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== planegeometry.rs ==
<syntaxhighlight lang="rs">
// plane_geometry.rs
// Geometry of points and lines in the plane, implemented with rational numbers. The implementation is janky, though.
// Can be used to enumerate ternary billiard scales.
use std::ops::Add;
use std::ops::Sub;
use std::ops::Neg;
use std::iter::zip;
use num_traits::sign::Signed;
use std::fmt;


use num_rational::Rational64 as r64;
#[derive(Copy, Clone, Debug, Hash, PartialEq, Eq)]
/// The possible configurations of a point and an oriented line on the plane.
pub enum PointLineConfiguration {
    Left, // The point is on the left half-plane.
    Right, // The point is on the right half-plane.
    OnTheLine, // The point is on the line.
}
fn is_between(a:r64, b:r64, c:r64) -> bool {
    if b == c {
        a == b
    } else if b < c {
        b < a && a < c
    } else {
        c < a && a < b
    }
}
/// Gives the greatest common denominator of the two inputs, unless that's 2^63.
/// 2^63 doesn't fit in an `i64`, so it returns -2^63, which does.
pub fn gcd(u: i64, v: i64) -> i64 {
    // `wrapping_abs` gives a number's absolute value, unless that's 2^63. 2^63
    // won't fit in `i64`, so it gives -2^63 instead.
    let mut v = v.wrapping_abs() as u64;
    if u == 0 {
        return v as i64;
    }
    let mut u = u.wrapping_abs() as u64;
    if v == 0 {
        return u as i64;
    }
    // `|` is bitwise OR. `trailing_zeros` quickly counts a binary number's
    // trailing zeros, giving its prime factorization's exponent on two.
    let gcd_exponent_on_two = (u | v).trailing_zeros();
    // `>>=` divides the left by two to the power of the right, storing that in
    // the left variable. `u` divided by its prime factorization's power of two
    // turns it odd.
    u >>= u.trailing_zeros();
    v >>= v.trailing_zeros();
    while u != v {
        if u < v {
            // Swap the variables' values with each other.
            core::mem::swap(&mut u, &mut v);
        }
        u -= v;
        u >>= u.trailing_zeros();
    }
    // `<<` multiplies the left by two to the power of the right.
    (u << gcd_exponent_on_two) as i64
}
/// A rational number or unsigned infinity; represents a valid slope for a line in Q^2.
#[derive(Copy, Clone, Debug, Hash)]
pub struct Slope {
    numer: i64,
    denom: i64,
}
impl PartialEq for Slope {
    fn eq(&self, other: &Self) -> bool {
        self.numer * other.denom == other.numer * self.denom
    }
}
impl fmt::Display for Slope {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{}/{}", self.numer, self.denom)
    }
}
impl Slope {
    /// Converts a `Slope` to a rational; returns Err if `denom` is 0.
    pub fn as_rational(&self) -> Result<r64, String> {
        if self.denom != 0 {
            Ok(r64::new(self.numer, self.denom))
        } else {
            Err("Attempted to convert a Slope with `denom` == 0 into a Rational64".to_string())
        }
    }
   
    /// Converts the projective rational to a rational; panics if the denominator is zero.
    pub fn as_rational_raw(&self) -> r64 {
        r64::new(self.numer, self.denom)
    }
   
    /// Create a new reduced Slope; panics if both numer and denom are 0.
    pub fn new(n: i64, d: i64) -> Result<Self, String> {
        let (mut numer, mut denom) = (n, d);
        if numer == 0 && denom == 0 {
            Err("Attempted to create a Slope with both `numer` and `denom` equal to 0".to_string())
        } else {
            if denom < 0 {
                numer = -numer;
                denom = -denom;
            }
            let d = gcd(numer, denom);
            if d > 1 {
                numer = numer/d;
                denom = denom/d;
            }
            Ok(Self {
                numer,
                denom,
            })
        }
    }
   
    /// Create a new Slope without checking that `numer` == `denom` == 0, or reducing the rational afterwards.
    pub fn raw(numer: i64, denom: i64) -> Self {
        Self {
            numer,
            denom,
        }
    }
   
    /// Create a new `Slope` from a rational.
    pub fn rational(rat: r64) -> Self {
        Self {
            numer: *rat.numer(),
            denom: *rat.denom(),
        }
    }
   
    /// Create a new `Slope` from an integer.
    pub fn integer(n: i64) -> Self {
        // use 'raw' since an integer is always reduced
        Self::raw(n, 1)
    }
   
    /// Shorthand for slope 0.
    pub fn zero() -> Self {
        Self::raw(0, 1)
    }
    /// Shorthand for slope 1.
    pub fn one() -> Self {
        Self::raw(1, 1)
    }
   
    /// Shorthand for infinite slope.
    pub fn infinity() -> Self {
        Self::raw(1, 0)
    }
}
/// A finite point; a member of Q^2.
#[derive(Copy, Clone, Debug, Hash, PartialEq)]
pub struct Point {
    // The x-coordinate.
    x: r64,
    // The y-coordinate.
    y: r64,
}
impl Add for Point {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        Self {
            x: self.x + other.x,
            y: self.y + other.y,
        }
    }
}
impl Sub for Point{
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        Self {
            x: self.x - other.x,
            y: self.y - other.y,
        }
    }
}
impl Neg for Point{
    type Output = Self;
    fn neg(self) -> Self {
        Self {
            x: -self.x,
            y: -self.y,
        }
    }
}
impl Point {
    pub fn new(x: r64, y: r64) -> Self {
        Self {
            x,
            y,
        }
    }
   
    pub fn zero() -> Self {
        Self {
            x: r64::new(0,1),
            y: r64::new(0,1),
        }
    }
   
    pub fn scalar_mult(lambda: r64, v: Point) -> Self {
        Self {
            x: lambda*v.x,
            y: lambda*v.y,
        }
    }
    pub fn average(points: &Vec<Self>) -> Self {
        let mut sum = Self::zero();
        for p in points {
            sum = sum + *p;
        }
        Self::scalar_mult(r64::new(1,1)/r64::new(points.len() as i64,1), sum)
    }
   
    pub fn theta(v: Point) -> f64 {
        ( *v.y.numer() as f64 / *v.y.denom() as f64 ).atan2( *v.x.numer() as f64 / *v.x.denom() as f64 )
    }
   
