.1),
+            (-0.7885281374238573, 11.351471862576142),
+            (8.757413408594534, 3.5025865914054624),
+        );
+
+        assert_eq!(test, expected);
+    }
+
     #[test]
     fn from_centroid_distances() {
         let test = Triangle::from_centroid_distances((0.6, 12.2), [11.9, 1.2, 12.3]);
-        let expected = Triangle::new((0.0, 0.0), (0.1882, 4.3293), (0.8494, 18.1853));
+        let expected = Triangle::from_coords(
+            (0.6, 24.1),
+            (-0.24852813742385726, 11.351471862576142),
+            (9.297413408594533, 3.5025865914054624),
+        );
+
+        assert_eq!(test, expected);
+    }
+
+    #[test]
+    fn from_radius() {
+        let test = Triangle::from_radius(10.1);
+        let expected = Triangle::from_coords(
+            (0.0, 20.199999999999996),
+            (-17.493713156445658, -10.099999999999998),
+            (17.493713156445658, -10.099999999999998),
+        );
 
         assert_eq!(test, expected);
     }
 
     #[test]
-    fn from_center_radius() {
-        let test = Triangle::from_center_radius((0.2, 3.3), 10.1);
-        let expected = Triangle::new((20.4, 3.3), (-9.9, 20.779), (-9.9, -14.179));
+    fn with_centroid() {
+        let test = Triangle::EQUILATERAL.with_centroid((12.2, -2.3));
+        let expected = Triangle::from_coords((12.2, 1.7000000000000002), (9.2, -4.3), (15.2, -4.3));
 
         assert_eq!(test, expected);
     }
 
     #[test]
     fn centroid() {
-        let test = Triangle::new((-90.02, 3.5), (7.2, -9.3), (8.0, 9.1)).centroid();
+        let test = Triangle::from_coords((-90.02, 3.5), (7.2, -9.3), (8.0, 9.1)).centroid();
         let expected = Point::new(-24.939999999999998, 1.0999999999999996);
 
         assert_eq!(test, expected);
@@ -533,7 +575,7 @@ mod tests {
 
     #[test]
     fn sizes() {
-        let test = Triangle::new((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).sizes();
+        let test = Triangle::from_coords((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).sizes();
         let expected = [
             Size::new(-110.39999999999999, 86.8),
             Size::new(-89.19999999999999, -93.39999999999999),
@@ -571,7 +613,7 @@ mod tests {
 
     #[test]
     fn right_angled_area() {
-        let test = Triangle::new((1.2, 5.3), (1.2, 1.6), (10.0, 1.6)).right_angled_area();
+        let test = Triangle::from_coords((1.2, 5.3), (1.2, 1.6), (10.0, 1.6)).right_angled_area();
         let expected = 16.28;
 
         assert_eq!(test, expected);
@@ -579,7 +621,7 @@ mod tests {
 
     #[test]
     fn vertex_from_x() {
-        let test = Triangle::new((1.0, 3.2), (63.8, 30.2), (2.0, 2.0))
+        let test = Triangle::from_coords((1.0, 3.2), (63.8, 30.2), (2.0, 2.0))
             .vertex_from_x(63.8)
             .unwrap();
         let expected = Point::new(63.8, 30.2);
@@ -589,8 +631,8 @@ mod tests {
 
     #[test]
     fn organise() {
-        let test = Triangle::new((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).organise();
-        let expected = Triangle::new((12.3, 12.3), (-20.1, 3.2), (9.2, -100.8));
+        let test = Triangle::from_coords((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).organise();
+        let expected = Triangle::from_coords((12.3, 12.3), (-20.1, 3.2), (9.2, -100.8));
 
         assert_eq!(test, expected);
     }
diff --git a/src/vec2.rs b/src/vec2.rs
index c6a3b937..5ed8059b 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -142,16 +142,6 @@ impl Vec2 {
         }
     }
 
-    /// A [`Vec2`] with magnitude `magnitude` with components in `direction` direction
-    ///
-    /// see [`Self::from_angle`] to get a unit vector from an angle
-    ///
-    /// NOTE: direction should be a unit vector because it is not [`Self::normalize`]d in this function
-    // #[inline]
-    pub fn from_magnitude(magnitude: f64, direction: Vec2) -> Vec2 {
-        todo!()
-    }
-
     /// Linearly interpolate between two vectors.
     #[inline]
     pub fn lerp(self, other: Vec2, t: f64) -> Vec2 {

From 8b03193f6f932807b723c9d693a4010ba5e5076d Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sun, 2 Jun 2024 08:44:04 +1000
Subject: [PATCH 09/23] working `organise`\(\)

---
 src/triangle.rs | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 8f78c078..f153b3a1 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -212,9 +212,13 @@ impl Triangle {
     /// such that [`Triangle::a`] is topmost, [`Triangle::b`] is leftmost, and [`Triangle::c`] is rightmost
     #[inline]
     pub fn organise(self) -> Self {
-        let t = Self::new(self.topmost(), self.leftmost(), self.rightmost());
+        let mut points = self.as_array();
+        points.sort_by(|x, y| x.rightmost(y));
 
-        t
+        let a = self.topmost();
+        let b = *points.iter().find(|&&p| p != a).unwrap();
+        let c = *points.iter().rev().find(|&&p| p != a).unwrap();
+        Self::new(a, b, c)
     }
 
     /// Vertex coordinate ([`Point`]) of [`Triangle`] with `x` ordinate

From e40449c0dc964c8626129fcd320b12fcce8bc3c9 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sun, 2 Jun 2024 09:02:27 +1000
Subject: [PATCH 10/23] proper ellipse size

---
 src/ellipse.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ellipse.rs b/src/ellipse.rs
index c6217f52..f332e8da 100644
--- a/src/ellipse.rs
+++ b/src/ellipse.rs
@@ -70,8 +70,8 @@ impl Ellipse {
         let radius = triangle.radius();
         Ellipse::private_new(
             triangle.centroid().to_vec2(),
-            radius / 2.0,
-            radius / 2.0,
+            radius,
+            radius,
             0.0,
         )
     }

From 30d9e1c6cf5bae6cc12dfc23dff43f41a63bc075 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sun, 2 Jun 2024 11:04:56 +1000
Subject: [PATCH 11/23] fix ci

---
 src/ellipse.rs  |  7 +------
 src/triangle.rs | 13 +++++++++----
 2 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/src/ellipse.rs b/src/ellipse.rs
index f332e8da..6c1f4b92 100644
--- a/src/ellipse.rs
+++ b/src/ellipse.rs
@@ -68,12 +68,7 @@ impl Ellipse {
     #[inline]
     pub fn from_triangle(triangle: Triangle) -> Self {
         let radius = triangle.radius();
-        Ellipse::private_new(
-            triangle.centroid().to_vec2(),
-            radius,
-            radius,
-            0.0,
-        )
+        Ellipse::private_new(triangle.centroid().to_vec2(), radius, radius, 0.0)
     }
 
     /// Create an ellipse from an affine transformation of the unit circle.
diff --git a/src/triangle.rs b/src/triangle.rs
index f153b3a1..b52e3326 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -525,6 +525,11 @@ impl Iterator for TrianglePathIter {
 mod tests {
     use crate::{Point, Size, Triangle};
 
+    fn assert_approx_eq(x: f64, y: f64) {
+        assert!((x - y).abs() < 1e-7);
+    }
+
+
     #[test]
     fn from_centroid_sizes() {
         let test = Triangle::from_centroid_distances((0.06, 12.2), [11.9, 1.2, 12.3]);
@@ -599,7 +604,7 @@ mod tests {
         .perimeter();
         let expected = 1380963.0638877784;
 
