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use crate::bounding_volume::Aabb;
use crate::math::{Isometry, Point, Real, UnitVector, Vector};
use crate::query::visitors::BoundingVolumeIntersectionsVisitor;
use crate::query::{IntersectResult, PointQuery, SplitResult};
use crate::shape::{Cuboid, FeatureId, Polyline, Segment, Shape, TriMesh, TriMeshFlags, Triangle};
use crate::transformation;
use crate::utils::{hashmap::HashMap, SortedPair, WBasis};
use spade::{handles::FixedVertexHandle, ConstrainedDelaunayTriangulation, Triangulation as _};
use std::cmp::Ordering;
struct Triangulation {
delaunay: ConstrainedDelaunayTriangulation<spade::Point2<Real>>,
basis: [Vector<Real>; 2],
basis_origin: Point<Real>,
spade2index: HashMap<FixedVertexHandle, u32>,
index2spade: HashMap<u32, FixedVertexHandle>,
}
impl Triangulation {
fn new(axis: UnitVector<Real>, basis_origin: Point<Real>) -> Self {
Triangulation {
delaunay: ConstrainedDelaunayTriangulation::new(),
basis: axis.orthonormal_basis(),
basis_origin,
spade2index: HashMap::default(),
index2spade: HashMap::default(),
}
}
fn project(&self, pt: Point<Real>) -> spade::Point2<Real> {
let dpt = pt - self.basis_origin;
spade::Point2::new(dpt.dot(&self.basis[0]), dpt.dot(&self.basis[1]))
}
fn add_edge(&mut self, id1: u32, id2: u32, points: &[Point<Real>]) {
let proj1 = self.project(points[id1 as usize]);
let proj2 = self.project(points[id2 as usize]);
let handle1 = *self.index2spade.entry(id1).or_insert_with(|| {
let h = self.delaunay.insert(proj1).unwrap();
let _ = self.spade2index.insert(h, id1);
h
});
let handle2 = *self.index2spade.entry(id2).or_insert_with(|| {
let h = self.delaunay.insert(proj2).unwrap();
let _ = self.spade2index.insert(h, id2);
h
});
// NOTE: the naming of the `ConstrainedDelaunayTriangulation::can_add_constraint` method is misleading.
if !self.delaunay.can_add_constraint(handle1, handle2) {
let _ = self.delaunay.add_constraint(handle1, handle2);
}
}
}
impl TriMesh {
/// Splits this `TriMesh` along the given canonical axis.
///
/// This will split the Aabb by a plane with a normal with it’s `axis`-th component set to 1.
/// The splitting plane is shifted wrt. the origin by the `bias` (i.e. it passes through the point
/// equal to `normal * bias`).
///
/// # Result
/// Returns the result of the split. The first mesh returned is the piece lying on the negative
/// half-space delimited by the splitting plane. The second mesh returned is the piece lying on the
/// positive half-space delimited by the splitting plane.
pub fn canonical_split(&self, axis: usize, bias: Real, epsilon: Real) -> SplitResult<Self> {
// TODO: optimize this.
self.local_split(&Vector::ith_axis(axis), bias, epsilon)
}
/// Splits this mesh, transformed by `position` by a plane identified by its normal `local_axis`
/// and the `bias` (i.e. the plane passes through the point equal to `normal * bias`).
pub fn split(
&self,
position: &Isometry<Real>,
axis: &UnitVector<Real>,
bias: Real,
epsilon: Real,
) -> SplitResult<Self> {
let local_axis = position.inverse_transform_unit_vector(axis);
let added_bias = -position.translation.vector.dot(axis);
self.local_split(&local_axis, bias + added_bias, epsilon)
}
/// Splits this mesh by a plane identified by its normal `local_axis`
/// and the `bias` (i.e. the plane passes through the point equal to `normal * bias`).
pub fn local_split(
&self,
local_axis: &UnitVector<Real>,
bias: Real,
epsilon: Real,
) -> SplitResult<Self> {
let mut triangulation = if self.pseudo_normals().is_some() {
Some(Triangulation::new(*local_axis, self.vertices()[0]))
} else {
None
};
// 1. Partition the vertices.
let vertices = self.vertices();
let indices = self.indices();
let mut colors = vec![0u8; self.vertices().len()];
// Color 0 = on plane.
