path: root/src/math/polygon/polygon_graph.rs

use super::Polygon;
use crate::math::{self, LineSegment, Vec2};
use nalgebra::{RealField, Scalar};
use std::cmp::{Ordering, PartialOrd};

#[derive(Debug)]
struct Node<T: Scalar + Copy> {
    pub vec: Vec2<T>,
    pub adjacent: Vec<Vec2<T>>,
}

struct EdgeIterator<'a, T: Scalar + Copy> {
    nodes: &'a [Node<T>],
    pos: (usize, usize),
}

/// An undirected graph, that is optimised for polygon edge operations. Since edges of a polygon
/// are an undirected graph, this structure also holds both directions. This makes it rather space
/// inefficient, but makes edge operations rather swift. ß
#[derive(Debug)]
pub struct PolygonGraph<T: Scalar + Copy + PartialOrd> {
    /// The nodes of the graph, together with their adjacency list.
    nodes: Vec<Node<T>>,
}
// Helper functions to find nodes/vecs in sorted fields, so It doesn't always have to be written
// out.
#[inline]
fn find_vec2<T: Scalar + Copy + PartialOrd>(
    field: &[Vec2<T>],
    lookup: &Vec2<T>,
) -> Result<usize, usize> {
    field.binary_search_by(|n| n.partial_cmp(lookup).unwrap_or(Ordering::Greater))
}
#[inline]
fn find_node<T: Scalar + Copy + PartialOrd>(
    field: &[Node<T>],
    lookup: &Vec2<T>,
) -> Result<usize, usize> {
    field.binary_search_by(|n| n.vec.partial_cmp(lookup).unwrap_or(Ordering::Greater))
}

impl<'a, T: Scalar + Copy> EdgeIterator<'a, T> {
    pub fn new(nodes: &'a [Node<T>]) -> Self {
        Self { nodes, pos: (0, 0) }
    }
}

impl<'a, T: Scalar + Copy> Iterator for EdgeIterator<'a, T> {
    type Item = LineSegment<T>;

    fn next(&mut self) -> Option<Self::Item> {
        // Try to find the element in the nodes vector, if it exists.
        if let Some(node) = self.nodes.get(self.pos.0) {
            let end = node.adjacent[self.pos.1];

            // Advance the iterator to the next possible element
            if self.pos.1 + 1 < node.adjacent.len() {
                self.pos.1 += 1;
            } else {
                self.pos.1 = 0;
                self.pos.0 += 1;
            }

            Some(LineSegment::new(node.vec, end))
        } else {
            None
        }
    }
}

impl<T: Scalar + Copy + PartialOrd> PolygonGraph<T> {
    /// Create a new, empty polygon graph.
    pub fn new() -> Self {
        Self { nodes: Vec::new() }
    }

    /// Count the number of edges in the graph. Internally, for each two connected points there are
    /// two edges, but this returns the amount of polygon edges.
    pub fn num_edges(&self) -> usize {
        let mut num_edges = 0;
        for node in &self.nodes {
            for _ in &node.adjacent {
                num_edges += 1;
            }
        }

        assert!(num_edges % 2 == 0);
        num_edges / 2
    }

    /// Count the number of nodes in this graph. If this graph consists of multiple polygons, this
    /// can be different than the amount of corners, since corners with the same position are only
    /// counted once.
    pub fn num_nodes(&self) -> usize {
        self.nodes.len()
    }

    /// Checks if there is an edge between the two given vectors. Is commutative in respect to the
    /// two arguments.
    pub fn has_edge(&self, from: &Vec2<T>, to: &Vec2<T>) -> bool {
        // Binary search the starting and then the end node.
        if let Ok(from) = find_node(&self.nodes, from) {
            find_vec2(&self.nodes[from].adjacent, to).is_ok()
        } else {
            false
        }
    }

