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use num_traits::{Float, Signed};
use ::{MultiPoint, MultiPolygon, Point, Polygon};
use algorithm::convexhull::ConvexHull;
use ::{ExtremePoint, Extremes};
// Useful direction vectors, aligned with x and y axes:
// 1., 0. = largest x
// 0., 1. = largest y
// 0., -1. = smallest y
// -1, 0. = smallest x
// various tests for vector orientation relative to a direction vector u
// Not currently used, but maybe useful in the future
#[allow(dead_code)]
fn up<T>(u: &Point<T>, v: &Point<T>) -> bool
where
T: Float,
{
u.dot(v) > T::zero()
}
fn direction_sign<T>(u: &Point<T>, vi: &Point<T>, vj: &Point<T>) -> T
where
T: Float,
{
u.dot(&(*vi - *vj))
}
// true if Vi is above Vj
fn above<T>(u: &Point<T>, vi: &Point<T>, vj: &Point<T>) -> bool
where
T: Float,
{
direction_sign(u, vi, vj) > T::zero()
}
// true if Vi is below Vj
// Not currently used, but maybe useful in the future
#[allow(dead_code)]
fn below<T>(u: &Point<T>, vi: &Point<T>, vj: &Point<T>) -> bool
where
T: Float,
{
direction_sign(u, vi, vj) < T::zero()
}
// wrapper for extreme-finding function
fn find_extreme_indices<T, F>(func: F, polygon: &Polygon<T>) -> Result<Extremes, ()>
where
T: Float + Signed,
F: Fn(&Point<T>, &Polygon<T>) -> Result<usize, ()>,
{
if !polygon.is_convex() {
return Err(());
}
let directions = vec![
Point::new(T::zero(), -T::one()),
Point::new(T::one(), T::zero()),
Point::new(T::zero(), T::one()),
Point::new(-T::one(), T::zero()),
];
Ok(directions
.iter()
.map(|p| func(p, polygon).unwrap())
.collect::<Vec<usize>>()
.into())
}
// find a convex, counter-clockwise oriented polygon's maximum vertex in a specified direction
// u: a direction vector. We're using a point to represent this, which is a hack but works fine
fn polymax_naive_indices<T>(u: &Point<T>, poly: &Polygon<T>) -> Result<usize, ()>
where
T: Float,
{
let vertices = &poly.exterior.0;
let mut max: usize = 0;
for (i, _) in vertices.iter().enumerate() {
// if vertices[i] is above prior vertices[max]
if above(u, &vertices[i], &vertices[max]) {
max = i;
}
}
Ok(max)
}
pub trait ExtremeIndices<T: Float + Signed> {
/// Find the extreme `x` and `y` indices of a convex Polygon
///
/// The polygon **must be convex and properly (ccw) oriented**.
///
/// ```
/// use geo::{Point, LineString, Polygon};
/// use geo::extremes::ExtremeIndices;
/// // a diamond shape
/// let points_raw = vec![(1.0, 0.0), (2.0, 1.0), (1.0, 2.0), (0.0, 1.0), (1.0, 0.0)];
/// let points = points_raw.iter().map(|e| Point::new(e.0, e.1)).collect::<Vec<_>>();
/// let poly = Polygon::new(LineString(points), vec![]);
/// // Polygon is both convex and oriented counter-clockwise
/// let extremes = poly.extreme_indices().unwrap();
/// assert_eq!(extremes.ymin, 0);
/// assert_eq!(extremes.xmax, 1);
/// assert_eq!(extremes.ymax, 2);
/// assert_eq!(extremes.xmin, 3);
/// ```
fn extreme_indices(&self) -> Result<Extremes, ()>;
}
impl<T> ExtremeIndices<T> for Polygon<T>
where
T: Float + Signed,
{
fn extreme_indices(&self) -> Result<Extremes, ()> {
find_extreme_indices(polymax_naive_indices, self)
}
}
impl<T> ExtremeIndices<T> for MultiPolygon<T>
where
T: Float + Signed,
{
fn extreme_indices(&self) -> Result<Extremes, ()> {
find_extreme_indices(polymax_naive_indices, &self.convex_hull())
}
}
impl<T> ExtremeIndices<T> for MultiPoint<T>
where
T: Float + Signed,
{
fn extreme_indices(&self) -> Result<Extremes, ()> {
find_extreme_indices(polymax_naive_indices, &self.convex_hull())
}
}
pub trait ExtremePoints<T: Float> {
/// Find the extreme `x` and `y` points of a Geometry
///