// 1 = on negative half-space.
// 2 = on positive half-space.
let mut found_negative = false;
let mut found_positive = false;
for (i, pt) in vertices.iter().enumerate() {
let dist_to_plane = pt.coords.dot(local_axis) - bias;
if dist_to_plane < -epsilon {
found_negative = true;
colors[i] = 1;
} else if dist_to_plane > epsilon {
found_positive = true;
colors[i] = 2;
}
}
// Exit early if `self` isn’t crossed by the plane.
if !found_negative {
return SplitResult::Positive;
}
if !found_positive {
return SplitResult::Negative;
}
// 2. Split the triangles.
let mut intersections_found = HashMap::default();
let mut new_indices = indices.to_vec();
let mut new_vertices = vertices.to_vec();
for (tri_id, idx) in indices.iter().enumerate() {
let mut intersection_features = (FeatureId::Unknown, FeatureId::Unknown);
// First, find where the plane intersects the triangle.
for ia in 0..3 {
let ib = (ia + 1) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let fid = match (colors[idx_a as usize], colors[idx_b as usize]) {
(1, 2) | (2, 1) => FeatureId::Edge(ia),
// NOTE: the case (_, 0) will be dealt with in the next loop iteration.
(0, _) => FeatureId::Vertex(ia),
_ => continue,
};
if intersection_features.0 == FeatureId::Unknown {
intersection_features.0 = fid;
} else {
// TODO: this assertion may fire if the triangle is coplanar with the edge?
// assert_eq!(intersection_features.1, FeatureId::Unknown);
intersection_features.1 = fid;
}
}
// Helper that intersects an edge with the plane.
let mut intersect_edge = |idx_a, idx_b| {
*intersections_found
.entry(SortedPair::new(idx_a, idx_b))
.or_insert_with(|| {
let segment = Segment::new(
new_vertices[idx_a as usize],
new_vertices[idx_b as usize],
);
// Intersect the segment with the plane.
if let Some((intersection, _)) = segment
.local_split_and_get_intersection(local_axis, bias, epsilon)
.1
{
new_vertices.push(intersection);
colors.push(0);
(new_vertices.len() - 1) as u32
} else {
unreachable!()
}
})
};
// Perform the intersection, push new triangles, and update
// triangulation constraints if needed.
match intersection_features {
(_, FeatureId::Unknown) => {
// The plane doesn’t intersect the triangle, or intersects it at
// a single vertex, so we don’t have anything to do.
assert!(
matches!(intersection_features.0, FeatureId::Unknown)
|| matches!(intersection_features.0, FeatureId::Vertex(_))
);
}
(FeatureId::Vertex(v1), FeatureId::Vertex(v2)) => {
// The plane intersects the triangle along one of its edge.
// We don’t have to split the triangle, but we need to add
// a constraint to the triangulation.
if let Some(triangulation) = &mut triangulation {
let id1 = idx[v1 as usize];
let id2 = idx[v2 as usize];
triangulation.add_edge(id1, id2, &new_vertices);
}
}
(FeatureId::Vertex(iv), FeatureId::Edge(ie))
| (FeatureId::Edge(ie), FeatureId::Vertex(iv)) => {
// The plane splits the triangle into exactly two triangles.
let ia = ie;
let ib = (ie + 1) % 3;
let ic = (ie + 2) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let idx_c = idx[ic as usize];
assert_eq!(iv, ic);
let intersection_idx = intersect_edge(idx_a, idx_b);
// Compute the indices of the two triangles.
let new_tri_a = [idx_c, idx_a, intersection_idx];
let new_tri_b = [idx_b, idx_c, intersection_idx];
new_indices[tri_id] = new_tri_a;
new_indices.push(new_tri_b);
if let Some(triangulation) = &mut triangulation {
triangulation.add_edge(intersection_idx, idx_c, &new_vertices);
}
}
(FeatureId::Edge(mut e1), FeatureId::Edge(mut e2)) => {
// The plane splits the triangle into 1 + 2 triangles.
