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use static_aabb2d_index::{StaticAABB2DIndex, StaticAABB2DIndexBuilder, AABB};
use crate::{
core::{
math::{
angle, angle_from_bulge, bulge_from_angle, delta_angle, dist_squared, is_left,
is_left_or_equal, point_on_circle, Vector2,
},
traits::{ControlFlow, FuzzyEq, FuzzyOrd, Real},
},
polyline::{seg_arc_radius_and_center, SelfIntersectsInclude},
};
use super::{
arc_seg_bounding_box,
internal::{
pline_boolean::polyline_boolean,
pline_intersects::{
find_intersects, visit_global_self_intersects, visit_local_self_intersects,
},
pline_offset::parallel_offset,
},
seg_bounding_box, seg_closest_point, seg_fast_approx_bounding_box, seg_length,
seg_split_at_point, BooleanOp, BooleanResult, ClosestPointResult, FindIntersectsOptions,
PlineBooleanOptions, PlineIntersectVisitor, PlineIntersectsCollection, PlineOffsetOptions,
PlineOrientation, PlineSelfIntersectOptions, PlineVertex,
};
use num_traits::cast::NumCast;
use num_traits::One;
use num_traits::ToPrimitive;
use num_traits::Zero;
/// Trait representing a readonly source of polyline data. This trait has all the methods and
/// operations that can be performed on a readonly polyline.
///
/// A polyline is a sequence of vertexes and a bool indicating whether the polyline is closed (last
/// vertex forms segment with first vertex) or open (no segment between last and first vertex). For
/// related traits see [PlineSourceMut] and [PlineCreation].
///
/// Each vertex has a 2d xy position and bulge value. See [PlineVertex] for more information.
pub trait PlineSource {
/// Numeric type used for the polyline.
type Num: Real;
/// Type used for output when invoking methods that return a new polyline.
type OutputPolyline: PlineCreation<Num = Self::Num>;
/// Total number of vertexes.
fn vertex_count(&self) -> usize;
/// Whether the polyline is closed (true) or open (false).
fn is_closed(&self) -> bool;
/// Get the vertex at given `index` position. Returns `None` if `index` out of bounds.
fn get(&self, index: usize) -> Option<PlineVertex<Self::Num>>;
/// Same as [PlineSource::get] but panics if `index` is out of bounds.
///
/// # Panics
///
/// Panics if `index` is out of bounds.
fn at(&self, index: usize) -> PlineVertex<Self::Num>;
/// Return iterator to iterate over all the polyline segments.
#[inline]
fn iter_segments(&self) -> SegmentIter<'_, Self> {
SegmentIter::new(self)
}
/// Return iterator to iterate over all the polyline vertexes.
#[inline]
fn iter_vertexes(&self) -> VertexIter<'_, Self> {
VertexIter::new(self)
}
/// Returns true if vertex count is 0.
#[inline]
fn is_empty(&self) -> bool {
self.vertex_count() == 0
}
/// Fuzzy compare with another polyline using `eps` epsilon value for fuzzy comparison of
/// vertexes.
#[inline]
fn fuzzy_eq_eps<P>(&self, other: &P, eps: Self::Num) -> bool
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.is_closed() == other.is_closed()
&& self.vertex_count() == other.vertex_count()
&& self
.iter_vertexes()
.zip(other.iter_vertexes())
.all(|(v1, v2)| v1.fuzzy_eq_eps(v2, eps))
}
/// Same as [PlineSource::fuzzy_eq_eps] but uses default `Self::Num::fuzzy_epsilon()`.
#[inline]
fn fuzzy_eq<P>(&self, other: &P) -> bool
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.fuzzy_eq_eps(other, Self::Num::fuzzy_epsilon())
}
/// Get the last vertex of the polyline or `None` if polyline is empty.
#[inline]
fn last(&self) -> Option<PlineVertex<Self::Num>> {
self.get(self.vertex_count() - 1)
}
/// Total number of segments in the polyline.
#[inline]
fn segment_count(&self) -> usize {
let vc = self.vertex_count();
if vc < 2 {
0
} else if self.is_closed() {
vc
} else {
vc - 1
}
}
/// Iterate through all the polyline segment vertex positional indexes.
///
/// Segments are represented by polyline vertex pairs, for each vertex there is an associated
/// positional index in the polyline, this method iterates through those positional indexes as
/// segment pairs starting at (0, 1) and ending at (n-2, n-1) if open polyline or (n-1, 0) if
/// closed polyline where n is the number of vertexes.
#[inline]
fn iter_segment_indexes(&self) -> PlineSegIndexIterator {
PlineSegIndexIterator::new(self.vertex_count(), self.is_closed())
}
/// Returns the next wrapping vertex index for the polyline.
///
/// If `i + 1 >= self.len()` then 0 is returned, otherwise `i + 1` is returned.
#[inline]
fn next_wrapping_index(&self, i: usize) -> usize {
let next = i + 1;
if next >= self.vertex_count() {
0
} else {
next
}
}
/// Returns the previous wrapping vertex index for the polyline.
///
/// If `i == 0` then `self.len() - 1` is returned, otherwise `i - 1` is returned.
#[inline]
fn prev_wrapping_index(&self, i: usize) -> usize {
if i == 0 {
self.vertex_count() - 1
} else {
i - 1
}
}
/// Returns the forward wrapping distance between two vertex indexes.
///
/// Assumes `start_index` is valid, debug asserts `start_index < self.len()`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new_closed();
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// assert_eq!(polyline.fwd_wrapping_dist(0, 2), 2);
/// assert_eq!(polyline.fwd_wrapping_dist(3, 1), 2);
/// ```
#[inline]
fn fwd_wrapping_dist(&self, start_index: usize, end_index: usize) -> usize {
let vc = self.vertex_count();
debug_assert!(
start_index < vc,
"start_index is out of polyline range bounds"
);
if start_index <= end_index {
end_index - start_index
} else {
vc - start_index + end_index
}
}
/// Returns the vertex index after applying `offset` to `start_index` in a wrapping manner.
///
/// Assumes `start_index` is valid, debug asserts `start_index < self.len()`.
/// Assumes `offset` does not wrap multiple times, debug asserts `offset <= self.len()`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new_closed();
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// polyline.add(0.0, 0.0, 0.0);
/// assert_eq!(polyline.fwd_wrapping_index(0, 2), 2);
/// assert_eq!(polyline.fwd_wrapping_index(1, 2), 3);
/// assert_eq!(polyline.fwd_wrapping_index(1, 3), 0);
/// assert_eq!(polyline.fwd_wrapping_index(2, 3), 1);
/// ```
#[inline]
fn fwd_wrapping_index(&self, start_index: usize, offset: usize) -> usize {
let vc = self.vertex_count();
debug_assert!(
start_index < vc,
"start_index is out of polyline range bounds"
);
debug_assert!(offset <= vc, "offset wraps multiple times");
let sum = start_index + offset;
if sum < vc {
sum
} else {
sum - vc
}
}
/// Compute the XY extents of the polyline.