-        assert_eq!(test, expected);
+        assert_approx_eq(test, expected);
     }
 
     #[test]
@@ -612,7 +617,7 @@ mod tests {
         .area();
         let expected = 1079952.91574081;
 
-        assert_eq!(test, expected);
+        assert_approx_eq(test, expected);
     }
 
     #[test]
@@ -620,7 +625,7 @@ mod tests {
         let test = Triangle::from_coords((1.2, 5.3), (1.2, 1.6), (10.0, 1.6)).right_angled_area();
         let expected = 16.28;
 
-        assert_eq!(test, expected);
+        assert_approx_eq(test, expected);
     }
 
     #[test]
@@ -646,6 +651,6 @@ mod tests {
         let test = Triangle::EQUILATERAL.radius();
         let expected = 1.8541019662496845;
 
-        assert_eq!(test, expected);
+        assert_approx_eq(test, expected);
     }
 }

From 5580aefd85eb1ae4175986041bc8f68f320ba2f4 Mon Sep 17 00:00:00 2001
From: amy <fabianpaci@protonmail.com>
Date: Sun, 2 Jun 2024 11:08:15 +1000
Subject: [PATCH 12/23] chore: format

---
 src/triangle.rs | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index b52e3326..5d4afdbd 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -529,7 +529,6 @@ mod tests {
         assert!((x - y).abs() < 1e-7);
     }
 
-
     #[test]
     fn from_centroid_sizes() {
         let test = Triangle::from_centroid_distances((0.06, 12.2), [11.9, 1.2, 12.3]);

From 4d8f906af02ebe9bdff84ffe75b35161da5e736f Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Thu, 15 Aug 2024 14:17:39 +1000
Subject: [PATCH 13/23] apply suggestions

---
 src/ellipse.rs  |  15 +-
 src/size.rs     |  10 --
 src/triangle.rs | 386 +++++++-----------------------------------------
 src/vec2.rs     |   3 -
 4 files changed, 52 insertions(+), 362 deletions(-)

diff --git a/src/ellipse.rs b/src/ellipse.rs
index 6c1f4b92..af1c11e6 100644
--- a/src/ellipse.rs
+++ b/src/ellipse.rs
@@ -9,7 +9,7 @@ use core::{
     ops::{Add, Mul, Sub},
 };
 
-use crate::{Affine, Arc, ArcAppendIter, Circle, PathEl, Point, Rect, Shape, Size, Triangle, Vec2};
+use crate::{Affine, Arc, ArcAppendIter, Circle, PathEl, Point, Rect, Shape, Size, Vec2};
 
 #[cfg(not(feature = "std"))]
 use crate::common::FloatFuncs;
@@ -58,19 +58,6 @@ impl Ellipse {
         Ellipse::private_new(center, width, height, 0.0)
     }
 
-    // TODO: this returns the largest circle not ellipse
-    /// Returns the largest ellipse that can be bounded by this [`Triangle`].
-    ///
-    /// This ellipse is always axis-aligned; to apply rotation you can call
-    /// [`with_rotation`] with the result.
-    ///
-    /// [`with_rotation`]: Ellipse::with_rotation
-    #[inline]
-    pub fn from_triangle(triangle: Triangle) -> Self {
-        let radius = triangle.radius();
-        Ellipse::private_new(triangle.centroid().to_vec2(), radius, radius, 0.0)
-    }
-
     /// Create an ellipse from an affine transformation of the unit circle.
     #[inline]
     pub fn from_affine(affine: Affine) -> Self {
diff --git a/src/size.rs b/src/size.rs
index a352659d..009d612a 100644
--- a/src/size.rs
+++ b/src/size.rs
@@ -336,16 +336,6 @@ impl SubAssign<Size> for Size {
     }
 }
 
-impl From<f64> for Size {
-    #[inline]
-    fn from(s: f64) -> Size {
-        Size {
-            width: s,
-            height: s,
-        }
-    }
-}
-
 impl From<(f64, f64)> for Size {
     #[inline]
     fn from(v: (f64, f64)) -> Size {
diff --git a/src/triangle.rs b/src/triangle.rs
index 5d4afdbd..d7c8ccf9 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,7 +2,7 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{Ellipse, PathEl, Point, Rect, Shape, Size, Vec2};
+use crate::{PathEl, Point, Rect, Shape, Vec2};
 
 use core::cmp::*;
 use core::f64::consts::FRAC_PI_4;
@@ -30,18 +30,6 @@ pub struct Triangle {
     pub c: Point,
 }
 
-impl Default for Triangle {
-    fn default() -> Self {
-        Self::EQUILATERAL
-    }
-}
-
-macro_rules! most_ordering {
-    ($x: ident, $by: block) => {
-        *$x.as_array().iter().max_by($by).unwrap()
-    };
-}
-
 impl Triangle {
     /// The empty [`Triangle`] at the origin
     pub const ZERO: Self = Self::from_coords((0., 0.), (0., 0.), (0., 0.));
@@ -49,8 +37,15 @@ impl Triangle {
     /// empty [`Triangle`] at (1.0, 1.0)
     pub const ONE: Self = Self::from_coords((1.0, 1.0), (1.0, 1.0), (1.0, 1.0));
 
-    /// equilateral [`Triangle`] identity
-    pub const EQUILATERAL: Self = Self::from_coords((3.0, 6.0), (0.0, 0.0), (6.0, 0.0));
+    /// equilateral [`Triangle`]
+    pub const EQUILATERAL: Self = Self::from_coords(
+        (
+            1.0 / 2.0,
+            1.732050807568877293527446341505872367_f64 / 2.0, /* (sqrt 3)/2 */
+        ),
+        (0.0, 0.0),
+        (1.0, 0.0),
+    );
 
     /// A new [`Triangle`] from three vertices ([`Points`])
     #[inline]
@@ -72,213 +67,41 @@ impl Triangle {
         }
     }
 
-    /// A new [`Triangle`] from centroid and sizes ([`Size`]) - offset of each vertex from the centroid
+    /// A new [`Triangle`] from centroid and offsets ([`Vec2`]) - offset of each vertex from the centroid
     #[inline]
-    pub fn from_centroid_sizes(centroid: impl Into<Point>, sizes: [impl Into<Size>; 3]) -> Self {
+    fn from_centroid_offsets(centroid: impl Into<Point>, offsets: [impl Into<Vec2>; 3]) -> Self {
         let centroid = centroid.into();
 
         let mut points: [Point; 3] = Default::default();
-        for (i, size) in sizes.into_iter().enumerate() {
-            points[i] = centroid + size.into().to_vec2();
+        for (i, offset) in offsets.into_iter().enumerate() {
+            points[i] = centroid + offset.into();
         }
 