// First, make sure the edge indices are consecutive.
if e2 != (e1 + 1) % 3 {
std::mem::swap(&mut e1, &mut e2);
}
let ia = e2; // The first point of the second edge is the vertex shared by both edges.
let ib = (e2 + 1) % 3;
let ic = (e2 + 2) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let idx_c = idx[ic as usize];
let intersection1 = intersect_edge(idx_c, idx_a);
let intersection2 = intersect_edge(idx_a, idx_b);
let new_tri1 = [idx_a, intersection2, intersection1];
let new_tri2 = [intersection2, idx_b, idx_c];
let new_tri3 = [intersection2, idx_c, intersection1];
new_indices[tri_id] = new_tri1;
new_indices.push(new_tri2);
new_indices.push(new_tri3);
if let Some(triangulation) = &mut triangulation {
triangulation.add_edge(intersection1, intersection2, &new_vertices);
}
}
_ => unreachable!(),
}
}
// 3. Partition the new triangles into two trimeshes.
let mut vertices_lhs = vec![];
let mut vertices_rhs = vec![];
let mut indices_lhs = vec![];
let mut indices_rhs = vec![];
let mut remap = vec![];
for i in 0..new_vertices.len() {
match colors[i] {
0 => {
remap.push((vertices_lhs.len() as u32, vertices_rhs.len() as u32));
vertices_lhs.push(new_vertices[i]);
vertices_rhs.push(new_vertices[i]);
}
1 => {
remap.push((vertices_lhs.len() as u32, u32::MAX));
vertices_lhs.push(new_vertices[i]);
}
2 => {
remap.push((u32::MAX, vertices_rhs.len() as u32));
vertices_rhs.push(new_vertices[i]);
}
_ => unreachable!(),
}
}
for idx in new_indices {
let idx = [idx[0] as usize, idx[1] as usize, idx[2] as usize]; // Convert to usize.
let colors = [colors[idx[0]], colors[idx[1]], colors[idx[2]]];
let remap = [remap[idx[0]], remap[idx[1]], remap[idx[2]]];
if colors[0] == 1 || colors[1] == 1 || colors[2] == 1 {
assert!(colors[0] != 2 && colors[1] != 2 && colors[2] != 2);
indices_lhs.push([remap[0].0, remap[1].0, remap[2].0]);
} else if colors[0] == 2 || colors[1] == 2 || colors[2] == 2 {
assert!(colors[0] != 1 && colors[1] != 1 && colors[2] != 1);
indices_rhs.push([remap[0].1, remap[1].1, remap[2].1]);
} else {
// The colors are all 0, so push into both trimeshes.
indices_lhs.push([remap[0].0, remap[1].0, remap[2].0]);
indices_rhs.push([remap[0].1, remap[1].1, remap[2].1]);
}
}
// Push the triangulation if there is one.
if let Some(triangulation) = triangulation {
for face in triangulation.delaunay.inner_faces() {
let vtx = face.vertices();
let mut idx1 = [0; 3];
let mut idx2 = [0; 3];
for k in 0..3 {
let vid = triangulation.spade2index[&vtx[k].fix()];
assert_eq!(colors[vid as usize], 0);
idx1[k] = remap[vid as usize].0;
idx2[k] = remap[vid as usize].1;
}
let tri = Triangle::new(
vertices_lhs[idx1[0] as usize],
vertices_lhs[idx1[1] as usize],
vertices_lhs[idx1[2] as usize],
);
if self.contains_local_point(&tri.center()) {
indices_lhs.push(idx1);
idx2.swap(1, 2); // Flip orientation for the second half of the split.
indices_rhs.push(idx2);
}
}
}
// TODO: none of the index buffers should be empty at this point unless perhaps
// because of some rounding errors?
// Should we just panic if they are empty?
if indices_rhs.is_empty() {
SplitResult::Negative
} else if indices_lhs.is_empty() {
SplitResult::Positive
} else {
let mesh_lhs = TriMesh::new(vertices_lhs, indices_lhs);
let mesh_rhs = TriMesh::new(vertices_rhs, indices_rhs);
SplitResult::Pair(mesh_lhs, mesh_rhs)
}
}
/// Computes the intersection [`Polyline`]s between this mesh and the plane identified by
/// the given canonical axis.