    /// Return a copy of `points` sorted using the direction they make from the centroid, according to theta(v-centroid) in (-pi, pi].
    fn ordered_ccw(mut points: Vec<Self>) -> Vec<Self> {
        let centroid = Self::average(&points);
        points.sort_by(|a,b| Self::theta(*a-centroid).partial_cmp(&Self::theta(*b-centroid)).unwrap() );
        points
    }
   
    pub fn midpoint(p1: &Self, p2: &Self) -> Self {
        Self {
            x: (p1.x+p2.x)/r64::new(2,1),
            y: (p1.y+p2.y)/r64::new(2,1),
        }
    }
    // Use the slope-intercept formula including the case where the slope is infinite.
    pub fn are_collinear(p1: Self, p2: Self, p3: Self) -> bool {
        (p1.y - p3.y)*(p1.x - p2.x) == (p1.y-p2.y)*(p1.x - p3.x)
    }
}
impl fmt::Display for Point {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "({}, {})", self.x, self.y)
    }
}
/// An oriented line in Q^2 of rational or infinite slope.
#[derive(Copy, Clone, Debug, Hash)]
pub struct Line {
    point1: Point,
    point2: Point,
}
impl PartialEq for Line {
    fn eq(&self, other: &Self) -> bool {
        self.slope() == other.slope() && self.has_point(other.point())
    }
}
impl Line {
    pub fn slope(self: Line) -> Slope {
        Slope::new(
            (*(self.point2.y-self.point1.y).numer()) * (*(self.point2.x-self.point1.x).denom()),
            (*(self.point2.x-self.point1.x).numer()) * (*(self.point2.y-self.point1.y).denom())).unwrap()
    }
   
    pub fn point(self: Line) -> Point {
        self.point1
    }
   
    pub fn from_slope_and_point(sl: Slope, point: Point) -> Self {
        Self {
            point1: point,
            point2: point + Point::new(r64::new_raw(sl.denom, 1), r64::new_raw(sl.numer, 1)),
        }
    }
    pub fn from_points(point1: Point, point2: Point) -> Result<Self, String> {
        if point1 == point2 {
            Err("The points {point1} and {point2} are equal".to_string())
        } else {
            Ok(Line{point1, point2})
        }
    }
   
    /// Test whether a line is vertical.
    fn is_vertical(&self) -> bool {
        self.point1.x == self.point2.x
    }
    /// Test whether a line is horizontal.
    fn is_horizontal(&self) -> bool {
        self.point1.y == self.point2.y
    }
   
    /// Test whether two lines are parallel.
    fn is_parallel(&self, other: Self) -> bool {
        self.slope() == other.slope()
    }
   
    /// Test whether `p` satisfies the equation of the line.
    fn has_point(&self, p: Point) -> bool {
        (p.y - self.point().y)*r64::new_raw(self.slope().denom,1) == r64::new_raw(self.slope().numer,1)*(p.x - self.point().x)
    }
   
    /// Determine whether `p1` and `p2` are on the same side of the line.
    fn on_same_side(&self, p1: Point, p2: Point) -> bool {
        if self.is_vertical() {
            (p1.x < self.point1.x && p2.x < self.point1.x ) || (p1.x > self.point1.x && p2.x > self.point1.x)
        } else { // both `p1` and `p2` are above `self`
            ((p1.y - self.point1.y)*r64::new_raw(self.slope().denom,1) > r64::new_raw(self.slope().numer,1)*(p1.x - self.point1.x) &&
                (p2.y - self.point1.y)*r64::new_raw(self.slope().denom,1) > r64::new_raw(self.slope().numer,1)*(p2.x - self.point1.x))
            || // ... or both are below `self`
            ((p1.y - self.point1.y)*r64::new_raw(self.slope().denom,1) < r64::new_raw(self.slope().numer,1)*(p1.x - self.point1.x) &&
                (p2.y - self.point1.y)*r64::new_raw(self.slope().denom,1) < r64::new_raw(self.slope().numer,1)*(p2.x - self.point1.x))
        }
    }
   
