use core::convert::From;
use std::cmp::Reverse;
use std::collections::{BTreeSet, BinaryHeap};
use std::ops::Bound::{Excluded, Unbounded};
use std::ops::{Div, Neg};
use traiter::numbers::Signed;
use crate::operations::{
to_sorted_pair, DotMultiply, IntersectCrossingSegments, Orient, Square,
SquaredMetric,
};
use crate::oriented::Orientation;
use crate::relatable::Relation;
use crate::sweeping::traits::{EventsContainer, EventsQueue, SweepLine};
use crate::traits::{Elemental, Segmental};
use super::event::{
is_event_left, is_event_right, left_event_to_position,
segment_id_to_left_event, segment_id_to_right_event, Event,
};
use super::events_queue_key::EventsQueueKey;
use super::sweep_line_key::SweepLineKey;
use super::utils::all_equal;
pub(crate) struct Operation<Point> {
first_segments_count: usize,
#[allow(clippy::box_collection)]
endpoints: Box<Vec<Point>>,
events_queue_data: BinaryHeap<Reverse<EventsQueueKey<Point>>>,
#[allow(clippy::box_collection)]
opposites: Box<Vec<Event>>,
segments_ids: Vec<usize>,
sweep_line_data: BTreeSet<SweepLineKey<Point>>,
}
struct RelationState {
first_is_subset: bool,
second_is_subset: bool,
has_crossing: bool,
has_intersection: bool,
has_overlap: bool,
}
impl RelationState {
fn update<
Output: Div<Output = Output>
+ Neg<Output = Output>
+ Ord
+ Square<Output = Output>,
Point: PartialEq,
>(
&mut self,
same_start_events: &[Event],
operation: &Operation<Point>,
) where
for<'a> &'a Output: Signed,
for<'a> &'a Point: DotMultiply<Output = Output>
+ Orient
+ SquaredMetric<Output = Output>,
{
debug_assert!(!same_start_events.is_empty());
if operation.has_intersection(same_start_events) {
if !self.has_intersection {
self.has_intersection = true
}
self.detect_touch_or_overlap(same_start_events, operation);
self.detect_crossing(same_start_events, operation);
} else if operation.is_event_from_first_operand(same_start_events[0]) {
if self.first_is_subset {
self.first_is_subset = false
}
} else if self.second_is_subset {
self.second_is_subset = false
}
}
fn detect_touch_or_overlap<Point: PartialEq>(
&mut self,
same_start_events: &[Event],
operation: &Operation<Point>,
) {
let mut left_events = same_start_events
.iter()
.copied()
.filter(|&event| is_event_left(event));
if let Some(mut prev_event) = left_events.next() {
loop {
if let Some(event) = left_events.next() {
if operation.get_event_end(event)
== operation.get_event_end(prev_event)
{
if !self.has_overlap {
self.has_overlap = true;
}
if let Some(event) = left_events.next() {
prev_event = event;
} else {
break;
}
} else {
if operation.is_event_from_first_operand(prev_event) {
if self.first_is_subset {
self.first_is_subset = false
}
} else if self.second_is_subset {
self.second_is_subset = false
}
prev_event = event;
}
} else {
if operation.is_event_from_first_operand(prev_event) {
if self.first_is_subset {
self.first_is_subset = false
}
} else if self.second_is_subset {
self.second_is_subset = false
}
break;
}
}
}
}
fn detect_crossing<
Output: Div<Output = Output>
+ Neg<Output = Output>
+ Ord
+ Square<Output = Output>,
Point,
>(
&mut self,
same_start_events: &[Event],
operation: &Operation<Point>,
) where
for<'a> &'a Output: Signed,
for<'a> &'a Point: DotMultiply<Output = Output>
+ Orient
+ SquaredMetric<Output = Output>,
{
if !self.has_crossing && operation.has_crossing(same_start_events) {
self.has_crossing = true;
}
}
}
impl<Point: Ord, Segment: Clone + Segmental<Endpoint = Point>>
From<(&[&Segment], &[&Segment])> for Operation<Point>
where
for<'a> &'a Point: Orient,
{
fn from((first, second): (&[&Segment], &[&Segment])) -> Self {
let first_segments_count = first.len();
let second_segments_count = second.len();
let mut result =
Self::with_capacity(first_segments_count, second_segments_count);
result.extend(first.iter().copied().cloned());
result.extend(second.iter().copied().cloned());
result
}
}
impl<Point: Clone + PartialOrd, Scalar> Operation<Point>
where
Self: EventsQueue<Event = Event> + SweepLine<Event = Event>,
for<'a> &'a Point: Elemental<Coordinate = &'a Scalar>
+ IntersectCrossingSegments<Output = Point>
