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```
```use crate::geom::{Circle, Line, Rectangle, Triangle, Vector, Transform, about_equal};

/// The collision and positional attributes of shapes
pub trait Shape {
/// If the point lies on the shape's boundary or within it
#[must_use]
fn contains(&self, point: impl Into<Vector>) -> bool;
/// If any area bounded by the shape falls on the line
#[must_use]
fn intersects(&self, line: &Line) -> bool { self.overlaps(line) }
/// If any area is bounded by both the shape and the circle
#[must_use]
fn overlaps_circle(&self, circle: &Circle) -> bool { self.overlaps(circle) }
/// If any area is bounded by both the shape and the rectangle
#[must_use]
fn overlaps_rectangle(&self, rectangle: &Rectangle) -> bool { self.overlaps(rectangle) }
/// If any area is bounded by both either shape
#[must_use]
fn overlaps(&self, other: &impl Shape) -> bool;

/// The point all other points are equidistant to in the shape
#[must_use]
fn center(&self) -> Vector;
/// A Rectangle that contains the entire shape
#[must_use]
fn bounding_box(&self) -> Rectangle;
/// Apply a transform to a shape then get the bounding box for the transformed shape
///
/// Note: if you want to get the collision of rotated shapes, you probably
/// want to use [ncollide](https://crates.io/crates/ncollide)
#[must_use]
fn transformed_bounding_box(&self, transform: Transform) -> Rectangle {
let bb = self.bounding_box();
// Build the transform to rotate the shape
let transform = Transform::translate(bb.center() + bb.pos)
* transform
* Transform::translate(-bb.pos - bb.center());
// Get new corner position
let tl = transform * bb.pos;
let tr = transform * (bb.pos + Vector::new(bb.size.x, 0));
let bl = transform * (bb.pos + Vector::new(0, bb.size.y));
let br = transform * (bb.pos + bb.size);
// Get min and max points
let min = tr.min(tl).min(bl).min(br);
let max = tr.max(tl).max(bl).max(br);
// Make new bounding box
Rectangle::new(min, max - min)
}
/// Create a copy of the shape with an offset center
#[must_use]
fn translate(&self, amount: impl Into<Vector>) -> Self where Self: Sized;
/// Create a copy of the shape that is contained within the bound
#[must_use]
fn constrain(&self, outer: &Rectangle) -> Self where Self: Sized {
let area = self.bounding_box();
let clamped = area.top_left().clamp(outer.top_left(), outer.top_left() + outer.size() - area.size());
self.translate(clamped - area.top_left())
}
/// Create a copy of the shape with an offset center
#[must_use]
fn with_center(&self, center: impl Into<Vector>) -> Self where Self: Sized {
self.translate(center.into() - self.center())
}
}

impl Shape for Circle {
fn contains(&self, v: impl Into<Vector>) -> bool {
}
fn overlaps_circle(&self, c: &Circle) -> bool {
}
fn overlaps(&self, shape: &impl Shape) -> bool {
shape.overlaps_circle(self)
}

fn center(&self) -> Vector { self.pos }
fn bounding_box(&self) -> Rectangle {
}
fn translate(&self, v: impl Into<Vector>) -> Self {
Circle {
pos: self.pos + v.into(),
}
}
}

impl Shape for Rectangle {
fn contains(&self, point: impl Into<Vector>) -> bool {
let p = point.into();

return p.x >= self.x()
&& p.y >= self.y()
&& p.x < self.x() + self.width()
&& p.y < self.y() + self.height()
}
fn overlaps_circle(&self, c: &Circle) -> bool {
(c.center().clamp(self.top_left(), self.top_left() + self.size()) - c.center()).len2() < c.radius.powi(2)
}
fn overlaps_rectangle(&self, b: &Rectangle) -> bool {
self.x() < b.pos.x + b.size.x && self.x() + self.width() > b.pos.x && self.y() < b.pos.y + b.size.y &&
self.y() + self.height() > b.pos.y
}

fn intersects(&self, l: &Line) -> bool { l.overlaps_rectangle(self) }
fn overlaps(&self, shape: &impl Shape) -> bool { shape.overlaps_rectangle(self) }

fn center(&self) -> Vector { self.pos + self.size / 2 }
fn bounding_box(&self) -> Rectangle { *self }
fn translate(&self, v: impl Into<Vector>) -> Self {
Rectangle {
pos: self.pos + v.into(),
size: self.size
}
}
}

impl Shape for Triangle {
fn contains(&self, v: impl Into<Vector>) -> bool {
let v = v.into();
// form three triangles with this new vector
let t_1 = Triangle::new(v, self.a, self.b);
let t_2 = Triangle::new(v, self.b, self.c);