    /// Depending on the orientation of the line, determine whether the point `p` is to the left, to the right, or on the line.
    pub fn point_line_config(&self, p: Point) -> PointLineConfiguration {
        if self.point2.x != self.point1.x { // For non-vertical lines
                if ((p.y - self.point().y)*r64::new_raw(self.slope().denom, 1) - r64::new_raw(self.slope().numer, 1)*(p.x - self.point().x)) * (self.point2.x - self.point1.x).signum() > r64::new_raw(0,1) {
                    PointLineConfiguration::Left
                } else if ((p.y - self.point().y)*r64::new_raw(self.slope().denom, 1) - r64::new_raw(self.slope().numer, 1)*(p.x - self.point().x)) * (self.point2.x - self.point1.x).signum() == r64::new_raw(0,1) {
                    PointLineConfiguration::OnTheLine
                } else {
                    PointLineConfiguration::Right
                }
        } else { // For vertical lines
                // If point2.y < point1.y, then the line is oriented downwards, so multiply by -1 to compensate.
            if (p.x-self.point().x) * (self.point2.y-self.point1.y) < r64::new_raw(0,1) {  // upwards vertical line and point to the left of it, or downwards vertical line and point to the right of it.
                PointLineConfiguration::Left
            } else if (p.x-self.point().x) * (self.point2.y-self.point1.y) == r64::new_raw(0,1)  {
                PointLineConfiguration::OnTheLine
            } else {
                PointLineConfiguration::Right
            }
        }
    }
}
impl fmt::Display for Line {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "(slope: {}, point: {})", self.slope(), self.point1)
    }
}
/// For two non-parallel ones, find the intersection; for two parallel lines, return `None`.
pub fn intersection(l1: Line, l2: Line) -> Option<Point> {
    let (x1, y1, x2, y2) = (l1.point().x, l1.point().y, l2.point().x, l2.point().y);
    match (l1.slope(), l2.slope()) {
        (s1, s2) if s1 == s2 => None, // Same slope
        (s1, s2) if s1 == Slope::infinity() && s2 != Slope::infinity() => Some(Point {
            x: x1,
            y: s2.as_rational_raw() * (x1 - x2) + y2,
        }),
        (s1, s2) if s1 != Slope::infinity() && s2 == Slope::infinity() => Some(Point {
            x: x2,
            y: s1.as_rational_raw() * (x2 - x1) + y1,
        }),
        (s1, s2) => Some(Point {
            x: (y1 - s1.as_rational_raw() * x1 + s2.as_rational_raw() * x2 - y2)
                / (s2.as_rational_raw() - s1.as_rational_raw()),
            y: (s1.as_rational_raw() * s2.as_rational_raw() * (x2 - x1) + s2.as_rational_raw() * y1 - s1.as_rational_raw() * y2)
                / (s2.as_rational_raw() - s1.as_rational_raw()),
        }),
    }
}
#[derive(Clone, Debug, Hash)]
pub struct ConvexPolygon {
    vertices: Vec<Point>, // Assumes that the vertices are ordered in clockwise or counterclockwise order.
}
impl PartialEq for ConvexPolygon {
    fn eq(&self, other: &Self) -> bool {
        // If all the points in both polygons are equal then they are equal; we ensure this by enforcing a standard order when a `ConvexPolygon` is created.
        if other.vertices.len() != self.vertices.len() {
            return false;
        }
        for (a, b) in zip(self.vertices.iter(), other.vertices.iter()) {
            if a != b {
                return false;
            }
        }
        true
    }
}
impl ConvexPolygon { // Assumes that the vertices form a convex polygon. Does not check if the `Vec` of vertices consists of distinct elements.
    pub fn new(vertices: Vec<Point>) -> Option<Self> {
        if vertices.len() >= 3 {
            Some(Self {
                vertices: Point::ordered_ccw(vertices), // This will work for vertices of a convex polygon.
            })
        } else {
            None
        }
    }
   
    fn raw(vertices: Vec<Point>) -> Self { // Does not check for ordering.
        Self {
            vertices: Point::ordered_ccw(vertices), // This will work for vertices of a convex polygon.
        }
           
    }
   
    pub fn centroid(&self) -> Point {
        Point::average(&self.vertices)
    }
   
    pub fn has_point_inside(&self, point: Point) -> bool {
        // Do `point` and edge_i+1 x edge_i+2 lie on the same side of edge_i?
        for i in 0..self.vertices.len()-2 {
            if !Line::from_points(self.vertices[i], self.vertices[i+1]).unwrap().on_same_side(point, self.vertices[i+2]) {
                return false;
            }
        }
        // Check last two triples.
        if !Line::from_points(self.vertices[self.vertices.len()-2], self.vertices[self.vertices.len()-1]).unwrap().on_same_side(point, self.vertices[0]) {
            return false;
        } else if !Line::from_points(self.vertices[self.vertices.len()-1], self.vertices[0]).unwrap().on_same_side(point, self.vertices[1]) {
            return false;
        } else {
            return true;
        }
    }
   
    /// A vector storing the edges of the polygon in order.
    fn lines_for_edges(&self) -> Vec<Line> {
        let mut result: Vec<Line> = (0..self.vertices.len()-1).into_iter().map(|i| Line::from_points(self.vertices[i], self.vertices[i+1]).unwrap()).collect();
        result.push(Line::from_points(self.vertices[self.vertices.len()-1], self.vertices[0]).unwrap());
        result
    }
   
    /// Subdivide a polygon with the given line and return the two pieces.
    pub fn subdivide(&self, line: Line) -> (Option<ConvexPolygon>, Option<ConvexPolygon>) {
        // Collect vertices that fall to the left, on thhe line, and to the right, respectively. The left and right collections are missing two vertices.
        let mut vertices_left: Vec<Point> = self.vertices
                .iter()
                .filter(|&x| line.point_line_config(*x) == PointLineConfiguration::Left).cloned().collect();
        let mut vertices_right: Vec<Point> = self.vertices
                .iter()
                .filter(|&x| line.point_line_config(*x) == PointLineConfiguration::Right).cloned().collect();
        let vertices_on_line: Vec<Point> = self.vertices
                .iter()
                .filter(|&x| line.point_line_config(*x) == PointLineConfiguration::OnTheLine).cloned().collect();
        if !vertices_left.is_empty() || !vertices_right.is_empty() {
            // Add any vertices on the line both to the new left polygon and the new right polygon.
            for point in &vertices_on_line {
                vertices_left.push(*point);
                vertices_right.push(*point);
            }
            // Look for intersection points on edges with the line. 
            for edge in &self.lines_for_edges() {
                if let Some(intsn) = intersection(*edge, line) {
                    if is_between(intsn.x, edge.point1.x, edge.point2.x) && is_between(intsn.y, edge.point1.y, edge.point2.y) {
                        vertices_left.push(intsn);
                        vertices_right.push(intsn);
                    }
                }
            }
            // At most two vertices are added, so if there was no vertex to one side originally, that side doesn't have a polygon.
        }
        (ConvexPolygon::new(vertices_left), ConvexPolygon::new(vertices_right))
    }
   