///
/// Returns `None` if polyline has less than 2 vertexes.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// let mut polyline = Polyline::new();
/// assert_eq!(polyline.extents(), None);
/// polyline.add(1.0, 1.0, 1.0);
/// assert_eq!(polyline.extents(), None);
///
/// polyline.add(3.0, 1.0, 1.0);
/// let extents = polyline.extents().unwrap();
/// assert!(extents.min_x.fuzzy_eq(1.0));
/// assert!(extents.min_y.fuzzy_eq(0.0));
/// assert!(extents.max_x.fuzzy_eq(3.0));
/// assert!(extents.max_y.fuzzy_eq(1.0));
///
/// polyline.set_is_closed(true);
/// let extents = polyline.extents().unwrap();
/// assert!(extents.min_x.fuzzy_eq(1.0));
/// assert!(extents.min_y.fuzzy_eq(0.0));
/// assert!(extents.max_x.fuzzy_eq(3.0));
/// assert!(extents.max_y.fuzzy_eq(2.0));
/// ```
fn extents(&self) -> Option<AABB<Self::Num>> {
if self.segment_count() == 0 {
return None;
}
let v1 = self.at(0);
let mut result = AABB::new(v1.x, v1.y, v1.x, v1.y);
for (v1, v2) in self.iter_segments() {
if v1.bulge_is_zero() {
// line segment, just look at end of line point (result seeded with first point)
if v2.x < result.min_x {
result.min_x = v2.x;
} else if v2.x > result.max_x {
result.max_x = v2.x;
}
if v2.y < result.min_y {
result.min_y = v2.y;
} else if v2.y > result.max_y {
result.max_y = v2.y;
}
continue;
}
// else arc segment
let arc_extents = arc_seg_bounding_box(v1, v2);
result.min_x = num_traits::real::Real::min(result.min_x, arc_extents.min_x);
result.min_y = num_traits::real::Real::min(result.min_y, arc_extents.min_y);
result.max_x = num_traits::real::Real::max(result.max_x, arc_extents.max_x);
result.max_y = num_traits::real::Real::max(result.max_y, arc_extents.max_y);
}
Some(result)
}
/// Returns the total path length of the polyline.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// let mut polyline: Polyline = Polyline::new();
/// // open polyline half circle
/// polyline.add(0.0, 0.0, 1.0);
/// polyline.add(2.0, 0.0, 1.0);
/// assert!(polyline.path_length().fuzzy_eq(std::f64::consts::PI));
/// // close into full circle
/// polyline.set_is_closed(true);
/// assert!(polyline.path_length().fuzzy_eq(2.0 * std::f64::consts::PI));
/// ```
#[inline]
fn path_length(&self) -> Self::Num {
self.iter_segments()
.fold(Self::Num::zero(), |acc, (v1, v2)| acc + seg_length(v1, v2))
}
/// Compute the closed signed area of the polyline.
///
/// If [PlineSource::is_closed] is false (open polyline) then 0.0 is always returned.
/// The area is signed such that if the polyline direction is counter clockwise
/// then the area is positive, otherwise it is negative.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// let mut polyline: Polyline = Polyline::new();
/// assert!(polyline.area().fuzzy_eq(0.0));
/// polyline.add(1.0, 1.0, 1.0);
/// assert!(polyline.area().fuzzy_eq(0.0));
///
/// polyline.add(3.0, 1.0, 1.0);
/// // polyline is still open so area is 0
/// assert!(polyline.area().fuzzy_eq(0.0));
/// polyline.set_is_closed(true);
/// assert!(polyline.area().fuzzy_eq(std::f64::consts::PI));
/// polyline.invert_direction_mut();
/// assert!(polyline.area().fuzzy_eq(-std::f64::consts::PI));
/// ```
fn area(&self) -> Self::Num {
use num_traits::real::Real;
if !self.is_closed() {
return Self::Num::zero();
}
// Implementation notes:
// Using the shoelace formula (https://en.wikipedia.org/wiki/Shoelace_formula) modified to
// support arcs defined by a bulge value. The shoelace formula returns a negative value for
// clockwise oriented polygons and positive value for counter clockwise oriented polygons.
// The area of each circular segment defined by arcs is then added if it is a counter
// clockwise arc or subtracted if it is a clockwise arc. The area of the circular segments
// are computed by finding the area of the arc sector minus the area of the triangle
// defined by the chord and center of circle.
// See https://en.wikipedia.org/wiki/Circular_segment
let mut double_total_area = Self::Num::zero();
for (v1, v2) in self.iter_segments() {
double_total_area = double_total_area + v1.x * v2.y - v1.y * v2.x;
if !v1.bulge_is_zero() {
// add arc segment area
let b = v1.bulge.abs();
let sweep_angle = angle_from_bulge(b);
let triangle_base = (v2.pos() - v1.pos()).length();
let radius = triangle_base * ((b * b + Self::Num::one()) / (Self::Num::four() * b));
let sagitta = b * triangle_base / Self::Num::two();
let triangle_height = radius - sagitta;
let double_sector_area = sweep_angle * radius * radius;
let double_triangle_area = triangle_base * triangle_height;
let mut double_arc_area = double_sector_area - double_triangle_area;
if v1.bulge_is_neg() {
double_arc_area = -double_arc_area;
}
double_total_area = double_total_area + double_arc_area;
}
}
double_total_area / Self::Num::two()
}
/// Returns the orientation of the polyline.
///
/// This method just uses the [PlineSource::area] function to determine directionality of a closed
/// polyline which may not yield a useful result if the polyline has self intersects.
fn orientation(&self) -> PlineOrientation {
if !self.is_closed() {
return PlineOrientation::Open;
}
if self.area() < Self::Num::zero() {
PlineOrientation::Clockwise
} else {
PlineOrientation::CounterClockwise
}
}
/// Remove all repeat position vertexes from the polyline.
///
/// Returns `None` to avoid allocation and copy in the case that no vertexes are removed.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new_closed();
/// polyline.add(2.0, 2.0, 0.5);
/// polyline.add(2.0, 2.0, 1.0);
/// polyline.add(3.0, 3.0, 1.0);
/// polyline.add(3.0, 3.0, 0.5);
/// let result = polyline.remove_repeat_pos(1e-5).expect("repeat position vertexes were removed");
/// assert_eq!(result.vertex_count(), 2);
/// assert!(result[0].fuzzy_eq(PlineVertex::new(2.0, 2.0, 1.0)));
/// assert!(result[1].fuzzy_eq(PlineVertex::new(3.0, 3.0, 0.5)));
/// ```
fn remove_repeat_pos(&self, pos_equal_eps: Self::Num) -> Option<Self::OutputPolyline> {
if self.vertex_count() < 2 {
return None;
}
let mut result: Option<Self::OutputPolyline> = None;
let mut prev_pos = self.at(0).pos();
for (i, v) in self.iter_vertexes().enumerate().skip(1) {
let is_repeat = v.pos().fuzzy_eq_eps(prev_pos, pos_equal_eps);
if is_repeat {
// repeat position just update bulge (remove vertex by not adding it to result)
let r = result.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(self.iter_vertexes().take(i), self.is_closed())
});
let last = r.last().unwrap();
r.set_last(last.with_bulge(v.bulge));
} else {
if let Some(ref mut r) = result {
// not repeat position and result is initialized
r.add_vertex(v);
}
// else not repeat position and result is not initialized, do nothing
// update previous position for next iteration
prev_pos = v.pos();
}
}
// check if is_closed and last repeats position on first
if self.is_closed()
&& self
.last()
.unwrap()
.pos()
.fuzzy_eq_eps(self.at(0).pos(), pos_equal_eps)
{
result
.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(self.iter_vertexes(), self.is_closed())
})
.remove_last();
}
result
}
/// Remove all redundant vertexes from the polyline.
///
/// Redundant vertexes can arise with multiple vertexes on top of each other, along a straight
/// line, or forming a concentric arc with sweep angle less than or equal to PI.
///
/// Returns `None` to avoid allocation and copy in the case that no vertexes are removed.
