Add player movementHEADmain

3 files changed, 527 insertions, 0 deletions

diff --git a/src/math/mod.rs b/src/math/mod.rs
new file mode 100644
index 0000000..8b22972
--- /dev/null
+++ b/src/math/mod.rs
@@ -0,0 +1,93 @@
+//! Useful mathematical operations in graphical contexts.
+
+pub mod rect;
+pub mod vec2;
+
+use std::cmp::Ordering;
+
+use nalgebra::RealField;
+use num_traits::Pow;
+
+pub use self::rect::*;
+pub use self::vec2::*;
+
+/// Round a floating point number to the nearest step given by the step
+/// argument. For instance, if the step is 0.5, then all numbers from 0.0 to
+/// 0.24999... will be 0., while all numbers from 0.25 to 0.74999... will be 0.5
+/// and so on.
+pub fn round<T>(num: T, step: T) -> T
+where
+    T: RealField,
+{
+    // Only positive steps will be accepted.
+    assert!(step > T::zero());
+
+    let lower_bound = (num / step).floor() * step;
+    let upper_bound = lower_bound + step;
+
+    // Compare the distances and prefer the smaller. If they are the same, prefer
+    // the upper bound.
+    if (num - lower_bound) < (upper_bound - num) {
+        lower_bound
+    }
+    else {
+        upper_bound
+    }
+}
+
+/// Like round, but instead of rounding to a certain fraction, rounds to the nth
+/// decimal place instead of taking a granularity.
+pub fn round_nth_decimal<T>(num: T, decimal_place: u16) -> T
+where
+    T: RealField + Pow<u16, Output = T>,
+{
+    round(num, nalgebra::convert::<f64, T>(0.1).pow(decimal_place))
+}
+
+/// Works like `std::cmp::max`, however also allows partial comparisons. It is
+/// specifically designed so functions that should be able to use f32 and f64
+/// work, eventhough these do not implement Ord. The downside of this function
+/// however is, that its behaviour is undefined when `f32::NaN` for instance
+/// were to be passed.
+pub(crate) fn partial_max<T>(a: T, b: T) -> T
+where
+    T: PartialOrd,
+{
+    match a.partial_cmp(&b) {
+        Some(Ordering::Greater) => a,
+        _ => b,
+    }
+}
+/// Like `partial_max`, but for minimum values. Comes with the same downside,
+/// too.
+pub(crate) fn partial_min<T>(a: T, b: T) -> T
+where
+    T: PartialOrd,
+{
+    match a.partial_cmp(&b) {
+        Some(Ordering::Less) => a,
+        _ => b,
+    }
+}
+
+#[cfg(test)]
+mod test
+{
+    #[test]
+    fn partial_max()
+    {
+        assert_eq!(super::partial_max(0., 0.), 0.);
+        assert_eq!(super::partial_max(-1., 1.), 1.);
+        assert_eq!(super::partial_max(-2., -1.), -1.);
+        assert_eq!(super::partial_max(2., 1.), 2.);
+    }
+
+    #[test]
+    fn partial_min()
+    {
+        assert_eq!(super::partial_min(0., 0.), 0.);
+        assert_eq!(super::partial_min(-1., 1.), -1.);
+        assert_eq!(super::partial_min(-2., -1.), -2.);
+        assert_eq!(super::partial_min(2., 1.), 1.);
+    }
+}
diff --git a/src/math/rect.rs b/src/math/rect.rs
new file mode 100644
index 0000000..55e0b1c
--- /dev/null
+++ b/src/math/rect.rs
@@ -0,0 +1,203 @@
+//! Rectangles where the sides are parallel to the x and y-axes.
+
+use std::ops::{Add, AddAssign, Sub};
+
+//use alga::general::{Additive, Identity};
+use nalgebra::Scalar;
+use num_traits::sign::{self, Signed};
+use num_traits::Zero;
+use serde::{Deserialize, Serialize};
+
+use super::Vec2;
+
+/// Represents a Rectangle with the value type T.
+#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Serialize, Deserialize)]
+pub struct Rect<T: Scalar + Copy>
+{
+    /// The x coordinate, or leftmost coordinate of the Rect.
+    pub x: T,
+    /// The y coordinate, or rightmost coordinate of the Rect.
+    pub y: T,
+    /// The width of the Rect.
+    pub w: T,
+    /// The height of the Rect.
+    pub h: T,
+}
+
+impl<T: Scalar + Copy> Rect<T>
+{
+    /// Create a new Rectangle from the internal values, where it might be nicer
+    /// to use a function instead of setting the values directly.
+    pub fn new(x: T, y: T, w: T, h: T) -> Self { Self { x, y, w, h } }
+
+    /// Create a Rectangle from a slice. Indices are [x, y, w, h].
+    pub fn from_slice(slice: [T; 4]) -> Rect<T>
+    where
+        T: Copy,
+    {
+        Rect {
+            x: slice[0],
+            y: slice[1],
+            w: slice[2],
+            h: slice[3],
+        }
+    }
+
+    /// Move by the Vec provided.
