1 files changed, 231 insertions, 0 deletions
diff --git a/src/math/vec2.rs b/src/math/vec2.rs
new file mode 100644
index 0000000..5ae0024
--- /dev/null
+++ b/src/math/vec2.rs
@@ -0,0 +1,231 @@
+//! Two-dimensional vectors and useful operations on them.
+
+use std::cmp::Ordering;
+use std::ops::{Add, AddAssign, Div, Mul, MulAssign, Neg, Sub, SubAssign};
+use std::{fmt, mem};
+
+use nalgebra::{RealField, Scalar};
+use num_traits::One;
+use serde::{Deserialize, Serialize};
+
+use crate::math::Rect;
+
+/// Describes a vector, which may be a point or a directed length, depending on
+/// the interpretation.
+#[allow(missing_docs)]
+#[derive(Clone, Copy, Debug, Default, PartialEq, Serialize, Deserialize, Eq, Hash)]
+pub struct Vec2<T: Scalar + Copy>
+{
+    pub x: T,
+    pub y: T,
+}
+
+impl<T: Scalar + Copy> Vec2<T>
+{
+    /// Create a new vector from its internal values.
+    pub fn new(x: T, y: T) -> Self { Self { x, y } }
+
+    /// Finds the euclidian length and returns it.
+    pub fn length(&self) -> T
+    where
+        T: RealField,
+    {
+        (self.x * self.x + self.y * self.y).sqrt()
+    }
+
+    /// Consumes the vector and returns a vector that is rotated by Pi/2 in
+    /// clockwise direction. This is a special case of rotation and the
+    /// function is faster than using the nonspecific rotation function.
+    pub fn rotated_90_clockwise(mut self) -> Vec2<T>
+    where
+        T: One + Neg<Output = T> + MulAssign,
+    {
+        mem::swap(&mut self.x, &mut self.y);
+        self.y *= -T::one();
+        self
+    }
+
+    /// Consumes the vector and returns a vector that is rotated by Pi/2 in
+    /// counterclockwise direction. This is a special case of rotation and
+    /// the function is faster than using the nonspecific rotation function.
+    pub fn rotated_90_counterclockwise(mut self) -> Vec2<T>
+    where
+        T: One + Neg<Output = T> + MulAssign,
+    {
+        mem::swap(&mut self.x, &mut self.y);
+        self.x *= -T::one();
+        self
+    }
+}
+
+// Begin mathematical operators -----------------------------------------------
+
+// Addition
+impl<T: Scalar + Add<Output = T> + Copy> Add for Vec2<T>
+{
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self { Vec2::new(self.x + rhs.x, self.y + rhs.y) }
+}
+
+impl<T: Scalar + Add<Output = T> + Copy> Add<(T, T)> for Vec2<T>
+{
+    type Output = Self;
+
+    fn add(self, (x, y): (T, T)) -> Self { Vec2::new(self.x + x, self.y + y) }
+}
+
+impl<T: Scalar + Add<Output = T> + Copy> Add<T> for Vec2<T>
+{
+    type Output = Self;
+
+    fn add(self, rhs: T) -> Self { Vec2::new(self.x + rhs, self.y + rhs) }
+}
+
+impl<T: Scalar + AddAssign + Copy> AddAssign for Vec2<T>
+{
+    fn add_assign(&mut self, rhs: Self)
+    {
+        self.x += rhs.x;
+        self.y += rhs.y;
+    }
+}
+
+impl<T: Scalar + AddAssign + Copy> AddAssign<(T, T)> for Vec2<T>
+{
+    fn add_assign(&mut self, (x, y): (T, T))
+    {
+        self.x += x;
+        self.y += y;
+    }
+}
+
+// Subtraction
+impl<T: Scalar + Sub<Output = T> + Copy> Sub for Vec2<T>
+{
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self { Vec2::new(self.x - rhs.x, self.y - rhs.y) }
+}
+
+impl<T: Scalar + Sub<Output = T> + Copy> Sub<(T, T)> for Vec2<T>
+{
+    type Output = Self;
+
+    fn sub(self, (x, y): (T, T)) -> Self { Vec2::new(self.x - x, self.y - y) }
+}
+
+impl<T: Scalar + Sub<Output = T> + Copy> Sub<T> for Vec2<T>
+{
+    type Output = Self;
+
+    fn sub(self, rhs: T) -> Self { Vec2::new(self.x - rhs, self.y - rhs) }
+}
+
+impl<T: Scalar + SubAssign + Copy> SubAssign for Vec2<T>
+{
+    fn sub_assign(&mut self, rhs: Self)
+    {
+        self.x -= rhs.x;
+        self.y -= rhs.y;
+    }
+}
+
+impl<T: Scalar + SubAssign + Copy> SubAssign<(T, T)> for Vec2<T>
+{
+    fn sub_assign(&mut self, (x, y): (T, T))
+    {
+        self.x -= x;
+        self.y -= y;
+    }
+}
+
+// Scalar multiplication
+impl<T: Scalar + Add<Output = T> + Mul<Output = T> + Copy> Mul for Vec2<T>
+{
+    type Output = T;
+
+    fn mul(self, rhs: Self) -> T { self.x * rhs.x + self.y * rhs.y }
+}
+
+impl<T: Scalar + Mul<Output = T> + Copy> Mul<T> for Vec2<T>
+{
+    type Output = Self;
+
+    fn mul(self, rhs: T) -> Self { Vec2::new(self.x * rhs, self.y * rhs) }
+}
+
+impl<T: Scalar + Div<Output = T> + Copy> Div<T> for Vec2<T>
+{
+    type Output = Self;
+
+    fn div(self, rhs: T) -> Self { Vec2::new(self.x / rhs, self.y / rhs) }
+}
+
+// End of mathematical operators ----------------------------------------------
+
+// By default, the coordinates are first compared by their y-coordinates, then
+// their x-coordinates
+impl<T: fmt::Debug> PartialOrd for Vec2<T>
+where
+    T: PartialOrd + Copy + 'static,
+{
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering>
+    {
+        match self.y.partial_cmp(&other.y) {
+            Some(Ordering::Equal) | None => self.x.partial_cmp(&other.x),
+            y_order => y_order,
+        }
+    }
+}
+
+impl<T: fmt::Debug> Ord for Vec2<T>
+where
+    T: Ord + Copy + 'static,
+{
+    fn cmp(&self, other: &Self) -> Ordering
+    {
+        match self.y.cmp(&other.y) {
+            Ordering::Equal => self.x.cmp(&other.x),
+            y_order => y_order,
+        }
+    }
+}
+
+// Helper function to determine the absolute positive difference between two
+// Values, which don't have to be signed.
+fn difference_abs<T>(a: T, b: T) -> T
+where
+    T: Sub<Output = T> + PartialOrd,
+{
+    if a > b {
+        a - b
+    }
+    else {
+        b - a
+    }
+}
+
+// Helper function that removes all points inside the vector that are not
+// contained inside the optional limit Rect
+fn retain_inside_limits<T: 'static>(items: Vec<Vec2<T>>, limits: Option<Rect<T>>) -> Vec<Vec2<T>>
+where
+    T: PartialOrd + std::fmt::Debug + Copy + Add<Output = T>,
+{
+    // Fast return in case there are no limits
+    if limits.is_none() {
+        return items;
+    }
+    let limits = limits.unwrap();
+
+    // Retain only items that are within the bounds of the limits rect
+    items
+        .into_iter()
+        .filter(|v| {
+            v.x >= limits.x
+                && v.x <= limits.x + limits.w
+                && v.y >= limits.y
+                && v.y <= limits.y + limits.h
+        })
+        .collect()
+}