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use crate::util::{Dir, Plane, Projection};
use core::f32::consts::{FRAC_PI_2, PI, TAU};
use serde::{Deserialize, Serialize};
use specs::Component;
use vek::{Quaternion, Vec2, Vec3};
// Orientation
#[derive(Copy, Clone, Debug, PartialEq, Serialize, Deserialize)]
#[serde(into = "SerdeOri")]
#[serde(from = "SerdeOri")]
pub struct Ori(Quaternion<f32>);
impl Default for Ori {
/// Returns the default orientation (no rotation; default Dir)
fn default() -> Self { Self(Quaternion::identity()) }
}
impl Ori {
pub fn new(quat: Quaternion<f32>) -> Self {
#[cfg(debug_assertions)]
{
let v4 = quat.into_vec4();
debug_assert!(v4.map(f32::is_finite).reduce_and());
debug_assert!(v4.is_normalized());
}
Self(quat)
}
/// Tries to convert into a Dir and then the appropriate rotation
pub fn from_unnormalized_vec<T>(vec: T) -> Option<Self>
where
T: Into<Vec3<f32>>,
{
Dir::from_unnormalized(vec.into()).map(Self::from)
}
/// Look direction as a vector (no pedantic normalization performed)
pub fn look_vec(self) -> Vec3<f32> { self.to_quat() * *Dir::default() }
/// Get the internal quaternion representing the rotation from
/// `Dir::default()` to this orientation.
///
/// The operation is a cheap copy.
pub fn to_quat(self) -> Quaternion<f32> {
debug_assert!(self.is_normalized());
self.0
}
/// Look direction (as a Dir it is pedantically normalized)
pub fn look_dir(&self) -> Dir { self.to_quat() * Dir::default() }
pub fn up(&self) -> Dir { self.pitched_up(PI / 2.0).look_dir() }
pub fn down(&self) -> Dir { self.pitched_down(PI / 2.0).look_dir() }
pub fn left(&self) -> Dir { self.yawed_left(PI / 2.0).look_dir() }
pub fn right(&self) -> Dir { self.yawed_right(PI / 2.0).look_dir() }
pub fn slerp(ori1: Self, ori2: Self, s: f32) -> Self {
Self(Quaternion::slerp(ori1.0, ori2.0, s).normalized())
}
#[must_use]
pub fn slerped_towards(self, ori: Ori, s: f32) -> Self { Self::slerp(self, ori, s) }
/// Multiply rotation quaternion by `q`
/// (the rotations are in local vector space).
///
/// ```
/// use vek::{Quaternion, Vec3};
/// use veloren_common::{comp::Ori, util::Dir};
///
/// let ang = 90_f32.to_radians();
/// let roll_right = Quaternion::rotation_y(ang);
/// let pitch_up = Quaternion::rotation_x(ang);
///
/// let ori1 = Ori::from(Dir::new(Vec3::unit_x()));
/// let ori2 = Ori::default().rotated(roll_right).rotated(pitch_up);
///
/// assert!((ori1.look_dir().dot(*ori2.look_dir()) - 1.0).abs() <= f32::EPSILON);
/// ```
#[must_use]
pub fn rotated(self, q: Quaternion<f32>) -> Self {
Self((self.to_quat() * q.normalized()).normalized())
}
/// Premultiply rotation quaternion by `q`
/// (the rotations are in global vector space).