///
/// This will intersect the mesh by a plane with a normal with it’s `axis`-th component set to 1.
/// The splitting plane is shifted wrt. the origin by the `bias` (i.e. it passes through the point
/// equal to `normal * bias`).
///
/// Note that the resultant polyline may have multiple connected components
pub fn canonical_intersection_with_plane(
&self,
axis: usize,
bias: Real,
epsilon: Real,
) -> IntersectResult<Polyline> {
self.intersection_with_local_plane(&Vector::ith_axis(axis), bias, epsilon)
}
/// Computes the intersection [`Polyline`]s between this mesh, transformed by `position`,
/// and a plane identified by its normal `axis` and the `bias`
/// (i.e. the plane passes through the point equal to `normal * bias`).
pub fn intersection_with_plane(
&self,
position: &Isometry<Real>,
axis: &UnitVector<Real>,
bias: Real,
epsilon: Real,
) -> IntersectResult<Polyline> {
let local_axis = position.inverse_transform_unit_vector(axis);
let added_bias = -position.translation.vector.dot(axis);
self.intersection_with_local_plane(&local_axis, bias + added_bias, epsilon)
}
/// Computes the intersection [`Polyline`]s between this mesh
/// and a plane identified by its normal `local_axis`
/// and the `bias` (i.e. the plane passes through the point equal to `normal * bias`).
pub fn intersection_with_local_plane(
&self,
local_axis: &UnitVector<Real>,
bias: Real,
epsilon: Real,
) -> IntersectResult<Polyline> {
// 1. Partition the vertices.
let vertices = self.vertices();
let indices = self.indices();
let mut colors = vec![0u8; self.vertices().len()];
// Color 0 = on plane.
// 1 = on negative half-space.
// 2 = on positive half-space.
let mut found_negative = false;
let mut found_positive = false;
for (i, pt) in vertices.iter().enumerate() {
let dist_to_plane = pt.coords.dot(local_axis) - bias;
if dist_to_plane < -epsilon {
found_negative = true;
colors[i] = 1;
} else if dist_to_plane > epsilon {
found_positive = true;
colors[i] = 2;
}
}
// Exit early if `self` isn’t crossed by the plane.
if !found_negative {
return IntersectResult::Positive;
}
if !found_positive {
return IntersectResult::Negative;
}
// 2. Split the triangles.
let mut index_adjacencies: Vec<Vec<usize>> = Vec::new(); // Adjacency list of indices
// Helper functions for adding polyline segments to the adjacency list
let mut add_segment_adjacencies = |idx_a: usize, idx_b| {
assert!(idx_a <= index_adjacencies.len());
match idx_a.cmp(&index_adjacencies.len()) {
Ordering::Less => index_adjacencies[idx_a].push(idx_b),
Ordering::Equal => index_adjacencies.push(vec![idx_b]),
Ordering::Greater => {}
}
};
let mut add_segment_adjacencies_symmetric = |idx_a: usize, idx_b| {
if idx_a < idx_b {
add_segment_adjacencies(idx_a, idx_b);
add_segment_adjacencies(idx_b, idx_a);
} else {
add_segment_adjacencies(idx_b, idx_a);
add_segment_adjacencies(idx_a, idx_b);
}
};
let mut intersections_found = HashMap::default();
let mut existing_vertices_found = HashMap::default();
let mut new_vertices = Vec::new();
for idx in indices.iter() {
let mut intersection_features = (FeatureId::Unknown, FeatureId::Unknown);
// First, find where the plane intersects the triangle.
for ia in 0..3 {
let ib = (ia + 1) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let fid = match (colors[idx_a as usize], colors[idx_b as usize]) {
(1, 2) | (2, 1) => FeatureId::Edge(ia),
// NOTE: the case (_, 0) will be dealt with in the next loop iteration.
(0, _) => FeatureId::Vertex(ia),
_ => continue,
};
if intersection_features.0 == FeatureId::Unknown {
intersection_features.0 = fid;
} else {
// TODO: this assertion may fire if the triangle is coplanar with the edge?
