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//! Ear-clipping algorithm for creating a triangle mesh from a simple polygon.
//! Based on <https://github.com/ivanfratric/polypartition>, contributed by embotech AG.
use crate::{
math::{Real, Vector},
utils::point_in_triangle::{corner_direction, is_point_in_triangle, Orientation},
};
use alloc::{vec, vec::Vec};
/// The information stored for each vertex in the ear clipping algorithm.
#[derive(Clone, Default)]
struct VertexInfo {
/// Whether the vertex is still active i.e. it has not been clipped yet.
is_active: bool,
/// Whether the vertex is the tip of an ear and should be clipped.
is_ear: bool,
/// How small the angle of the ear is. Ears with a smaller angle are clipped first.
pointiness: Real,
/// The index of the previous vertex.
p_prev: usize,
/// The index of the next vertex.
p_next: usize,
}
/// Updates the fields `pointiness` and `is_ear` for a given vertex index.
fn update_vertex(idx: usize, vertex_info: &mut VertexInfo, points: &[Vector]) -> bool {
// Get the point and its neighbors.
let p = points[idx];
let p1 = points[vertex_info.p_prev];
let p3 = points[vertex_info.p_next];
// Get the pointiness.
let vec1 = (p1 - p).normalize();
let vec3 = (p3 - p).normalize();
vertex_info.pointiness = vec1.dot(vec3);
if vertex_info.pointiness.is_nan() {
return false;
}
// A point is considered an ear when it is convex and no other points are
// inside the triangle spanned by it and its two neighbors.
let mut error = false;
vertex_info.is_ear = corner_direction(p1, p, p3) == Orientation::Ccw
&& (0..points.len())
.filter(|&i| i != vertex_info.p_prev && i != idx && i != vertex_info.p_next)
.all(|i| {
if let Some(is) = is_point_in_triangle(points[i], p1, p, p3) {
!is
} else {
error = true;
true
}
});
!error
}
/// Ear clipping triangulation algorithm.
pub(crate) fn triangulate_ear_clipping(vertices: &[Vector]) -> Option<Vec<[u32; 3]>> {
let n_vertices = vertices.len();
// Create a new vector to hold the information about vertices.
let mut vertex_info = vec![VertexInfo::default(); n_vertices];
// Initialize information for each vertex.
let success = vertex_info.iter_mut().enumerate().all(|(i, info)| {
info.is_active = true;
info.p_prev = if i == 0 { n_vertices - 1 } else { i - 1 };
info.p_next = if i == n_vertices - 1 { 0 } else { i + 1 };
update_vertex(i, info, vertices)
});
if !success {
return None;
}
// The output shapes
let mut output_indices = Vec::new();
for i in 0..n_vertices - 3 {
// Search through all active ears and pick out the pointiest.
let maybe_ear = vertex_info
.iter()
.enumerate()
.filter(|(_, info)| info.is_active && info.is_ear)
.max_by(|(_, info1), (_, info2)| {
// The unwrap here is safe since we check for NaN when
// we assign the pointiness value.
info1.pointiness.partial_cmp(&info2.pointiness).unwrap()
});
// If we found an ear, clip it. Else the algorithm failed.
let (ear_i, _) = maybe_ear?;
// Deactivate the tip of the ear.
vertex_info[ear_i].is_active = false;
// Get the indices of the neighbors.
let VertexInfo { p_prev, p_next, .. } = vertex_info[ear_i];
// Extract the triangle that is the ear and add it to the index buffer.
let triangle_points = [p_prev as u32, ear_i as u32, p_next as u32];
output_indices.push(triangle_points);
// Connect the remaining two vertices.
vertex_info[p_prev].p_next = vertex_info[ear_i].p_next;
vertex_info[p_next].p_prev = vertex_info[ear_i].p_prev;
// Only three vertices remain and those are guaranteed to be convex so
// there is no point in updating the remaining vertex information.
if i == n_vertices - 4 {
break;
};
// Update the info for the remaining two vertices.
if !update_vertex(p_prev, &mut vertex_info[p_prev], vertices)
|| !update_vertex(p_next, &mut vertex_info[p_next], vertices)
{
return None;
}
}
// Add the remaining triangle.
if let Some((i, info)) = vertex_info
.iter()
.enumerate()
.find(|(_, info)| info.is_active)
{
let triangle_points = [info.p_prev as u32, i as u32, info.p_next as u32];
output_indices.push(triangle_points);
}
Some(output_indices)
}
// --- Unit tests ----------------------------------------------------------------------------
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn triangle_ccw() {
let vertices = vec![
Vector::new(0., 0.),
Vector::new(1., 0.),
Vector::new(1., 1.),
];
let triangles = triangulate_ear_clipping(&vertices);
assert_eq!(triangles.unwrap(), vec![[2, 0, 1]]);
}
#[test]
fn square_ccw() {
let vertices = vec![
Vector::new(0., 0.), // 0
Vector::new(1., 0.), // 1
Vector::new(1., 1.), // 2
Vector::new(0., 1.), // 3
];
let triangles = triangulate_ear_clipping(&vertices);
assert_eq!(triangles.unwrap(), vec![[2, 3, 0], [2, 0, 1]]);
}
#[test]
fn square_cw() {
let vertices = vec![
Vector::new(0., 1.), // 0
Vector::new(1., 1.), // 1
Vector::new(1., 0.), // 2
Vector::new(0., 0.), // 3
];
// This fails because we expect counter-clockwise ordering.
let triangles = triangulate_ear_clipping(&vertices);
assert!(triangles.is_none());
}
#[test]
fn square_with_dent() {
let vertices = vec![
Vector::new(0., 0.), // 0
Vector::new(1., 0.), // 1
Vector::new(0.5, 0.5), // 2
Vector::new(1., 1.), // 3
Vector::new(0., 1.), // 4
];
let triangles = triangulate_ear_clipping(&vertices);
assert_eq!(triangles.unwrap(), vec![[2, 3, 4], [2, 4, 0], [2, 0, 1],]);
}
#[test]
/// Checks the case where the origin is outside the shape.
/// 4-----------------------3
/// | |
/// | |
/// | 7-------0 |
/// | | | |
/// | | ° | |
/// 5-------6 1-------2
fn origin_outside_shape() {
let vertices = vec![
Vector::new(2.0, 2.0), // 0
Vector::new(2.0, -2.0), // 1
Vector::new(4.0, -2.0), // 2
Vector::new(4.0, 4.0), // 3
Vector::new(-4.0, 4.0), // 4
Vector::new(-4.0, -2.0), // 5
Vector::new(-2.0, -2.0), // 6
Vector::new(-2.0, 2.0), // 7
];
let triangles = triangulate_ear_clipping(&vertices).unwrap();
assert_eq!(
triangles,
vec![
[5, 6, 7],
[4, 5, 7],
[3, 4, 7],
[3, 7, 0],
[2, 3, 0],
[2, 0, 1],
]
);
}
}