///
/// # Examples
///
/// ### Removing repeat vertexes along a line
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new_closed();
/// polyline.add(2.0, 2.0, 0.0);
/// polyline.add(3.0, 3.0, 0.0);
/// polyline.add(3.0, 3.0, 0.0);
/// polyline.add(4.0, 4.0, 0.0);
/// polyline.add(2.0, 4.0, 0.0);
/// let result = polyline.remove_redundant(1e-5).expect("redundant vertexes were removed");
/// assert_eq!(result.vertex_count(), 3);
/// assert!(result.is_closed());
/// assert!(result[0].fuzzy_eq(PlineVertex::new(2.0, 2.0, 0.0)));
/// assert!(result[1].fuzzy_eq(PlineVertex::new(4.0, 4.0, 0.0)));
/// assert!(result[2].fuzzy_eq(PlineVertex::new(2.0, 4.0, 0.0)));
/// ```
///
/// ### Simplifying a circle defined by 5 vertexes
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let bulge = (std::f64::consts::PI / 8.0).tan();
/// let mut polyline = Polyline::new_closed();
/// polyline.add(-0.5, 0.0, bulge);
/// polyline.add(0.0, -0.5, bulge);
/// // repeat vertex thrown in
/// polyline.add(0.0, -0.5, bulge);
/// polyline.add(0.5, 0.0, bulge);
/// polyline.add(0.0, 0.5, bulge);
/// let result = polyline.remove_redundant(1e-5).expect("redundant vertexes were removed");
/// assert_eq!(result.vertex_count(), 2);
/// assert!(result.is_closed());
/// assert!(result[0].fuzzy_eq(PlineVertex::new(-0.5, 0.0, 1.0)));
/// assert!(result[1].fuzzy_eq(PlineVertex::new(0.5, 0.0, 1.0)));
/// ```
fn remove_redundant(&self, pos_equal_eps: Self::Num) -> Option<Self::OutputPolyline> {
use num_traits::real::Real;
let vc = self.vertex_count();
if vc < 2 {
return None;
}
if vc == 2 {
let v1 = self.at(0);
let v2 = self.at(1);
if v1.pos().fuzzy_eq_eps(v2.pos(), pos_equal_eps) {
let mut result = Self::OutputPolyline::with_capacity(1, self.is_closed());
result.add_vertex(v2); // take bulge from last vertex
return Some(result);
}
return None;
}
// helper to test if v1->v2->v3 are collinear and all going in the same direction
let is_collinear_same_dir =
|v1: &PlineVertex<Self::Num>,
v2: &PlineVertex<Self::Num>,
v3: &PlineVertex<Self::Num>| {
// check if v2 on top of v3 (considered collinear for the purposes of discarding v2)
if v2.pos().fuzzy_eq_eps(v3.pos(), pos_equal_eps) {
return true;
}
let collinear =
(v1.x * (v2.y - v3.y) + v2.x * (v3.y - v1.y) + v3.x * (v1.y - v2.y))
.fuzzy_eq_zero_eps(pos_equal_eps);
let same_direction =
(v3.pos() - v2.pos()).dot(v2.pos() - v1.pos()) > -pos_equal_eps;
collinear && same_direction
};
let mut v1 = self.at(0);
let mut v2 = self.at(1);
// remove all repeat positions at the start
let mut i = 2;
while v1.pos().fuzzy_eq_eps(v2.pos(), pos_equal_eps) {
v1.bulge = v2.bulge;
// check for reaching the end of polyline
if i >= vc {
break;
}
v2 = self.at(i);
i += 1;
}
let mut result: Option<Self::OutputPolyline> = if i == 2 {
None
} else {
let mut pl = Self::OutputPolyline::with_capacity(1, self.is_closed());
pl.add_vertex(v1);
Some(pl)
};
// if end is reached return polyline with the only vertex
if i >= vc {
return result;
}
let mut v1_v2_arc: Option<(Self::Num, Vector2<Self::Num>)> = None;
let mut v1_bulge_is_zero = v1.bulge_is_zero();
let mut v2_bulge_is_zero = v2.bulge_is_zero();
let mut v1_bulge_is_pos = v1.bulge_is_pos();
let mut v2_bulge_is_pos = v2.bulge_is_pos();
let iter_count = if self.is_closed() { vc - 1 } else { vc - 2 };
enum RemoveRedundantCase<U>
where
U: Real,
{
/// Include the vertex in the result.
IncludeVertex,
/// Discard the current vertex.
DiscardVertex,
/// Discard the current vertex and update the previous vertex bulge with the value computed.
UpdateV1BulgeForArc(U),
}
// loop through processing/considering to discard the middle vertex v2
for (i, v3) in self
.iter_vertexes()
.cycle()
.enumerate()
.skip(i)
.take(iter_count)
{
use RemoveRedundantCase::*;
let state: RemoveRedundantCase<Self::Num> =
if v2.pos().fuzzy_eq_eps(v3.pos(), pos_equal_eps) {
// repeat position, just update bulge
DiscardVertex
} else if v1_bulge_is_zero && v2_bulge_is_zero {
// two line segments in a row, check if collinear
let is_final_vertex_for_open = !self.is_closed() && i == vc;
if !is_final_vertex_for_open && is_collinear_same_dir(&v1, &v2, &v3) {
DiscardVertex
} else {
IncludeVertex
}
} else if !v1_bulge_is_zero
&& !v2_bulge_is_zero
&& (v1_bulge_is_pos == v2_bulge_is_pos)
&& !v2.pos().fuzzy_eq_eps(v3.pos(), pos_equal_eps)
{
// two arc segments in a row with same orientation, check if v2 can be removed by
// updating v1 bulge
let &mut (arc_radius1, arc_center1) =
v1_v2_arc.get_or_insert_with(|| seg_arc_radius_and_center(v1, v2));
let (arc_radius2, arc_center2) = seg_arc_radius_and_center(v2, v3);
if arc_radius1.fuzzy_eq_eps(arc_radius2, pos_equal_eps)
&& arc_center1.fuzzy_eq_eps(arc_center2, pos_equal_eps)
{
let angle1 = angle(arc_center1, v1.pos());
let angle2 = angle(arc_center1, v2.pos());
let angle3 = angle(arc_center1, v3.pos());
let total_sweep =
delta_angle(angle1, angle2).abs() + delta_angle(angle2, angle3).abs();
let avg_radius = (arc_radius1 + arc_radius2) / Self::Num::two();
// can only combine vertexes if total sweep will still be less than PI
// multiplying by average radius for fuzzy compare to have numbers in scale
// of epsilon
if (avg_radius * total_sweep)
.fuzzy_lt_eps(avg_radius * Self::Num::pi(), pos_equal_eps)
{
let bulge = if v1_bulge_is_pos {
bulge_from_angle(total_sweep)
} else {
-bulge_from_angle(total_sweep)
};
UpdateV1BulgeForArc(bulge)
} else {
IncludeVertex
}
} else {
IncludeVertex
}
} else {
IncludeVertex
};
let copy_self = || {
Self::OutputPolyline::from_iter(self.iter_vertexes().take(i - 1), self.is_closed())
};
match state {
IncludeVertex => {
if let Some(ref mut r) = result {
r.add_vertex(v2);
}
v1 = v2;
v2 = v3;
v1_v2_arc = None;
v1_bulge_is_zero = v2_bulge_is_zero;
v2_bulge_is_zero = v3.bulge_is_zero();
v1_bulge_is_pos = v2_bulge_is_pos;
v2_bulge_is_pos = v3.bulge_is_pos();
}
DiscardVertex => {
if result.is_none() {
result = Some(copy_self());
}
v2 = v3;
v1_v2_arc = None;
v2_bulge_is_zero = v3.bulge_is_zero();
v2_bulge_is_pos = v3.bulge_is_pos();
}
UpdateV1BulgeForArc(bulge) => {
let p = result.get_or_insert_with(copy_self);
let last = p.last().unwrap();
p.set_last(last.with_bulge(bulge));
v1.bulge = bulge;
v2 = v3;
v1_bulge_is_zero = v2_bulge_is_zero;
v2_bulge_is_zero = v3.bulge_is_zero();
v1_bulge_is_pos = v2_bulge_is_pos;
v2_bulge_is_pos = v3.bulge_is_pos();
}
}
}
if self.is_closed() {
// handle wrap around middle vertex at start
match result.as_mut() {
Some(pl) => {
if pl
.last()
.unwrap()
.pos()
.fuzzy_eq_eps(pl.at(0).pos(), pos_equal_eps)
{
pl.remove_last();
}
}
None => {
if self
.last()
.unwrap()
.pos()
.fuzzy_eq_eps(self.at(0).pos(), pos_equal_eps)
{