///
/// ```
/// use vek::{Quaternion, Vec3};
/// use veloren_common::{comp::Ori, util::Dir};
///
/// let ang = 90_f32.to_radians();
/// let roll_right = Quaternion::rotation_y(ang);
/// let pitch_up = Quaternion::rotation_x(ang);
///
/// let ori1 = Ori::from(Dir::up());
/// let ori2 = Ori::default().prerotated(roll_right).prerotated(pitch_up);
///
/// assert!((ori1.look_dir().dot(*ori2.look_dir()) - 1.0).abs() <= f32::EPSILON);
/// ```
#[must_use]
pub fn prerotated(self, q: Quaternion<f32>) -> Self {
Self((q.normalized() * self.to_quat()).normalized())
}
/// Take `global` into this Ori's local vector space
///
/// ```
/// use vek::Vec3;
/// use veloren_common::{comp::Ori, util::Dir};
///
/// let ang = 90_f32.to_radians();
/// let (fw, left, up) = (Dir::default(), Dir::left(), Dir::up());
///
/// let ori = Ori::default().rolled_left(ang).pitched_up(ang);
/// approx::assert_relative_eq!(ori.global_to_local(fw).dot(*-up), 1.0);
/// approx::assert_relative_eq!(ori.global_to_local(left).dot(*fw), 1.0);
/// let ori = Ori::default().rolled_right(ang).pitched_up(2.0 * ang);
/// approx::assert_relative_eq!(ori.global_to_local(up).dot(*left), 1.0);
/// ```
pub fn global_to_local<T>(&self, global: T) -> <Quaternion<f32> as std::ops::Mul<T>>::Output
where
Quaternion<f32>: std::ops::Mul<T>,
{
self.to_quat().inverse() * global
}
/// Take `local` into the global vector space
///
/// ```
/// use vek::Vec3;
/// use veloren_common::{comp::Ori, util::Dir};
///
/// let ang = 90_f32.to_radians();
/// let (fw, left, up) = (Dir::default(), Dir::left(), Dir::up());
///
/// let ori = Ori::default().rolled_left(ang).pitched_up(ang);
/// approx::assert_relative_eq!(ori.local_to_global(fw).dot(*left), 1.0);
/// approx::assert_relative_eq!(ori.local_to_global(left).dot(*-up), 1.0);
/// let ori = Ori::default().rolled_right(ang).pitched_up(2.0 * ang);
/// approx::assert_relative_eq!(ori.local_to_global(up).dot(*left), 1.0);
/// ```
pub fn local_to_global<T>(&self, local: T) -> <Quaternion<f32> as std::ops::Mul<T>>::Output
where
Quaternion<f32>: std::ops::Mul<T>,
{
self.to_quat() * local
}
#[must_use]
pub fn to_horizontal(self) -> Self {
// We don't use Self::look_dir to avoid the extra normalization step within
// Dir's Quaternion Mul impl
let fw = self.to_quat() * Dir::default().to_vec();
// Check that dir is not straight up/down
// Uses a multiple of EPSILON to be safe
// We can just check z since beyond floating point errors `fw` should be
// normalized
if 1.0 - fw.z.abs() > f32::EPSILON * 4.0 {
// We know direction lies in the xy plane so we only need to compute a rotation
// about the z-axis
let Vec2 { x, y } = fw.xy().normalized();
// Negate x and swap coords since we want to compute the angle from y+
let quat = rotation_2d(Vec2::new(y, -x), Vec3::unit_z());
Self(quat)
} else {
// if the direction is straight down, pitch up, or if straight up, pitch down
if fw.z < 0.0 {
self.pitched_up(FRAC_PI_2)
} else {
self.pitched_down(FRAC_PI_2)
}
// TODO: test this alternative for speed and correctness compared to
// current impl
//
// removes a branch
//
// use core::f32::consts::FRAC_1_SQRT_2;
// let cos = FRAC_1_SQRT_2;
// let sin = -FRAC_1_SQRT_2 * fw.z.signum();
// let axis = Vec3::unit_x();
// let scalar = cos;
// let vector = sin * axis;
// Self((self.0 * Quaternion::from_scalar_and_vec3((scalar,
// vector))).normalized())
}
}
/// Find the angle between two `Ori`s
///
/// NOTE: This finds the angle of the quaternion between the two `Ori`s
/// which can involve rolling and thus can be larger than simply the
/// angle between vectors at the start and end points.