+    pub fn translate(&mut self, by: Vec2<T>)
+    where
+        T: AddAssign,
+    {
+        self.x += by.x;
+        self.y += by.y;
+    }
+
+    /// Set the posiotien of the rectangle to the given one without changing its
+    /// size
+    pub fn set_pos(&mut self, pos: Vec2<T>)
+    {
+        self.x = pos.x;
+        self.y = pos.y;
+    }
+
+    /// Test if two rectangles intersect.
+    pub fn intersect<'a>(this: &'a Rect<T>, other: &'a Rect<T>) -> bool
+    where
+        T: Add<Output = T> + PartialOrd + Copy,
+    {
+        !(this.x > other.x + other.w
+            || this.x + this.w < other.x
+            || this.y > other.y + other.h
+            || this.y + this.h < other.y)
+    }
+
+    /// Function to calculate the bounding rectangle that is between two
+    /// vectors. The order of the vectors is irrelevent for this. As long as
+    /// they are diagonally opposite of each other, this function will work.
+    pub fn bounding_rect(pos1: Vec2<T>, pos2: Vec2<T>) -> Self
+    where
+        T: PartialOrd + Sub<Output = T>,
+    {
+        let vertices = [pos1, pos2];
+
+        Self::bounding_rect_n(&vertices)
+    }
+
+    /// Function to calculate the bounding rectangle of n vertices provided. The
+    /// order of them is not relevant and a point that is contained by the
+    /// vertices will not change the result.
+    ///
+    /// # Panics
+    /// If there is not at least one vertex in the vertices slice, the function
+    /// will panic, since it is impossible to calculate any bounds in such a
+    /// case.
+    pub fn bounding_rect_n(vertices: &[Vec2<T>]) -> Self
+    where
+        T: PartialOrd + Sub<Output = T>,
+    {
+        if vertices.is_empty() {
+            panic!("Cannot create bounding rectangle without any vertices");
+        }
+
+        let mut min = vertices[0];
+        let mut max = vertices[0];
+
+        for vertex in vertices.iter().skip(1) {
+            min.x = super::partial_min(min.x, vertex.x);
+            min.y = super::partial_min(min.y, vertex.y);
+            max.x = super::partial_max(max.x, vertex.x);
+            max.y = super::partial_max(max.y, vertex.y);
+        }
+
+        Self {
+            x: min.x,
+            y: min.y,
+            w: max.x - min.x,
+            h: max.y - min.y,
+        }
+    }
+
+    /// Get the shortest way that must be applied to this Rect to clear out of
+    /// another Rect of the same type so that they would not intersect any more.
+    pub fn shortest_way_out(&self, of: &Rect<T>) -> Vec2<T>
+    where
+        T: Add<Output = T> + Sub<Output = T> + Signed + PartialOrd,
+    {
+        // Check upwards
+        let mut move_y = of.y - self.y - self.h;
+        // Check downwards
+        let move_down = of.y + of.h - self.y;
+        if move_down < -move_y {
+            move_y = move_down;
+        }
+
+        // Check left
+        let mut move_x = of.x - self.x - self.w;
+        // Check right
+        let move_right = of.x + of.w - self.x;
+        if move_right < -move_x {
+            move_x = move_right;
+        }
+
+        if move_x.abs() < move_y.abs() {
+            Vec2::new(move_x, T::zero())
+        }
+        else {
+            Vec2::new(T::zero(), move_y)
+        }
+    }
+
+    /// Calculate the area of the rectangle.
+    pub fn area(&self) -> T
+    where
+        T: Signed,
+    {
+        sign::abs(self.w) * sign::abs(self.h)
+    }
+
+    fn contains_point(&self, point: &Vec2<T>) -> bool
+    where
+        T: Add<Output = T> + PartialOrd,
+    {
+        point.x >= self.x
+            && point.x <= self.x + self.w
+            && point.y >= self.y
+            && point.y <= self.y + self.h
+    }
+
+    fn contains_rect(&self, rect: &Rect<T>) -> bool
+    where
+        T: Add<Output = T> + Sub<Output = T> + Zero + PartialOrd,
+    {
+        /* True, if the rightmost x-coordinate of the called rectangle is further
+         * right or the same as the rightmost coordinate of the given rect.
+         */
+        let x_exceeds = self.x + self.w - rect.x - rect.w >= T::zero();
+        // The same for the y-coordinates
+        let y_exceeds = self.y + self.h - rect.y - rect.h >= T::zero();
+
+        x_exceeds && y_exceeds && self.x <= rect.x && self.y <= rect.y
+    }
+
+    fn is_inside_rect(&self, rect: &Rect<T>) -> bool
+    where
+        T: Add<Output = T> + Sub<Output = T> + Zero + PartialOrd,
+    {
+        rect.contains_rect(&self)
+    }
+}
+
+#[cfg(test)]
+mod test
+{
+    use super::*;
+
+    #[test]
+    fn test_intersect()
+    {
+        let a = Rect::from_slice([0, 0, 4, 4]);
+        let b = Rect::from_slice([-1, -1, 1, 1]);
+
+        assert!(Rect::intersect(&a, &b));
+    }
+}
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()
+}