3 files changed, 115 insertions, 0 deletions
diff --git a/src/geom/angle.rs b/src/geom/angle.rs
index 888442f7..65270ebd 100644
--- a/src/geom/angle.rs
+++ b/src/geom/angle.rs
@@ -64,6 +64,51 @@ impl Angle {
     pub fn cos(self) -> f64 {
         self.to_rad().cos()
     }
+
+    /// Get the control points for a bezier curve that describes a circular arc
+    /// of this angle with the given radius.
+    pub fn bezier_arc(
+        self,
+        radius: Length,
+        rotate: bool,
+        mirror_x: bool,
+        mirror_y: bool,
+    ) -> [Point; 4] {
+        let end = Point::new(self.cos() * radius - radius, self.sin() * radius);
+        let center = Point::new(-radius, Length::zero());
+
+        let mut ts = if mirror_y {
+            Transform::mirror_y()
+        } else {
+            Transform::identity()
+        };
+
+        if mirror_x {
+            ts = ts.pre_concat(Transform::mirror_x());
+        }
+
+        if rotate {
+            ts = ts.pre_concat(Transform::rotate(Angle::deg(90.0)));
+        }
+
+        let a = center * -1.0;
+        let b = end - center;
+
+        let q1 = a.x.to_raw() * a.x.to_raw() + a.y.to_raw() * a.y.to_raw();
+        let q2 = q1 + a.x.to_raw() * b.x.to_raw() + a.y.to_raw() * b.y.to_raw();
+        let k2 = (4.0 / 3.0) * ((2.0 * q1 * q2).sqrt() - q2)
+            / (a.x.to_raw() * b.y.to_raw() - a.y.to_raw() * b.x.to_raw());
+
+        let control_1 = Point::new(center.x + a.x - k2 * a.y, center.y + a.y + k2 * a.x);
+        let control_2 = Point::new(center.x + b.x + k2 * b.y, center.y + b.y - k2 * b.x);
+
+        [
+            Point::zero(),
+            control_1.transform(ts),
+            control_2.transform(ts),
+            end.transform(ts),
+        ]
+    }
 }
 
 impl Numeric for Angle {
diff --git a/src/geom/sides.rs b/src/geom/sides.rs
index 3584a1ce..255c21ee 100644
--- a/src/geom/sides.rs
+++ b/src/geom/sides.rs
@@ -31,6 +31,32 @@ impl<T> Sides<T> {
             bottom: value,
         }
     }
+
+    /// Maps the individual fields with `f`.
+    pub fn map<F, U>(self, mut f: F) -> Sides<U>
+    where
+        F: FnMut(T) -> U,
+    {
+        Sides {
+            left: f(self.left),
+            top: f(self.top),
+            right: f(self.right),
+            bottom: f(self.bottom),
+        }
+    }
+
+    /// Returns an iterator over the sides.
+    pub fn iter(&self) -> impl Iterator<Item = &T> {
+        [&self.left, &self.top, &self.right, &self.bottom].into_iter()
+    }
+
+    /// Returns whether all sides are equal.
+    pub fn is_uniform(&self) -> bool
+    where
+        T: PartialEq,
+    {
+        self.left == self.top && self.top == self.right && self.right == self.bottom
+    }
 }
 
 impl<T> Sides<T>
@@ -100,4 +126,24 @@ impl Side {
             Self::Bottom => Self::Top,
         }
     }
+
+    /// The next side, clockwise.
+    pub fn clockwise(self) -> Self {
+        match self {
+            Self::Left => Self::Top,
+            Self::Top => Self::Right,
+            Self::Right => Self::Bottom,
+            Self::Bottom => Self::Left,
+        }
+    }
+
+    /// The next side, counter-clockwise.
+    pub fn counter_clockwise(self) -> Self {
+        match self {
+            Self::Left => Self::Bottom,
+            Self::Top => Self::Left,
+            Self::Right => Self::Top,
+            Self::Bottom => Self::Right,
+        }
+    }
 }
diff --git a/src/geom/transform.rs b/src/geom/transform.rs
index 28a1af80..de2a9781 100644
--- a/src/geom/transform.rs
+++ b/src/geom/transform.rs
@@ -24,6 +24,30 @@ impl Transform {
         }
     }
 
+    /// Transform by mirroring along the x-axis.
+    pub fn mirror_x() -> Self {
+        Self {
+            sx: Ratio::one(),
+            ky: Ratio::zero(),
+            kx: Ratio::zero(),
+            sy: -Ratio::one(),
+            tx: Length::zero(),
+            ty: Length::zero(),
+        }
+    }
+
+    /// Transform by mirroring along the y-axis.
+    pub fn mirror_y() -> Self {
+        Self {
+            sx: -Ratio::one(),
+            ky: Ratio::zero(),
+            kx: Ratio::zero(),
+            sy: Ratio::one(),
+            tx: Length::zero(),
+            ty: Length::zero(),
+        }
+    }
+
     /// A translate transform.
     pub const fn translate(tx: Length, ty: Length) -> Self {
         Self { tx, ty, ..Self::identity() }