// last repeats position on first
result
.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(
self.iter_vertexes(),
self.is_closed(),
)
})
.remove_last();
}
}
}
// v1 => last
// v2 => first
// v3 => second
let v3 = match result.as_ref() {
Some(pl) => pl.at(1),
None => self.at(1),
};
if v1_bulge_is_zero && v2_bulge_is_zero && is_collinear_same_dir(&v1, &v2, &v3) {
// first vertex is in middle of line
let p = result.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(self.iter_vertexes(), self.is_closed())
});
let last = p.remove_last();
p.set_vertex(0, last);
} else if !v1_bulge_is_zero
&& !v2_bulge_is_zero
&& (v1_bulge_is_pos == v2_bulge_is_pos)
&& !v2.pos().fuzzy_eq_eps(v3.pos(), pos_equal_eps)
{
// check if arc can be simplified by removing first vertex
let &mut (arc_radius1, arc_center1) =
v1_v2_arc.get_or_insert_with(|| seg_arc_radius_and_center(v1, v2));
let (arc_radius2, arc_center2) = seg_arc_radius_and_center(v2, v3);
if arc_radius1.fuzzy_eq_eps(arc_radius2, pos_equal_eps)
&& arc_center1.fuzzy_eq_eps(arc_center2, pos_equal_eps)
{
let angle1 = angle(arc_center1, v1.pos());
let angle2 = angle(arc_center1, v2.pos());
let angle3 = angle(arc_center1, v3.pos());
let total_sweep =
delta_angle(angle1, angle2).abs() + delta_angle(angle2, angle3).abs();
let avg_radius = (arc_radius1 + arc_radius2) / Self::Num::two();
if (avg_radius * total_sweep)
.fuzzy_lt_eps(avg_radius * Self::Num::pi(), pos_equal_eps)
{
let bulge = if v1_bulge_is_pos {
bulge_from_angle(total_sweep)
} else {
-bulge_from_angle(total_sweep)
};
let p = result.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(self.iter_vertexes(), self.is_closed())
});
let last = p.remove_last();
p.set_vertex(0, last.with_bulge(bulge));
}
}
}
} else {
// handle adding last vertex
match result.as_mut() {
Some(pl) => {
pl.add_or_replace_vertex(self.last().unwrap(), pos_equal_eps);
}
None => {
if self.at(vc - 2).fuzzy_eq_eps(self.at(vc - 1), pos_equal_eps) {
result
.get_or_insert_with(|| {
Self::OutputPolyline::from_iter(
self.iter_vertexes(),
self.is_closed(),
)
})
.remove_last();
}
}
}
}
result
}
/// Rotates the vertexes in a closed polyline such that the first vertex's position is at
/// `point`. `start_index` indicates which segment `point` lies on before rotation. This does
/// not change the shape of the polyline curve. `pos_equal_eps` is epsilon value used for
/// comparing the positions of points. `None` is returned if the polyline is not closed, the
/// polyline length is less than 2, or the `start_index` is out of bounds.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::core::math::*;
/// let mut polyline = Polyline::new_closed();
/// assert!(matches!(polyline.rotate_start(0, Vector2::new(0.0, 0.0), 1e-5), None));
/// polyline.add(0.0, 0.0, 0.0);
/// assert!(matches!(polyline.rotate_start(0, Vector2::new(0.0, 0.0), 1e-5), None));
/// polyline.add(1.0, 0.0, 0.0);
/// polyline.add(1.0, 1.0, 0.0);
/// polyline.add(0.0, 1.0, 0.0);
///
/// let rot = polyline.rotate_start(0, Vector2::new(0.5, 0.0), 1e-5).unwrap();
/// let mut expected_rot = Polyline::new_closed();
/// expected_rot.add(0.5, 0.0, 0.0);
/// expected_rot.add(1.0, 0.0, 0.0);
/// expected_rot.add(1.0, 1.0, 0.0);
/// expected_rot.add(0.0, 1.0, 0.0);
/// expected_rot.add(0.0, 0.0, 0.0);
/// assert!(rot.fuzzy_eq(&expected_rot));
/// ```
fn rotate_start(
&self,
start_index: usize,
point: Vector2<Self::Num>,
pos_equal_eps: Self::Num,
) -> Option<Self::OutputPolyline> {
let vc = self.vertex_count();
if !self.is_closed() || vc < 2 || start_index > vc - 1 {
return None;
}
let wrapping_vertexes_starting_at = |start: usize| {
self.iter_vertexes()
.skip(start)
.take(vc - start)
.chain(self.iter_vertexes().take(start))
};
let mut result = Self::OutputPolyline::with_capacity(0, true);
let start_v = self.at(start_index);
if start_v.pos().fuzzy_eq_eps(point, pos_equal_eps) {
// point lies on top of start index vertex
result.extend_vertexes(wrapping_vertexes_starting_at(start_index))
} else {
// check if it's at the end of the segment, if it is then use that next index
let next_index = self.next_wrapping_index(start_index);
if point.fuzzy_eq_eps(self.at(next_index).pos(), pos_equal_eps) {
result.reserve(vc);
result.extend_vertexes(wrapping_vertexes_starting_at(next_index));
} else {
// must split at the point
result.reserve(vc + 1);
let split = seg_split_at_point(
self.at(start_index),
self.at(next_index),
point,
pos_equal_eps,
);
result.add_vertex(split.split_vertex);
result.extend_vertexes(wrapping_vertexes_starting_at(next_index));
result.set_last(split.updated_start);
}
}
Some(result)
}
/// Creates a fast approximate spatial index of all the polyline segments.
///
/// The starting vertex index position is used as the key to the segment bounding box in the
/// `StaticAABB2DIndex`. The bounding boxes are guaranteed to be no smaller than the actual
/// bounding box of the segment but may be larger, this is done for performance. If you want the
/// actual bounding box index use [PlineSource::create_aabb_index] instead.
///
/// Returns `None` if polyline vertex count is less than 2 or an error occurs in constructing
/// the spatial index.
fn create_approx_aabb_index(&self) -> Option<StaticAABB2DIndex<Self::Num>> {
let vc = self.vertex_count();
if vc < 2 {
return None;
}
let seg_count = if self.is_closed() { vc } else { vc - 1 };
let mut builder = StaticAABB2DIndexBuilder::new(seg_count);
for (v1, v2) in self.iter_segments() {
let approx_aabb = seg_fast_approx_bounding_box(v1, v2);
builder.add(
approx_aabb.min_x,
approx_aabb.min_y,
approx_aabb.max_x,
approx_aabb.max_y,
);
}
builder.build().ok()
}
/// Creates a spatial index of all the polyline segments.
///
/// The starting vertex index position is used as the key to the segment bounding box in the
/// `StaticAABB2DIndex`. The bounding boxes are the actual bounding box of the segment, for
/// performance reasons you may want to use [PlineSource::create_approx_aabb_index].
///
/// Returns `None` if polyline vertex count is less than 2 or an error occurs in constructing
/// the spatial index.
fn create_aabb_index(&self) -> Option<StaticAABB2DIndex<Self::Num>> {
let vc = self.vertex_count();
if vc < 2 {
return None;
}
let seg_count = if self.is_closed() { vc } else { vc - 1 };
let mut builder = StaticAABB2DIndexBuilder::new(seg_count);
for (v1, v2) in self.iter_segments() {
let approx_aabb = seg_bounding_box(v1, v2);
builder.add(
approx_aabb.min_x,
approx_aabb.min_y,
approx_aabb.max_x,
approx_aabb.max_y,
);
}
builder.build().ok()
}
/// Find the closest segment point on a polyline to a `point` given.
///
/// If the polyline is empty then `None` is returned.