// assert_eq!(intersection_features.1, FeatureId::Unknown);
intersection_features.1 = fid;
}
}
// Helper that intersects an edge with the plane.
let mut intersect_edge = |idx_a, idx_b| {
*intersections_found
.entry(SortedPair::new(idx_a, idx_b))
.or_insert_with(|| {
let segment =
Segment::new(vertices[idx_a as usize], vertices[idx_b as usize]);
// Intersect the segment with the plane.
if let Some((intersection, _)) = segment
.local_split_and_get_intersection(local_axis, bias, epsilon)
.1
{
new_vertices.push(intersection);
colors.push(0);
new_vertices.len() - 1
} else {
unreachable!()
}
})
};
// Perform the intersection, push new triangles, and update
// triangulation constraints if needed.
match intersection_features {
(_, FeatureId::Unknown) => {
// The plane doesn’t intersect the triangle, or intersects it at
// a single vertex, so we don’t have anything to do.
assert!(
matches!(intersection_features.0, FeatureId::Unknown)
|| matches!(intersection_features.0, FeatureId::Vertex(_))
);
}
(FeatureId::Vertex(iv1), FeatureId::Vertex(iv2)) => {
// The plane intersects the triangle along one of its edge.
// We don’t have to split the triangle, but we need to add
// the edge to the polyline indices
let id1 = idx[iv1 as usize];
let id2 = idx[iv2 as usize];
let out_id1 = *existing_vertices_found.entry(id1).or_insert_with(|| {
let v1 = vertices[id1 as usize];
new_vertices.push(v1);
new_vertices.len() - 1
});
let out_id2 = *existing_vertices_found.entry(id2).or_insert_with(|| {
let v2 = vertices[id2 as usize];
new_vertices.push(v2);
new_vertices.len() - 1
});
add_segment_adjacencies_symmetric(out_id1, out_id2);
}
(FeatureId::Vertex(iv), FeatureId::Edge(ie))
| (FeatureId::Edge(ie), FeatureId::Vertex(iv)) => {
// The plane splits the triangle into exactly two triangles.
let ia = ie;
let ib = (ie + 1) % 3;
let ic = (ie + 2) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let idx_c = idx[ic as usize];
assert_eq!(iv, ic);
let intersection_idx = intersect_edge(idx_a, idx_b);
let out_idx_c = *existing_vertices_found.entry(idx_c).or_insert_with(|| {
let v2 = vertices[idx_c as usize];
new_vertices.push(v2);
new_vertices.len() - 1
});
add_segment_adjacencies_symmetric(out_idx_c, intersection_idx);
}
(FeatureId::Edge(mut e1), FeatureId::Edge(mut e2)) => {
// The plane splits the triangle into 1 + 2 triangles.
// First, make sure the edge indices are consecutive.
if e2 != (e1 + 1) % 3 {
std::mem::swap(&mut e1, &mut e2);
}
let ia = e2; // The first point of the second edge is the vertex shared by both edges.
let ib = (e2 + 1) % 3;
let ic = (e2 + 2) % 3;
let idx_a = idx[ia as usize];
let idx_b = idx[ib as usize];
let idx_c = idx[ic as usize];
let intersection1 = intersect_edge(idx_c, idx_a);
let intersection2 = intersect_edge(idx_a, idx_b);
add_segment_adjacencies_symmetric(intersection1, intersection2);
}
_ => unreachable!(),
}
}
// 3. Ensure consistent edge orientation by traversing the adjacency list
let mut polyline_indices: Vec<[u32; 2]> = Vec::with_capacity(index_adjacencies.len() + 1);
let mut seen = vec![false; index_adjacencies.len()];
for (idx, neighbors) in index_adjacencies.iter().enumerate() {
if !seen[idx] {
// Start a new component
// Traverse the adjencies until the loop closes
let first = idx;
let mut prev = first;
let mut next = neighbors.first(); // Arbitrary neighbor
'traversal: while let Some(current) = next {
seen[*current] = true;
polyline_indices.push([prev as u32, *current as u32]);
for neighbor in index_adjacencies[*current].iter() {
if *neighbor != prev && *neighbor != first {
prev = *current;
next = Some(neighbor);
continue 'traversal;
} else if *neighbor != prev && *neighbor == first {
// If the next index is same as the first, close the polyline and exit
polyline_indices.push([*current as u32, first as u32]);
next = None;
continue 'traversal;
}
}
}
}
}
IntersectResult::Intersect(Polyline::new(new_vertices, Some(polyline_indices)))
}
/// Computes the intersection mesh between an Aabb and this mesh.
