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Explain in comments how to point-in-polygon checking method works

This commit is contained in:
Mikolaj Wielgus 2026-05-16 21:07:42 +02:00
parent fc3857072c
commit 36004b155b
1 changed files with 33 additions and 13 deletions
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46
topola/src/math.rs
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@ -53,35 +53,55 @@ impl<T: Copy> From<Vector2<T>> for [T; 2] {
macro_rules! impl_inside_polygon { macro_rules! impl_inside_polygon {
($type:ty) => { ($type:ty) => {
impl Vector2<$type> { impl Vector2<$type> {
// Checks if the point (px, py) is inside a polygon using the ray-casting // Checks if the point is inside a polygon by casting a ray to the
// algorithm. Division is not used to avoid integer truncation errors. // right. Division is not used to avoid integer truncation errors.
pub fn inside_polygon(&self, polygon: &[Vector2<$type>]) -> bool { pub fn inside_polygon(&self, polygon: &[Vector2<$type>]) -> bool {
let mut inside = false; let mut inside = false;
let n = polygon.len(); let n = polygon.len();
let px = self.x;
let py = self.y;
// `self` is `v0`.
// `v1` is the previous vertex.
let mut v1 = &polygon[n - 1]; let mut v1 = &polygon[n - 1];
// `v2` is the current vertex.
for v2 in polygon.iter() { for v2 in polygon.iter() {
let dy = v2.y - v1.y; let dx12 = v2.x - v1.x;
let zero = 0 as $type; let dy12 = v2.y - v1.y;
if dy != zero && (py > v1.y) != (py > v2.y) { // First, check if the line of the horizontal rightward ray
let dx = v2.x - v1.x; // cast to actually crosses the vertical span of the current
let t = py - v1.y; // `(v1, v2)` edge.
let s = px - v1.x; if dy12 != (0 as $type) && (self.y > v1.y) != (self.y > v2.y) {
let dx01 = self.x - v1.x;
let dy01 = self.y - v1.y;
let crosses = if dy > zero { // Now check if the (v1, v2) edge is actually on the
s * dy < dx * t // right side of the ray and not on the left.
//
// This just compares the X coordinate of `self` (`v0`)
// to the X coordinate of the intersection between the
// horizontal rightward ray and the current `(v1, v2)` edge:
//
// `self.x < v1.x + (self.y - v1.y) * (dx12 / dy12)`
//
// but is algebraically simplified and rewritten to not
// use division.
let crosses = if dy12 > (0 as $type) {
dx01 * dy12 < dx12 * dy01
} else { } else {
s * dy > dx * t dx01 * dy12 > dx12 * dy01
}; };
// Even-odd rule: flip whether the point is inside or
// outside upon each detected crossing.
if crosses { if crosses {
inside = !inside; inside = !inside;
} }
} }
// Make the current vertex previous for the next loop
// iteration.
v1 = v2; v1 = v2;
} }