    // Helper function to add the edge into the internal graph representation for one side only.
    // Since to the outside the graph should always be undirected, this must be private.
    fn add_edge_onesided(&mut self, from: &Vec2<T>, to: &Vec2<T>) -> bool {
        match find_node(&self.nodes, from) {
            Ok(pos) => match find_vec2(&self.nodes[pos].adjacent, to) {
                Ok(_) => return false,
                Err(i) => self.nodes[pos].adjacent.insert(i, *to),
            },
            Err(pos) => self.nodes.insert(
                pos,
                Node {
                    vec: *from,
                    adjacent: vec![*to],
                },
            ),
        }

        true
    }

    /// Add an edge between the given vectors. If the edge already exists, it does nothing and
    /// returns false, otherwise it returns true after addition.
    pub fn add_edge(&mut self, from: &Vec2<T>, to: &Vec2<T>) -> bool {
        if !self.add_edge_onesided(from, to) {
            return false;
        }

        let back_edge_succ = self.add_edge_onesided(to, from);
        assert!(back_edge_succ);

        true
    }

    // Helper function to remove the edge in the internal graph representation for one side only.
    // Since to the outside the graph should always be undirected, this must be private.
    fn remove_edge_onesided(&mut self, from: &Vec2<T>, to: &Vec2<T>) -> bool {
        if let Ok(from) = find_node(&self.nodes, from) {
            if let Ok(to) = find_vec2(&self.nodes[from].adjacent, to) {
                // Remove the edge from the vector.
                self.nodes[from].adjacent.remove(to);

                // If the node has no adjacent nodes anymore, remove it entirely.
                if self.nodes[from].adjacent.is_empty() {
                    self.nodes.remove(from);
                }

                true
            } else {
                false
            }
        } else {
            false
        }
    }

    /// Remove an edge between the given vectors. If there is no edge between them, it does nothing
    /// and returns false, otherwise it returns true after deletion.
    pub fn remove_edge(&mut self, from: &Vec2<T>, to: &Vec2<T>) -> bool {
        if !self.remove_edge_onesided(from, to) {
            return false;
        }

        let back_edge_succ = self.remove_edge_onesided(to, from);
        assert!(back_edge_succ);

        true
    }

    /// Constructs a new PolygonGraph from the provided polygon. Adds a node for every corner and
    /// an edge to all connected corners (which should be exactly two, for regular polygons)
    pub fn from_polygon(polygon: &Polygon<T>) -> Self {
        let mut graph = PolygonGraph {
            nodes: Vec::with_capacity(polygon.corners.len()),
        };

        graph.add_all(polygon);
        graph
    }

    /// Add all edges of the provided polygon into the graph. Requires roughly double as much space
    /// as the normal polygon.
    pub fn add_all(&mut self, polygon: &Polygon<T>) {
        for i in 0..polygon.corners.len() {
            self.add_edge(
                &polygon.corners[i],
                &polygon.corners[(i + 1) % polygon.corners.len()],
            );
        }
    }

    /// Calculates all points where the graph edges intersect with one another. It then adds them
    /// into the adjacency list such that the intersection point lies between the nodes of the
    /// lines.
    pub fn intersect_self(&mut self)
    where
        T: RealField,
    {
        // Find all intersections with all other edges.
        let mut to_delete: Vec<LineSegment<T>> = Vec::new();
        let mut to_add: Vec<(Vec2<T>, Vec2<T>)> = Vec::new();
        for segment in EdgeIterator::new(&self.nodes) {
            /* Save all intersections of this line with any other line, and the line that it's
             * intersecting with.
             */
            let mut intersections: Vec<Vec2<T>> = Vec::new();
            for compare_segment in EdgeIterator::new(&self.nodes) {
                if segment.eq_ignore_dir(&compare_segment) {
                    continue;
                }

                if let Some(intersection) = LineSegment::intersection(&segment, &compare_segment) {
                    intersections.push(intersection);
                }
            }

            if intersections.is_empty() {
                continue;
            }

            to_delete.push(segment.clone());