+ Orient,
Scalar: PartialOrd,
{
pub(super) fn into_relation<
Output: Div<Output = Output>
+ Neg<Output = Output>
+ Ord
+ Square<Output = Output>,
>(
mut self,
first_is_subset: bool,
second_is_subset: bool,
min_max_x: &Scalar,
) -> Relation
where
for<'a> &'a Output: Signed,
for<'a> &'a Point:
DotMultiply<Output = Output> + SquaredMetric<Output = Output>,
{
let mut state = RelationState {
first_is_subset,
second_is_subset,
has_crossing: false,
has_intersection: false,
has_overlap: false,
};
let mut first_same_start_event =
unsafe { self.pop().unwrap_unchecked() };
let mut same_start_events = vec![first_same_start_event];
self.process_event(first_same_start_event);
loop {
if let Some(event) = self.pop() {
let start = self.get_event_start(event);
if start == self.get_event_start(first_same_start_event) {
same_start_events.push(event);
} else {
state.update(&same_start_events, &self);
same_start_events.clear();
if state.has_overlap
&& !state.first_is_subset
&& !state.second_is_subset
{
break;
}
if start.x().gt(min_max_x) {
if self.is_event_from_first_operand(event) {
if state.first_is_subset {
state.first_is_subset = false
}
} else if state.second_is_subset {
state.second_is_subset = false
}
break;
}
first_same_start_event = event;
same_start_events.push(event);
}
self.process_event(event);
} else {
debug_assert!(!same_start_events.is_empty());
state.update(&same_start_events, &self);
same_start_events.clear();
break;
}
}
debug_assert!(same_start_events.is_empty());
if state.first_is_subset {
if state.second_is_subset {
Relation::Equal
} else {
Relation::Component
}
} else if state.second_is_subset {
Relation::Composite
} else if state.has_overlap {
Relation::Overlap
} else if state.has_crossing {
Relation::Cross
} else if state.has_intersection {
Relation::Touch
} else {
Relation::Disjoint
}
}
}
impl<Point: Clone + PartialOrd> Operation<Point>
where
Self: EventsQueue<Event = Event> + SweepLine<Event = Event>,
for<'a> &'a Point:
Elemental + IntersectCrossingSegments<Output = Point> + Orient,
for<'a> <&'a Point as Elemental>::Coordinate: PartialEq,
{
fn process_event(&mut self, event: Event) {
if is_event_right(event) {
let opposite_event = self.to_opposite_event(event);
debug_assert!(is_event_left(opposite_event));
if let Some(equal_segment_event) =
<Self as SweepLine>::find(self, opposite_event)
{
let (maybe_above_event, maybe_below_event) = (
self.above(equal_segment_event),
self.below(equal_segment_event),
);
self.remove(equal_segment_event);
if let (Some(above_event), Some(below_event)) =
(maybe_above_event, maybe_below_event)
{
self.detect_intersection(below_event, above_event);
}
}
} else if self.insert(event) {
debug_assert!(is_event_left(event));
let (maybe_above_event, maybe_below_event) =
(self.above(event), self.below(event));
if let Some(above_event) = maybe_above_event {
self.detect_intersection(event, above_event);
}
if let Some(below_event) = maybe_below_event {
self.detect_intersection(below_event, event);
}
}
}
}
impl<Point> EventsContainer for Operation<Point> {
type Endpoint = Point;
type Event = Event;
fn get_event_end(&self, event: Self::Event) -> &Self::Endpoint {
&self.endpoints[self.to_opposite_event(event)]
}
fn get_event_start(&self, event: Self::Event) -> &Self::Endpoint {
&self.endpoints[event]
}
}
impl<Point> Operation<Point> {
fn has_crossing<
Output: Div<Output = Output>
+ Neg<Output = Output>
+ Ord
+ Square<Output = Output>,
>(
&self,
same_start_events: &[Event],
) -> bool
where
for<'a> &'a Output: Signed,
for<'a> &'a Point: DotMultiply<Output = Output>
+ Orient
+ SquaredMetric<Output = Output>,
{
if same_start_events.len() < 4 {
return false;
}
let from_first_operand_events_count = same_start_events
.iter()
.filter(|&&event| self.is_event_from_first_operand(event))
.count();
if !(1 < from_first_operand_events_count
&& from_first_operand_events_count < same_start_events.len() - 1)
{
return false;
};
let (mut from_first_events, mut from_second_events) = (
Vec::with_capacity(same_start_events.len()),
Vec::with_capacity(same_start_events.len()),
