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// Boost.Polygon library voronoi_graphic_utils.hpp header file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// See http://www.boost.org for updates, documentation, and revision history of C++ code.
// Ported from C++ boost 1.76.0 to Rust in 2020/2021 by Eadf (github.com/eadf)
//! Graphical utilities.
use crate::{
cast,
geometry::{Line, Point},
BvError, InputType, OutputType,
};
use std::fmt;
/// Utilities class, that contains set of routines handful for visualization.
pub struct VoronoiVisualUtils {}
impl VoronoiVisualUtils {
/// Discretize parabolic Voronoi edge.
/// Parabolic Voronoi edges are always formed by one point and one segment
/// from the initial input set.
///
/// Args:
/// point: input point in diagram coordinate system
/// segment: input segment in diagram coordinate system
/// max_dist: maximum discretization distance in output coordinate system,
/// affine: an affine transform converting from diagram coordinate system to output coordinate system,
/// discretization: point discretization of the given Voronoi edge in output coordinate system,
///
/// Template arguments:
/// InCT: coordinate type of the input geometries (usually integer).
/// Point: point type, should model point concept.
/// Segment: segment type, should model segment concept.
///
/// Important:
/// discretization should contain both edge endpoints initially.
pub fn discretize<I: InputType, F: OutputType>(
point: &Point<I>,
segment: &Line<I>,
max_dist: F,
affine: &SimpleAffine<F>,
discretization: &mut Vec<[F; 2]>,
) {
// no need to discretize infinitely small distances
if discretization[0][0] == discretization[1][0]
&& discretization[0][1] == discretization[1][1]
{
return;
}
// Apply the linear transformation to move start point of the segment to
// the point with coordinates (0, 0) and the direction of the segment to
// coincide the positive direction of the x-axis.
let segm_vec_x: F =
affine.transform_ix(segment.end.x) - affine.transform_ix(segment.start.x);
let segm_vec_y: F =
affine.transform_iy(segment.end.y) - affine.transform_iy(segment.start.y);
let sqr_segment_length = segm_vec_x * segm_vec_x + segm_vec_y * segm_vec_y;
// Compute x-coordinates of the endpoints of the edge
// in the transformed space.
let projection_start =
sqr_segment_length * Self::point_projection(affine, &discretization[0], segment);
let projection_end =
sqr_segment_length * Self::point_projection(affine, &discretization[1], segment);
// Compute parabola parameters in the transformed space.
// Parabola has next representation:
// f(x) = ((x-rot_x)^2 + rot_y^2) / (2.0*rot_y).
let point_vec_x = affine.transform_ix(point.x) - affine.transform_ix(segment.start.x);
let point_vec_y = affine.transform_iy(point.y) - affine.transform_iy(segment.start.y);
let rot_x = segm_vec_x * point_vec_x + segm_vec_y * point_vec_y;
let rot_y = segm_vec_x * point_vec_y - segm_vec_y * point_vec_x;
// Save the last point.
let last_point = (*discretization)[1];
let _ = discretization.pop();
// Use stack to avoid recursion.
let mut point_stack = vec![projection_end];
let mut cur_x = projection_start;
let mut cur_y = Self::parabola_y::<F>(cur_x, rot_x, rot_y);
// Adjust max_dist parameter in the transformed space.
let max_dist_transformed = max_dist * max_dist * sqr_segment_length;
while !point_stack.is_empty() {
let new_x = point_stack[point_stack.len() - 1]; // was .top();
let new_y = Self::parabola_y::<F>(new_x, rot_x, rot_y);
// Compute coordinates of the point of the parabola that is
// furthest from the current line segment.
let mid_x = (new_y - cur_y) / (new_x - cur_x) * rot_y + rot_x;
let mid_y = Self::parabola_y::<F>(mid_x, rot_x, rot_y);
// Compute maximum distance between the given parabolic arc
// and line segment that discretize it.
let mut dist = (new_y - cur_y) * (mid_x - cur_x) - (new_x - cur_x) * (mid_y - cur_y);
#[allow(clippy::suspicious_operation_groupings)]
{
dist = dist * dist
/ ((new_y - cur_y) * (new_y - cur_y) + (new_x - cur_x) * (new_x - cur_x));
}
if dist.is_nan() {
break;
}
if dist <= max_dist_transformed {
// Distance between parabola and line segment is less than max_dist.
let _ = point_stack.pop();
let inter_x = (segm_vec_x * new_x - segm_vec_y * new_y) / sqr_segment_length
+ affine.transform_ix(segment.start.x);
let inter_y = (segm_vec_x * new_y + segm_vec_y * new_x) / sqr_segment_length
+ affine.transform_iy(segment.start.y);
discretization.push([inter_x, inter_y]);
cur_x = new_x;
cur_y = new_y;
} else {
point_stack.push(mid_x);
}
}
// Update last point.
let discretization_len = discretization.len();
discretization[discretization_len - 1] = last_point;
}
/// Compute y(x) = ((x - a) * (x - a) + b * b) / (2 * b).
