conspire 0.7.7

The Rust interface to conspire.
Documentation 
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#[cfg(test)]
mod test;

use crate::{
    geometry::{
        Coordinate, Coordinates, Direction,
        mesh::{
            Connectivity,
            tessellation::{D, Tessellation},
        },
    },
    math::{CrossProduct, FxHashMap, FxHashSet, Quantity, Scalar, Tensor},
    units::{Area, Dimensionless, Length},
};
use std::array::from_fn;

/// Cosine of the dihedral deviation past which an edge is a crease.
const CREASE_COSINE: Scalar = 0.866_025_403_784_438_6;

/// The sharp edges and points of a tessellation.
///
/// An edge is a crease when its two triangles turn through more than thirty
/// degrees. A vertex is a corner when the creases through it do not simply
/// pass through: it ends one, joins three or more, or turns sharply between
/// two.
///
/// Only edges with exactly two incident triangles are considered, so a
/// tessellation whose triangles do not share nodes has no features rather
/// than having every edge be one.
pub struct Features {
    corners: Vec<Coordinate<D>>,
    creases: Vec<[Coordinate<D>; 2]>,
}

/// The features of a tessellation, binned for lookup within a fixed radius.
pub struct FeatureIndex<'a> {
    features: &'a Features,
    corners: FxHashMap<[i64; D], Vec<usize>>,
    creases: FxHashMap<[i64; D], Vec<usize>>,
    /// Creases spanning too many cells to bin, scanned by every lookup.
    sprawling: Vec<usize>,
    spacing: Quantity<Length>,
}

/// How many cells a crease may be binned into before it is left sprawling.
const SPAN: i64 = 64;

fn triangles(tessellation: &Tessellation) -> Vec<[usize; D]> {
    match &tessellation.mesh().connectivities()[0] {
        Connectivity::Triangular(triangles) => triangles.iter().copied().collect(),
        _ => Vec::new(),
    }
}

fn key(one: usize, two: usize) -> [usize; 2] {
    if one < two { [one, two] } else { [two, one] }
}

pub(crate) fn crease_edges(
    triangles: &[[usize; D]],
    coordinates: &Coordinates<D>,
) -> Vec<[usize; 2]> {
    let normals: Vec<Direction<D>> = triangles
        .iter()
        .map(|&[a, b, c]| {
            (&coordinates[b] - &coordinates[a])
                .cross(&(&coordinates[c] - &coordinates[a]))
                .normalized()
        })
        .collect();
    let mut incident = FxHashMap::<[usize; 2], Vec<usize>>::default();
    triangles
        .iter()
        .enumerate()
        .for_each(|(index, &[a, b, c])| {
            [key(a, b), key(b, c), key(c, a)]
                .into_iter()
                .for_each(|edge| incident.entry(edge).or_default().push(index))
        });
    let mut sharp: Vec<[usize; 2]> = incident
        .iter()
        .filter(|(_, triangles)| triangles.len() == 2)
        .filter(|(_, triangles)| &normals[triangles[0]] * &normals[triangles[1]] < CREASE_COSINE)
        .map(|(&edge, _)| edge)
        .collect();
    sharp.sort_unstable();
    sharp
}

pub(crate) fn crease_nodes(
    triangles: &[[usize; D]],
    coordinates: &Coordinates<D>,
) -> FxHashSet<usize> {
    crease_edges(triangles, coordinates)
        .into_iter()
        .flatten()
        .collect()
}

