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plane.rs
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plane.rs
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use std::ops::{Mul, Neg};
use crate::{
dodeca::{Side, Vertex},
math::{lorentz_normalize, mip},
};
/// A hyperbolic plane
#[derive(Debug, Copy, Clone)]
pub struct Plane<N: na::RealField> {
normal: na::Vector4<N>,
}
impl From<Side> for Plane<f64> {
/// A surface overlapping with a particular dodecahedron side
fn from(side: Side) -> Self {
Self {
normal: *side.normal(),
}
}
}
impl<N: na::RealField + Copy> From<na::Unit<na::Vector3<N>>> for Plane<N> {
/// A plane passing through the origin
fn from(x: na::Unit<na::Vector3<N>>) -> Self {
Self {
normal: x.into_inner().push(na::zero()),
}
}
}
impl<N: na::RealField + Copy> Neg for Plane<N> {
type Output = Self;
fn neg(self) -> Self {
Self {
normal: -self.normal,
}
}
}
impl Mul<Plane<f64>> for Side {
type Output = Plane<f64>;
/// Reflect a plane across the side
fn mul(self, rhs: Plane<f64>) -> Plane<f64> {
self.reflection() * rhs
}
}
impl<'a, N: na::RealField + Copy> Mul<Plane<N>> for &'a na::Matrix4<N> {
type Output = Plane<N>;
fn mul(self, rhs: Plane<N>) -> Plane<N> {
Plane {
normal: lorentz_normalize(&(self * rhs.normal)),
}
}
}
impl<N: na::RealField + Copy> Plane<N> {
/// Hyperbolic normal vector identifying the plane
pub fn normal(&self) -> &na::Vector4<N> {
&self.normal
}
/// Shortest distance between the plane and a point
pub fn distance_to(&self, point: &na::Vector4<N>) -> N {
let mip_value = mip(&self.normal, point);
// Workaround for bug fixed in rust PR #72486
mip_value.abs().asinh() * mip_value.signum()
}
}
impl Plane<f64> {
/// Like `distance_to`, but using chunk coordinates for a chunk in the same node space
pub fn distance_to_chunk(&self, chunk: Vertex, coord: &na::Vector3<f64>) -> f64 {
let pos = lorentz_normalize(&(chunk.chunk_to_node() * coord.push(1.0)));
self.distance_to(&pos)
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::math::{origin, translate_along};
use approx::*;
#[test]
fn distance_sanity() {
for &axis in &[
na::Vector3::x_axis(),
na::Vector3::y_axis(),
na::Vector3::z_axis(),
] {
for &distance in &[-1.5, 0.0, 1.5] {
let plane = Plane::from(axis);
assert_abs_diff_eq!(
plane.distance_to(
&(translate_along(&(axis.into_inner() * distance)) * origin())
),
distance
);
}
}
}
#[test]
fn check_surface_flipped() {
let root = Plane::from(Side::A);
assert_abs_diff_eq!(
root.distance_to_chunk(Vertex::A, &na::Vector3::new(-1.0, 1.0, 1.0)),
root.distance_to_chunk(Vertex::J, &na::Vector3::new(-1.0, 1.0, 1.0)) * -1.0,
epsilon = 1e-5
);
}
#[test]
fn check_surface_on_plane() {
assert_abs_diff_eq!(
Plane::from(Side::A).distance_to_chunk(
Vertex::from_sides(Side::A, Side::B, Side::C).unwrap(),
&na::Vector3::new(0.0, 0.7, 0.1), // The first 0.0 is important, the plane is the midplane of the cube in Side::A direction
),
0.0,
epsilon = 1e-8,
);
}
#[test]
fn check_elevation_consistency() {
let abc = Vertex::from_sides(Side::A, Side::B, Side::C).unwrap();
// A cube corner should have the same elevation seen from different cubes
assert_abs_diff_eq!(
Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(1.0, 1.0, 1.0)),
Plane::from(Side::A).distance_to_chunk(
Vertex::from_sides(Side::F, Side::H, Side::J).unwrap(),
&na::Vector3::new(1.0, 1.0, 1.0),
),
epsilon = 1e-8,
);
// The same corner should have the same distance_to_chunk when represented from the same cube at different corners
assert_abs_diff_eq!(
Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(0.0, 1.0, 1.0)),
(Side::A * Plane::from(Side::A))
.distance_to_chunk(abc, &na::Vector3::new(0.0, 1.0, 1.0),),
epsilon = 1e-8,
);
// Corners of midplane cubes separated by the midplane should have the same distance_to_chunk with a different sign
assert_abs_diff_eq!(
Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(1.0, 1.0, 1.0)),
-Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(-1.0, 1.0, 1.0)),
epsilon = 1e-8,
);
// Corners of midplane cubes not separated by the midplane should have the same distance_to_chunk
assert_abs_diff_eq!(
Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(1.0, 1.0, 1.0)),
Plane::from(Side::A).distance_to_chunk(abc, &na::Vector3::new(1.0, 1.0, -1.0)),
epsilon = 1e-8,
);
}
}