#[inline(always)]
#[allow(clippy::suspicious_operation_groupings)]
fn parabola_y<F: OutputType>(x: F, a: F, b: F) -> F {
((x - a) * (x - a) + b * b) / (b + b)
}
// Get normalized length of the distance between:
// 1) point projection onto the segment
// 2) start point of the segment
// Return this length divided by the segment length. This is made to avoid
// sqrt computation during transformation from the initial space to the
// transformed one and vice versa. The assumption is made that projection of
// the point lies between the start-point and endpoint of the segment.
pub fn point_projection<I: InputType, F: OutputType>(
affine: &SimpleAffine<F>,
point: &[F; 2],
segment: &Line<I>,
) -> F {
let segment_vec_x: F =
affine.transform_ix(segment.end.x) - affine.transform_ix(segment.start.x);
let segment_vec_y: F =
affine.transform_iy(segment.end.y) - affine.transform_iy(segment.start.y);
let point_vec_x = point[0] - affine.transform_ix(segment.start.x);
let point_vec_y = point[1] - affine.transform_iy(segment.start.y);
let sqr_segment_length = segment_vec_x * segment_vec_x + segment_vec_y * segment_vec_y;
let vec_dot = segment_vec_x * point_vec_x + segment_vec_y * point_vec_y;
vec_dot / sqr_segment_length
}
}
/// A simple 2d axis aligned bounding box.
///
/// If `min_max` is `None` no data has been assigned.
#[derive(PartialEq, Eq, Clone, fmt::Debug)]
pub struct Aabb2<F: OutputType> {
min_max_: Option<([F; 2], [F; 2])>,
}
impl<F: OutputType> Default for Aabb2<F> {
#[inline]
fn default() -> Self {
Self { min_max_: None }
}
}
impl<F: OutputType> Aabb2<F> {
/// Creates a new AABB with the limits defined by `p1` & `p2`
pub fn new<I: InputType>(p1: &Point<I>, p2: &Point<I>) -> Self {
let mut rv = Self::default();
rv.update_point(p1);
rv.update_point(p2);
rv
}
/// Creates a new AABB with `i32` coordinates
pub fn new_from_i32<I: InputType>(x1: i32, y1: i32, x2: i32, y2: i32) -> Self {
let mut rv = Self::default();
rv.update_coordinate::<I>(x1, y1);
rv.update_coordinate::<I>(x2, y2);
rv
}
#[inline(always)]
pub fn update_point<I: InputType>(&mut self, point: &Point<I>) {
let x = cast::<I, F>(point.x);
let y = cast::<I, F>(point.y);
self.update_vertex(x, y);
}
#[inline(always)]
pub fn update_coordinate<I: InputType>(&mut self, x: i32, y: i32) {
self.update_vertex(cast::<i32, F>(x), cast::<i32, F>(y));
}
#[inline]
pub fn update_vertex(&mut self, x: F, y: F) {
if self.min_max_.is_none() {
self.min_max_ = Some(([x, y], [x, y]));
return;
}
let (mut aabb_min, mut aabb_max) = self.min_max_.take().unwrap();
if x < aabb_min[0] {
aabb_min[0] = x;
}
if y < aabb_min[1] {
aabb_min[1] = y;
}
if x > aabb_max[0] {
aabb_max[0] = x;
}
if y > aabb_max[1] {
aabb_max[1] = y;
}
self.min_max_ = Some((aabb_min, aabb_max));
}
#[inline]
pub fn update_i64(&mut self, x: i64, y: i64) {
self.update_vertex(cast::<i64, F>(x), cast::<i64, F>(y))
}
#[inline]
pub fn update_f64(&mut self, x: f64, y: f64) {
self.update_vertex(cast::<f64, F>(x), cast::<f64, F>(y))
}
#[inline(always)]
pub fn update_line<I: InputType>(&mut self, line: &Line<I>) {
self.update_point(&line.start);
self.update_point(&line.end);
}
#[inline(always)]
pub fn get_high(&self) -> Option<[F; 2]> {
if let Some((_, high)) = self.min_max_ {
return Some(high);
}
None
}
#[inline(always)]
pub fn get_low(&self) -> Option<[F; 2]> {
if let Some((low, _)) = self.min_max_ {
return Some(low);
}
None
}
/// grows the aabb uniformly by some percent.