impl Features {
    pub fn corners(&self) -> &[Coordinate<D>] {
        &self.corners
    }
    pub fn creases(&self) -> &[[Coordinate<D>; 2]] {
        &self.creases
    }
    pub(super) fn of(tessellation: &Tessellation) -> Self {
        let coordinates = tessellation.mesh().coordinates();
        let triangles = triangles(tessellation);
        let sharp = crease_edges(&triangles, coordinates);
        let mut through = FxHashMap::<usize, Vec<usize>>::default();
        sharp.iter().for_each(|&[a, b]| {
            through.entry(a).or_default().push(b);
            through.entry(b).or_default().push(a)
        });
        let mut nodes: Vec<usize> = through.keys().copied().collect();
        nodes.sort_unstable();
        let corners = nodes
            .into_iter()
            .filter(|node| {
                let others = &through[node];
                match others.len() {
                    2 => {
                        let one = (&coordinates[others[0]] - &coordinates[*node]).normalized();
                        let two = (&coordinates[others[1]] - &coordinates[*node]).normalized();
                        &one * &two > -CREASE_COSINE
                    }
                    _ => true,
                }
            })
            .map(|node| coordinates[node].clone())
            .collect();
        let creases = sharp
            .into_iter()
            .map(|[a, b]| [coordinates[a].clone(), coordinates[b].clone()])
            .collect();
        Self { corners, creases }
    }
    /// Bins the features so that everything within `radius` of a point is
    /// found in the twenty-seven cells about it.
    pub fn index(&self, radius: Quantity<Length>) -> FeatureIndex<'_> {
        let spacing = if radius > Quantity::new(0.0) {
            radius
        } else {
            Quantity::new(1.0)
        };
        let mut corners = FxHashMap::<[i64; D], Vec<usize>>::default();
        self.corners.iter().enumerate().for_each(|(index, point)| {
            corners.entry(cell(point, spacing)).or_default().push(index)
        });
        let mut creases = FxHashMap::<[i64; D], Vec<usize>>::default();
        let mut sprawling = Vec::new();
        self.creases.iter().enumerate().for_each(|(index, [a, b])| {
            let (low, high) = (cell(a, spacing), cell(b, spacing));
            let span: [i64; D] = from_fn(|axis| (high[axis] - low[axis]).abs() + 1);
            if span.iter().product::<i64>() > SPAN {
                return sprawling.push(index);
            }
            for i in low[0].min(high[0])..=low[0].max(high[0]) {
                for j in low[1].min(high[1])..=low[1].max(high[1]) {
                    for k in low[2].min(high[2])..=low[2].max(high[2]) {
                        creases.entry([i, j, k]).or_default().push(index)
                    }
                }
            }
        });
        FeatureIndex {
            features: self,
            corners,
            creases,
            sprawling,
            spacing,
        }
    }
}

fn cell(point: &Coordinate<D>, spacing: Quantity<Length>) -> [i64; D] {
    from_fn(|axis| (point[axis] / spacing).floor().value() as i64)
}

fn closest_on(segment: &[Coordinate<D>; 2], point: &Coordinate<D>) -> Coordinate<D> {
    let along = &segment[1] - &segment[0];
    let length = &along * &along;
    if length == Quantity::<Area>::new(0.0) {
        return segment[0].clone();
    }
    let fraction = Quantity::<Dimensionless>::new(
        ((point - &segment[0]) * &along / length)
            .value()
            .clamp(0.0, 1.0),
    );
    &segment[0] + &(along * fraction)
}

impl FeatureIndex<'_> {
    fn about(&self, point: &Coordinate<D>) -> Vec<[i64; D]> {
        let middle = cell(point, self.spacing);
        (-1..=1)
            .flat_map(|i| {
                (-1..=1).flat_map(move |j| {
                    (-1..=1).map(move |k| [middle[0] + i, middle[1] + j, middle[2] + k])
                })
            })
            .collect()
    }
    /// The corner nearest `point` within `radius`, and how far away it is.
    pub fn nearest_corner(
        &self,
        point: &Coordinate<D>,
        radius: Quantity<Length>,
    ) -> Option<(usize, Quantity<Length>)> {
        self.about(point)
            .iter()
            .filter_map(|cell| self.corners.get(cell))
            .flatten()
            .map(|&index| (index, (&self.features.corners[index] - point).norm()))
            .filter(|&(_, distance)| distance < radius)
            .min_by(|(_, one), (_, two)| one.total_cmp(two))
    }
    /// The point on a crease nearest `point` within `radius`.
    pub fn nearest_crease(
        &self,
        point: &Coordinate<D>,
        radius: Quantity<Length>,
    ) -> Option<Coordinate<D>> {
        self.about(point)
            .iter()
            .filter_map(|cell| self.creases.get(cell))
            .flatten()
            .chain(self.sprawling.iter())
            .map(|&index| closest_on(&self.features.creases[index], point))
            .map(|closest| {
                let distance = (&closest - point).norm();
                (closest, distance)
            })
            .filter(|&(_, distance)| distance < radius)
            .min_by(|(_, one), (_, two)| one.total_cmp(two))
            .map(|(closest, _)| closest)
    }
    pub fn corner(&self, index: usize) -> &Coordinate<D> {
        &self.features.corners[index]
    }
    pub fn is_empty(&self) -> bool {
        self.features.corners.is_empty() && self.features.creases.is_empty()
    }
}