            // Safe, since at least the line segment itself is represented.
            let segments = segment.segments(&intersections);
            for i in 1..segments.len() {
                to_add.push((segments[i - 1], segments[i]));
            }
        }

        for segment in to_delete {
            self.remove_edge(&segment.start, &segment.end);
        }
        for (start, end) in to_add {
            self.add_edge(&start, &end);
        }
    }

    /// Finds the minimal polygon that could hold this graph together, i.e. could contain the
    /// entire graph, but with the minimal amount of space. It may however still contain extra
    /// corner points, meaning an extra edge for three collinear points on this edge, that can be
    /// cleaned up.
    pub fn bounding_polygon(mut self) -> Polygon<T>
    where
        T: RealField,
    {
        assert!(self.num_nodes() >= 3);
        self.intersect_self();

        /* Start with the top-left node. Since the nodes are always sorted by y over x from top to
         * bottom and left to right, this is the very first element in the vector. This is also a
         * corner, because for such a node to be enveloped, there would have to be a node further
         * to the top, in which case that node would have been selected.
         */
        let mut current_node = &self.nodes[0];
        // Pretend we're coming from the top to start in the right direction.
        let mut last_vec = current_node.vec - Vec2::new(T::zero(), T::one());
        let mut bounding_polygon = Polygon::new(vec![current_node.vec]);
        loop {
            /* Find the next point by choosing the one with the greatest angle. This means we are
             * "bending" to the leftmost edge at each step. Since we are going around the polygon
             * in a clockwise direction, this yields the hull around the polygon.
             * NOTE: Going left is just as viable, but we would have to handle the case where the
             * algorithm would try to go back because the edge back has 0 degrees, which would be
             * always preferred. Going right makes going back the absolute worst option.
             */
            let next_corner = current_node
                .adjacent
                .iter()
                .max_by(|&a, &b| {
                    math::triplet_angle(last_vec, current_node.vec, *a)
                        .partial_cmp(&math::triplet_angle(last_vec, current_node.vec, *b))
                        .unwrap_or(Ordering::Equal)
                })
                .expect("Adjacency list is empty. The polygon has an open edge (is broken)");

            // When we have come back to the start, the traversal is completed
            if *next_corner == bounding_polygon.corners[0] {
                break;
            }

            bounding_polygon.corners.push(*next_corner);
            last_vec = current_node.vec;
            current_node = &self.nodes[find_node(&self.nodes, &next_corner)
                .expect("Failure to find node that should be inside list.")];
        }

        bounding_polygon
    }
}

impl<T: Scalar + Copy + PartialOrd> Default for PolygonGraph<T> {
    fn default() -> Self {
        Self::new()
    }
}

#[cfg(test)]
mod test {
    use super::*;

    #[test]
    fn from_polygon() {
        let a = Vec2::new(0., 0.);
        let b = Vec2::new(0., 1.);
        let c = Vec2::new(0.5, 1.);

        let triangle = Polygon::new(vec![a, b, c]);

        let graph = PolygonGraph::from_polygon(&triangle);
        assert_eq!(graph.num_edges(), 3);

        assert!(graph.has_edge(&a, &b));
        assert!(graph.has_edge(&b, &a));

        assert!(graph.has_edge(&a, &c));
        assert!(graph.has_edge(&c, &a));

        assert!(graph.has_edge(&b, &c));
        assert!(graph.has_edge(&c, &b));
    }

    #[test]
    fn add_all() {
        let top_left = Vec2::new(0., 0.);
        let top_right = Vec2::new(1., 0.);
        let bot_left = Vec2::new(0., 1.);
        let bot_right = Vec2::new(1., 1.);

        let triangle = Polygon::new(vec![top_left, bot_right, top_right]);

        let square = Polygon::new(vec![bot_left, bot_right, top_right, top_left]);

        let mut graph = PolygonGraph::new();
        graph.add_all(&triangle);
        graph.add_all(&square);

        assert_eq!(graph.num_edges(), 5);
        assert_eq!(graph.num_nodes(), 4);

        assert!(graph.has_edge(&top_left, &top_right));
        assert!(graph.has_edge(&top_right, &top_left));

        assert!(graph.has_edge(&top_left, &bot_left));
        assert!(graph.has_edge(&bot_left, &top_left));

        assert!(graph.has_edge(&bot_left, &bot_right));
        assert!(graph.has_edge(&bot_right, &bot_left));

        assert!(graph.has_edge(&bot_right, &top_right));
        assert!(graph.has_edge(&top_right, &bot_right));

        assert!(graph.has_edge(&top_left, &bot_right));
        assert!(graph.has_edge(&bot_right, &top_left));
    }