         Self::new(points[0], points[1], points[2])
     }
 
-    /// A new [`Triangle`] with vertex distances of `distances` from the `centroid`
-    ///
-    /// NOTE: the new [`Triangle`] does not keep `centroid`
-    #[inline]
-    pub fn from_centroid_distances(centroid: impl Into<Point>, distances: [f64; 3]) -> Self {
-        let centroid = centroid.into();
-
-        Self::new(
-            centroid + (0.0, distances[0]),
-            centroid + distances[1] * Vec2::from_angle(5.0 * FRAC_PI_4),
-            centroid + distances[2] * Vec2::from_angle(7.0 * FRAC_PI_4),
-        )
-    }
-
-    /// A new equilateral [`Triangle`]
-    /// takes the center and a point equidistant to the midpoints of the vertices (radius)
-    #[inline]
-    pub fn from_radius(radius: f64) -> Self {
-        // sqrt(3) (until https://github.com/rust-lang/rust/issues/103883)
-        pub const SQRT_3: f64 = 1.732050807568877293527446341505872367_f64;
-
-        let center = Point::new(0.0, 0.0); // self.centroid().to_vec2();
-
-        let length = 2.0 * SQRT_3 * radius;
-        let height = length * SQRT_3 / 2.0;
-        let distance = height / 3.0;
-
-        let sizes: [Size; 3] = [
-            (0.0, 2.0 * distance).into(),
-            (-length / 2.0, -height / 3.0).into(),
-            (length / 2.0, -height / 3.0).into(),
-        ];
-
-        // let a = (center.x, center.y + 2.0 * distance);
-        // let b = (center + Vec2::ONE * h;
-        // let c = center - Vec2::ONE * h;
-
-        // Self::new(a, b.to_point(), c.to_point())
-        Self::from_centroid_sizes(center, sizes)
-    }
-
-    /// A new [`Triangle`] moved to `centroid`
-    #[inline]
-    pub fn with_centroid(&self, centroid: impl Into<Point>) -> Self {
-        Self::from_centroid_sizes(centroid, self.sizes())
-    }
-
-    /// Creates a new [`Triangle`] with `sizes`
-    #[inline]
-    pub fn with_sizes(self, sizes: [impl Into<Size>; 3]) -> Self {
-        Self::from_centroid_sizes(self.centroid(), sizes)
-    }
-
-    /// Creates a new [`Triangle`] with each vertice's `distances` offset from centroid
-    #[inline]
-    pub fn with_distances(self, distances: [f64; 3]) -> Self {
-        Self::from_centroid_distances(self.centroid(), distances)
-    }
-
     /// The centroid of the [`Triangle`]
     #[inline]
     pub fn centroid(&self) -> Point {
-        Point::new(
-            (self.a.x + self.b.x + self.c.x) / 3.0,
-            (self.a.y + self.b.y + self.c.y) / 3.0,
-        )
-    }
-
-    /// The euclidean distance of each vertex from the centroid
-    #[inline]
-    pub fn distance(&self) -> [f64; 3] {
-        let centroid = self.centroid();
-
-        [
-            self.a.distance(centroid),
-            self.b.distance(centroid),
-            self.c.distance(centroid),
-        ]
+        (1.0 / 3.0 * (self.a.to_vec2() + self.b.to_vec2() + self.c.to_vec2())).to_point()
     }
 
     /// The offset of each vertex from the centroid
     #[inline]
-    pub fn sizes(&self) -> [Size; 3] {
+    pub fn offsets(&self) -> [Vec2; 3] {
         let centroid = self.centroid().to_vec2();
 
         [
-            (self.a.to_vec2() - centroid).to_size(),
-            (self.b.to_vec2() - centroid).to_size(),
-            (self.c.to_vec2() - centroid).to_size(),
+            (self.a.to_vec2() - centroid),
+            (self.b.to_vec2() - centroid),
+            (self.c.to_vec2() - centroid),
         ]
     }
 
-    /// The perimeter of the [`Triangle`]
-    #[inline]
-    fn perimeter(&self) -> f64 {
-        self.a.distance(self.b) + self.b.distance(self.c) + self.c.distance(self.a)
-    }
-
     /// The area of the [`Triangle`]
     #[inline]
     pub fn area(&self) -> f64 {
-        let ab = self.a.distance(self.b);
-        let ac = self.a.distance(self.c);
-        let bc = self.b.distance(self.c);
-
-        // cos rule
-        let theta = ((bc * bc - ab * ab - ac * ac) / (-2.0 * ab * ac)).acos();
-
-        // A = 1/2*a*b*sin(C)
-        (ab * ac * theta.sin()) / 2.0
-    }
-
-    // TODO: maybe make height functions for right and non right angled triangles
-
-    /// The area of a right angled [`Triangle`]
-    ///
-    /// NOTE: assumed [`Triangle::organise`]d positions
-    #[inline]
-    pub fn right_angled_area(&self) -> f64 {
-        // A = 1/2*b*h
-        (self.b.distance(self.c) * (self.a.y - self.b.y)) / 2.0
-    }
-
-    /// Updates [`Triangle`]'s vertice positions
-    /// such that [`Triangle::a`] is topmost, [`Triangle::b`] is leftmost, and [`Triangle::c`] is rightmost
-    #[inline]
-    pub fn organise(self) -> Self {
-        let mut points = self.as_array();
-        points.sort_by(|x, y| x.rightmost(y));
-
-        let a = self.topmost();
-        let b = *points.iter().find(|&&p| p != a).unwrap();
-        let c = *points.iter().rev().find(|&&p| p != a).unwrap();
-        Self::new(a, b, c)
-    }
-
-    /// Vertex coordinate ([`Point`]) of [`Triangle`] with `x` ordinate
-    #[inline]
-    pub fn vertex_from_x(&self, x: f64) -> Option<Point> {
-        self.as_array().iter().find(|&v| v.x == x).copied()
-    }
-
-    /// Vertex coordinate ([`Point`]) of [`Triangle`] with `y` ordinate
-    #[inline]
-    pub fn vertex_from_y(&self, y: f64) -> Option<Point> {
-        self.as_array().iter().find(|&v| v.y == y).copied()
-    }
-
-    /// The topmost vertex of `self` as a [`Point`]
-    #[inline]
-    pub fn topmost(&self) -> Point {
-        most_ordering!(self, { |x, y| x.topmost(y) })
-    }
-
-    /// The bottommost vertex of `self` as a [`Point`]
-    #[inline]
-    pub fn bottommost(&self) -> Point {
-        most_ordering!(self, { |x, y| x.bottommost(y) })
-    }
-
-    /// The rightmost vertex of `self` as a [`Point`]
-    #[inline]
-    pub fn rightmost(&self) -> Point {
-        most_ordering!(self, { |x, y| x.x.total_cmp(&y.x) })
-    }
-
-    /// The leftmost vertex of `self` as a [`Point`]
-    #[inline]
-    pub fn leftmost(&self) -> Point {
-        most_ordering!(self, { |x, y| y.x.total_cmp(&x.x) })
-    }
-
-    /// Maximum x-coordinate of the [`Triangle`]'s vertices
-    #[inline]
-    pub fn max_x(&self) -> f64 {
-        self.a.x.max(self.b.x.max(self.c.x))
-    }
-
-    /// Minimum x-coordinate of the [`Triangle`]'s vertices
-    #[inline]
-    pub fn min_x(&self) -> f64 {
-        self.a.x.min(self.b.x.min(self.c.x))
-    }
-
-    /// Mayimum y-coordinate of the [`Triangle`]'s vertices
-    #[inline]
-    pub fn max_y(&self) -> f64 {
-        self.a.y.max(self.b.y.max(self.c.y))
-    }
-
-    /// Minimum y-coordinate of the [`Triangle`]'s vertices
-    #[inline]
-    pub fn min_y(&self) -> f64 {
-        self.a.y.min(self.b.y.min(self.c.y))
+        0.5 * (self.b - self.a).cross(self.c - self.a)
     }
 
     /// Whether this [`Triangle`] has no (zero) area
@@ -287,102 +110,37 @@ impl Triangle {
         self.area() == 0.0
     }
 