/// This trait is available to any struct implementing both `ConvexHull` amd `ExtremeIndices`
///
/// ```
/// use geo::{Point, LineString, Polygon};
/// use geo::extremes::ExtremePoints;
/// let points_raw = vec![(1.0, 0.0), (2.0, 1.0), (1.0, 2.0), (0.0, 1.0), (1.0, 0.0)];
/// let points = points_raw
/// .iter()
/// .map(|e| Point::new(e.0, e.1))
/// .collect::<Vec<_>>();
/// let poly1 = Polygon::new(LineString(points), vec![]);
/// let extremes = poly1.extreme_points();
/// let correct = Point::new(0.0, 1.0);
/// assert_eq!(extremes.xmin, correct);
/// ```
fn extreme_points(&self) -> ExtremePoint<T>;
}
impl<T, G> ExtremePoints<T> for G
where
T: Float + Signed,
G: ConvexHull<T> + ExtremeIndices<T>,
{
// Any Geometry implementing `ConvexHull` and `ExtremeIndices` gets this automatically
fn extreme_points(&self) -> ExtremePoint<T> {
let ch = self.convex_hull();
// safe to unwrap, since we're guaranteeing the polygon's convexity
let indices = ch.extreme_indices().unwrap();
ExtremePoint {
ymin: ch.exterior.0[indices.ymin],
xmax: ch.exterior.0[indices.xmax],
ymax: ch.exterior.0[indices.ymax],
xmin: ch.exterior.0[indices.xmin],
}
}
}
#[cfg(test)]
mod test {
use ::{LineString, Point};
use super::*;
#[test]
fn test_polygon_extreme_x() {
// a diamond shape
let points_raw = vec![(1.0, 0.0), (2.0, 1.0), (1.0, 2.0), (0.0, 1.0), (1.0, 0.0)];
let points = points_raw
.iter()
.map(|e| Point::new(e.0, e.1))
.collect::<Vec<_>>();
let poly1 = Polygon::new(LineString(points), vec![]);
let min_x = polymax_naive_indices(&Point::new(-1., 0.), &poly1).unwrap();
let correct = 3_usize;
assert_eq!(min_x, correct);
}
#[test]
#[should_panic]
fn test_extreme_indices_bad_polygon() {
// non-convex, with a bump on the top-right edge
let points_raw = vec![
(1.0, 0.0),
(1.3, 1.),
(2.0, 1.0),
(1.75, 1.75),
(1.0, 2.0),
(0.0, 1.0),
(1.0, 0.0),
];
let points = points_raw
.iter()
.map(|e| Point::new(e.0, e.1))
.collect::<Vec<_>>();
let poly1 = Polygon::new(LineString(points), vec![]);
let extremes = find_extreme_indices(polymax_naive_indices, &poly1).unwrap();
let correct = Extremes {
ymin: 0,
xmax: 1,
ymax: 3,
xmin: 4,
};
assert_eq!(extremes, correct);
}
#[test]
fn test_extreme_indices_good_polygon() {
// non-convex, with a bump on the top-right edge
let points_raw = vec![
(1.0, 0.0),
(1.3, 1.),
(2.0, 1.0),
(1.75, 1.75),
(1.0, 2.0),
(0.0, 1.0),
(1.0, 0.0),
];
let points = points_raw
.iter()
.map(|e| Point::new(e.0, e.1))
.collect::<Vec<_>>();
let poly1 = Polygon::new(LineString(points), vec![]);
let extremes = find_extreme_indices(polymax_naive_indices, &poly1.convex_hull()).unwrap();
let correct = Extremes {
ymin: 0,
xmax: 1,
ymax: 3,
xmin: 4,
};
assert_eq!(extremes, correct);
}
#[test]
fn test_polygon_extreme_wrapper_convex() {
// convex, with a bump on the top-right edge
let points_raw = vec![
(1.0, 0.0),
(2.0, 1.0),
(1.75, 1.75),
(1.0, 2.0),
(0.0, 1.0),
(1.0, 0.0),
];
let points = points_raw
.iter()
.map(|e| Point::new(e.0, e.1))
.collect::<Vec<_>>();
let poly1 = Polygon::new(LineString(points), vec![]);
let extremes = find_extreme_indices(polymax_naive_indices, &poly1.convex_hull()).unwrap();
let correct = Extremes {
ymin: 0,
xmax: 1,
ymax: 3,
xmin: 4,
};
assert_eq!(extremes, correct);
}
#[test]
fn test_polygon_extreme_point_x() {
// a diamond shape
let points_raw = vec![(1.0, 0.0), (2.0, 1.0), (1.0, 2.0), (0.0, 1.0), (1.0, 0.0)];
let points = points_raw
.iter()
.map(|e| Point::new(e.0, e.1))
.collect::<Vec<_>>();
let poly1 = Polygon::new(LineString(points), vec![]);
let extremes = poly1.extreme_points();
let correct = Point::new(0.0, 1.0);
assert_eq!(extremes.xmin, correct);
}
}