    fn triangle_from_lines(l1: Line, l2: Line, l3: Line) -> Option<Self> {
        if !l1.is_parallel(l2) && !l2.is_parallel(l3) && !l3.is_parallel(l1) {
            let p1 = intersection(l1, l2).unwrap();
            let p2 = intersection(l2, l3).unwrap();
            let p3 = intersection(l3, l1).unwrap();
            Self::new(vec![p1, p2, p3])
        } else {
            None
        }
    }
   
    fn parallelogram_from_lines(l1: Line, l2: Line, m1: Line, m2: Line) -> Option<Self> {
        if l1.is_parallel(l2) && l1 != l2 && m1.is_parallel(m2) && m1 != m2 {
            let p1 = intersection(l1, m1).unwrap();
            let p2 = intersection(l1, m2).unwrap();
            let p3 = intersection(l2, m1).unwrap();
            let p4 = intersection(l2, m2).unwrap();
            Self::new(vec![p1, p2, p3, p4])
        } else {
            None
        }
    }
}
fn projected_constraint_planes(a: u32, b: u32, c: u32) -> (Vec<Line>, Vec<Line>, Vec<Line>) {
    let first = (0..b+c+1).map(|i| Line::from_slope_and_point(Slope::raw(0, 1), Point::new(r64::new(0, 1), r64::new(-(b as i64) + (i as i64), c as i64 ) ) )).collect(); // horizontal lines going up (Left)
    let second = (0..a+c+1).map(|j| Line::from_slope_and_point(Slope::raw(1, 0), Point::new(r64::new((c as i64)-(j as i64), c as i64), r64::new(0, 1) ) )).collect(); // vertical lines going left (Left)
    let third = (0..a+b+1).map(|k| Line::from_slope_and_point(Slope::raw(b as i64, a as i64), Point::new( r64::new(0, 1), r64::new(-(b as i64)+(k as i64), a as i64))) ).collect(); // lines of pos. slope going up (Left)
    (first, second, third)
}
/// Project the unit cube in R^3 via a linear map that has (a,b,c) in its kernel.
pub fn projected_cube(a: u32, b: u32, c: u32) -> Option<ConvexPolygon> {
    if a > 0 && b > 0 && c > 0 {
        let projected_cube_vertices = vec![Point::new(r64::new(0,1), r64::new(1,1)), 
                    Point::new(r64::new(1,1), r64::new(1,1)),
                    Point::new(r64::new(1,1), r64::new(0,1)),
                    Point::new(r64::new(-(a as i64), c as i64), r64::new(-(b as i64), c as i64) + r64::new(1,1)),
                    Point::new(r64::new(-(a as i64), c as i64), r64::new(-(b as i64), c as i64)),
                    Point::new(r64::new(-(a as i64), c as i64) + r64::new(1,1), r64::new(-(b as i64), c as i64))];
        ConvexPolygon::new(projected_cube_vertices)
    } else {
        None
    }
}
/// Partition the projected unit cube with the projected constraint planes.
pub fn project_and_partition(a: u32, b: u32, c: u32) -> Vec<ConvexPolygon> {
    let projected_cube = projected_cube(a, b, c).unwrap();
    let lineses = projected_constraint_planes(a, b, c);  // it's a vector of vector of `Line`s
    let mut first_shapes = Vec::<ConvexPolygon>::new();
    let mut second_shapes = Vec::<ConvexPolygon>::new();
    let mut third_shapes = Vec::<ConvexPolygon>::new();
    let mut i: usize = 0;
    let mut remaining: ConvexPolygon = projected_cube;
    while let (maybe_remaining, maybe_next) = remaining.subdivide((lineses.0)[i]) { // The remaining portion is to the Left.
        match (maybe_remaining, maybe_next) {
            (Some(r), None) => {
                remaining = r;
            },
            (Some(r), Some(next)) => {
                remaining = r;
                first_shapes.push(next);
            },
            (None, Some(next)) => { // This is the last `next` you need to look at.
                first_shapes.push(next);
                break;
            },
            (_, _) => {
                break;
            },
        }
        i = i+1;
    }
    for polygon in first_shapes {
        let mut j: usize = 0;
        let mut remaining2: ConvexPolygon = polygon;       
        loop {
            let (maybe_remaining, maybe_next) = remaining2.subdivide((lineses.1)[j]); // The remaining portion is to the Left.
            match (maybe_remaining, maybe_next) {
                (Some(r), None) => {
                    remaining2 = r;
                },
                (Some(r), Some(next)) => {
                    remaining2 = r;
                    second_shapes.push(next);
                },
                (None, Some(next)) => {
                    second_shapes.push(next);
                    break;
                },
                (_, _) => {
                    break;
                },
            }
            j = j+1;
        }
    }
    for polygon in second_shapes {
        let mut j: usize = 0;
        let mut remaining3: ConvexPolygon = polygon;
        while let (maybe_remaining, maybe_next) = remaining3.subdivide((lineses.2)[j]) { // The remaining portion is to the Left.
            match (maybe_remaining, maybe_next) {
                (Some(r), None) => {
                    remaining3 = r;
                },
                (Some(r), Some(next)) => {
                    remaining3 = r;
                    third_shapes.push(next);
                },
                (None, Some(next)) => {
                    third_shapes.push(next);
                    break;
                },
                (_, _) => {
                    break;
                },
            }
            j = j+1;
        }
    }
    for polygon in third_shapes.clone() {
    }
    third_shapes
}
/// Advance a projected point, `pt`, by one letter according to what integer coordinate it next hits as it traverses in the given velocity,
/// and return the next point and the corresponding letter, one of "x", "y", and "z".
pub fn advance(a: u32, b: u32, c: u32, pt: Point) -> Result<(Point, String), String> {
    let projected_cube = projected_cube(a, b, c).unwrap();
    // Consider: _ /
    //            |
    if !projected_cube.has_point_inside(pt) {
        Err(format!("Point passed to `advance`, {}, is not inside the projected cube", pt))
    } else {
        let projected_x_y_equals_1_1 = Line::from_slope_and_point(Slope::raw(b as i64, a as i64), Point::new( r64::new(0, 1), r64::new(-(b as i64)+(a as i64), a as i64))); // the /
        let projected_x_z_equals_1_1 = Line::from_slope_and_point(Slope::raw(0, 1), Point::new(r64::new(0, 1), r64::new(-(b as i64)+(c as i64), c as i64))); // the _, oriented right
        let projected_y_z_equals_1_1 = Line::from_slope_and_point(Slope::raw(1, 0), Point::new(r64::new((c as i64)-(a as i64), c as i64), r64::new(0, 1))); // the |, oriented up
        if projected_x_y_equals_1_1.point_line_config(pt) == PointLineConfiguration::Right
                && projected_y_z_equals_1_1.point_line_config(pt) == PointLineConfiguration::Right  { // Below the / and to the right of the | => x has changed, change x coordinate to 0 and project; move x coordinate to the left
            Ok((pt - Point::new(r64::new(1,1), r64::new(0,1)), "x".to_string())) // new point is one unit to the left
        } else if projected_x_z_equals_1_1.point_line_config(pt) == PointLineConfiguration::Left
                && projected_x_y_equals_1_1.point_line_config(pt) == PointLineConfiguration::Left { // Above the _ and to the left of the / => y has changed, change y coordinate to 0 and project; move y coordinate down
            Ok((pt - Point::new(r64::new(0,1), r64::new(1,1)), "y".to_string())) // new point is one unit below
        } else if projected_x_z_equals_1_1.point_line_config(pt) == PointLineConfiguration::Right
                && projected_y_z_equals_1_1.point_line_config(pt) == PointLineConfiguration::Left { // Below the _ and to the left of the | => z has changed, change y coordinate to 0 and project
            Ok((pt + Point::new(r64::new((a as i64), (c as i64)), r64::new((b as i64), (c as i64) ) ), "z".to_string())) // new point is one unit below in the z-direction, and e3 is projected to (-a/c, -b/c)
        } else {
            Err(format!("Point passed to `advance`, {}, is inside the projected cube but falls on a projected constraint plane", pt))
        }
    }
}
#[cfg(test)]
mod tests {
    use num_rational::Rational64 as r64;
    use crate::plane_geometry::Slope;
    use crate::plane_geometry::Point;
    use crate::plane_geometry::Line;
    use crate::plane_geometry::intersection;
    use crate::plane_geometry::ConvexPolygon;
    use crate::plane_geometry::PointLineConfiguration;
    use crate::plane_geometry::projected_cube;
   