-    /// Whether this right angled [`Triangle`] has no (zero) area
-    #[inline]
-    pub fn is_empty_right_angled(&self) -> bool {
-        self.right_angled_area() == 0.0
-    }
-
-    /// `true` if `point` lies within `self`
-    #[inline]
-    pub fn contains(&self, point: Point) -> bool {
-        point.x >= self.min_x()
-            && point.x < self.max_x()
-            && point.y >= self.min_y()
-            && point.y < self.max_y()
-    }
-
     /// The greatest radius of a circle that is within the [`Triangle`]
     #[inline]
-    pub fn radius(&self) -> f64 {
+    pub fn incircle(&self) -> f64 {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
-        // semi perimeter
-        let s = (ab + bc + ac) / 2.0;
-
-        // Heron's formula
-        let area = (s * (s - ab) * (s - bc) * (s - ac)).sqrt();
-
-        area / s
+        self.area() / (ab + bc + ac) / 2.0
     }
 
-    /// Expand the triangle by a constant amount (`sizes`) in all directions
-    pub fn inflate(&self, size: impl Into<Size>) -> Self {
-        let size = size.into();
-
-        Self::new(
-            (self.a.to_vec2() + size.to_vec2()).to_point(),
-            (self.b.to_vec2() + size.to_vec2()).to_point(),
-            (self.c.to_vec2() + size.to_vec2()).to_point(),
-        )
-    }
-
-    /// A new [`Triangle`] with each vertecie's ordinates rounded to the nearest integer
-    #[inline]
-    pub fn round(self) -> Self {
-        Self::new(self.a.round(), self.b.round(), self.c.round())
-    }
-
-    /// A new [`Triangle`] with each vertecie's ordinates rounded up to the nearest integer
+    /// Circumcircle of the [`Triangle`]
     #[inline]
-    pub fn ceil(self) -> Self {
-        Self::new(self.a.ceil(), self.b.ceil(), self.c.ceil())
-    }
-
-    /// A new [`Triangle`] with each vertecie's ordinates rounded down to the nearest integer
-    #[inline]
-    pub fn floor(self) -> Self {
-        Self::new(self.a.floor(), self.b.floor(), self.c.floor())
-    }
+    pub fn circumcircle(&self) -> f64 {
+        let ab = self.a.distance(self.b);
+        let bc = self.b.distance(self.c);
+        let ac = self.a.distance(self.c);
 
-    /// A new [`Triangle`],
-    /// with each coordinate value rounded towards the center of the [`Triangle`]
-    /// to the nearest integer, unless they are already an integer.
-    /// That is to say this function will return the biggest possible [`Triangle`]
-    /// with integer coordinates that is a subset of `self`.
-    #[inline]
-    pub fn expand(self) -> Self {
-        Self::new(self.a.expand(), self.b.expand(), self.c.expand())
+        ab * bc * ac / (((ab + bc + ac) * (bc + ac - ab) * (ab + ac - bc) * (ab + bc - ac)).sqrt())
     }
 
-    /// Returns a new [`Triangle`],
-    /// with each coordinate value rounded towards the center of the [`Triangle`]
-    /// to the nearest integer, unless they are already an integer.
-    /// That is to say this function will return the biggest possible [`Triangle`]
-    /// with integer coordinates that is a subset of `self`.
-    #[inline]
-    pub fn trunc(self) -> Self {
-        Self::new(self.a.trunc(), self.b.trunc(), self.c.trunc())
-    }
+    /// Expand the triangle by a constant amount (`sizes`) in all directions
+    pub fn inflate(&self, scalar: f64) -> Self {
+        let centroid = self.centroid();
 
-    /// Scales the [`Triangle`] by a `factor`
-    #[inline]
-    pub fn scale(self, factor: f64) -> Self {
         Self::new(
-            (self.a.to_vec2() * factor).to_point(),
-            (self.b.to_vec2() * factor).to_point(),
-            (self.c.to_vec2() * factor).to_point(),
+            centroid + (0.0, scalar),
+            centroid + scalar * Vec2::from_angle(5.0 * FRAC_PI_4),
+            centroid + scalar * Vec2::from_angle(7.0 * FRAC_PI_4),
         )
     }
 
-    /// Returns the [`Ellipse`] that is bounded by this [`Triangle`].
-    #[inline]
-    pub fn to_ellipse(self) -> Ellipse {
-        Ellipse::from_triangle(self)
-    }
-
     /// Is this [`Triangle`] finite?
     #[inline]
     pub fn is_finite(&self) -> bool {
@@ -408,12 +166,6 @@ impl From<(Point, Point, Point)> for Triangle {
     }
 }
 
-impl From<(Point, f64)> for Triangle {
-    fn from(params: (Point, f64)) -> Triangle {
-        Triangle::from_radius(params.1).with_centroid(params.0)
-    }
-}
-
 impl Add<Vec2> for Triangle {
     type Output = Triangle;
 
@@ -465,45 +217,33 @@ impl Shape for Triangle {
 
     #[inline]
     fn perimeter(&self, _accuracy: f64) -> f64 {
-        self.perimeter()
+        self.a.distance(self.b) + self.b.distance(self.c) + self.c.distance(self.a)
     }
 
     #[inline]
     fn winding(&self, pt: Point) -> i32 {
-        let xmin = self.min_x();
-        let xmax = self.max_x();
-        let ymin = self.min_y();
-        let ymax = self.max_y();
-
-        // TODO: may not be correct
-        if pt.x >= xmin && pt.x < xmax && pt.y >= ymin && pt.y < ymax {
-            if (self.c.x > self.b.x) ^ (self.a.y > self.b.y || self.a.y > self.c.y) {
-                -1
-            } else {
-                1
-            }
-        } else {
-            0
-        }
+        let s0 = (self.b - self.a).cross(pt - self.a).signum();
+        let s1 = (self.c - self.b).cross(pt - self.b).signum();
+        let s2 = (self.a - self.c).cross(pt - self.c).signum();
+        if s0 == s1 && s1 == s2 { s0 as i32 } else { 0 }
     }
 
     #[inline]
     fn bounding_box(&self) -> Rect {
-        Rect::new(self.min_x(), self.min_y(), self.max_x(), self.max_y())
+        Rect::new(
+            self.a.x.min(self.b.x.min(self.c.x)),
+            self.a.y.min(self.b.y.min(self.c.y)),
+            self.a.x.max(self.b.x.max(self.c.x)),
+            self.a.y.max(self.b.y.max(self.c.y)),
+        )
     }
 
     #[inline]
     fn as_rect(&self) -> Option<Rect> {
         Some(self.bounding_box())
     }
-
-    #[inline]
-    fn contains(&self, pt: Point) -> bool {
-        self.contains(pt)
-    }
 }
 
-// Anticlockwise direction from vertices a, b, c
 // NOTE: vertices a, b and c are not garunteed to be in order as described in the struct comments
 //       (i.e. as "vertex a is topmost, vertex b is leftmost, and vertex c is rightmost")
 impl Iterator for TrianglePathIter {
@@ -523,36 +263,12 @@ impl Iterator for TrianglePathIter {
 
 #[cfg(test)]
 mod tests {
-    use crate::{Point, Size, Triangle};
+    use crate::{Point, Triangle, Vec2};
 
     fn assert_approx_eq(x: f64, y: f64) {
         assert!((x - y).abs() < 1e-7);
     }
 