pub fn intersection_with_aabb(
&self,
position: &Isometry<Real>,
flip_mesh: bool,
aabb: &Aabb,
flip_cuboid: bool,
epsilon: Real,
) -> Option<Self> {
let cuboid = Cuboid::new(aabb.half_extents());
let cuboid_pos = Isometry::from(aabb.center());
self.intersection_with_cuboid(
position,
flip_mesh,
&cuboid,
&cuboid_pos,
flip_cuboid,
epsilon,
)
}
/// Computes the intersection mesh between a cuboid and this mesh transformed by `position`.
pub fn intersection_with_cuboid(
&self,
position: &Isometry<Real>,
flip_mesh: bool,
cuboid: &Cuboid,
cuboid_position: &Isometry<Real>,
flip_cuboid: bool,
epsilon: Real,
) -> Option<Self> {
self.intersection_with_local_cuboid(
flip_mesh,
cuboid,
&position.inv_mul(cuboid_position),
flip_cuboid,
epsilon,
)
}
/// Computes the intersection mesh between a cuboid and this mesh.
pub fn intersection_with_local_cuboid(
&self,
flip_mesh: bool,
cuboid: &Cuboid,
cuboid_position: &Isometry<Real>,
flip_cuboid: bool,
_epsilon: Real,
) -> Option<Self> {
if self.topology().is_some() && self.pseudo_normals().is_some() {
let (cuboid_vtx, cuboid_idx) = cuboid.to_trimesh();
let cuboid_trimesh = TriMesh::with_flags(
cuboid_vtx,
cuboid_idx,
TriMeshFlags::HALF_EDGE_TOPOLOGY | TriMeshFlags::ORIENTED,
);
return transformation::intersect_meshes(
&Isometry::identity(),
self,
flip_mesh,
cuboid_position,
&cuboid_trimesh,
flip_cuboid,
)
.ok()
.flatten();
}
let cuboid_aabb = cuboid.compute_aabb(cuboid_position);
let mut intersecting_tris = vec![];
let mut visitor = BoundingVolumeIntersectionsVisitor::new(&cuboid_aabb, |id| {
intersecting_tris.push(*id);
true
});
let _ = self.qbvh().traverse_depth_first(&mut visitor);
if intersecting_tris.is_empty() {
return None;
}
// First, very naive version that outputs a triangle soup without
// index buffer (shared vertices are duplicated).
let vertices = self.vertices();
let indices = self.indices();
let mut clip_workspace = vec![];
let mut new_vertices = vec![];
let mut new_indices = vec![];
let aabb = cuboid.local_aabb();
let inv_pos = cuboid_position.inverse();
let mut to_clip = vec![];
for tri in intersecting_tris {
let idx = indices[tri as usize];
to_clip.extend_from_slice(&[
inv_pos * vertices[idx[0] as usize],
inv_pos * vertices[idx[1] as usize],
inv_pos * vertices[idx[2] as usize],
]);
// There is no need to clip if the triangle is fully inside of the Aabb.
// Note that we can’t take a shortcut for the case where all the vertices are
// outside of the Aabb, because the Aabb can still instersect the edges or face.
if !(aabb.contains_local_point(&to_clip[0])
&& aabb.contains_local_point(&to_clip[1])
&& aabb.contains_local_point(&to_clip[2]))
{
aabb.clip_polygon_with_workspace(&mut to_clip, &mut clip_workspace);
}
if to_clip.len() >= 3 {
let base_i = new_vertices.len();
for i in 1..to_clip.len() - 1 {
new_indices.push([base_i as u32, (base_i + i) as u32, (base_i + i + 1) as u32]);
}
new_vertices.append(&mut to_clip);
}
}
// The clipping outputs points in the local-space of the cuboid.
// So we need to transform it back.
for pt in &mut new_vertices {
*pt = cuboid_position * *pt;
}
if new_vertices.len() >= 3 {
Some(TriMesh::new(new_vertices, new_indices))
} else {
None
}
}
}