/// method does nothing if not initialized
pub fn grow_percent<I: InputType>(&mut self, percent: i32) {
if self.min_max_.is_some() {
let size_x = self.get_high().unwrap()[0] - self.get_low().unwrap()[0];
let size_y = self.get_high().unwrap()[1] - self.get_low().unwrap()[1];
let size = if size_x > size_y { size_x } else { size_y };
let delta = size * cast::<f32, F>((percent as f32) / 100.0);
let mut p = self.get_high().unwrap();
p[0] = p[0] + delta;
p[1] = p[1] + delta;
self.update_vertex(p[0], p[1]);
let mut p = self.get_low().unwrap();
p[0] = p[0] - delta;
p[1] = p[1] - delta;
self.update_vertex(p[0], p[1]);
}
}
/// returns `Some(true)` if the aabb contains the point (inclusive)
/// returns `None` if the aabb is uninitialized
///```
/// # use boostvoronoi_core::geometry::Point;
/// # use boostvoronoi_core::visual_utils::Aabb2;
/// let p0 = Point::from([0,0]);
/// let p1 = Point::from([1,1]);
///
/// let aabb = Aabb2::<f32>::new(&p0,&p1);
/// assert!(aabb.contains_point(&Point::from([1,1])).unwrap_or(false));
/// assert!(!aabb.contains_point(&Point::from([2,1])).unwrap_or(true));
/// ```
#[inline]
pub fn contains_point<I: InputType>(&self, point: &Point<I>) -> Option<bool> {
if let Some(min_max) = self.min_max_ {
let x = cast::<I, F>(point.x);
let y = cast::<I, F>(point.y);
Some(x >= min_max.0[0] && x <= min_max.1[0] && y >= min_max.0[1] && y <= min_max.1[1])
} else {
None
}
}
/// returns `Some(true)` if the aabb contains the line (inclusive)
/// returns `None` if the aabb is uninitialized
/// ```
/// # use boostvoronoi_core::BvError;
/// # use boostvoronoi_core::geometry::{Line, Point};
/// # use boostvoronoi_core::visual_utils::Aabb2;
/// let p0 = Point::from([0,0]);
/// let p1 = Point::from([10,10]);
///
/// let aabb = Aabb2::<f32>::new(&p0,&p1);
/// assert!( aabb.contains_line(&Line::from([1,1,10,10])).unwrap_or(false));
/// assert!(!aabb.contains_line(&Line::from([1,-1,10,10])).unwrap_or(true));
/// ```
#[inline]
pub fn contains_line<I: InputType>(&self, line: &Line<I>) -> Option<bool> {
if self.min_max_.is_some() {
// unwrap is now safe
Some(
self.contains_point(&line.start).unwrap()
&& self.contains_point(&line.end).unwrap(),
)
} else {
None
}
}
}
/// This is a simple affine transformation object.
/// Inadvertently it also serves as a type converter F<->I<->i32
/// It can pan and zoom but not rotate.
#[derive(PartialEq, Clone, fmt::Debug)]
pub struct SimpleAffine<F: OutputType> {
/// The offsets used to center the 'source' coordinate system. Typically the input geometry
/// in this case.
to_center_: [F; 2],
/// A zoom scale
pub scale: [F; 2],
/// The offsets needed to center coordinates of interest on the 'dest' coordinate system.
/// i.e. the screen coordinate system.
pub to_offset: [F; 2],
}
impl<F: OutputType> Default for SimpleAffine<F> {
#[inline]
fn default() -> Self {
Self {
to_center_: [F::zero(), F::zero()],
scale: [F::one(), F::one()],
to_offset: [F::zero(), F::zero()],
}
}
}
impl<F: OutputType> SimpleAffine<F> {
pub fn new<I: InputType>(
source_aabb: &Aabb2<F>,
dest_aabb: &Aabb2<F>,
) -> Result<Self, BvError> {
let min_dim = cast::<i32, F>(10);
if let Some(s_low) = source_aabb.get_low() {
if let Some(s_high) = source_aabb.get_high() {
if let Some(d_low) = dest_aabb.get_low() {
if let Some(d_high) = dest_aabb.get_high() {
//println!("s_low:{:?},s_high:{:?},d_low:{:?},d_high:{:?}", s_low, s_high, d_low, d_high);
let source_aabb_center = [
-(s_low[0] + s_high[0]) / cast::<i32, F>(2_i32),
-(s_low[1] + s_high[1]) / cast::<i32, F>(2_i32),
];
let source_aabb_size = [
(s_high[0] - s_low[0]).max(min_dim),
(s_high[1] - s_low[1]).max(min_dim),
];
let dest_aabb_center = [
(d_low[0] + d_high[0]) / cast::<i32, F>(2_i32),
(d_low[1] + d_high[1]) / cast::<i32, F>(2_i32),
];
let dest_aabb_size = [
(d_high[0] - d_low[0]).max(min_dim),
(d_high[1] - d_low[1]).max(min_dim),
];
// make sure the larges dimension of source fits inside smallest of dest
let source_aabb_size = source_aabb_size[0].max(source_aabb_size[1]);