-    #[test]
-    fn from_centroid_sizes() {
-        let test = Triangle::from_centroid_distances((0.06, 12.2), [11.9, 1.2, 12.3]);
-        let expected = Triangle::from_coords(
-            (0.06, 24.1),
-            (-0.7885281374238573, 11.351471862576142),
-            (8.757413408594534, 3.5025865914054624),
-        );
-
-        assert_eq!(test, expected);
-    }
-
-    #[test]
-    fn from_centroid_distances() {
-        let test = Triangle::from_centroid_distances((0.6, 12.2), [11.9, 1.2, 12.3]);
-        let expected = Triangle::from_coords(
-            (0.6, 24.1),
-            (-0.24852813742385726, 11.351471862576142),
-            (9.297413408594533, 3.5025865914054624),
-        );
-
-        assert_eq!(test, expected);
-    }
-
     #[test]
     fn from_radius() {
         let test = Triangle::from_radius(10.1);
@@ -582,12 +298,12 @@ mod tests {
     }
 
     #[test]
-    fn sizes() {
-        let test = Triangle::from_coords((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).sizes();
+    fn offsets() {
+        let test = Triangle::from_coords((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).offsets();
         let expected = [
-            Size::new(-110.39999999999999, 86.8),
-            Size::new(-89.19999999999999, -93.39999999999999),
-            Size::new(199.60000000000002, 6.6000000000000085),
+            Vec2::new(-110.39999999999999, 86.8),
+            Vec2::new(-89.19999999999999, -93.39999999999999),
+            Vec2::new(199.60000000000002, 6.6000000000000085),
         ];
 
         assert_eq!(test, expected);
diff --git a/src/vec2.rs b/src/vec2.rs
index 5ed8059b..8b148d1a 100644
--- a/src/vec2.rs
+++ b/src/vec2.rs
@@ -31,9 +31,6 @@ impl Vec2 {
     /// The vector (0, 0).
     pub const ZERO: Vec2 = Vec2::new(0., 0.);
 
-    /// The vector (1, 1)
-    pub const ONE: Vec2 = Vec2::new(1., 1.);
-
     /// Create a new vector.
     #[inline]
     pub const fn new(x: f64, y: f64) -> Vec2 {

From 0438fae28e081dc810fe1108cc1c85135866d0e6 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Thu, 15 Aug 2024 18:03:56 +1000
Subject: [PATCH 14/23] tests

fix old tests + add new circle tests
---
 src/triangle.rs | 105 +++++++++++++++++++++---------------------------
 1 file changed, 45 insertions(+), 60 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index d7c8ccf9..299af03d 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -86,6 +86,27 @@ impl Triangle {
         (1.0 / 3.0 * (self.a.to_vec2() + self.b.to_vec2() + self.c.to_vec2())).to_point()
     }
 
+    /// The circumcenter of the [`Triangle`]
+    #[inline]
+    pub fn circumcenter(&self) -> Point {
+        let d = 2.0
+            * (self.a.x * (self.b.y - self.c.y)
+                + self.b.x * (self.c.y - self.a.y)
+                + self.c.x * (self.a.y - self.b.y));
+
+        let ux = ((self.a.x.powi(2) + self.a.y.powi(2)) * (self.b.y - self.c.y)
+            + (self.b.x.powi(2) + self.b.y.powi(2)) * (self.c.y - self.a.y)
+            + (self.c.x.powi(2) + self.c.y.powi(2)) * (self.a.y - self.b.y))
+            / d;
+
+        let uy = ((self.a.x.powi(2) + self.a.y.powi(2)) * (self.c.x - self.b.x)
+            + (self.b.x.powi(2) + self.b.y.powi(2)) * (self.a.x - self.c.x)
+            + (self.c.x.powi(2) + self.c.y.powi(2)) * (self.b.x - self.a.x))
+            / d;
+
+        Point::new(ux, uy)
+    }
+
     /// The offset of each vertex from the centroid
     #[inline]
     pub fn offsets(&self) -> [Vec2; 3] {
@@ -101,7 +122,7 @@ impl Triangle {
     /// The area of the [`Triangle`]
     #[inline]
     pub fn area(&self) -> f64 {
-        0.5 * (self.b - self.a).cross(self.c - self.a)
+        0.5 * (self.b - self.a).cross(self.c - self.a).abs()
     }
 
     /// Whether this [`Triangle`] has no (zero) area
@@ -111,26 +132,29 @@ impl Triangle {
     }
 
     /// The greatest radius of a circle that is within the [`Triangle`]
+    /// with center [`Triangle::circumcenter`]
     #[inline]
     pub fn incircle(&self) -> f64 {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
-        self.area() / (ab + bc + ac) / 2.0
+        2.0 * self.area() / (ab + bc + ac)
     }
 
     /// Circumcircle of the [`Triangle`]
+    /// with center [`Triangle::circumcenter`]
     #[inline]
     pub fn circumcircle(&self) -> f64 {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
-        ab * bc * ac / (((ab + bc + ac) * (bc + ac - ab) * (ab + ac - bc) * (ab + bc - ac)).sqrt())
+        (ab * bc * ac) / (4.0 * self.area())
+        // ab * bc * ac / (((ab + bc + ac) * (bc + ac - ab) * (ab + ac - bc) * (ab + bc - ac)).sqrt())
     }
 
-    /// Expand the triangle by a constant amount (`sizes`) in all directions
+    /// Expand the triangle by a constant amount (`scalar`) in all directions
     pub fn inflate(&self, scalar: f64) -> Self {
         let centroid = self.centroid();
 
@@ -192,8 +216,6 @@ impl Sub<Vec2> for Triangle {
     }
 }
 
-// TODO: Insets
-
 #[doc(hidden)]
 pub struct TrianglePathIter {
     triangle: Triangle,
@@ -225,7 +247,12 @@ impl Shape for Triangle {
         let s0 = (self.b - self.a).cross(pt - self.a).signum();
         let s1 = (self.c - self.b).cross(pt - self.b).signum();
         let s2 = (self.a - self.c).cross(pt - self.c).signum();
-        if s0 == s1 && s1 == s2 { s0 as i32 } else { 0 }
+
+        if s0 == s1 && s1 == s2 {
+            s0 as i32
+        } else {
+            0
+        }
     }
 
     #[inline]
@@ -261,6 +288,7 @@ impl Iterator for TrianglePathIter {
     }
 }
 
+// TODO: better and more tests
 #[cfg(test)]
 mod tests {
     use crate::{Point, Triangle, Vec2};
@@ -269,26 +297,6 @@ mod tests {
         assert!((x - y).abs() < 1e-7);
     }
 
-    #[test]
-    fn from_radius() {
-        let test = Triangle::from_radius(10.1);
-        let expected = Triangle::from_coords(
-            (0.0, 20.199999999999996),
-            (-17.493713156445658, -10.099999999999998),
-            (17.493713156445658, -10.099999999999998),
-        );
-
-        assert_eq!(test, expected);
-    }
-
-    #[test]
-    fn with_centroid() {
-        let test = Triangle::EQUILATERAL.with_centroid((12.2, -2.3));
-        let expected = Triangle::from_coords((12.2, 1.7000000000000002), (9.2, -4.3), (15.2, -4.3));
-
-        assert_eq!(test, expected);
-    }
-
     #[test]
     fn centroid() {
         let test = Triangle::from_coords((-90.02, 3.5), (7.2, -9.3), (8.0, 9.1)).centroid();
@@ -309,19 +317,6 @@ mod tests {
         assert_eq!(test, expected);
     }
 
