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use crate::math::Vector;
use na::{self, RealField, Unit};
/// A cone with a circular basis and its apex at the origin.
///
/// A circular cone is a set of half-lines emanating from its apex and forming an angle of at most `angle` with its `axis`.
/// It is usually used to bound a set of directions like normals and tangents.
/// It is convex and have a circular basis.
#[derive(Copy, Clone, Debug, PartialEq, Eq)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub enum CircularCone<N: RealField + Copy> {
/// A cone which is the whole space.
Full,
/// An empty cone containing only the zero vector.
Empty,
/// All the vectors emanating from the origin, with a maximal `angle` wrt the given `axis`.
Spread {
/// The cone axis.
axis: Unit<Vector<N>>,
/// Half of the cone apex angle, i.e., the largest angle possible between the axis and a vector contained by this cone.
angle: N,
},
}
// FIXME: rewrite all those without calls to acos()
// (by performing tests on the cos themselves instead of the actual angles).
impl<N: RealField + Copy> CircularCone<N> {
/// Creates a circular cone from a set of vectors.
pub fn from_vectors(dirs: &[Unit<Vector<N>>]) -> Self {
let mut res = CircularCone::Empty;
for dir in dirs {
res.push(*dir)
}
res
}
/// Returns `true` if this cone is empty.
pub fn is_empty(&self) -> bool {
*self == CircularCone::Empty
}
/// Enlarge this cone so it contains `dir` too.
pub fn push(&mut self, dir: Unit<Vector<N>>) {
match *self {
CircularCone::Full => {}
CircularCone::Empty => {
*self = CircularCone::Spread {
axis: dir,
angle: N::zero(),
}
}
CircularCone::Spread {
ref mut axis,
ref mut angle,
} => {
let dot = axis.dot(&dir);
let delta_ang = dot.acos();
if delta_ang <= *angle {
// The current cone already contains dir.
} else {
let ortho = *dir - **axis * dot;
if let Some(basis2) = Unit::try_new(ortho, N::zero()) {
let hang = delta_ang * na::convert(0.5);
let (s, c) = hang.sin_cos();
*axis = Unit::new_unchecked(**axis * c + *basis2 * s);
*angle = hang + *angle * na::convert(0.5);
}
// Otherwise, dir and axis are collinear so there is nothing more to do.
}
}
}
}
/// Returns `true` if this cone intersects `other`.
pub fn intersects(&self, other: &Self) -> bool {
match (self, other) {
(CircularCone::Empty, _) => false,
(_, CircularCone::Empty) => false,
(CircularCone::Full, _) => true,
(_, CircularCone::Full) => true,
(
CircularCone::Spread {
axis: axis1,
angle: angle1,
},
CircularCone::Spread {
axis: axis2,
angle: angle2,
},
) => {
let ang = axis1.dot(&axis2).acos();
ang <= *angle1 + *angle2
}
}
}
/// Tests if this circular cone, extended to be a double cone, intersects the `other` circular cone, also seen as a double cone.
pub fn double_cones_intersect(&self, other: &Self) -> bool {
match (self, other) {
(CircularCone::Empty, _) => false,
(_, CircularCone::Empty) => false,
(CircularCone::Full, _) => true,
(_, CircularCone::Full) => true,
(
CircularCone::Spread {
axis: axis1,
angle: angle1,
},
CircularCone::Spread {
axis: axis2,
angle: angle2,
},
) => {
let ang = axis1.dot(&axis2).acos();
ang <= *angle1 + *angle2 || (N::pi() - ang) <= *angle1 + *angle2
}
}
}
/// Returns `true` if this cone contains `other`.
pub fn contains(&self, other: &Self) -> bool {
match (self, other) {
(CircularCone::Empty, _) => false,
(CircularCone::Full, _) => *other != CircularCone::Empty,
(_, CircularCone::Full) => false,
(_, CircularCone::Empty) => true,
(
CircularCone::Spread {
axis: axis1,
angle: angle1,
},
CircularCone::Spread {
axis: axis2,
angle: angle2,
},
) => {
let ang = axis1.dot(&axis2).acos();
ang + *angle2 <= *angle1
}
}
}
/// Merges this cone with `other` in-place.
pub fn merge(&mut self, other: &Self) {
*self = self.merged(other)
}
/// Merges this cone with `other`.
pub fn merged(&self, other: &Self) -> Self {
match (self, other) {
(CircularCone::Empty, _) => *other,
(CircularCone::Full, _) => CircularCone::Full,
(_, CircularCone::Empty) => *self,
(_, CircularCone::Full) => CircularCone::Full,
(
CircularCone::Spread {
axis: axis1,
angle: angle1,
},
CircularCone::Spread {
axis: axis2,
angle: angle2,
},
) => {
let dot = axis1.dot(&axis2);
let ang = dot.acos();
if ang + *angle1 <= *angle2 {
// self is contained in other
// so there is nothing to do for the merge.
*self
} else if ang + *angle2 <= *angle1 {
// other is contained in self
*other
} else {
let ortho = **axis2 - **axis1 * dot;
if let Some(basis2) = Unit::try_new(ortho, N::zero()) {
let partial_sum = (ang + *angle2) * na::convert(0.5);
let (s, c) = partial_sum.sin_cos();
let new_axis = **axis1 * c + *basis2 * s;
CircularCone::Spread {
axis: Unit::new_unchecked(new_axis),
angle: partial_sum + *angle1 * na::convert(0.5),
}
} else {
// This should be unreachable because that means both axii are superimposed so one
// of the first `if` statements above should have kicked in already.
// But this might happen due to rounding errors. Just return the
// cone with the largest angle.
if *angle2 > *angle1 {
*other
} else {
*self
}
}
}
}
}
}
}
///// Checks if the unit vector `dir` is inside of the circular cone described by the given `axis` and apex half-angle `angle`.
//pub fn cone_contains_dir<N: RealField + Copy>(axis: &Unit<Vector<N>>, angle: N, dir: &Unit<Vector<N>>) -> bool {
// let ang = axis.dot(dir).acos();
// ang <= angle
//}
//
///// Checks if the unit vector `dir` is inside of the polar of the circular cone described by the given `axis` and apex half-angle `angle`.
//pub fn cone_polar_contains_dir<N: RealField + Copy>(
// axis: &Unit<Vector<N>>,
// angle: N,
// dir: &Unit<Vector<N>>,
//) -> bool
//{
// let ang = axis.dot(dir).acos();
// ang >= angle + N::frac_pi_2()
//}