let t_3 = Triangle::new(v, self.c, self.a);

// calculate the area these smaller triangles make
// if they add up to be the area of this triangle, the point is inside it
about_equal(t_1.area() + t_2.area() + t_3.area(), self.area())
}
fn intersects(&self, line: &Line) -> bool {
// check each the vertices and each edge if it overlaps the line
self.contains(line.a)
|| self.contains(line.b)
|| Line::new(self.a, self.b).intersects(line)
|| Line::new(self.b, self.c).intersects(line)
|| Line::new(self.c, self.a).intersects(line)
}
fn overlaps_circle(&self, circ: &Circle) -> bool{
Line::new(self.a, self.b).overlaps_circle(circ)
|| Line::new(self.b, self.c).overlaps_circle(circ)
|| Line::new(self.c, self.a).overlaps_circle(circ)
}
fn overlaps_rectangle(&self, rect: &Rectangle) ->bool {
Line::new(self.a, self.b).overlaps_rectangle(rect)
|| Line::new(self.b, self.c).overlaps_rectangle(rect)
|| Line::new(self.c, self.a).overlaps_rectangle(rect)
}
fn overlaps(&self, other: &impl Shape) -> bool {
self.contains(other.center())
|| other.intersects(&Line::new(self.a, self.b))
|| other.intersects(&Line::new(self.b, self.c))
|| other.intersects(&Line::new(self.a, self.c))
}

fn center(&self) -> Vector {
(self.a + self.b + self.c) / 3
}
fn bounding_box(&self) -> Rectangle {
let min = self.a.min(self.b.min(self.c));
let max = self.a.max(self.b.max(self.c));
Rectangle::new(min, max - min)
}
fn translate(&self, v: impl Into<Vector>) -> Self {
let v = v.into();
Triangle {
a: self.a + v,
b: self.b + v,
c: self.c + v
}
}
}

impl Shape for Line {
fn contains(&self, v: impl Into<Vector>) -> bool {
let v = v.into();
}
fn intersects(&self, l: &Line) -> bool {
// calculate the distance to intersection point
let d1 = ((l.b.x - l.a.x) * (self.a.y - l.a.y) - (l.b.y - l.a.y) * (self.a.x - l.a.x))
/ ((l.b.y - l.a.y) * (self.b.x - self.a.x) - (l.b.x - l.a.x) * (self.b.y - self.a.y));
let d2 = ((self.b.x - self.a.x) * (self.a.y - l.a.y) - (self.b.y - self.a.y) * (self.a.x - l.a.x))
/ ((l.b.y - l.a.y) * (self.b.x - self.a.x) - (l.b.x - l.a.x) * (self.b.y - self.a.y));

// if d1 and d2 are between 0-1, lines are colliding
if d1 >= 0.0 && d1 <= 1.0 && d2 >= 0.0 && d2 <= 1.0 {
return true;

// for anyone interested, here is the intersection point:
// let intersect_x = self.a.x + (d1 * (self.b.x-self.a.x));
// let intersect_y = self.a.y + (d1 * (self.b.y-self.a.y));
}
false
}
fn overlaps_circle(&self, c: &Circle) -> bool {
// check if start or end point is in the circle
if c.contains(self.a) || c.contains(self.b) {
true
} else {
let length = self.b - self.a;
// get dot product of the line and circle
let dot = length.dot(c.center() - self.a) / length.len2();
// find the closest point on the line
let closest = self.a + length * dot;
// make sure the point is on the line, and in the circle
self.contains(closest)
&& (closest - c.center()).len2() <= c.radius.powi(2)
}
}
fn overlaps_rectangle(&self, b: &Rectangle) -> bool {
// check each edge (top, bottom, left, right) if it overlaps our line
let top_left = b.top_left();
let top_right = top_left + Vector::new(b.width(), 0.0);
let bottom_left = top_left + Vector::new(0.0, b.height());
let bottom_right = top_left + Vector::new(b.width(), b.height());

b.contains(self.a) || b.contains(self.b)
|| self.intersects(&Line::new(top_left, top_right))
|| self.intersects(&Line::new(top_left, bottom_left))
|| self.intersects(&Line::new(top_right, bottom_right))
|| self.intersects(&Line::new(bottom_left, bottom_right))
}
fn overlaps(&self, shape: &impl Shape) -> bool {
shape.intersects(self)
}

fn center(&self) -> Vector { (self.a + self.b) / 2 }
fn bounding_box(&self) -> Rectangle {
let min = self.a.min(self.b);
let max = self.a.max(self.b);
Rectangle::new(min, max - min)
}
fn translate(&self, v: impl Into<Vector>) -> Self {
let v = v.into();
Line {
a: self.a + v,
b: self.b + v,
t: self.t
}
}
}

impl Shape for Vector {
fn contains(&self, v: impl Into<Vector>) -> bool {
*self == v.into()
}
fn overlaps(&self, shape: &impl Shape) -> bool {
shape.contains(*self)
}

fn center(&self) -> Vector { *self }
fn bounding_box(&self) -> Rectangle { Rectangle::new(*self, Vector::ONE) }
fn translate(&self, v: impl Into<Vector>) -> Vector { *self + v.into() }
}
```