-    #[test]
-    fn perimeter() {
-        let test = Triangle::new(
-            (781239.273894, 789234.234789),
-            (234897.823471, 378902.234789),
-            (789241.789234, 789234.234897),
-        )
-        .perimeter();
-        let expected = 1380963.0638877784;
-
-        assert_approx_eq(test, expected);
-    }
-
     #[test]
     fn area() {
         let test = Triangle::new(
@@ -336,35 +331,25 @@ mod tests {
     }
 
     #[test]
-    fn right_angled_area() {
-        let test = Triangle::from_coords((1.2, 5.3), (1.2, 1.6), (10.0, 1.6)).right_angled_area();
-        let expected = 16.28;
-
-        assert_approx_eq(test, expected);
-    }
-
-    #[test]
-    fn vertex_from_x() {
-        let test = Triangle::from_coords((1.0, 3.2), (63.8, 30.2), (2.0, 2.0))
-            .vertex_from_x(63.8)
-            .unwrap();
-        let expected = Point::new(63.8, 30.2);
+    fn circumcenter() {
+        let test = Triangle::EQUILATERAL.circumcenter();
+        let expected = Point::new(0.5, 0.2886751345948128);
 
         assert_eq!(test, expected);
     }
 
     #[test]
-    fn organise() {
-        let test = Triangle::from_coords((-20.1, 3.2), (12.3, 12.3), (9.2, -100.8)).organise();
-        let expected = Triangle::from_coords((12.3, 12.3), (-20.1, 3.2), (9.2, -100.8));
+    fn incircle() {
+        let test = Triangle::EQUILATERAL.incircle();
+        let expected = 0.28867513459481287;
 
-        assert_eq!(test, expected);
+        assert_approx_eq(test, expected);
     }
 
     #[test]
-    fn radius() {
-        let test = Triangle::EQUILATERAL.radius();
-        let expected = 1.8541019662496845;
+    fn circumcircle() {
+        let test = Triangle::EQUILATERAL.circumcircle();
+        let expected = 0.5773502691896258;
 
         assert_approx_eq(test, expected);
     }

From 7d1e41d922a2d05983a4e62d5620dfec9b075e17 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Tue, 27 Aug 2024 06:41:02 +1000
Subject: [PATCH 15/23] apply cleanup suggestions

---
 src/triangle.rs | 55 ++++++++++++++++++-------------------------------
 1 file changed, 20 insertions(+), 35 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 299af03d..7e53e482 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,7 +2,7 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{PathEl, Point, Rect, Shape, Vec2};
+use crate::{Line, PathEl, Point, Rect, Shape, Vec2};
 
 use core::cmp::*;
 use core::f64::consts::FRAC_PI_4;
@@ -67,19 +67,6 @@ impl Triangle {
         }
     }
 
-    /// A new [`Triangle`] from centroid and offsets ([`Vec2`]) - offset of each vertex from the centroid
-    #[inline]
-    fn from_centroid_offsets(centroid: impl Into<Point>, offsets: [impl Into<Vec2>; 3]) -> Self {
-        let centroid = centroid.into();
-
-        let mut points: [Point; 3] = Default::default();
-        for (i, offset) in offsets.into_iter().enumerate() {
-            points[i] = centroid + offset.into();
-        }
-
-        Self::new(points[0], points[1], points[2])
-    }
-
     /// The centroid of the [`Triangle`]
     #[inline]
     pub fn centroid(&self) -> Point {
@@ -122,7 +109,7 @@ impl Triangle {
     /// The area of the [`Triangle`]
     #[inline]
     pub fn area(&self) -> f64 {
-        0.5 * (self.b - self.a).cross(self.c - self.a).abs()
+        0.5 * (self.b - self.a).cross(self.c - self.a)
     }
 
     /// Whether this [`Triangle`] has no (zero) area
@@ -131,10 +118,10 @@ impl Triangle {
         self.area() == 0.0
     }
 
-    /// The greatest radius of a circle that is within the [`Triangle`]
+    /// Inradius of [`Triangle`] (the greatest radius of a circle that is within the [`Triangle`])
     /// with center [`Triangle::circumcenter`]
     #[inline]
-    pub fn incircle(&self) -> f64 {
+    pub fn inradius(&self) -> f64 {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
@@ -142,16 +129,15 @@ impl Triangle {
         2.0 * self.area() / (ab + bc + ac)
     }
 
-    /// Circumcircle of the [`Triangle`]
+    /// Circumradius of [`Triangle`] (the smallest radius of a circle such that it intercepts each vertex)
     /// with center [`Triangle::circumcenter`]
     #[inline]
-    pub fn circumcircle(&self) -> f64 {
+    pub fn circumradius(&self) -> f64 {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
         (ab * bc * ac) / (4.0 * self.area())
-        // ab * bc * ac / (((ab + bc + ac) * (bc + ac - ab) * (ab + ac - bc) * (ab + bc - ac)).sqrt())
     }
 
     /// Expand the triangle by a constant amount (`scalar`) in all directions
@@ -190,16 +176,18 @@ impl From<(Point, Point, Point)> for Triangle {
     }
 }
 
+impl From<(Line, Line)> for Triangle {
+    fn from(lines: (Line, Line)) -> Triangle {
+        Triangle::new(lines.0.p0, lines.0.p1, lines.1.p0)
+    }
+}
+
 impl Add<Vec2> for Triangle {
     type Output = Triangle;
 
     #[inline]
     fn add(self, v: Vec2) -> Triangle {
-        Triangle::new(
-            (self.a.to_vec2() + v).to_point(),
-            (self.b.to_vec2() + v).to_point(),
-            (self.c.to_vec2() + v).to_point(),
-        )
+        Triangle::new(self.a + v, self.b + v, self.c + v)
     }
 }
 
@@ -208,11 +196,7 @@ impl Sub<Vec2> for Triangle {
 
     #[inline]
     fn sub(self, v: Vec2) -> Triangle {
-        Triangle::new(
-            (self.a.to_vec2() - v).to_point(),
-            (self.b.to_vec2() - v).to_point(),
-            (self.c.to_vec2() - v).to_point(),
-        )
+        Triangle::new(self.a - v, self.b - v, self.c - v)
     }
 }
 
@@ -335,20 +319,21 @@ mod tests {
         let test = Triangle::EQUILATERAL.circumcenter();
         let expected = Point::new(0.5, 0.2886751345948128);
 
-        assert_eq!(test, expected);
+        assert_eq!(test.x, expected.x);
+        assert_approx_eq(test.y, expected.y);
     }
 
     #[test]
-    fn incircle() {
-        let test = Triangle::EQUILATERAL.incircle();
+    fn inradius() {
+        let test = Triangle::EQUILATERAL.inradius();
         let expected = 0.28867513459481287;
 
         assert_approx_eq(test, expected);
     }
 
     #[test]
-    fn circumcircle() {
-        let test = Triangle::EQUILATERAL.circumcircle();
+    fn circumradius() {
+        let test = Triangle::EQUILATERAL.circumradius();
         let expected = 0.5773502691896258;
 
         assert_approx_eq(test, expected);

From 8bac853bcb59f0d080f2548e543b056bde273c16 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Tue, 27 Aug 2024 20:38:38 +1000
Subject: [PATCH 16/23] signed area test

one with and without permutated vertices
---
 src/triangle.rs | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 7e53e482..e515928d 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -307,11 +307,14 @@ mod tests {
             (12123.423, 2382.7834),
             (7892.729, 238.459),
             (7820.2, 712.23),
-        )
-        .area();
+        );
         let expected = 1079952.91574081;
 