///
/// Returns angle in radians
pub fn angle_between(self, other: Self) -> f32 {
// Compute quaternion from one ori to the other
// https://www.mathworks.com/matlabcentral/answers/476474-how-to-find-the-angle-between-two-quaternions#answer_387973
let between = self.to_quat().conjugate() * other.to_quat();
// Then compute it's angle
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/
//
// NOTE: acos is very sensitive to errors at small angles
// - https://www.researchgate.net/post/How_do_I_calculate_the_smallest_angle_between_two_quaternions
// - see angle_between unit test epislons
let angle = 2.0 * between.w.clamp(-1.0, 1.0).acos();
if angle < PI { angle } else { TAU - angle }
}
pub fn dot(self, other: Self) -> f32 { self.look_vec().dot(other.look_vec()) }
#[must_use]
pub fn pitched_up(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_x(angle_radians))
}
#[must_use]
pub fn pitched_down(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_x(-angle_radians))
}
#[must_use]
pub fn yawed_left(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_z(angle_radians))
}
#[must_use]
pub fn yawed_right(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_z(-angle_radians))
}
#[must_use]
pub fn rolled_left(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_y(-angle_radians))
}
#[must_use]
pub fn rolled_right(self, angle_radians: f32) -> Self {
self.rotated(Quaternion::rotation_y(angle_radians))
}
/// Returns a version which is rolled such that its up points towards `dir`
/// as much as possible without pitching or yawing
#[must_use]
pub fn rolled_towards(self, dir: Dir) -> Self {
dir.projected(&Plane::from(self.look_dir()))
.map_or(self, |dir| self.prerotated(self.up().rotation_between(dir)))
}
/// Returns a version which has been pitched towards `dir` as much as
/// possible without yawing or rolling
#[must_use]
pub fn pitched_towards(self, dir: Dir) -> Self {
dir.projected(&Plane::from(self.right()))
.map_or(self, |dir_| {
self.prerotated(self.look_dir().rotation_between(dir_))
})
}
/// Returns a version which has been yawed towards `dir` as much as possible
/// without pitching or rolling
#[must_use]
pub fn yawed_towards(self, dir: Dir) -> Self {
dir.projected(&Plane::from(self.up())).map_or(self, |dir_| {
self.prerotated(self.look_dir().rotation_between(dir_))
})
}
/// Returns a version without sideways tilt (roll)
///
/// ```
/// use veloren_common::comp::Ori;
///
/// let ang = 45_f32.to_radians();
/// let zenith = vek::Vec3::unit_z();
///
/// let rl = Ori::default().rolled_left(ang);
/// assert!((rl.up().angle_between(zenith) - ang).abs() <= f32::EPSILON);
/// assert!(rl.uprighted().up().angle_between(zenith) <= f32::EPSILON);
///
/// let pd_rr = Ori::default().pitched_down(ang).rolled_right(ang);
/// let pd_upr = pd_rr.uprighted();
///
/// assert!((pd_upr.up().angle_between(zenith) - ang).abs() <= f32::EPSILON);
///
/// let ang1 = pd_upr.rolled_right(ang).up().angle_between(zenith);
/// let ang2 = pd_rr.up().angle_between(zenith);
/// assert!((ang1 - ang2).abs() <= f32::EPSILON);
/// ```
#[must_use]
pub fn uprighted(self) -> Self { self.look_dir().into() }
fn is_normalized(&self) -> bool { self.0.into_vec4().is_normalized() }
}
/// Produce a quaternion from an axis to rotate about and a 2D point on the unit
/// circle to rotate to
///
/// NOTE: the provided axis and 2D vector must be normalized
fn rotation_2d(Vec2 { x, y }: Vec2<f32>, axis: Vec3<f32>) -> Quaternion<f32> {
