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use crate::math::Vector;
#[cfg(feature = "alloc")]
use crate::{math::Vector3, query::details::NormalConstraints};
// NOTE: ideally, the normal cone should take into account the point where the normal cone is
// considered. But as long as we assume that the triangles are one-way we can get away with
// just relying on the normal directions.
// Taking the point into account would be technically doable (and desirable if we wanted
// to define, e.g., a one-way mesh) but requires:
// 1. To make sure the edge pseudo-normals are given in the correct edge order.
// 2. To have access to the contact feature.
// We can have access to both during the narrow-phase, but leave that as a future
// potential improvements.
// NOTE: this isn’t equal to the "true" normal cones since concave edges will have pseudo-normals
// still pointing outward (instead of inward or being empty).
/// The pseudo-normals of a triangle providing approximations of its feature’s normal cones.
#[derive(Clone, Debug)]
pub struct TrianglePseudoNormals {
/// The triangle’s face normal.
pub face: Vector,
// TODO: if we switch this to providing pseudo-normals in a specific order
// (e.g. in the same order as the triangle’s edges), then we should
// think of fixing that order in the heightfield
// triangle_pseudo_normals code.
/// The edges pseudo-normals, in no particular order.
pub edges: [Vector; 3],
}
#[cfg(feature = "alloc")]
impl NormalConstraints for TrianglePseudoNormals {
/// Projects the given direction to it is contained in the polygonal
/// cone defined `self`.
fn project_local_normal_mut(&self, dir: &mut Vector) -> bool {
let dot_face = dir.dot(self.face);
// Find the closest pseudo-normal.
let dots = Vector3::new(
dir.dot(self.edges[0]),
dir.dot(self.edges[1]),
dir.dot(self.edges[2]),
);
let closest_dot = dots.max_position();
let closest_edge = self.edges[closest_dot];
// Apply the projection. Note that this isn’t 100% accurate since this approximates the
// vertex normal cone using the closest edge’s normal cone instead of the
// true polygonal cone on S² (but taking into account this polygonal cone exactly
// would be quite computationally expensive).
if closest_edge == self.face {
// The normal cone is degenerate, there is only one possible direction.
*dir = self.face;
return dot_face >= 0.0;
}
// TODO: take into account the two closest edges instead for better continuity
// of vertex normals?
let dot_edge_face = self.face.dot(closest_edge);
let dot_dir_face = self.face.dot(*dir);
let dot_corrected_dir_face = 2.0 * dot_edge_face * dot_edge_face - 1.0; // cos(2 * angle(closest_edge, face))
if dot_dir_face >= dot_corrected_dir_face {
// The direction is in the pseudo-normal cone. No correction to apply.
return true;
}
// We need to correct.
let edge_on_normal = self.face * dot_edge_face;
let edge_orthogonal_to_normal = closest_edge - edge_on_normal;
let dir_on_normal = self.face * dot_dir_face;
let dir_orthogonal_to_normal = *dir - dir_on_normal;
let Some(unit_dir_orthogonal_to_normal) = dir_orthogonal_to_normal.try_normalize() else {
return dot_face >= 0.0;
};
// NOTE: the normalization might be redundant as the result vector is guaranteed to be
// unit sized. Though some rounding errors could throw it off.
let adjusted_pseudo_normal =
edge_on_normal + unit_dir_orthogonal_to_normal * edge_orthogonal_to_normal.length();
let (adjusted_pseudo_normal, length) = adjusted_pseudo_normal.normalize_and_length();
if length <= 1.0e-6 {
return dot_face >= 0.0;
};
// The reflection of the face normal wrt. the adjusted pseudo-normal gives us the
// second end of the pseudo-normal cone the direction is projected on.