///
/// `pos_equal_eps` is epsilon value used for fuzzy float comparisons.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::core::math::*;
/// let mut polyline: Polyline = Polyline::new();
/// assert!(matches!(polyline.closest_point(Vector2::zero(), 1e-5), None));
/// polyline.add(1.0, 1.0, 1.0);
/// let result = polyline.closest_point(Vector2::new(1.0, 0.0), 1e-5).unwrap();
/// assert_eq!(result.seg_start_index, 0);
/// assert!(result.seg_point.fuzzy_eq(polyline[0].pos()));
/// assert!(result.distance.fuzzy_eq(1.0));
/// ```
fn closest_point(
&self,
point: Vector2<Self::Num>,
pos_equal_eps: Self::Num,
) -> Option<ClosestPointResult<Self::Num>> {
use num_traits::real::Real;
if self.is_empty() {
return None;
}
let mut result = ClosestPointResult {
seg_start_index: 0,
seg_point: self.at(0).pos(),
distance: Real::max_value(),
};
if self.vertex_count() == 1 {
result.distance = (result.seg_point - point).length();
return Some(result);
}
let mut dist_squared = Real::max_value();
for (i, j) in self.iter_segment_indexes() {
let v1 = self.at(i);
let v2 = self.at(j);
let cp = seg_closest_point(v1, v2, point, pos_equal_eps);
let diff_v = point - cp;
let dist2 = diff_v.length_squared();
if dist2 < dist_squared {
result.seg_start_index = i;
result.seg_point = cp;
dist_squared = dist2;
}
}
result.distance = dist_squared.sqrt();
Some(result)
}
/// Calculate the winding number for a `point` relative to the polyline.
///
/// The winding number calculates the number of turns/windings around a point that the polyline
/// path makes. For a closed polyline without self intersects there are only three
/// possibilities:
///
/// * -1 (polyline winds around point clockwise)
/// * 0 (point is outside the polyline)
/// * 1 (polyline winds around the point counter clockwise).
///
/// For a self intersecting closed polyline the winding number may be less than -1 (if the
/// polyline winds around the point more than once in the counter clockwise direction) or
/// greater than 1 (if the polyline winds around the point more than once in the clockwise
/// direction).
///
/// This function always returns 0 if polyline [PlineSource::is_closed] is false.
///
/// If the point lies directly on top of one of the polyline segments the result is not defined
/// (it may return any integer). To handle the case of the point lying directly on the polyline
/// [PlineSource::closest_point] may be used to check if the distance from the point to the
/// polyline is zero.
///
/// # Examples
///
/// ### Polyline without self intersects
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::math::*;
/// let mut polyline: Polyline = Polyline::new_closed();
/// polyline.add(0.0, 0.0, 1.0);
/// polyline.add(2.0, 0.0, 1.0);
/// assert_eq!(polyline.winding_number(Vector2::new(1.0, 0.0)), 1);
/// assert_eq!(polyline.winding_number(Vector2::new(0.0, 2.0)), 0);
/// polyline.invert_direction_mut();
/// assert_eq!(polyline.winding_number(Vector2::new(1.0, 0.0)), -1);
/// ```
///
/// ### Multiple windings with self intersecting polyline
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::math::*;
/// let mut polyline: Polyline = Polyline::new_closed();
/// polyline.add(0.0, 0.0, 1.0);
/// polyline.add(2.0, 0.0, 1.0);
/// polyline.add(0.0, 0.0, 1.0);
/// polyline.add(4.0, 0.0, 1.0);
/// assert_eq!(polyline.winding_number(Vector2::new(1.0, 0.0)), 2);
/// assert_eq!(polyline.winding_number(Vector2::new(-1.0, 0.0)), 0);
/// polyline.invert_direction_mut();
/// assert_eq!(polyline.winding_number(Vector2::new(1.0, 0.0)), -2);
/// ```
fn winding_number(&self, point: Vector2<Self::Num>) -> i32 {
if !self.is_closed() || self.vertex_count() < 2 {
return 0;
}
// Helper function for processing a line segment when computing the winding number.
let process_line_winding =
|v1: PlineVertex<Self::Num>, v2: PlineVertex<Self::Num>, point: Vector2<Self::Num>| {
let mut result = 0;
if v1.y <= point.y {
if v2.y > point.y && is_left(v1.pos(), v2.pos(), point) {
// left and upward crossing
result += 1;
}
} else if v2.y <= point.y && !is_left(v1.pos(), v2.pos(), point) {
// right an downward crossing
result -= 1;
}
result
};
// Helper function for processing an arc segment when computing the winding number.
let process_arc_winding =
|v1: PlineVertex<Self::Num>, v2: PlineVertex<Self::Num>, point: Vector2<Self::Num>| {
let is_ccw = v1.bulge_is_pos();
let point_is_left = if is_ccw {
is_left(v1.pos(), v2.pos(), point)
} else {
is_left_or_equal(v1.pos(), v2.pos(), point)
};
let dist_to_arc_center_less_than_radius = || {
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
let dist2 = dist_squared(arc_center, point);
dist2 < arc_radius * arc_radius
};
let mut result = 0;
if v1.y <= point.y {
if v2.y > point.y {
// upward crossing of arc chord
if is_ccw {
if point_is_left {
// counter clockwise arc left of chord
result += 1;
} else {
// counter clockwise arc right of chord
if dist_to_arc_center_less_than_radius() {
result += 1;
}
}
} else if point_is_left {
// clockwise arc left of chord
if !dist_to_arc_center_less_than_radius() {
result += 1;
}
// else clockwise arc right of chord, no crossing
}
} else {
// not crossing arc chord and chord is below, check if point is inside arc sector
if is_ccw
&& !point_is_left
&& v2.x < point.x
&& point.x < v1.x
&& dist_to_arc_center_less_than_radius()
{
result += 1;
} else if !is_ccw
&& point_is_left
&& v1.x < point.x
&& point.x < v2.x
&& dist_to_arc_center_less_than_radius()
{
result -= 1;
}
}
} else if v2.y <= point.y {
// downward crossing of arc chord
if is_ccw {
if !point_is_left {
// counter clockwise arc right of chord
if !dist_to_arc_center_less_than_radius() {
result -= 1;
}
}
// else counter clockwise arc left of chord, no crossing
} else if point_is_left {
// clockwise arc left of chord
if dist_to_arc_center_less_than_radius() {
result -= 1;
}
} else {
// clockwise arc right of chord
result -= 1;
}
} else {
// not crossing arc chord and chord is above, check if point is inside arc sector
if is_ccw
&& !point_is_left
&& v1.x < point.x
&& point.x < v2.x
&& dist_to_arc_center_less_than_radius()
{
result += 1;
} else if !is_ccw
&& point_is_left
&& v2.x < point.x
&& point.x < v1.x
&& dist_to_arc_center_less_than_radius()
{
result -= 1;
}
}
result
};
let mut winding = 0;
for (v1, v2) in self.iter_segments() {
if v1.bulge_is_zero() {
winding += process_line_winding(v1, v2, point);
} else {
winding += process_arc_winding(v1, v2, point);
}
}
winding
}
/// Returns a new polyline with all arc segments converted to line segments with some
/// `error_distance` or None if T fails to cast to or from usize.
///
/// `error_distance` is the maximum distance from any line segment to the arc it is
/// approximating. Line segments are circumscribed by the arc (all line end points lie on the
/// arc path).
fn arcs_to_approx_lines(&self, error_distance: Self::Num) -> Option<Self::OutputPolyline> {
use num_traits::real::Real;
let mut result = Self::OutputPolyline::with_capacity(0, self.is_closed());
// catch case where polyline is empty since we may index into the last vertex later
if self.is_empty() {
return Some(result);
}
let abs_error = error_distance.abs();
for (v1, v2) in self.iter_segments() {
if v1.bulge_is_zero() {
result.add_vertex(v1);
continue;
}
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
if arc_radius.fuzzy_lt(error_distance) {
result.add(v1.x, v1.y, Self::Num::zero());
continue;
}
let start_angle = angle(arc_center, v1.pos());
let end_angle = angle(arc_center, v2.pos());
let angle_diff = delta_angle(start_angle, end_angle).abs();
let seg_sub_angle =
Self::Num::two() * (Self::Num::one() - abs_error / arc_radius).acos().abs();
let seg_count = (angle_diff / seg_sub_angle).ceil();
// create angle offset such that all lines have an equal part of the arc
let seg_angle_offset = if v1.bulge_is_neg() {
-angle_diff / seg_count
} else {
angle_diff / seg_count
};
// add start vertex
result.add(v1.x, v1.y, Self::Num::zero());
let usize_count = seg_count.to_usize()?;
// add all vertex points along arc
for i in 1..usize_count {
let angle_pos = <Self::Num as NumCast>::from(i)?;
let angle = angle_pos * seg_angle_offset + start_angle;
let pos = point_on_circle(arc_radius, arc_center, angle);
result.add(pos.x, pos.y, Self::Num::zero());
}
}
if !self.is_closed() {
// add the final missing vertex in the case that the polyline is not closed
result.add_vertex(self.last().unwrap());
}
Some(result)
}
/// Visit self intersects of the polyline using default options.