// Skip needing the angle for quaternion construction by computing cos/sin
// directly from the normalized x value
//
// scalar = cos(theta / 2)
// vector = axis * sin(theta / 2)
//
// cos(a / 2) = +/- ((1 + cos(a)) / 2)^0.5
// sin(a / 2) = +/- ((1 - cos(a)) / 2)^0.5
//
// scalar = +/- sqrt((1 + cos(a)) / 2)
// vector = vec3(0, 0, 1) * +/- sqrt((1 - cos(a)) / 2)
//
// cos(a) = x / |xy| => x (when normalized)
// Prevent NaNs from negative sqrt (float errors can put this slightly over 1.0)
let x = x.clamp(-1.0, 1.0);
let scalar = ((1.0 + x) / 2.0).sqrt() * y.signum();
let vector = axis * ((1.0 - x) / 2.0).sqrt();
// This is normalized by our construction above
Quaternion::from_scalar_and_vec3((scalar, vector))
}
impl From<Dir> for Ori {
fn from(dir: Dir) -> Self {
// Check that dir is not straight up/down
// Uses a multiple of EPSILON to be safe
let quat = if 1.0 - dir.z.abs() > f32::EPSILON * 4.0 {
// Compute rotation that will give an "upright" orientation (no
// rolling):
let xy_len = dir.xy().magnitude();
let xy_norm = dir.xy() / xy_len;
// Rotation to get to this projected point from the default direction of y+
// Negate x and swap coords since we want to compute the angle from y+
let yaw = rotation_2d(Vec2::new(xy_norm.y, -xy_norm.x), Vec3::unit_z());
// Rotation to then rotate up/down to the match the input direction
// In this rotated space the xy_len becomes the distance along the x axis
// And since we rotated around the z-axis the z value is unchanged
let pitch = rotation_2d(Vec2::new(xy_len, dir.z), Vec3::unit_x());
(yaw * pitch).normalized()
} else {
// Nothing in particular can be considered upright if facing up or down
// so we just produce a quaternion that will rotate to that direction
// (once again rotating from y+)
let pitch = PI / 2.0 * dir.z.signum();
Quaternion::rotation_x(pitch)
};
Self(quat)
}
}
impl From<Vec3<f32>> for Ori {
fn from(dir: Vec3<f32>) -> Self { Dir::from_unnormalized(dir).unwrap_or_default().into() }
}
impl From<Quaternion<f32>> for Ori {
fn from(quat: Quaternion<f32>) -> Self { Self::new(quat) }
}
impl From<vek::quaternion::repr_simd::Quaternion<f32>> for Ori {
fn from(
vek::quaternion::repr_simd::Quaternion { x, y, z, w }: vek::quaternion::repr_simd::Quaternion<f32>,
) -> Self {
Self::from(Quaternion { x, y, z, w })
}
}
impl From<Ori> for Quaternion<f32> {
fn from(Ori(q): Ori) -> Self { q }
}
impl From<Ori> for vek::quaternion::repr_simd::Quaternion<f32> {
fn from(Ori(Quaternion { x, y, z, w }): Ori) -> Self {
vek::quaternion::repr_simd::Quaternion { x, y, z, w }
}
}
impl From<Ori> for Dir {
fn from(ori: Ori) -> Self { ori.look_dir() }
}
impl From<Ori> for Vec3<f32> {
fn from(ori: Ori) -> Self { ori.look_vec() }
}
impl From<Ori> for vek::vec::repr_simd::Vec3<f32> {
fn from(ori: Ori) -> Self { vek::vec::repr_simd::Vec3::from(ori.look_vec()) }
}
impl From<Ori> for Vec2<f32> {
fn from(ori: Ori) -> Self { ori.look_dir().to_horizontal().unwrap_or_default().xy() }
}
impl From<Ori> for vek::vec::repr_simd::Vec2<f32> {
fn from(ori: Ori) -> Self { vek::vec::repr_simd::Vec2::from(ori.look_vec().xy()) }
}
// Validate at Deserialization
#[derive(Copy, Clone, Default, Debug, PartialEq, Serialize, Deserialize)]
struct SerdeOri(Quaternion<f32>);
impl From<SerdeOri> for Ori {
fn from(serde_quat: SerdeOri) -> Self {
let quat: Quaternion<f32> = serde_quat.0;
if quat.into_vec4().map(f32::is_nan).reduce_or() {