    // Tests for the struct `Slope`.
    #[test]
    fn slope_bad_slope() {
        let bad_slope : Result<Slope, String> = Slope::new(0,0);
            assert_eq!(bad_slope,
                    Err("Attempted to create a Slope with both `numer` and `denom` equal to 0".to_string()));
    }
   
    #[test]
    fn slope_infinite_slope() {
        let infinite_slope : Result<Slope, String> = Slope::new(1,0);
        assert_eq!(infinite_slope, Ok(Slope::infinity()));
    }
   
    #[test]
    fn slope_zero_slope() {
        let zero_slope : Result<Slope, String> = Slope::new(0,1);
        assert_eq!(zero_slope, Ok(Slope::zero()));
    }
   
    #[test]
    fn slope_integer_slope() {
        let slope_four : Slope = Slope::integer(4i64);
        assert_eq!(slope_four, Slope::raw(4,1));
    }
   
    #[test]
    fn slope_reduction() {
        let slope_two : Result<Slope, String> = Slope::new(8,4);
        assert_eq!(slope_two, Ok(Slope::raw(2,1)));
        let slope_half : Result<Slope, String> = Slope::new(4,8);
        assert_eq!(slope_half, Ok(Slope::raw(1,2)));
    }
   
    #[test]
    fn slope_as_rational() {
        let good_rational : Result<r64, String> = Slope::new(3,2).expect("Bad slope").as_rational();
        assert_eq!(good_rational, Ok(r64::new(3,2)));
       
        let bad_rational : Result<r64, String> = Slope::new(3,0).expect("Bad slope").as_rational();
        assert_eq!(bad_rational,
            Err("Attempted to convert a Slope with `denom` == 0 into a Rational64".to_string()));
    }
    // Tests for the module `Point`.
   