#[inline]
fn visit_self_intersects<C, V>(&self, visitor: &mut V) -> C
where
C: ControlFlow,
V: PlineIntersectVisitor<Self::Num, C>,
{
self.visit_self_intersects_opt(visitor, &Default::default())
}
/// Visit self intersects of the polyline using options provided.
fn visit_self_intersects_opt<C, V>(
&self,
visitor: &mut V,
options: &PlineSelfIntersectOptions<Self::Num>,
) -> C
where
C: ControlFlow,
V: PlineIntersectVisitor<Self::Num, C>,
{
if self.vertex_count() < 2 {
return C::continuing();
}
if options.include == SelfIntersectsInclude::Local {
// local intersects only
return visit_local_self_intersects(self, visitor, options.pos_equal_eps);
}
let constructed_index;
let index = if let Some(x) = options.aabb_index {
x
} else {
constructed_index = self.create_approx_aabb_index().unwrap();
&constructed_index
};
if options.include == SelfIntersectsInclude::Global {
// global intersects only
return visit_global_self_intersects(self, index, visitor, options.pos_equal_eps);
}
// else all intersects
try_cf!(visit_local_self_intersects(
self,
visitor,
options.pos_equal_eps
));
visit_global_self_intersects(self, index, visitor, options.pos_equal_eps)
}
/// Find all intersects between two polylines using default options.
#[inline]
fn find_intersects<P>(&self, other: &P) -> PlineIntersectsCollection<Self::Num>
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.find_intersects_opt(other, &Default::default())
}
/// Find all intersects between two polylines using the options provided.
#[inline]
fn find_intersects_opt<P>(
&self,
other: &P,
options: &FindIntersectsOptions<Self::Num>,
) -> PlineIntersectsCollection<Self::Num>
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
find_intersects(self, other, options)
}
/// Compute the parallel offset polylines of the polyline using default options.
///
/// `offset` determines what offset polylines are generated, if it is positive then the
/// direction of the offset is to the left of the polyline segment tangent vectors otherwise it
/// is to the right.
///
/// Algorithm will use [PlineOffsetOptions::default] for algorithm options.
///
/// # Examples
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::pline_closed;
/// let pline = pline_closed![(0.0, 0.0, 1.0), (1.0, 0.0, 1.0)];
/// let offset_plines = pline.parallel_offset(0.2);
/// assert_eq!(offset_plines.len(), 1);
/// let offset_pline = &offset_plines[0];
/// assert!(offset_pline[0].fuzzy_eq(PlineVertex::new(0.2, 0.0, 1.0)));
/// assert!(offset_pline[1].fuzzy_eq(PlineVertex::new(0.8, 0.0, 1.0)));
/// ```
fn parallel_offset(&self, offset: Self::Num) -> Vec<Self::OutputPolyline> {
self.parallel_offset_opt(offset, &Default::default())
}
/// Compute the parallel offset polylines of the polyline with options given.
///
/// `offset` determines what offset polylines are generated, if it is positive then the
/// direction of the offset is to the left of the polyline segment tangent vectors otherwise it
/// is to the right.
///
/// `options` is a struct that holds optional parameters. See
/// [PlineOffsetOptions](crate::polyline::PlineOffsetOptions) for specific parameters.
///
/// # Examples
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::pline_closed;
/// let pline = pline_closed![(0.0, 0.0, 1.0), (1.0, 0.0, 1.0)];
/// let aabb_index = pline.create_approx_aabb_index().unwrap();
/// let options = PlineOffsetOptions {
/// // setting option to handle possible self intersects in the polyline
/// handle_self_intersects: true,
/// // passing in existing spatial index of the polyline segments
/// aabb_index: Some(&aabb_index),
/// ..Default::default()
/// };
/// let offset_plines = pline.parallel_offset_opt(0.2, &options);
/// assert_eq!(offset_plines.len(), 1);
/// let offset_pline = &offset_plines[0];
/// assert!(offset_pline[0].fuzzy_eq(PlineVertex::new(0.2, 0.0, 1.0)));
/// assert!(offset_pline[1].fuzzy_eq(PlineVertex::new(0.8, 0.0, 1.0)));
/// ```
fn parallel_offset_opt(
&self,
offset: Self::Num,
options: &PlineOffsetOptions<Self::Num>,
) -> Vec<Self::OutputPolyline> {
parallel_offset(self, offset, options)
}
/// Perform a boolean `operation` between this polyline and another using default options.
///
/// See [PlineSource::boolean_opt] for more information.
///
/// # Examples
/// ```
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::pline_closed;
/// let rectangle = pline_closed![
/// (-1.0, -2.0, 0.0),
/// (3.0, -2.0, 0.0),
/// (3.0, 2.0, 0.0),
/// (-1.0, 2.0, 0.0),
/// ];
/// let circle = pline_closed![(0.0, 0.0, 1.0), (2.0, 0.0, 1.0)];
/// let results = rectangle.boolean(&circle, BooleanOp::Not);
/// // since the circle is inside the rectangle we get back 1 positive polyline and 1 negative
/// // polyline where the positive polyline is the rectangle and the negative polyline is the
/// // circle
/// assert_eq!(results.pos_plines.len(), 1);
/// assert_eq!(results.neg_plines.len(), 1);
/// assert!(matches!(results.result_info, BooleanResultInfo::Pline2InsidePline1));
/// assert!(results.pos_plines[0].pline.area().fuzzy_eq(rectangle.area()));
/// assert!(results.neg_plines[0].pline.area().fuzzy_eq(circle.area()));
/// ```
fn boolean<P>(&self, other: &P, operation: BooleanOp) -> BooleanResult<Self::OutputPolyline>
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.boolean_opt(other, operation, &Default::default())
}
/// Perform a boolean `operation` between this polyline and another with options provided.
///
/// Returns the boolean result polylines and their associated slices that were stitched together
/// end to end to form them. For the result `pline1` refers to `self`, and `pline2` refers to
/// `other`.
///
/// # Examples
/// ```
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::pline_closed;
/// let rectangle = pline_closed![
/// (-1.0, -2.0, 0.0),
/// (3.0, -2.0, 0.0),
/// (3.0, 2.0, 0.0),
/// (-1.0, 2.0, 0.0),
/// ];
/// let circle = pline_closed![(0.0, 0.0, 1.0), (2.0, 0.0, 1.0)];
/// let aabb_index = rectangle.create_approx_aabb_index().unwrap();
/// let options = PlineBooleanOptions {
/// // passing in existing spatial index of the polyline segments for the first polyline
/// pline1_aabb_index: Some(&aabb_index),
/// ..Default::default()
/// };
/// let results = rectangle.boolean_opt(&circle, BooleanOp::Not, &options);
/// // since the circle is inside the rectangle we get back 1 positive polyline and 1 negative
/// // polyline where the positive polyline is the rectangle and the negative polyline is the
/// // circle
/// assert_eq!(results.pos_plines.len(), 1);
/// assert_eq!(results.neg_plines.len(), 1);
/// assert!(matches!(results.result_info, BooleanResultInfo::Pline2InsidePline1));
/// assert!(results.pos_plines[0].pline.area().fuzzy_eq(rectangle.area()));
/// assert!(results.neg_plines[0].pline.area().fuzzy_eq(circle.area()));
/// ```
fn boolean_opt<P>(
&self,
other: &P,
operation: BooleanOp,
options: &PlineBooleanOptions<Self::Num>,
) -> BooleanResult<Self::OutputPolyline>
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
polyline_boolean(self, other, operation, options)
}
/// Find the segment index and point on the polyline corresponding to the path length given.
