src/sets.rs

/*!
This module provides various sets and traits for them.
*/

use crate::euclidean::Euclidean;
use crate::instance::{Instance, Space};
use crate::loc::Loc;
use crate::types::*;
use serde::Serialize;
use std::ops::{Range, RangeFrom, RangeFull, RangeInclusive, RangeTo, RangeToInclusive};

pub mod cube;
pub use cube::Cube;

/// Trait for arbitrary sets. The parameter `U` is the element type.
pub trait Set<U>
where
    U: Space,
{
    /// Check for element containment
    fn contains<I: Instance<U>>(&self, item: I) -> bool;
}

/// Additional ordering (besides [`PartialOrd`]) of a subfamily of sets:
/// greatest lower bound and least upper bound.
pub trait SetOrd: Sized {
    /// Returns the smallest set of same class contain both parameters.
    fn common(&self, other: &Self) -> Self;

    /// Returns the greatest set of same class contaied by n both parameter sets.
    fn intersect(&self, other: &Self) -> Option<Self>;
}

impl<U, const N: usize> Set<Loc<N, U>> for Cube<N, U>
where
    U: Num + PartialOrd + Sized,
{
    fn contains<I: Instance<Loc<N, U>>>(&self, item: I) -> bool {
        self.0
            .iter()
            .zip(item.ref_instance().iter())
            .all(|(s, x)| s.contains(x))
    }
}

impl<U: Space> Set<U> for RangeFull {
    fn contains<I: Instance<U>>(&self, _item: I) -> bool {
        true
    }
}

macro_rules! impl_ranges {
    ($($range:ident),*) => { $(
        impl<U,Idx> Set<U> for $range<Idx>
        where
            Idx : PartialOrd<U>,
            U : PartialOrd<Idx> + Space,
            Idx : PartialOrd
        {
            #[inline]
            fn contains<I : Instance<U>>(&self, item : I) -> bool {
                item.eval(|x| $range::contains(&self, x))
            }
        }
    )* }
}

impl_ranges!(RangeFrom, Range, RangeInclusive, RangeTo, RangeToInclusive);

/// Halfspaces described by an orthogonal vector and an offset.
///
/// The halfspace is $H = \\{ t v + a \mid a^⊤ v = 0 \\}$, where $v$ is the orthogonal
/// vector and $t$ the offset.
#[derive(Clone, Copy, Debug, Serialize, Eq, PartialEq)]
pub struct Halfspace<A>
where
    A: Euclidean,
{
    pub orthogonal: A,
    pub offset: A::Field,
}

impl<A> Halfspace<A>
where
    A: Euclidean,
{
    #[inline]
    pub fn new(orthogonal: A, offset: A::Field) -> Self {
        Halfspace {
            orthogonal: orthogonal,
            offset: offset,
        }
    }
}

/// Trait for generating a halfspace spanned by another set `Self` of elements of type `U`.
pub trait SpannedHalfspace {
    /// Type of the orthogonal vector describing the halfspace.
    type A: Euclidean;
    /// Returns the halfspace spanned by this set.
    fn spanned_halfspace(&self) -> Halfspace<Self::A>;
}

// TODO: Gram-Schmidt for higher N.
impl<F: Float> SpannedHalfspace for [Loc<1, F>; 2] {
    type A = Loc<1, F>;
    fn spanned_halfspace(&self) -> Halfspace<Self::A> {
        let (x0, x1) = (self[0], self[1]);
        Halfspace::new(x1 - x0, x0[0])
    }
}

// TODO: Gram-Schmidt for higher N.
impl<F: Float> SpannedHalfspace for [Loc<2, F>; 2] {
    type A = Loc<2, F>;
    fn spanned_halfspace(&self) -> Halfspace<Self::A> {
        let (x0, x1) = (&self[0], &self[1]);
        let d = x1 - x0;
        let orthog = loc![d[1], -d[0]]; // We don't normalise for efficiency
        let offset = x0.dot(&orthog);
        Halfspace::new(orthog, offset)
    }
}

impl<A> Set<A> for Halfspace<A>
where
    A: Euclidean,
{
    #[inline]
    fn contains<I: Instance<A>>(&self, item: I) -> bool {
        self.orthogonal.dot(item) >= self.offset
    }
}

/// Polygons defined by `N` `Halfspace`s.
#[derive(Clone, Copy, Debug, PartialEq)]
pub struct NPolygon<A: Euclidean, const N: usize>(pub [Halfspace<A>; N]);

impl<A: Euclidean, const N: usize> Set<A> for NPolygon<A, N> {
    fn contains<I: Instance<A>>(&self, item: I) -> bool {
        let r = item.ref_instance();
        self.0.iter().all(|halfspace| halfspace.contains(r))
    }
}