    #[test]
    fn point_create_point() {
        let point : Point = Point::new(r64::new(2,1),r64::new(2,1));
        assert_eq!(point, Point{ x: r64::new(2,1), y: r64::new(2,1)})
    }
   
    #[test]
    fn point_midpoint_vertical() {
        let point1 : Point = Point::new(r64::new(2,1),r64::new(2,1));
        let point2 : Point = Point::new(r64::new(2,1),r64::new(1,1));
        assert_eq!(Point::midpoint(&point1, &point2), Point{ x: r64::new(2,1), y: r64::new(3,2)})
    }
   
    #[test]
    fn point_midpoint_nonvertical() {
        let point1 : Point = Point::new(r64::new(1,1),r64::new(2,1));
        let point2 : Point = Point::new(r64::new(2,1),r64::new(1,1));
        assert_eq!(Point::midpoint(&point1, &point2), Point{ x: r64::new(3,2), y: r64::new(3,2)})
    }
    #[test]
    fn point_midpoint_identical() {
        let point1 : Point = Point::new(r64::new(1,1),r64::new(1,1));
        let point2 : Point = Point::new(r64::new(1,1),r64::new(1,1));
        assert_eq!(Point::midpoint(&point1, &point2), Point{ x: r64::new(1,1), y: r64::new(1,1)})
    }
   
    #[test]
    fn point_collinear() {
        let point1 : Point = Point::new(r64::new(1,1),r64::new(1,1));
        let point2 : Point = Point::new(r64::new(3,1),r64::new(4,1));
        let point3 : Point = Point::new(r64::new(1,1),r64::new(4,1));
        let point4 : Point = Point::new(r64::new(2,1),r64::new(5,2));
       
        assert!(Point::are_collinear(point1, point1, point1));
        assert!(Point::are_collinear(point1, point1, point2));
        assert!(Point::are_collinear(point1, point2, point1));
        assert!(Point::are_collinear(point2, point1, point1));
        assert!(Point::are_collinear(point1, point2, point4));
        assert!(!Point::are_collinear(point1, point2, point3));
    }
   
    #[test]
    fn line_parallel_implies_equal_slope() {
        let line1 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(1,1))).unwrap();
        let line2 = Line::from_points(Point::new(r64::new(0,1),r64::new(1,1)), Point::new(r64::new(1,1),r64::new(2,1))).unwrap();
        assert_eq!(line1.slope(), line2.slope());
    }
    // Tests for the module `Line`.
    #[test]
    fn line_equality() {
        let line1 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(1,1))).unwrap();
        let line2 = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(2,1),r64::new(2,1))); // equal to `line1`
        assert_eq!(line1, line2);
        let line3 = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(1,2),r64::new(1,2)));
        assert_eq!(line3, line2);
       
        let line4 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(2,1),r64::new(1,1))).unwrap();
        assert_ne!(line1, line4);
        let line5 = Line::from_points(Point::new(r64::new(1,1),r64::new(2,1)), Point::new(r64::new(0,1),r64::new(1,1))).unwrap();
        assert_ne!(line1, line5);
    }
   
    #[test]
    fn line_intersection_parallel_equal() {
        let line1 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(1,1))).unwrap();
        let line2 = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(2,1),r64::new(2,1))); // equal to `line1`
        assert_eq!(intersection(line1, line2), None);
    }
   
    #[test]
    fn line_intersection_parallel_unequal() {
        let line1 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(1,1))).unwrap();
        let line2 = Line::from_points(Point::new(r64::new(0,1),r64::new(1,2)), Point::new(r64::new(1,1),r64::new(3,2))).unwrap(); // not equal but parallel to `line1`
        assert_eq!(intersection(line1, line2), None);
        let line3 = Line::from_points(Point::new(r64::new(0,1),r64::new(1,1)), Point::new(r64::new(1,1),r64::new(2,1))).unwrap(); // not equal but parallel to `line1`
        assert_eq!(intersection(line1, line3), None);
    }
   
    #[test]
    fn line_intersection_nonparallel() {
        let line1 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(1,1))).unwrap();
        let line2 = Line::from_points(Point::new(r64::new(0,1),r64::new(0,1)), Point::new(r64::new(1,1),r64::new(2,1))).unwrap();
        assert_eq!(intersection(line1, line2), Some(Point::new(r64::new(0,1), r64::new(0,1))));
    }
   
    #[test]
    fn point_order_coordinate_vecs() {
        let e1 = Point::new(r64::new(1,1),r64::new(0,1));
        let e2 = Point::new(r64::new(0,1),r64::new(1,1));
        let mut points = vec![e1, -e1, e2, -e2, e1+e2, e1-e2, -e1-e2, -e1+e2];
        points = Point::ordered_ccw(points);
        assert!(points[0] == -e1-e2 && points[1] == -e2 && points[2] == e1-e2 && points[3] == e1 && points[4] == e1+e2 && points[5] == e2 && points[6] == -e1+e2 && points[7] == -e1 );
    }
   
    #[test]
    fn convexpolygon_disallow_polygon_with_fewer_than_3_vertices() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let result0 = ConvexPolygon::new(vec![]);
        assert_eq!(result0, None);
        let result1 = ConvexPolygon::new(vec![p1]);
        assert_eq!(result1, None);
        let result2 = ConvexPolygon::new(vec![p1, p2]);
        assert_eq!(result2, None);
    }
   
    #[test]
    fn convexpolygon_vertices_of_triangle_are_sorted() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let triangle = ConvexPolygon::new(vec![p1, p2, p3]);
        assert!(triangle.is_some());
        let vertices = triangle.unwrap().vertices;
        assert_eq!(vertices, vec![p3, p1, p2]);
    }
   