let dest_aabb_size = dest_aabb_size[0].min(dest_aabb_size[1]);
let scale = dest_aabb_size / source_aabb_size;
return Ok(Self {
to_center_: source_aabb_center,
scale: [scale, scale],
to_offset: dest_aabb_center,
});
}
}
}
}
Err(BvError::InternalError(format!(
"could not get dimension of the AABB. {}:{}",
file!(),
line!()
)))
}
/// transform from destination coordinate system to source coordinate system
#[inline(always)]
pub fn reverse_transform<I: InputType>(&self, x: F, y: F) -> Result<[I; 2], BvError> {
let x = self.reverse_transform_x(x)?;
let y = self.reverse_transform_y(y)?;
Ok([x, y])
}
/// transform from destination coordinate system to source coordinate system
#[inline(always)]
pub fn reverse_transform_x<I: InputType>(&self, x: F) -> Result<I, BvError> {
super::try_cast::<F, I>(
((x - self.to_offset[0]) / self.scale[0] - self.to_center_[0]).round(),
)
}
/// transform from dest coordinate system to source coordinate system
#[inline(always)]
pub fn reverse_transform_y<I: InputType>(&self, y: F) -> Result<I, BvError> {
super::try_cast::<F, I>(
((y - self.to_offset[1]) / self.scale[1] - self.to_center_[1]).round(),
)
}
/// transform from source coordinate system to dest coordinate system
#[inline(always)]
pub fn transform(&self, x: F, y: F) -> [F; 2] {
[self.transform_x(x), self.transform_y(y)]
}
/// transform from source coordinate system to dest coordinate system
/// float x coordinate
#[inline(always)]
pub fn transform_x(&self, x: F) -> F {
(x + self.to_center_[0]) * self.scale[0] + self.to_offset[0]
}
/// transform from source coordinate system to dest coordinate system
/// float y coordinate
#[inline(always)]
pub fn transform_y(&self, y: F) -> F {
(y + self.to_center_[1]) * self.scale[1] + self.to_offset[1]
}
/// transform from source coordinate system to dest coordinate system
#[inline(always)]
pub fn transform_i<I: InputType>(&self, point: [I; 2]) -> [F; 2] {
[self.transform_ix(point[0]), self.transform_iy(point[1])]
}
/// transform from source coordinate system to dest coordinate system
#[inline(always)]
pub fn transform_f(&self, point: [F; 2]) -> [F; 2] {
[self.transform_fx(point[0]), self.transform_fy(point[1])]
}
/// transform from source coordinate system to dest coordinate system
#[inline(always)]
pub fn transform_p<I: InputType>(&self, point: &Point<I>) -> [F; 2] {
[self.transform_ix(point.x), self.transform_iy(point.y)]
}
/// transform from source coordinate system to dest coordinate system
/// integer x coordinate
#[inline(always)]
pub fn transform_ix<I: InputType>(&self, x: I) -> F {
(cast::<I, F>(x) + self.to_center_[0]) * self.scale[0] + self.to_offset[0]
}
/// transform from source coordinate system to dest coordinate system
/// integer y coordinate
#[inline(always)]
pub fn transform_iy<I: InputType>(&self, y: I) -> F {
(cast::<I, F>(y) + self.to_center_[1]) * self.scale[1] + self.to_offset[1]
}
/// transform from source coordinate system to destination coordinate system
/// float x coordinate
#[inline(always)]
pub fn transform_fx(&self, x: F) -> F {
(x + self.to_center_[0]) * self.scale[0] + self.to_offset[0]
}
/// transform from source coordinate system to destination coordinate system
/// float y coordinate
#[inline(always)]
pub fn transform_fy(&self, y: F) -> F {
(y + self.to_center_[1]) * self.scale[1] + self.to_offset[1]
}
/// multiply the scale by a factor f
#[inline(always)]
pub fn zoom(&mut self, f: F) {
self.scale = [self.scale[0] * f, self.scale[1] * f];
}
}
/// Helper function: Affine transforms and casts a slice of `[[integer,integer,integer,integer]]` into
/// input data for the Builder.
pub fn to_segments_offset<I1: InputType, I2: InputType>(
points: &[[I1; 4]],
scale_x: f64,
scale_y: f64,
dx: i64,
dy: i64,
) -> Vec<Line<I2>> {
let fx = |x: I1| cast::<f64, I2>(cast::<I1, f64>(x) * scale_x) + cast::<i64, I2>(dx);
let fy = |y: I1| cast::<f64, I2>(cast::<I1, f64>(y) * scale_y) + cast::<i64, I2>(dy);
points
.iter()
.map(|x| Line {
start: Point {
x: fx(x[0]),
y: fy(x[1]),
},
end: Point {
x: fx(x[2]),
y: fy(x[3]),
},
})
.collect()
}