tracing::warn!(
?quat,
"Deserialized rotation quaternion containing NaNs, replacing with default"
);
Default::default()
} else if !Self(quat).is_normalized() {
tracing::warn!(
?quat,
"Deserialized unnormalized rotation quaternion (magnitude: {}), replacing with \
default",
quat.magnitude()
);
Default::default()
} else {
Self::new(quat)
}
}
}
impl From<Ori> for SerdeOri {
fn from(other: Ori) -> SerdeOri { SerdeOri(other.to_quat()) }
}
impl Component for Ori {
type Storage = specs::VecStorage<Self>;
}
#[cfg(test)]
mod tests {
use super::*;
// Helper method to produce Dirs at different angles to test
fn dirs() -> impl Iterator<Item = Dir> {
let angles = 32;
(0..angles).flat_map(move |i| {
let theta = PI * 2.0 * (i as f32) / (angles as f32);
let v = Vec3::unit_y();
let q = Quaternion::rotation_x(theta);
let dir_1 = Dir::new(q * v);
let v = Vec3::unit_z();
let q = Quaternion::rotation_y(theta);
let dir_2 = Dir::new(q * v);
let v = Vec3::unit_x();
let q = Quaternion::rotation_z(theta);
let dir_3 = Dir::new(q * v);
[dir_1, dir_2, dir_3]
})
}
#[test]
fn to_horizontal() {
let to_horizontal = |dir: Dir| {
let ori = Ori::from(dir);
let horizontal = ori.to_horizontal();
approx::assert_relative_eq!(horizontal.look_dir().xy().magnitude(), 1.0);
approx::assert_relative_eq!(horizontal.look_dir().z, 0.0);
// Check correctness by comparing with Dir::to_horizontal
if let Some(dir_h) = ori.look_dir().to_horizontal() {
let quat_correct = Quaternion::<f32>::rotation_from_to_3d(Dir::default(), dir_h);
#[rustfmt::skip]
assert!(
dir_h
.map2(*horizontal.look_dir(), |d, o| approx::relative_eq!(d, o, epsilon = f32::EPSILON * 4.0))
.reduce_and(),
"\n\
Original: {:?}\n\
Dir::to_horizontal: {:?}\n\
Ori::to_horizontal(as dir): {:?}\n\
Ori::to_horizontal(as quat): {:?}\n\
Correct quaternion {:?}",
ori.look_dir(),
dir_h,
horizontal.look_dir(),
horizontal,
quat_correct,
);
}
};
dirs().for_each(to_horizontal);
}
#[test]
fn angle_between() {
let axis_list = (-16..17)
.map(|i| i as f32 / 16.0)
.flat_map(|fraction| {
[
Vec3::new(1.0 - fraction, fraction, 0.0),
Vec3::new(0.0, 1.0 - fraction, fraction),
Vec3::new(fraction, 0.0, 1.0 - fraction),
]
})
.collect::<Vec<_>>();
// Iterator over some angles between 0 and 180
let angles = (0..129).map(|i| i as f32 / 128.0 * PI);
for angle_a in angles.clone() {
for angle_b in angles.clone() {
for axis in axis_list.iter().copied() {
let ori_a = Ori(Quaternion::rotation_3d(angle_a, axis));
let ori_b = Ori(Quaternion::rotation_3d(angle_b, axis));
let angle = (angle_a - angle_b).abs();
let epsilon = match angle {
angle if angle > 0.5 => f32::EPSILON * 20.0,
angle if angle > 0.2 => 0.00001,
angle if angle > 0.01 => 0.0001,
_ => 0.002,
};
approx::assert_relative_eq!(
ori_a.angle_between(ori_b),
angle,
epsilon = epsilon,
);
}
}
}
}
#[test]
fn from_to_dir() {
let from_to = |dir: Dir| {
let ori = Ori::from(dir);
assert!(ori.is_normalized(), "ori {:?}\ndir {:?}", ori, dir);
assert!(
approx::relative_eq!(ori.look_dir().dot(*dir), 1.0),
"Ori::from(dir).look_dir() != dir\ndir: {:?}\nOri::from(dir).look_dir(): {:?}",
dir,
ori.look_dir(),
);
approx::assert_relative_eq!((ori.to_quat() * Dir::default()).dot(*dir), 1.0);
};
dirs().for_each(from_to);
}
#[test]
fn orthogonal_dirs() {
let ori = Ori::default();
let def = Dir::default();
for dir in &[ori.up(), ori.down(), ori.left(), ori.right()] {
approx::assert_relative_eq!(dir.dot(*def), 0.0);
}
}
}