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/// Represents a line segment
#[derive(Debug, Clone, Copy)]
pub struct Line {
pub start: (f64, f64),
pub end: (f64, f64),
}
impl Line {
pub fn new(start: (f64, f64), end: (f64, f64)) -> Self {
Self { start, end }
}
}
/// Represents a rectangle
#[derive(Debug, Clone, Copy)]
pub struct Rect {
pub x: f64,
pub y: f64,
pub width: f64,
pub height: f64,
}
impl Rect {
pub fn new(x: f64, y: f64, width: f64, height: f64) -> Self {
Self {
x,
y,
width,
height,
}
}
}
/// Checks if a point is inside a rectangle
pub fn point_in_rect(point: (f64, f64), rect: &Rect) -> bool {
point.0 >= rect.x
&& point.0 <= rect.x + rect.width
&& point.1 >= rect.y
&& point.1 <= rect.y + rect.height
}
/// Checks if two rectangles intersect (AABB collision)
pub fn rect_intersects_rect(r1: &Rect, r2: &Rect) -> bool {
!(r1.x + r1.width < r2.x
|| r2.x + r2.width < r1.x
|| r1.y + r1.height < r2.y
|| r2.y + r2.height < r1.y)
}
/// Checks if two line segments intersect using parametric equations
pub fn line_intersects_line(l1: &Line, l2: &Line) -> bool {
let x1 = l1.start.0;
let y1 = l1.start.1;
let x2 = l1.end.0;
let y2 = l1.end.1;
let x3 = l2.start.0;
let y3 = l2.start.1;
let x4 = l2.end.0;
let y4 = l2.end.1;
let denom = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
if denom.abs() < 1e-10 {
return false; // Parallel or coincident
}
let t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / denom;
let u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / denom;
(0.0..=1.0).contains(&t) && (0.0..=1.0).contains(&u)
}
/// Checks if a line segment intersects a rectangle
pub fn line_intersects_rect(line: &Line, rect: &Rect) -> bool {
if point_in_rect(line.start, rect) || point_in_rect(line.end, rect) {
return true;
}
let edges = [
Line::new((rect.x, rect.y), (rect.x + rect.width, rect.y)),
Line::new(
(rect.x + rect.width, rect.y),
(rect.x + rect.width, rect.y + rect.height),
),
Line::new(
(rect.x + rect.width, rect.y + rect.height),
(rect.x, rect.y + rect.height),
),
Line::new((rect.x, rect.y + rect.height), (rect.x, rect.y)),
];
edges.iter().any(|edge| line_intersects_line(line, edge))
}
/// Spatial hash grid for fast collision detection
/// that stores cells as indices of lines.
pub struct SpatialGrid {
cell_size: f64,
cells: Vec<Vec<usize>>,
columns: usize,
rows: usize,
}
impl SpatialGrid {
/// Creates a new spatial grid for the given dimensions
pub fn new(width: f64, height: f64, cell_size: f64) -> Self {
let columns = ((width / cell_size).ceil() as usize).max(1);
let rows = ((height / cell_size).ceil() as usize).max(1);
let cells = vec![Vec::new(); columns * rows];
Self {
cell_size,
cells,
columns,
rows,
}
}
/// Inserts a line into the spatial grid
pub fn insert_line(&mut self, line_idx: usize, line: &Line) {
let min_x = line.start.0.min(line.end.0);
let max_x = line.start.0.max(line.end.0);
let min_y = line.start.1.min(line.end.1);
let max_y = line.start.1.max(line.end.1);
let start_column = ((min_x / self.cell_size).floor() as usize).min(self.columns - 1);
let end_column = ((max_x / self.cell_size).floor() as usize).min(self.columns - 1);
let start_row = ((min_y / self.cell_size).floor() as usize).min(self.rows - 1);
let end_row = ((max_y / self.cell_size).floor() as usize).min(self.rows - 1);
for row in start_row..=end_row {
for col in start_column..=end_column {
let cell_idx = row * self.columns + col;
self.cells[cell_idx].push(line_idx);
}
}
}
/// Queries the spatial grid for lines that might intersect with the given rectangle
/// Returns line indices without duplicates
pub fn query_rect(&self, rect: &Rect) -> impl Iterator<Item = usize> + '_ {
let min_x = rect.x;
let max_x = rect.x + rect.width;
let min_y = rect.y;
let max_y = rect.y + rect.height;
let start_column = ((min_x / self.cell_size).floor() as isize)
.max(0)
.min(self.columns as isize - 1) as usize;
let end_column = ((max_x / self.cell_size).floor() as isize)
.max(0)
.min(self.columns as isize - 1) as usize;
let start_row = ((min_y / self.cell_size).floor() as isize)
.max(0)
.min(self.rows as isize - 1) as usize;
let end_row = ((max_y / self.cell_size).floor() as isize)
.max(0)
.min(self.rows as isize - 1) as usize;
let mut line_indices = Vec::new();
for row in start_row..=end_row {
for column in start_column..=end_column {
let cell_idx = row * self.columns + column;
line_indices.extend_from_slice(&self.cells[cell_idx]);
}
}
line_indices.sort_unstable();
line_indices.dedup();
line_indices.into_iter()
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_point_in_rect() {
let rect = Rect::new(10.0, 10.0, 20.0, 20.0);
assert!(point_in_rect((15.0, 15.0), &rect));
assert!(point_in_rect((10.0, 10.0), &rect));
assert!(point_in_rect((30.0, 30.0), &rect));
assert!(!point_in_rect((5.0, 15.0), &rect));
assert!(!point_in_rect((35.0, 15.0), &rect));
}
#[test]
fn test_rect_intersects_rect() {
let r1 = Rect::new(0.0, 0.0, 10.0, 10.0);
let r2 = Rect::new(5.0, 5.0, 10.0, 10.0);
let r3 = Rect::new(20.0, 20.0, 10.0, 10.0);
assert!(rect_intersects_rect(&r1, &r2));
assert!(rect_intersects_rect(&r2, &r1));
assert!(!rect_intersects_rect(&r1, &r3));
}
#[test]
fn test_line_intersects_line() {
let l1 = Line::new((0.0, 0.0), (10.0, 10.0));
let l2 = Line::new((0.0, 10.0), (10.0, 0.0));
let l3 = Line::new((20.0, 20.0), (30.0, 30.0));
assert!(line_intersects_line(&l1, &l2));
assert!(!line_intersects_line(&l1, &l3));
}
#[test]
fn test_line_intersects_rect() {
let rect = Rect::new(10.0, 10.0, 20.0, 20.0);
let l1 = Line::new((0.0, 15.0), (40.0, 15.0)); // Horizontal through
let l2 = Line::new((15.0, 0.0), (15.0, 40.0)); // Vertical through
let l3 = Line::new((0.0, 0.0), (5.0, 5.0)); // Outside
assert!(line_intersects_rect(&l1, &rect));
assert!(line_intersects_rect(&l2, &rect));
assert!(!line_intersects_rect(&l3, &rect));
}
}
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