///
/// Returns `Ok((0, first_vertex_position))` if `target_path_length` is negative.
///
/// Returns `Ok((seg_index, point))` if `target_path_length` is less than or equal to the
/// polyline's total path length. Where `seg_index` is the index of the segment the point lies
/// on, e.g. if point is on the second segment of the polyline then `seg_index = 1`.
///
/// Returns `Err((total_path_length))` if `target_path_length` is greater than total path
/// length of the polyline.
fn find_point_at_path_length(
&self,
target_path_length: Self::Num,
) -> Result<(usize, Vector2<Self::Num>), Self::Num> {
if target_path_length <= Self::Num::zero() {
return Ok((0, self.at(0).pos()));
}
let mut acc_length = Self::Num::zero();
for (i, (v1, v2)) in self.iter_segments().enumerate() {
let seg_len = seg_length(v1, v2);
let sum_len = acc_length + seg_len;
if sum_len < target_path_length {
acc_length = sum_len;
continue;
}
// parametric value (from 0 to 1) along the segment where the point lies
let t = (target_path_length - acc_length) / seg_len;
if v1.bulge_is_zero() {
// line segment
let pt = v1.pos() + (v2.pos() - v1.pos()).scale(t);
return Ok((i, pt));
} else {
// arc segment
let (radius, center) = seg_arc_radius_and_center(v1, v2);
let start_angle = angle(center, v1.pos());
let total_sweep_angle = angle_from_bulge(v1.bulge);
let target_angle = start_angle + total_sweep_angle * t;
let pt = point_on_circle(radius, center, target_angle);
return Ok((i, pt));
}
}
Err(acc_length)
}
}
/// Trait representing a mutable source of polyline data. This trait has all the methods and
/// operations that can be performed on a mutable polyline.
///
/// See other core polyline traits: [PlineSource] and [PlineCreation] for more information.
pub trait PlineSourceMut: PlineSource {
/// Set the vertex data at the given `index` position of the polyline.
fn set_vertex(&mut self, index: usize, vertex: PlineVertex<Self::Num>);
/// Same as [PlineSourceMut::set_vertex] but accepts each component of the vertex rather than a
/// vertex structure.
#[inline]
fn set(&mut self, index: usize, x: Self::Num, y: Self::Num, bulge: Self::Num) {
self.set_vertex(index, PlineVertex::new(x, y, bulge))
}
/// Set the last vertex of the polyline.
///
/// # Panics
///
/// Panics if polyline is empty.
#[inline]
fn set_last(&mut self, vertex: PlineVertex<Self::Num>) {
self.set_vertex(self.vertex_count() - 1, vertex);
}
/// Insert a new vertex into the polyline at the given `index` position.
fn insert_vertex(&mut self, index: usize, vertex: PlineVertex<Self::Num>);
/// Same as [PlineSourceMut::insert_vertex] but accepts each component of the vertex rather than
/// a vertex structure.
#[inline]
fn insert(&mut self, index: usize, x: Self::Num, y: Self::Num, bulge: Self::Num) {
self.insert_vertex(index, PlineVertex::new(x, y, bulge));
}
/// Remove vertex at the given `index` position and return it.
fn remove(&mut self, index: usize) -> PlineVertex<Self::Num>;
/// Remove the last vertex from the polyline and return it.
///
/// # Panics
///
/// Panics if polyline is empty.
#[inline]
fn remove_last(&mut self) -> PlineVertex<Self::Num> {
self.remove(self.vertex_count() - 1)
}
/// Clear all vertexes of the polyline.
fn clear(&mut self);
/// Add a vertex to the end of the polyline.
fn add_vertex(&mut self, vertex: PlineVertex<Self::Num>);
/// Same as [PlineSourceMut::add_vertex] but accepts each component of the vertex rather than a
/// vertex structure.
#[inline]
fn add(&mut self, x: Self::Num, y: Self::Num, bulge: Self::Num) {
self.add_vertex(PlineVertex::new(x, y, bulge));
}
/// Same as [PlineSourceMut::add_vertex] but accepts each component as elements in an array,
/// 0 = x, 1 = y, 2 = bulge.
#[inline]
fn add_from_array(&mut self, data: [Self::Num; 3]) {
self.add(data[0], data[1], data[2]);
}
/// Append all vertexes from an iterator to the end of this polyline.
fn extend_vertexes<I>(&mut self, vertexes: I)
where
I: IntoIterator<Item = PlineVertex<Self::Num>>;
/// Copy all vertexes from `other` to the end of this polyline.
#[inline]
fn extend<P>(&mut self, other: &P)
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.extend_vertexes(other.iter_vertexes());
}
/// Same as [PlineSourceMut::extend] but removes any consecutive repeat position vertexes in the
/// process of copying (using `pos_equal_eps` for compare).
#[inline]
fn extend_remove_repeat<P>(&mut self, other: &P, pos_equal_eps: Self::Num)
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
self.reserve(other.vertex_count());
for v in other.iter_vertexes() {
self.add_or_replace_vertex(v, pos_equal_eps)
}
}
/// Reserves capacity for at least `additional` more vertexes.
fn reserve(&mut self, additional: usize);
/// Add a vertex if it's position is not fuzzy equal to the last vertex in the polyline.
///
/// If the vertex position is fuzzy equal then just update the bulge of the last vertex with
/// the bulge given.
#[inline]
fn add_or_replace_vertex(&mut self, vertex: PlineVertex<Self::Num>, pos_equal_eps: Self::Num) {
let vc = self.vertex_count();
if vc == 0 {
self.add_vertex(vertex);
return;
}
let last = self.at(vc - 1);
if last.pos().fuzzy_eq_eps(vertex.pos(), pos_equal_eps) {
self.set_vertex(vc - 1, last.with_bulge(vertex.bulge));
return;
}
self.add_vertex(vertex);
}
/// Same as [PlineSourceMut::add_or_replace_vertex] but accepts each component of the vertex
/// rather than a vertex structure.
#[inline]
fn add_or_replace(
&mut self,
x: Self::Num,
y: Self::Num,
bulge: Self::Num,
pos_equal_eps: Self::Num,
) {
self.add_or_replace_vertex(PlineVertex::new(x, y, bulge), pos_equal_eps);
}
/// Set whether the polyline is closed (`is_closed = true`) or open (`is_closed = false`).
fn set_is_closed(&mut self, is_closed: bool);
/// Uniformly scale the polyline (mutably) in the xy plane by `scale_factor`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new();
/// polyline.add(2.0, 2.0, 0.5);
/// polyline.add(4.0, 4.0, 1.0);
/// polyline.scale_mut(2.0);
/// let mut expected = Polyline::new();
/// expected.add(4.0, 4.0, 0.5);
/// expected.add(8.0, 8.0, 1.0);
/// assert!(polyline.fuzzy_eq(&expected));
/// ```
fn scale_mut(&mut self, scale_factor: Self::Num) {
for i in 0..self.vertex_count() {
let v = self.at(i);
self.set(i, scale_factor * v.x, scale_factor * v.y, v.bulge);
}
}
/// Translate the polyline (mutably) by some `x_offset` and `y_offset`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// let mut polyline = Polyline::new();
/// polyline.add(2.0, 2.0, 0.5);
/// polyline.add(4.0, 4.0, 1.0);
/// polyline.translate_mut(-3.0, 1.0);
/// let mut expected = Polyline::new();
/// expected.add(-1.0, 3.0, 0.5);
/// expected.add(1.0, 5.0, 1.0);
/// assert!(polyline.fuzzy_eq(&expected));
/// ```
fn translate_mut(&mut self, x: Self::Num, y: Self::Num) {
for i in 0..self.vertex_count() {
let v = self.at(i);
self.set(i, v.x + x, v.y + y, v.bulge);
}
}
/// Invert/reverse the direction of the polyline in place (mutably).