);
for &event in same_start_events {
(if self.is_event_from_first_operand(event) {
&mut from_first_events
} else {
&mut from_second_events
})
.push(event);
}
let start = self.get_event_start(same_start_events[0]);
let base_event = unsafe {
from_second_events
.iter()
.min_by_key(|&&event| {
self.to_signed_point_event_squared_cosine(
self.get_event_end(from_second_events[0]),
event,
)
})
.copied()
.unwrap_unchecked()
};
let base_end = self.get_event_end(base_event);
let largest_angle_event = unsafe {
from_second_events
.into_iter()
.min_by_key(|&event| {
self.to_signed_point_event_squared_cosine(base_end, event)
})
.unwrap_unchecked()
};
let largest_angle_end = self.get_event_end(largest_angle_event);
let base_orientation = start.orient(base_end, largest_angle_end);
!all_equal(from_first_events.into_iter().map(|event| {
is_point_in_angle(
self.get_event_end(event),
start,
base_end,
largest_angle_end,
base_orientation,
)
}))
}
fn has_intersection(&self, same_start_events: &[Event]) -> bool {
debug_assert!(!same_start_events.is_empty());
!all_equal(
same_start_events
.iter()
.map(|&event| self.is_event_from_first_operand(event)),
)
}
fn is_event_from_first_operand(&self, event: Event) -> bool {
self.is_left_event_from_first_operand(self.to_left_event(event))
}
fn get_endpoints(&self) -> &Vec<Point> {
&self.endpoints
}
fn get_opposites(&self) -> &Vec<Event> {
&self.opposites
}
fn is_left_event_from_first_operand(&self, event: Event) -> bool {
self.left_event_to_segment_id(event) < self.first_segments_count
}
fn left_event_to_segment_id(&self, event: Event) -> usize {
self.segments_ids[left_event_to_position(event)]
}
fn to_events_queue_key(&self, event: Event) -> EventsQueueKey<Point> {
EventsQueueKey::new(
event,
self.is_event_from_first_operand(event),
self.get_endpoints(),
self.get_opposites(),
)
}
fn to_left_event(&self, event: Event) -> Event {
if is_event_left(event) {
event
} else {
self.to_opposite_event(event)
}
}
fn to_opposite_event(&self, event: Event) -> Event {
self.opposites[event]
}
fn to_signed_point_event_squared_cosine<
Output: Div<Output = Output> + Neg<Output = Output> + Square<Output = Output>,
>(
&self,
point: &Point,
event: Event,
) -> Output
where
for<'a> &'a Output: Signed,
for<'a> &'a Point:
DotMultiply<Output = Output> + SquaredMetric<Output = Output>,
{
let start = self.get_event_start(event);
let end = self.get_event_end(event);
let dot_product = DotMultiply::dot_multiply(start, point, start, end);
(if dot_product.is_positive() {
dot_product.square()
} else {
-dot_product.square()
}) / start.squared_distance_to(end)
}
fn to_sweep_line_key(&self, event: Event) -> SweepLineKey<Point> {
SweepLineKey::new(
event,
self.is_left_event_from_first_operand(event),
&self.endpoints,
&self.opposites,
)
}
}
impl<Point: Clone + PartialOrd> Operation<Point>
where
Self: EventsQueue<Event = Event> + SweepLine<Event = Event>,
for<'a> &'a Point: IntersectCrossingSegments<Output = Point> + Orient,
{
fn detect_intersection(&mut self, below_event: Event, event: Event) {
debug_assert_ne!(below_event, event);
let event_start = self.get_event_start(event);
let event_end = self.get_event_end(event);
let below_event_start = self.get_event_start(below_event);
let below_event_end = self.get_event_end(below_event);
let event_start_orientation =
below_event_end.orient(below_event_start, event_start);
let event_end_orientation =
below_event_end.orient(below_event_start, event_end);
if event_start_orientation == event_end_orientation {
if event_start_orientation == Orientation::Collinear {
debug_assert_ne!(
self.is_left_event_from_first_operand(below_event),
self.is_left_event_from_first_operand(event)
);
if event_start == below_event_start {
if event_end != below_event_end {
let (max_end_event, min_end_event) =
if event_end < below_event_end {
(below_event, event)
} else {
(event, below_event)
};
let min_end =
self.get_event_end(min_end_event).clone();
let (min_end_to_start_event, min_end_to_max_end_event) =
self.divide(max_end_event, min_end);
self.push(min_end_to_start_event);
