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-rw-r--r--src/math/polygon_graph.rs462
1 files changed, 0 insertions, 462 deletions
diff --git a/src/math/polygon_graph.rs b/src/math/polygon_graph.rs
deleted file mode 100644
index 14b2b0d..0000000
--- a/src/math/polygon_graph.rs
+++ /dev/null
@@ -1,462 +0,0 @@
-use super::{LineSegment, Polygon, 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| {
- super::triplet_angle(last_vec, current_node.vec, *a)
- .partial_cmp(&super::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.)
- );
- }
-}
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