///
/// This method works by simply reversing the order of the vertexes, shifting by 1 position all
/// the vertexes, and inverting the sign of all the bulge values. E.g. after reversing the
/// vertex the bulge at index 0 becomes negative bulge at index 1. The end result for a is_closed
/// polyline is the direction will be changed from clockwise to counter clockwise or vice versa.
fn invert_direction_mut(&mut self) {
let vc = self.vertex_count();
if vc < 2 {
return;
}
let mut start = 0;
let mut end = vc - 1;
while start < end {
let s = self.at(start);
let e = self.at(end);
self.set_vertex(start, e);
self.set_vertex(end, s);
start += 1;
end -= 1;
}
let first_bulge = self.at(0).bulge;
for i in 1..vc {
let b = -self.at(i).bulge;
self.set_vertex(i - 1, self.at(i - 1).with_bulge(b));
}
if self.is_closed() {
self.set_vertex(vc - 1, self.at(vc - 1).with_bulge(-first_bulge));
}
}
}
/// Trait representing a creatable source of polyline data. This trait acts as a mutable polyline
/// source and also exposes associated functions for construction. This trait is used when new
/// polylines need to be returned from a function.
///
/// See other core polyline traits: [PlineSource] and [PlineSourceMut] for more information.
pub trait PlineCreation: PlineSourceMut + Sized {
/// Create a new empty polyline with `capacity` given and `is_closed` indicating whether it is
/// a closed or open polyline.
fn with_capacity(capacity: usize, is_closed: bool) -> Self;
/// Create a new polyline by constructing from vertexes given by an iterator, `is_closed` sets
/// whether the created polyline is closed or open.
fn from_iter<I>(iter: I, is_closed: bool) -> Self
where
I: Iterator<Item = PlineVertex<Self::Num>>;
/// Create a new polyline by cloning from an existing polyline.
#[inline]
fn create_from<P>(pline: &P) -> Self
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
Self::from_iter(pline.iter_vertexes(), pline.is_closed())
}
/// Same as [PlineCreation::create_from] but removes any repeat position vertexes in the
/// process using `pos_equal_eps` for positional comparisons.
#[inline]
fn create_from_remove_repeat<P>(pline: &P, pos_equal_eps: Self::Num) -> Self
where
P: PlineSource<Num = Self::Num> + ?Sized,
{
let mut result = Self::with_capacity(pline.vertex_count(), pline.is_closed());
for v in pline.iter_vertexes() {
result.add_or_replace_vertex(v, pos_equal_eps);
}
if pline.is_closed() && result.vertex_count() >= 2 {
// catch last position overlapping first for closed polyline case
let last = result.last().unwrap();
if last.pos().fuzzy_eq_eps(result.at(0).pos(), pos_equal_eps) {
result.remove_last();
}
}
result
}
/// Create empty polyline with `is_closed` set to false.
#[inline]
fn empty() -> Self {
Self::with_capacity(0, false)
}
}
/// An iterator that traverses polyline vertexes.
#[derive(Debug)]
pub struct VertexIter<'a, P>
where
P: ?Sized,
{
pline: &'a P,
pos: usize,
end: usize,
}
impl<'a, P> VertexIter<'a, P>
where
P: PlineSource + ?Sized,
{
#[inline]
pub fn new(pline: &'a P) -> Self {
Self {
pline,
pos: 0,
end: pline.vertex_count(),
}
}
}
impl<'a, P> Clone for VertexIter<'a, P>
where
P: ?Sized,
{
#[inline]
fn clone(&self) -> Self {
Self {
pline: self.pline,
pos: self.pos,
end: self.end,
}
}
}
impl<'a, P> Iterator for VertexIter<'a, P>
where
P: PlineSource + ?Sized,
{
type Item = PlineVertex<P::Num>;
#[inline]
fn next(&mut self) -> Option<Self::Item> {
if self.pos == self.end {
return None;
}
let r = self.pline.get(self.pos);
self.pos += 1;
r
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
let remaining = self.end - self.pos;
(remaining, Some(remaining))
}
}
impl<'a, P> ExactSizeIterator for VertexIter<'a, P>
where
P: PlineSource,
{
#[inline]
fn len(&self) -> usize {
let (lower, upper) = self.size_hint();
assert_eq!(upper, Some(lower));
lower
}
}
impl<'a, P> DoubleEndedIterator for VertexIter<'a, P>
where
P: PlineSource + ?Sized,
{
fn next_back(&mut self) -> Option<Self::Item> {
if self.pos == self.end {
return None;
}
let r = self.pline.get(self.end - 1);
self.end -= 1;
r
}
}
/// An iterator that traverses polyline segments (as pairs of vertexes).
#[derive(Debug)]
pub struct SegmentIter<'a, P>
where
P: ?Sized,
{
pline: &'a P,
pos: usize,
exhausted: bool,
}
impl<'a, P> SegmentIter<'a, P>
where
P: PlineSource + ?Sized,
{
#[inline]
pub fn new(pline: &'a P) -> Self {
Self {
pline,
pos: 0,
exhausted: pline.vertex_count() < 2,
}
}
}
impl<'a, P> Clone for SegmentIter<'a, P>
where
P: ?Sized,
{
#[inline]
fn clone(&self) -> Self {
Self {
pline: self.pline,
pos: self.pos,
exhausted: self.exhausted,
}
}
}
impl<'a, P> Iterator for SegmentIter<'a, P>
where
P: PlineSource + ?Sized,
{
type Item = (PlineVertex<P::Num>, PlineVertex<P::Num>);
#[inline]
fn next(&mut self) -> Option<Self::Item> {
if self.exhausted {
return None;
}
let vc = self.pline.vertex_count();
if self.pos == vc - 1 {
if self.pline.is_closed() {
self.exhausted = true;
return Some((self.pline.at(vc - 1), self.pline.at(0)));
} else {
return None;
}
}
let r = (self.pline.at(self.pos), self.pline.at(self.pos + 1));
self.pos += 1;
Some(r)
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
if self.exhausted {
(0, Some(0))
} else {
let remaining = if self.pline.is_closed() {
self.pline.vertex_count() - self.pos
} else {
self.pline.vertex_count() - self.pos - 1
};
(remaining, Some(remaining))
}
}
}
impl<'a, P> ExactSizeIterator for SegmentIter<'a, P>
where
P: PlineSource,
{
#[inline]
fn len(&self) -> usize {
let (lower, upper) = self.size_hint();
assert_eq!(upper, Some(lower));
lower
}
}
/// An iterator that traverses all segment vertex pair index positions.
pub struct PlineSegIndexIterator {
pos: usize,
remaining: usize,
is_closed: bool,
}
impl PlineSegIndexIterator {
#[inline]
pub fn new(vertex_count: usize, is_closed: bool) -> PlineSegIndexIterator {
let remaining = if vertex_count < 2 {
0
} else if is_closed {
vertex_count
} else {
vertex_count - 1
};
PlineSegIndexIterator {
pos: 0,
remaining,
is_closed,
}
}
}
impl Iterator for PlineSegIndexIterator {
type Item = (usize, usize);
#[inline]
fn next(&mut self) -> Option<Self::Item> {
if self.remaining == 0 {
return None;
}
self.remaining -= 1;
if self.remaining == 0 && self.is_closed {
return Some((self.pos, 0));
}
let pos = self.pos;
self.pos += 1;
Some((pos, pos + 1))
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
(self.remaining, Some(self.remaining))
}
}