    #[test]
    fn convexpolygon_vertices_of_square_are_sorted() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
       
        let square = ConvexPolygon::new(vec![p1, p2, p3, p4]);
        assert!(square.is_some());
        let vertices = square.unwrap().vertices;
        assert_eq!(vertices, vec![p3, p1, p4, p2]);
    }
    #[test]
    fn convexpolygon_vertices_of_5gon_are_sorted() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let p5 = Point::new(r64::new(1,2),r64::new(2,1));
       
        let pentagon  = ConvexPolygon::new(vec![p1, p2, p3, p4, p5]);
        assert!(pentagon.is_some());
        let vertices = pentagon.unwrap().vertices;
        assert_eq!(vertices, vec![p3, p1, p4, p5, p2]);
    }
   
    #[test]
    fn convexpolygon_triangle_has_centroid_inside() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let triangle = ConvexPolygon::new(vec![p1, p2, p3]);
        let centroid = ConvexPolygon::centroid(&triangle.clone().unwrap());
        assert!(triangle.clone().unwrap().has_point_inside(centroid));
    }
   
    #[test]
    fn convexpolygon_vertex_is_not_inside() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let triangle = ConvexPolygon::new(vec![p1, p2, p3]);
        assert!(!triangle.unwrap().has_point_inside(p1));
    }
   
    #[test]
    fn convexpolygon_point_on_edge_is_not_inside() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let triangle = ConvexPolygon::new(vec![p1, p2, p3]);
        let p_edge = Point::midpoint(&p1, &p2);
        assert!(!triangle.unwrap().has_point_inside(p_edge)); 
    }
   
    #[test]
    fn convexpolygon_point_outside_is_not_inside() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let triangle = ConvexPolygon::new(vec![p1, p2, p3]);
        let p_outside = Point::new(r64::new(1,1),r64::new(1,1));
        assert!(!triangle.unwrap().has_point_inside(p_outside)); 
    }
    #[test]
    fn line_point_line_config_test_vertical_line() {
        let p_left = Point::new(r64::new(-1,1),r64::new(0,1));
        let p_on_line = Point::new(r64::new(0,1),r64::new(1,1));
        let p_right = Point::new(r64::new(1,1),r64::new(1,1));
        let vertical_line_up = Line::from_slope_and_point(Slope::infinity(), Point::zero());
        assert_eq!(vertical_line_up.point_line_config(p_left), PointLineConfiguration::Left);
        assert_eq!(vertical_line_up.point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(vertical_line_up.point_line_config(p_right), PointLineConfiguration::Right);
        let vertical_line_down = Line::from_points(Point::zero(), Point::new(r64::new(0,1), r64::new(-1,1)));
        assert_eq!(vertical_line_down.clone().unwrap().point_line_config(p_left), PointLineConfiguration::Right);
        assert_eq!(vertical_line_down.clone().unwrap().point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(vertical_line_down.clone().unwrap().point_line_config(p_right), PointLineConfiguration::Left);
    }
    #[test]
    fn line_point_line_config_test_pos_slope() {
        let p_above = Point::new(r64::new(0,1),r64::new(1,1));
        let p_on_line = Point::new(r64::new(1,1),r64::new(1,1));
        let p_below = Point::new(r64::new(1,1),r64::new(0,1));
        let line_up_right = Line::from_slope_and_point(Slope::integer(1), Point::zero());
        assert_eq!(line_up_right.point_line_config(p_above), PointLineConfiguration::Left);
        assert_eq!(line_up_right.point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(line_up_right.point_line_config(p_below), PointLineConfiguration::Right);
        let line_down_left = Line::from_points(Point::zero(), Point::new(r64::new(-1,1), r64::new(-1,1)));
        assert_eq!(line_down_left.clone().unwrap().point_line_config(p_above), PointLineConfiguration::Right);
        assert_eq!(line_down_left.clone().unwrap().point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(line_down_left.clone().unwrap().point_line_config(p_below), PointLineConfiguration::Left);
    }
   
    #[test]
    fn line_point_line_config_test_neg_slope() {
        let p_below = Point::new(r64::new(-1,1),r64::new(0,1));
        let p_on_line = Point::new(r64::new(-1,1),r64::new(1,1));
        let p_above = Point::new(r64::new(0,1),r64::new(1,1));
        let line_down_right = Line::from_slope_and_point(Slope::integer(-1), Point::zero());
        assert_eq!(line_down_right.point_line_config(p_below), PointLineConfiguration::Right);
        assert_eq!(line_down_right.point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(line_down_right.point_line_config(p_above), PointLineConfiguration::Left);
        let line_up_left = Line::from_points(Point::zero(), Point::new(r64::new(-1,1), r64::new(1,1)));
        assert_eq!(line_up_left.clone().unwrap().point_line_config(p_below), PointLineConfiguration::Left);
        assert_eq!(line_up_left.clone().unwrap().point_line_config(p_on_line), PointLineConfiguration::OnTheLine);
        assert_eq!(line_up_left.clone().unwrap().point_line_config(p_above), PointLineConfiguration::Right);
    }
   
    #[test]
    fn convexpolygon_if_all_vertices_are_to_one_side() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line_to_the_right = Line::from_slope_and_point(Slope::infinity(), Point::new(r64::new(2,1), r64::new(0,1)));
        let line_to_the_left = Line::from_slope_and_point(Slope::infinity(), Point::new(r64::new(-1,1), r64::new(0,1)));
        let line_above = Line::from_slope_and_point(Slope::zero(), Point::new(r64::new(0,1), r64::new(2,1)));
        let line_below = Line::from_slope_and_point(Slope::zero(), Point::new(r64::new(0,1), r64::new(-1,1)));
       
        assert_eq!(square.subdivide(line_to_the_right), (Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), Option::<ConvexPolygon>::None) );
        assert_eq!(square.subdivide(line_to_the_left), (Option::<ConvexPolygon>::None, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2]))) );
        assert_eq!(square.subdivide(line_above), (Option::<ConvexPolygon>::None, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])))  );
        assert_eq!(square.subdivide(line_below), (Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), Option::<ConvexPolygon>::None) );
    }
   