    #[test]
    fn intersect_self() {
        let first = Polygon::new(vec![
            Vec2::new(0., 0.),
            Vec2::new(0., 2.),
            Vec2::new(2., 2.),
            Vec2::new(3., 1.),
            Vec2::new(2., 0.),
        ]);

        let second = Polygon::new(vec![
            Vec2::new(2.5, -0.5),
            Vec2::new(0., 2.),
            Vec2::new(2., 2.),
            Vec2::new(2., 0.5),
            Vec2::new(2.5, 0.),
        ]);

        let mut graph = PolygonGraph::from_polygon(&first);
        graph.add_all(&second);

        graph.intersect_self();

        println!("Intersected graph:");
        println!("{:#?}", &graph);

        assert_eq!(graph.num_nodes(), 9);
        assert_eq!(graph.num_edges(), 12);

        assert!(graph.has_edge(&Vec2::new(2., 0.), &Vec2::new(2.25, 0.25)));
        assert!(graph.has_edge(&Vec2::new(3., 1.), &Vec2::new(2.25, 0.25)));
        assert!(!graph.has_edge(&Vec2::new(2., 0.), &Vec2::new(3., 1.)));
        assert!(graph.has_edge(&Vec2::new(0., 2.), &Vec2::new(2., 2.)));
        assert!(graph.has_edge(&Vec2::new(2., 2.), &Vec2::new(0., 2.)));
        assert!(graph.has_edge(&Vec2::new(0., 2.), &Vec2::new(2., 0.)));
        assert!(!graph.has_edge(&Vec2::new(0., 2.), &Vec2::new(2.5, -0.5)));
    }

    #[test]
    fn bounding_polygon() {
        let first = Polygon::new(vec![
            Vec2::new(0., 0.),
            Vec2::new(0., 2.),
            Vec2::new(2., 2.),
            Vec2::new(3., 1.),
            Vec2::new(2., 0.),
        ]);

        let second = Polygon::new(vec![
            Vec2::new(2.5, -0.5),
            Vec2::new(0., 2.),
            Vec2::new(2., 2.),
            Vec2::new(2., 0.5),
            Vec2::new(2.5, 0.),
        ]);

        let mut graph = PolygonGraph::from_polygon(&first);
        graph.add_all(&second);

        let bounding = graph.bounding_polygon();

        let num_corners = 8;
        assert_eq!(bounding.corners.len(), num_corners);

        // Run around the polygon to see if it was constructed correctly.
        let start_i = bounding
            .corners
            .iter()
            .position(|&x| x == Vec2::new(0., 0.))
            .expect("Starting vector does not exist in polygon.");

        assert_eq!(
            bounding.corners[(start_i + 1) % num_corners],
            Vec2::new(2., 0.)
        );
        assert_eq!(
            bounding.corners[(start_i + 2) % num_corners],
            Vec2::new(2.5, -0.5)
        );
        assert_eq!(
            bounding.corners[(start_i + 3) % num_corners],
            Vec2::new(2.5, 0.0)
        );
        assert_eq!(
            bounding.corners[(start_i + 4) % num_corners],
            Vec2::new(2.25, 0.25)
        );
        assert_eq!(
            bounding.corners[(start_i + 5) % num_corners],
            Vec2::new(3., 1.)
        );
        assert_eq!(
            bounding.corners[(start_i + 6) % num_corners],
            Vec2::new(2., 2.)
        );
        assert_eq!(
            bounding.corners[(start_i + 7) % num_corners],
            Vec2::new(0., 2.)
        );
    }
}