self.push(min_end_to_max_end_event);
}
} else if event_end == below_event_end {
let (max_start_event, min_start_event) =
if event_start < below_event_start {
(below_event, event)
} else {
(event, below_event)
};
let max_start =
self.get_event_start(max_start_event).clone();
let (max_start_to_min_start_event, max_start_to_end_event) =
self.divide(min_start_event, max_start);
self.push(max_start_to_min_start_event);
self.push(max_start_to_end_event);
} else if below_event_start < event_start
&& event_start < below_event_end
{
if event_end < below_event_end {
let event_start = event_start.clone();
let event_end = event_end.clone();
self.divide_event_by_mid_segment_event_endpoints(
below_event,
event,
event_start,
event_end,
);
} else {
let (max_start, min_end) =
(event_start.clone(), below_event_end.clone());
self.divide_overlapping_events(
below_event,
event,
max_start,
min_end,
);
}
} else if event_start < below_event_start
&& below_event_start < event_end
{
if below_event_end < event_end {
let below_event_start = below_event_start.clone();
let below_event_end = below_event_end.clone();
self.divide_event_by_mid_segment_event_endpoints(
event,
below_event,
below_event_start,
below_event_end,
);
} else {
let (max_start, min_end) =
(below_event_start.clone(), event_end.clone());
self.divide_overlapping_events(
event,
below_event,
max_start,
min_end,
);
}
}
}
} else if event_start_orientation == Orientation::Collinear {
if below_event_start < event_start && event_start < below_event_end
{
let point = event_start.clone();
self.divide_event_by_midpoint(below_event, point);
}
} else if event_end_orientation == Orientation::Collinear {
if below_event_start < event_end && event_end < below_event_end {
let point = event_end.clone();
self.divide_event_by_midpoint(below_event, point);
}
} else {
let below_event_start_orientation =
event_start.orient(event_end, below_event_start);
let below_event_end_orientation =
event_start.orient(event_end, below_event_end);
if below_event_start_orientation == Orientation::Collinear {
debug_assert_ne!(
below_event_end_orientation,
Orientation::Collinear
);
if event_start < below_event_start
&& below_event_start < event_end
{
let point = below_event_start.clone();
self.divide_event_by_midpoint(event, point);
}
} else if below_event_end_orientation == Orientation::Collinear {
if event_start < below_event_end && below_event_end < event_end
{
let point = below_event_end.clone();
self.divide_event_by_midpoint(event, point);
}
} else if below_event_start_orientation
!= below_event_end_orientation
{
let cross_point =
IntersectCrossingSegments::intersect_crossing_segments(
event_start,
event_end,
below_event_start,
below_event_end,
);
self.divide_event_by_midpoint(
below_event,
cross_point.clone(),
);
self.divide_event_by_midpoint(event, cross_point);
}
}
}
fn divide_overlapping_events(
&mut self,
min_start_event: Event,
max_start_event: Event,
max_start: Point,
min_end: Point,
) {
self.divide_event_by_midpoint(max_start_event, min_end);
self.divide_event_by_midpoint(min_start_event, max_start);
}
fn divide_event_by_mid_segment_event_endpoints(
&mut self,
event: Event,
mid_segment_event: Event,
mid_segment_event_start: Point,
mid_segment_event_end: Point,
) where
Point: PartialEq,
{
debug_assert!(mid_segment_event_start
.eq(self.get_event_start(mid_segment_event)));
debug_assert!(
mid_segment_event_end.eq(self.get_event_end(mid_segment_event))
);
debug_assert!(mid_segment_event_start.ne(self.get_event_start(event)));
debug_assert!(mid_segment_event_end.ne(self.get_event_end(event)));
self.divide_event_by_midpoint(event, mid_segment_event_end);
self.divide_event_by_midpoint(event, mid_segment_event_start);
}
fn divide_event_by_midpoint(&mut self, event: Event, point: Point) {
let (point_to_event_start_event, point_to_event_end_event) =
self.divide(event, point);
self.push(point_to_event_start_event);
self.push(point_to_event_end_event);
}
}
impl<Point: Clone> Operation<Point> {
fn divide(&mut self, event: Event, mid_point: Point) -> (Event, Event) {
