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// https://en.wikipedia.org/wiki/Monotone_polygon
use crate::data::{Cursor, Point, Polygon, Vector};
use crate::{Error, Orientation, PolygonScalar, TotalOrd};

use std::cmp::Ordering;
use std::collections::VecDeque;
use std::ops::Bound::*;

///Check if the given polyon is monotone with resprect to given direction
pub fn is_monotone<T>(poly: &Polygon<T>, direction: &Vector<T, 2>) -> bool
where
T: PolygonScalar,
{
// We can only check polygons without. It would be nice to enforce this with types.
assert_eq!(poly.rings.len(), 1);

let cmp_cursors =
|a: &Cursor<'_, T>, b: &Cursor<'_, T>| direction.cmp_along(a, b).then_with(|| a.total_cmp(b));
// XXX: Is there a way to get both the min and max element at the same time?
let max_cursor = {
match poly.iter_boundary().max_by(cmp_cursors) {
Some(c) => c,
None => return false,
}
};
let min_cursor = {
match poly.iter_boundary().min_by(cmp_cursors) {
Some(c) => c,
None => return false,
}
};

// All points going counter-clockwise from min_cursor to max_cursor must be
// less-than or equal to the next point in the chain along the direction vector.
for pt in min_cursor.to(Excluded(max_cursor)) {
if direction.cmp_along(&pt, &pt.next()) == Ordering::Greater {
return false;
}
}

// Walking down the other chain, the condition is opposite: All points
// must be greater-than or equal to the next point in the chain along the direction vector.
for pt in max_cursor.to(Excluded(min_cursor)) {
if direction.cmp_along(&pt, &pt.next()) == Ordering::Less {
return false;
}
}

true
}

/// Generates a monotone polygon from given points with respect to given direction
pub fn new_monotone_polygon<T>(
mut points: Vec<Point<T, 2>>,
direction: &Vector<T, 2>,
) -> Result<Polygon<T>, Error>
where
T: PolygonScalar,
{
// First compare along the direction vector.
// If two points are the same distance along the vector, compare their X and Y components.
points.sort_by(|prev, curr| {
direction
.cmp_along(prev, curr)
.then_with(|| prev.total_cmp(curr))
});

points.dedup();
if points.len() < 3 {
return Err(Error::InsufficientVertices);
}

let (min_point, max_point) = (
points.first().unwrap().clone(),
points.last().unwrap().clone(),
);

let mut polygon_points: VecDeque<Point<T, 2>> = VecDeque::new();

while let Some(curr) = points.pop() {
match Orientation::new(&min_point, &max_point, &curr) {
Orientation::ClockWise => polygon_points.push_front(curr),
_ => polygon_points.push_back(curr),
}
}
let vec = Vec::from(polygon_points);

Polygon::new(vec)
}

//testing
#[cfg(test)]
mod monotone_testing {
use super::*;
use crate::data::{Point, Polygon, PolygonConvex, Vector};
use crate::Orientation;
use proptest::prelude::*;
use std::collections::BTreeSet;
use test_strategy::proptest;

#[proptest]
fn convex_polygon_is_montone(convex_polygon: PolygonConvex<i8>, direction: Vector<i8, 2>) {
prop_assert!(is_monotone(&convex_polygon.polygon(), &direction));
}

#[test]
//ToDo: Find a way to proptest the Non-monotone case
fn non_y_monotone() {
let polygon = Polygon::new(vec![
Point::new([0, 1]),
Point::new([1, 2]),
Point::new([1, -2]),
Point::new([0, -1]),
Point::new([-1, -2]),
Point::new([-1, 2]),
])
.unwrap();
assert!(!is_monotone(&polygon, &Vector::from(Point::new([0, 1]))));
}

#[test]
fn monotone_mountain() {
let polygon = Polygon::new(vec![
Point::new([0, 3]),
Point::new([1, 2]),
Point::new([1, -2]),
Point::new([0, -3]),
])
.unwrap();
assert!(is_monotone(&polygon, &Vector::from(Point::new([0, 1]))));
}

#[proptest]
fn monotone_is_monotone_prop(points: Vec<Point<i8, 2>>, direction: Vector<i8, 2>) {
if let Ok(p) = new_monotone_polygon(points, &direction) {
prop_assert!(is_monotone(&p, &direction));
prop_assert_eq!(p.validate().err(), None);
}
}

#[proptest]
fn valid_monotone(points: Vec<Point<i8, 2>>, direction: Vector<i8, 2>) {
// dedup points
let mut points = points;
let mut set = BTreeSet::new();
points.retain(|pt| set.insert(pt.clone()));
// If we have at least three, non-colinear points, then we must be able to
// create a monotone polygon.
if !points
.windows(3)
.all(|window| Orientation::new(&window[0], &window[1], &window[2]).is_colinear())
{
let p = new_monotone_polygon(points, &direction).unwrap();
prop_assert!(is_monotone(&p, &direction));
prop_assert_eq!(p.validate().err(), None);
}
}
}