    #[test]
    fn convexpolygon_new_line_cuts_two_edges() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line = Line::from_slope_and_point(Slope::infinity(), Point::new(r64::new(1,2), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
        assert_eq!(left_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(0,1),r64::new(0,1)),
                Point::new(r64::new(1,2),r64::new(0,1)),
                Point::new(r64::new(1,2),r64::new(1,1)),
                Point::new(r64::new(0,1),r64::new(1,1))
                ])), "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(1,2),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(1,2),r64::new(1,1))
                ])), "`right_polygon` is not right polygon");
    }
   
    #[test]
    fn convexpolygon_new_line_grazes_one_vertex() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(0,1), r64::new(1,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
       
        assert_eq!(left_polygon, None, "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), "`right_polygon` is not right polygon");
        let line2 = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(1,1), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line2);
       
        assert_eq!(left_polygon, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, None, "`right_polygon` is not right polygon");
    }
   
    #[test]
    fn convexpolygon_new_line_coincides_with_one_edge() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line = Line::from_slope_and_point(Slope::infinity(), Point::new(r64::new(0,1), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
       
        assert_eq!(left_polygon, None, "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), "`right_polygon` is not right polygon");
        let line = Line::from_slope_and_point(Slope::integer(0), Point::new(r64::new(1,1), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
       
        assert_eq!(left_polygon, Some(ConvexPolygon::raw(vec![p3, p1, p4, p2])), "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, None, "`right_polygon` is not right polygon");
    }
   
    #[test]
    fn convexpolygon_new_line_cuts_one_edge() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line = Line::from_slope_and_point(Slope::integer(2), Point::new(r64::new(0,1), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
       
        assert_eq!(left_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(0,1),r64::new(0,1)),
                Point::new(r64::new(1,2),r64::new(1,1)),
                Point::new(r64::new(0,1),r64::new(1,1)),
                ])), "`left_polygon is not right polygon");
        assert_eq!(right_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(0,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(1,2),r64::new(1,1))
                ])), "`right_polygon` is not right polygon");
    }
   
    #[test]
    fn convexpolygon_new_line_cuts_no_edges() {
        let p1 = Point::new(r64::new(1,1),r64::new(0,1));
        let p2 = Point::new(r64::new(0,1),r64::new(1,1));
        let p3 = Point::new(r64::new(0,1),r64::new(0,1));
        let p4 = Point::new(r64::new(1,1),r64::new(1,1));
        let square = ConvexPolygon::raw(vec![p3, p1, p4, p2]);
       
        let line = Line::from_slope_and_point(Slope::integer(1), Point::new(r64::new(0,1), r64::new(0,1)));
        let (left_polygon, right_polygon) = square.subdivide(line);
       
        assert_eq!(left_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(0,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(0,1),r64::new(1,1))
                ])), "`left_polygon` is not right polygon");
        assert_eq!(right_polygon, Some(ConvexPolygon::raw(vec![Point::new(r64::new(0,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(0,1)),
                Point::new(r64::new(1,1),r64::new(1,1))
                ])), "`right_polygon` is not right polygon");
    }
   
    #[test]
    fn convexpolygon_subdivide_test() {
        let hexagon = projected_cube(5, 2, 3);
        assert_eq!(hexagon, ConvexPolygon::new(vec![Point::new(r64::new(1,1),r64::new(0,1)), Point::new(r64::new(0,1),r64::new(1,1)), Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(-5,3),r64::new(-2,3)),  Point::new(r64::new(-2,3),r64::new(-2,3)), Point::new(r64::new(-5,3),r64::new(1,3))]) );
        let line = Line::from_slope_and_point(Slope::integer(0), Point::new(r64::new(0,1), r64::new(-1,3)));
        let divided = hexagon.unwrap().subdivide(line);
        assert_eq!(divided.0, ConvexPolygon::new(vec![Point::new(r64::new(1,1),r64::new(0,1)), Point::new(r64::new(0,1),r64::new(1,1)), Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(-5,3),r64::new(-1,3)),  Point::new(r64::new(1,6),r64::new(-1,3)), Point::new(r64::new(-5,3),r64::new(1,3))]) );
        assert_eq!(divided.1, ConvexPolygon::new(vec![ Point::new(r64::new(-5,3),r64::new(-1,3)),  Point::new(r64::new(1,6),r64::new(-1,3)),
                Point::new(r64::new(-5,3),r64::new(-2,3)), Point::new(r64::new(-2,3),r64::new(-2,3)) ]) );
        let line2 = Line::from_slope_and_point(Slope::integer(0), Point::new(r64::new(0,1), r64::new(0,1)));
        let divided_again = (divided.0).unwrap().subdivide(line2);
       
        assert_eq!(divided_again.0, ConvexPolygon::new(vec![Point::new(r64::new(1,1),r64::new(0,1)), Point::new(r64::new(0,1),r64::new(1,1)), Point::new(r64::new(1,1),r64::new(1,1)),
                Point::new(r64::new(-5,3),r64::new(0,1)), Point::new(r64::new(-5,3),r64::new(1,3))]) );
        assert_eq!(divided_again.1, ConvexPolygon::new(vec![Point::new(r64::new(1,1),r64::new(0,1)), Point::new(r64::new(1,6),r64::new(-1,3)),
                Point::new(r64::new(-5,3),r64::new(0,1)), Point::new(r64::new(-5,3),r64::new(-1,3))]) );
    }
   
}
</syntaxhighlight>

Latest revision as of 01:49, 31 December 2023

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