-        assert_approx_eq(test, expected);
+        // initial
+        assert_approx_eq(test.area(), -expected);
+        // permutate vertex
+        let test = Triangle::new(test.b, test.a, test.c);
+        assert_approx_eq(test.area(), expected);
     }
 
     #[test]

From 8da1a8c506fa99d3ca76ed36b39986d157143734 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Fri, 30 Aug 2024 17:07:27 +1000
Subject: [PATCH 17/23] match new style

`is_zero_area`, `is_nan`/`is_finite` docs, typo
---
 src/triangle.rs | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index e515928d..65f00f15 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -112,9 +112,9 @@ impl Triangle {
         0.5 * (self.b - self.a).cross(self.c - self.a)
     }
 
-    /// Whether this [`Triangle`] has no (zero) area
+    /// Whether this [`Triangle`] has zero area
     #[inline]
-    pub fn is_empty(&self) -> bool {
+    pub fn is_zero_area(&self) -> bool {
         self.area() == 0.0
     }
 
@@ -151,13 +151,17 @@ impl Triangle {
         )
     }
 
-    /// Is this [`Triangle`] finite?
+    /// Is this [`Triangle`] [finite]?
+    ///
+    /// [finite]: f64::is_finite
     #[inline]
     pub fn is_finite(&self) -> bool {
         self.a.is_finite() && self.b.is_finite() && self.c.is_finite()
     }
 
-    /// Is this [`Triangle`] NaN?
+    /// Is this [`Triangle`] [NaN]?
+    ///
+    /// [NaN]: f64::is_nan
     #[inline]
     pub fn is_nan(&self) -> bool {
         self.a.is_nan() || self.b.is_nan() || self.c.is_nan()
@@ -255,7 +259,7 @@ impl Shape for Triangle {
     }
 }
 
-// NOTE: vertices a, b and c are not garunteed to be in order as described in the struct comments
+// NOTE: vertices a, b and c are not guaranteed to be in order as described in the struct comments
 //       (i.e. as "vertex a is topmost, vertex b is leftmost, and vertex c is rightmost")
 impl Iterator for TrianglePathIter {
     type Item = PathEl;

From b2f4739aec1180f4c40b447d2a7ff62d9c133024 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Sat, 31 Aug 2024 18:34:39 +1000
Subject: [PATCH 18/23] add `is_zero_area` doc alias

see \#371
---
 src/triangle.rs | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/triangle.rs b/src/triangle.rs
index 65f00f15..5a93d1a1 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -113,6 +113,7 @@ impl Triangle {
     }
 
     /// Whether this [`Triangle`] has zero area
+    #[doc(alias = "is_empty")]
     #[inline]
     pub fn is_zero_area(&self) -> bool {
         self.area() == 0.0

From 57b4cb0b0e7587541938edaf4030eeef2eddbc3b Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Sat, 31 Aug 2024 19:53:57 +1000
Subject: [PATCH 19/23] remove from `Line`

wasnt supposed to be committed at all
---
 src/triangle.rs | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 5a93d1a1..f0cf0293 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,7 +2,7 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{Line, PathEl, Point, Rect, Shape, Vec2};
+use crate::{PathEl, Point, Rect, Shape, Vec2};
 
 use core::cmp::*;
 use core::f64::consts::FRAC_PI_4;
@@ -181,12 +181,6 @@ impl From<(Point, Point, Point)> for Triangle {
     }
 }
 
-impl From<(Line, Line)> for Triangle {
-    fn from(lines: (Line, Line)) -> Triangle {
-        Triangle::new(lines.0.p0, lines.0.p1, lines.1.p0)
-    }
-}
-
 impl Add<Vec2> for Triangle {
     type Output = Triangle;
 

From 4f171037e4f8bf59adc8dab622447465abf41b4c Mon Sep 17 00:00:00 2001
From: Julia <58243358+juliapaci@users.noreply.github.com>
Date: Mon, 23 Sep 2024 17:44:10 +1000
Subject: [PATCH 20/23] Apply explicit suggestions from derekdreery

Co-authored-by: Richard Dodd <richard.o.dodd@gmail.com>
---
 src/triangle.rs | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index f0cf0293..6733d8c3 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -119,7 +119,9 @@ impl Triangle {
         self.area() == 0.0
     }
 
-    /// Inradius of [`Triangle`] (the greatest radius of a circle that is within the [`Triangle`])
+    /// Inradius of [`Triangle`] 
+    /// 
+    /// This is defined as the greatest radius of a circle that is within the [`Triangle`] 
     /// with center [`Triangle::circumcenter`]
     #[inline]
     pub fn inradius(&self) -> f64 {
@@ -283,7 +285,7 @@ mod tests {
     #[test]
     fn centroid() {
         let test = Triangle::from_coords((-90.02, 3.5), (7.2, -9.3), (8.0, 9.1)).centroid();
-        let expected = Point::new(-24.939999999999998, 1.0999999999999996);
+        let expected = Point::new(-24.94, 1.1);
 
         assert_eq!(test, expected);
     }
@@ -292,9 +294,9 @@ mod tests {
     fn offsets() {
         let test = Triangle::from_coords((-20.0, 180.2), (1.2, 0.0), (290.0, 100.0)).offsets();
         let expected = [
-            Vec2::new(-110.39999999999999, 86.8),
-            Vec2::new(-89.19999999999999, -93.39999999999999),
-            Vec2::new(199.60000000000002, 6.6000000000000085),
+            Vec2::new(-110.4, 86.8),
+            Vec2::new(-89.2, -93.4),
+            Vec2::new(199.6, 6.6),
         ];
 
         assert_eq!(test, expected);

From 4d0afb9b6697855583dc7550d22d9c7fb72f9e1c Mon Sep 17 00:00:00 2001
From: Julia <58243358+juliapaci@users.noreply.github.com>
Date: Mon, 23 Sep 2024 17:46:43 +1000
Subject: [PATCH 21/23] remove point comparisons

Co-authored-by: Daniel McNab <36049421+DJMcNab@users.noreply.github.com>
---
 src/point.rs | 23 -----------------------
 1 file changed, 23 deletions(-)

diff --git a/src/point.rs b/src/point.rs
index 8f17af9e..cdd8e8a4 100644
--- a/src/point.rs
+++ b/src/point.rs
@@ -187,29 +187,6 @@ impl Point {
         self.x.is_nan() || self.y.is_nan()
     }
 
-    /// The topmost [`Point`]
-    #[inline]
-    pub fn topmost(&self, other: &Self) -> Ordering {
-        self.y.total_cmp(&other.y)
-    }
-
-    /// The bottommost [`Point`]
-    #[inline]
-    pub fn bottommost(&self, other: &Self) -> Ordering {
-        other.y.total_cmp(&self.y)
-    }
-
-    /// The rightmost [`Point`]
-    #[inline]
-    pub fn rightmost(&self, other: &Self) -> Ordering {
-        self.x.total_cmp(&other.x)
-    }
-
-    /// The leftmost [`Point`]
-    #[inline]
-    pub fn leftmost(&self, other: &Self) -> Ordering {
-        other.x.total_cmp(&self.x)
-    }
 }
 
 impl From<(f32, f32)> for Point {

From 3da32b722da480bde816b64e295f314a59711e5b Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Mon, 23 Sep 2024 17:48:43 +1000
Subject: [PATCH 22/23] apply implicit suggestions

private `from_coords` and  instead of `*radius` use `*circle`
---
 src/triangle.rs | 40 ++++++++++++++--------------------------
 1 file changed, 14 insertions(+), 26 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index 6733d8c3..b2a68a9e 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -2,7 +2,7 @@
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
 //! Triangle shape
-use crate::{PathEl, Point, Rect, Shape, Vec2};
+use crate::{Circle, PathEl, Point, Rect, Shape, Vec2};
 
 use core::cmp::*;
 use core::f64::consts::FRAC_PI_4;
@@ -34,9 +34,6 @@ impl Triangle {
     /// The empty [`Triangle`] at the origin
     pub const ZERO: Self = Self::from_coords((0., 0.), (0., 0.), (0., 0.));
 
