Improve utils by adding pixel conversion (#52)

Reviewed-on: corentin/border-wars#52
Reviewed-by: Tipragot <contact@tipragot.fr>
Co-authored-by: CoCoSol007 <solois.corentin@gmail.com>
Co-committed-by: CoCoSol007 <solois.corentin@gmail.com>

crates/border-wars/src/map/hex.rs

@@ -4,6 +4,7 @@ use std::collections::HashSet;
 use std::hash::Hash;
 use std::ops::{Add, AddAssign, Sub, SubAssign};
 
+use num::cast::AsPrimitive;
 use num::{FromPrimitive, Signed};
 use partial_min_max::{max, min};
 
@@ -24,7 +25,7 @@ pub struct HexPosition<T: HexNumber> {
     pub r: T,
 }
 
-impl<T: HexNumber> HexPosition<T> {
+impl<T: HexNumber + AsPrimitive<f32>> HexPosition<T> {
     /// Returns the distance between two [HexPosition]s.
     ///
     /// # How it works
@@ -55,6 +56,34 @@ impl<T: HexNumber> HexPosition<T> {
         // Manhattan distance = (abs(dq) + abs(dr) + abs(ds)) / 2
         (dq + dr + ds) / (T::one() + T::one())
     }
+
+    /// Converts the current [HexPosition] into a pixel coordinate.
+    /// Input: The size of the hexagon in pixels (witdh, height).
+    ///
+    /// If you want to learn more about pixel coordinates conversion,
+    /// you can check the
+    /// [documentation](https://www.redblobgames.com/grids/hexagons/#hex-to-pixel).
+    ///
+    /// # Example
+    ///
+    /// ```no_run
+    /// use border_wars::map::hex::HexPosition;
+    ///
+    /// let position = HexPosition { q: 1, r: 0 };
+    /// assert_eq!(
+    ///     position.to_pixel_coordinates((1.0, 1.0)),
+    ///     (3f32.sqrt(), 0.0)
+    /// );
+    /// ```
+    pub fn to_pixel_coordinates(&self, size: (f32, f32)) -> (f32, f32) {
+        (
+            size.0
+                * 3f32
+                    .sqrt()
+                    .mul_add(self.q.as_(), 3f32.sqrt() / 2.0 * (self.r.as_())),
+            size.1 * (3.0 / 2.0 * self.r.as_()),
+        )
+    }
 }
 
 impl<T: HexNumber + Eq + Hash + std::cmp::PartialOrd + num::ToPrimitive> HexPosition<T> {