*dir = adjusted_pseudo_normal * (2.0 * self.face.dot(adjusted_pseudo_normal)) - self.face;
dot_face >= 0.0
}
}
#[cfg(test)]
#[cfg(all(feature = "dim3", feature = "alloc"))]
mod test {
use super::NormalConstraints;
use crate::math::{Real, Vector};
use crate::shape::TrianglePseudoNormals;
fn bisector(v1: Vector, v2: Vector) -> Vector {
(v1 + v2).normalize()
}
fn bisector_y(v: Vector) -> Vector {
bisector(v, Vector::Y)
}
#[test]
fn trivial_pseudo_normals_projection() {
let pn = TrianglePseudoNormals {
face: Vector::Y,
edges: [Vector::Y; 3],
};
assert_eq!(
pn.project_local_normal(Vector::new(1.0, 1.0, 1.0)),
Some(Vector::Y)
);
assert!(pn.project_local_normal(-Vector::Y).is_none());
}
#[test]
fn edge_pseudo_normals_projection_strictly_positive() {
let bisector = |v1: Vector, v2: Vector| (v1 + v2).normalize();
let bisector_y = |v: Vector| bisector(v, Vector::Y);
// The normal cones for this test will be fully contained in the +Y half-space.
let cones_ref_dir = [
-Vector::Z,
-Vector::X,
Vector::new(1.0, 0.0, 1.0).normalize(),
];
let cones_ends = cones_ref_dir.map(bisector_y);
let cones_axes = cones_ends.map(bisector_y);
let pn = TrianglePseudoNormals {
face: Vector::Y,
edges: cones_axes.map(|v| v.normalize()),
};
for i in 0..3 {
assert!(pn
.project_local_normal(cones_ends[i])
.unwrap()
.abs_diff_eq(cones_ends[i], 1.0e-5));
assert_eq!(pn.project_local_normal(cones_axes[i]), Some(cones_axes[i]));
// Guaranteed to be inside the normal cone of edge i.
let subdivs = 100;
for k in 1..100 {
let v = Vector::Y
.lerp(cones_ends[i], k as Real / (subdivs as Real))
.normalize();
assert_eq!(pn.project_local_normal(v).unwrap(), v);
}
// Guaranteed to be outside the normal cone of edge i.
for k in 1..subdivs {
let v = cones_ref_dir[i]
.lerp(cones_ends[i], k as Real / (subdivs as Real))
.normalize();
assert!(pn
.project_local_normal(v)
.unwrap()
.abs_diff_eq(cones_ends[i], 1.0e-5));
}
// Guaranteed to be outside the normal cone, and in the -Y half-space.
for k in 1..subdivs {
let v = cones_ref_dir[i]
.lerp(-Vector::Y, k as Real / (subdivs as Real))
.normalize();
assert!(pn.project_local_normal(v).is_none(),);
}
}
}
#[test]
fn edge_pseudo_normals_projection_negative() {
// The normal cones for this test will be fully contained in the +Y half-space.
let cones_ref_dir = [
-Vector::Z,
-Vector::X,
Vector::new(1.0, 0.0, 1.0).normalize(),
];
let cones_ends = cones_ref_dir.map(|v| bisector(v, -Vector::Y));
let cones_axes = [
bisector(bisector_y(cones_ref_dir[0]), cones_ref_dir[0]),
bisector(bisector_y(cones_ref_dir[1]), cones_ref_dir[1]),
bisector(bisector_y(cones_ref_dir[2]), cones_ref_dir[2]),
];
let pn = TrianglePseudoNormals {
face: Vector::Y,
edges: cones_axes.map(|v| v.normalize()),
};
for i in 0..3 {
assert_eq!(pn.project_local_normal(cones_axes[i]), Some(cones_axes[i]));
// Guaranteed to be inside the normal cone of edge i.
let subdivs = 100;
for k in 1..subdivs {
let v = Vector::Y
.lerp(cones_ends[i], k as Real / (subdivs as Real))
.normalize();
assert_eq!(pn.project_local_normal(v).unwrap(), v);
}
// Guaranteed to be outside the normal cone of edge i.
// Since it is additionally guaranteed to be in the -Y half-space, we should get None.
for k in 1..subdivs {
let v = (-Vector::Y)
.lerp(cones_ends[i], k as Real / (subdivs as Real))
.normalize();
assert!(pn.project_local_normal(v).is_none());
}
}
}
}