debug_assert!(is_event_left(event));
let opposite_event = self.to_opposite_event(event);
let mid_point_to_event_end_event: Event = self.endpoints.len();
self.segments_ids.push(self.left_event_to_segment_id(event));
self.endpoints.push(mid_point.clone());
self.opposites.push(opposite_event);
self.opposites[opposite_event] = mid_point_to_event_end_event;
let mid_point_to_event_start_event: Event = self.endpoints.len();
self.endpoints.push(mid_point);
self.opposites.push(event);
self.opposites[event] = mid_point_to_event_start_event;
debug_assert_eq!(
self.is_left_event_from_first_operand(event),
self.is_event_from_first_operand(mid_point_to_event_start_event)
);
debug_assert_eq!(
self.is_left_event_from_first_operand(event),
self.is_left_event_from_first_operand(
mid_point_to_event_end_event
)
);
(mid_point_to_event_start_event, mid_point_to_event_end_event)
}
}
impl<Point: Ord> EventsQueue for Operation<Point>
where
for<'a> &'a Point: Orient,
{
type Event = Event;
fn peek(&mut self) -> Option<Self::Event> {
self.events_queue_data.peek().map(|key| key.0.event)
}
fn pop(&mut self) -> Option<Self::Event> {
self.events_queue_data.pop().map(|key| key.0.event)
}
fn push(&mut self, event: Self::Event) {
self.events_queue_data
.push(Reverse(self.to_events_queue_key(event)));
}
}
impl<Point> SweepLine for Operation<Point>
where
SweepLineKey<Point>: Ord,
{
type Event = Event;
fn above(&self, event: Self::Event) -> Option<Self::Event> {
self.sweep_line_data
.range((Excluded(&self.to_sweep_line_key(event)), Unbounded))
.next()
.map(|key| key.event)
}
fn below(&self, event: Self::Event) -> Option<Self::Event> {
self.sweep_line_data
.range((Unbounded, Excluded(&self.to_sweep_line_key(event))))
.last()
.map(|key| key.event)
}
fn find(&self, event: Self::Event) -> Option<Self::Event> {
self.sweep_line_data
.get(&self.to_sweep_line_key(event))
.map(|key| key.event)
}
fn insert(&mut self, event: Self::Event) -> bool {
self.sweep_line_data.insert(self.to_sweep_line_key(event))
}
fn remove(&mut self, event: Self::Event) -> bool {
self.sweep_line_data.remove(&self.to_sweep_line_key(event))
}
}
impl<Point: Ord> Operation<Point>
where
for<'a> &'a Point: Orient,
{
fn extend<Segment>(&mut self, segments: impl Iterator<Item = Segment>)
where
Segment: Segmental<Endpoint = Point>,
{
let segment_id_offset = self.endpoints.len() / 2;
for (segment_index, segment) in segments.enumerate() {
let (start, end) = to_sorted_pair(segment.endpoints());
debug_assert!(start != end);
let segment_id = segment_id_offset + segment_index;
let left_event = segment_id_to_left_event(segment_id);
let right_event = segment_id_to_right_event(segment_id);
self.endpoints.push(start);
self.endpoints.push(end);
self.opposites.push(right_event);
self.opposites.push(left_event);
self.push(left_event);
self.push(right_event);
}
}
fn with_capacity(
first_segments_count: usize,
second_segments_count: usize,
) -> Self {
let segments_count = first_segments_count + second_segments_count;
let initial_events_count = 2 * segments_count;
Self {
first_segments_count,
endpoints: Box::new(Vec::with_capacity(initial_events_count)),
events_queue_data: BinaryHeap::with_capacity(initial_events_count),
opposites: Box::new(Vec::with_capacity(initial_events_count)),
segments_ids: (0..segments_count).collect(),
sweep_line_data: BTreeSet::new(),
}
}
}
fn is_point_in_angle<Point>(
point: &Point,
vertex: &Point,
first_ray_point: &Point,
second_ray_point: &Point,
angle_orientation: Orientation,
) -> bool
where
for<'a> &'a Point: Orient,
{
let first_half_orientation = vertex.orient(first_ray_point, point);
let second_half_orientation = vertex.orient(point, second_ray_point);
if first_half_orientation == Orientation::Collinear {
second_half_orientation == angle_orientation
} else if second_half_orientation == Orientation::Collinear {
first_half_orientation == angle_orientation
} else {
(first_half_orientation == second_half_orientation)
&& first_half_orientation
== (if angle_orientation == Orientation::Collinear {
Orientation::Counterclockwise
} else {
angle_orientation
})
}
}