-    /// empty [`Triangle`] at (1.0, 1.0)
-    pub const ONE: Self = Self::from_coords((1.0, 1.0), (1.0, 1.0), (1.0, 1.0));
-
     /// equilateral [`Triangle`]
     pub const EQUILATERAL: Self = Self::from_coords(
         (
@@ -59,7 +56,7 @@ impl Triangle {
 
     /// A new [`Triangle`] from three float vertex coordinates
     #[inline]
-    pub const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
+    const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
         Self {
             a: Point::new(a.0, a.1),
             b: Point::new(b.0, b.1),
@@ -75,7 +72,7 @@ impl Triangle {
 
     /// The circumcenter of the [`Triangle`]
     #[inline]
-    pub fn circumcenter(&self) -> Point {
+    fn circumcenter(&self) -> Point {
         let d = 2.0
             * (self.a.x * (self.b.y - self.c.y)
                 + self.b.x * (self.c.y - self.a.y)
@@ -119,28 +116,24 @@ impl Triangle {
         self.area() == 0.0
     }
 
-    /// Inradius of [`Triangle`] 
-    /// 
-    /// This is defined as the greatest radius of a circle that is within the [`Triangle`] 
-    /// with center [`Triangle::circumcenter`]
+    /// Incircle of [`Triangle`] (the greatest [`Circle`] that lies within the [`Triangle`])
     #[inline]
-    pub fn inradius(&self) -> f64 {
+    pub fn incircle(&self) -> Circle {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
-        2.0 * self.area() / (ab + bc + ac)
+        Circle::new(self.circumcenter(), 2.0 * self.area() / (ab + bc + ac))
     }
 
-    /// Circumradius of [`Triangle`] (the smallest radius of a circle such that it intercepts each vertex)
-    /// with center [`Triangle::circumcenter`]
+    /// Circumcircle of [`Triangle`] (the smallest [`Circle`] such that it intercepts each vertex)
     #[inline]
-    pub fn circumradius(&self) -> f64 {
+    pub fn circumcircle(&self) -> Circle {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
 
-        (ab * bc * ac) / (4.0 * self.area())
+        Circle::new(self.circumcenter(), (ab * bc * ac) / (4.0 * self.area()))
     }
 
     /// Expand the triangle by a constant amount (`scalar`) in all directions
@@ -249,14 +242,9 @@ impl Shape for Triangle {
             self.a.y.max(self.b.y.max(self.c.y)),
         )
     }
-
-    #[inline]
-    fn as_rect(&self) -> Option<Rect> {
-        Some(self.bounding_box())
-    }
 }
 
-// NOTE: vertices a, b and c are not guaranteed to be in order as described in the struct comments
+// Note: vertices a, b and c are not guaranteed to be in order as described in the struct comments
 //       (i.e. as "vertex a is topmost, vertex b is leftmost, and vertex c is rightmost")
 impl Iterator for TrianglePathIter {
     type Item = PathEl;
@@ -329,17 +317,17 @@ mod tests {
 
     #[test]
     fn inradius() {
-        let test = Triangle::EQUILATERAL.inradius();
+        let test = Triangle::EQUILATERAL.incircle();
         let expected = 0.28867513459481287;
 
-        assert_approx_eq(test, expected);
+        assert_approx_eq(test.radius, expected);
     }
 
     #[test]
     fn circumradius() {
-        let test = Triangle::EQUILATERAL.circumradius();
+        let test = Triangle::EQUILATERAL.circumcircle();
         let expected = 0.5773502691896258;
 
-        assert_approx_eq(test, expected);
+        assert_approx_eq(test.radius, expected);
     }
 }

From 4823cb3472933d7daffa48c6366675dc30ae09e7 Mon Sep 17 00:00:00 2001
From: julia <me@juliapaci.com>
Date: Tue, 24 Sep 2024 16:27:15 +1000
Subject: [PATCH 23/23] meta cleanup

name and doc updates + public `from_coords`
---
 src/triangle.rs | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/src/triangle.rs b/src/triangle.rs
index b2a68a9e..f3b819c3 100644
--- a/src/triangle.rs
+++ b/src/triangle.rs
@@ -44,7 +44,7 @@ impl Triangle {
         (1.0, 0.0),
     );
 
-    /// A new [`Triangle`] from three vertices ([`Points`])
+    /// A new [`Triangle`] from three vertices ([`Point`]s)
     #[inline]
     pub fn new(a: impl Into<Point>, b: impl Into<Point>, c: impl Into<Point>) -> Self {
         Self {
@@ -55,8 +55,10 @@ impl Triangle {
     }
 
     /// A new [`Triangle`] from three float vertex coordinates
+    ///
+    /// Works as a constant [`Triangle::new`]
     #[inline]
-    const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
+    pub const fn from_coords(a: (f64, f64), b: (f64, f64), c: (f64, f64)) -> Self {
         Self {
             a: Point::new(a.0, a.1),
             b: Point::new(b.0, b.1),
@@ -116,9 +118,10 @@ impl Triangle {
         self.area() == 0.0
     }
 
-    /// Incircle of [`Triangle`] (the greatest [`Circle`] that lies within the [`Triangle`])
+    /// The inscribed circle of [`Triangle`] (the greatest [`Circle`] that lies within the [`Triangle`])
+    #[doc(alias = "incircle")]
     #[inline]
-    pub fn incircle(&self) -> Circle {
+    pub fn inscribed_circle(&self) -> Circle {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
@@ -126,9 +129,10 @@ impl Triangle {
         Circle::new(self.circumcenter(), 2.0 * self.area() / (ab + bc + ac))
     }
 
-    /// Circumcircle of [`Triangle`] (the smallest [`Circle`] such that it intercepts each vertex)
+    /// The circumscribed circle of [`Triangle`] (the smallest [`Circle`] which intercepts each vertex of the [`Triangle`])
+    #[doc(alias = "circumcircle")]
     #[inline]
-    pub fn circumcircle(&self) -> Circle {
+    pub fn circumscribed_circle(&self) -> Circle {
         let ab = self.a.distance(self.b);
         let bc = self.b.distance(self.c);
         let ac = self.a.distance(self.c);
@@ -317,7 +321,7 @@ mod tests {
 
     #[test]
     fn inradius() {
-        let test = Triangle::EQUILATERAL.incircle();
+        let test = Triangle::EQUILATERAL.inscribed_circle();
         let expected = 0.28867513459481287;
 
         assert_approx_eq(test.radius, expected);
@@ -325,7 +329,7 @@ mod tests {
 
     #[test]
     fn circumradius() {
-        let test = Triangle::EQUILATERAL.circumcircle();
+        let test = Triangle::EQUILATERAL.circumscribed_circle();
         let expected = 0.5773502691896258;
 
         assert_approx_eq(test.radius, expected);