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extern crate rand;
use rand::Rng;
use std::cmp::min;
#[derive(Debug)]
struct BackgroundGrid {
data: Vec<usize>,
dimensions: Vec<f64>,
min_dst_sqr: f64,
cell_size: f64,
cell_count: Vec<usize>,
cell_multiplicators: Vec<usize>,
}
impl BackgroundGrid {
pub fn new(dimensions: Vec<f64>, min_distance: f64) -> BackgroundGrid {
assert!(min_distance > 0.0);
let dimension = dimensions.len();
let cell_size = min_distance / (dimension as f64).sqrt();
let cell_count: Vec<usize> = dimensions.iter()
.map(|x| (x / (cell_size as f64)).ceil() as usize)
.collect();
let data_size = cell_count.iter().fold(1_usize, |accu, x| accu * x);
let mut cell_multiplicators = Vec::new();
let mut multi_accu = 1_usize;
for i in 0..dimension {
cell_multiplicators.push(multi_accu);
multi_accu *= cell_count[i];
}
BackgroundGrid {
data: vec![0; data_size],
dimensions: dimensions,
min_dst_sqr: min_distance * min_distance,
cell_size: cell_size,
cell_count: cell_count,
cell_multiplicators: cell_multiplicators,
}
}
pub fn dst_sqr(x: &Vec<f64>, y: &Vec<f64>) -> f64 {
debug_assert_eq!(x.len(), y.len());
x.iter().zip(y.iter()).fold(0_f64, |accu, (xx, yx)| {
let diff = xx - yx;
accu + diff * diff
})
}
fn calc_idx(&self, cell_id: &Vec<usize>) -> usize {
self.cell_multiplicators
.iter()
.zip(cell_id.iter())
.skip(1)
.fold(cell_id[0], |accu, (multi, cell)| accu + multi * cell)
}
pub fn insert(&mut self,
sample_position: Vec<f64>,
samples: &mut Vec<Vec<f64>>)
-> Result<usize, ()> {
if sample_position.iter()
.zip(self.dimensions.iter())
.any(|(samp_x, dim_x)| *samp_x < 0_f64 || samp_x >= dim_x) {
return Err(());
}
let dimension = self.dimensions.len();
debug_assert_eq!(sample_position.len(), dimension);
let cell_id: Vec<usize> = sample_position.iter()
.map(|x| (*x / self.cell_size) as usize)
.collect();
let samp_idx = self.calc_idx(&cell_id);
debug_assert!(cell_id.iter().zip(self.cell_count.iter()).all(|(cid, cc)| cid < cc));
let cell_offs = (self.min_dst_sqr / (self.cell_size as f64)).ceil() as usize;
let min_cell: Vec<usize> = cell_id.iter().map(|x| x.saturating_sub(cell_offs)).collect();
let max_cell: Vec<usize> = cell_id.iter()
.zip(self.cell_count.iter())
.map(|(x, size_x)| min(x + cell_offs, size_x - 1))
.collect();
debug_assert!(min_cell.iter()
.zip(max_cell.iter())
.zip(cell_id.iter())
.all(|((cmin, cmax), c)| cmin <= c && c <= cmax));
let mut indices = min_cell.clone();
let mut checked_own_idx = false;
loop {
debug_assert!(min_cell.iter()
.zip(max_cell.iter())
.zip(indices.iter())
.all(|((cmin, cmax), c)| cmin <= c && c <= cmax));
let idx = self.calc_idx(&indices);
if idx == samp_idx {
checked_own_idx = true;
}
match self.data[idx] {
0 => (),
other_id => {
let other_sample = &samples[other_id - 1];
if BackgroundGrid::dst_sqr(&sample_position, other_sample) < self.min_dst_sqr {
return Err(());
}
}
}
if indices == max_cell {
break;
}
for i in 0..dimension {
if indices[i] == max_cell[i] {
indices[i] = min_cell[i];
} else {
indices[i] += 1;
break;
}
}
}
debug_assert!(checked_own_idx,
format!("Didn't check own idx.\n\tMin cells: {:?}\n\tMax cells: \
{:?}\n\tself cells: {:?}",
min_cell,
max_cell,
cell_id));
samples.push(sample_position);
debug_assert_eq!(self.data[samp_idx], 0);
self.data[samp_idx] = samples.len();
Ok(samples.len())
}
}
fn polar_to_cartesian(radius: f64, angles: Vec<f64>) -> Vec<f64> {
let sines: Vec<f64> = angles.iter().map(|x| x.sin()).collect();
(0..angles.len() + 1)
.map(|i| {
sines.iter().take(i).fold(radius, |accu, sine| accu * sine) *
match angles.get(i) {
Some(ang) => ang.cos(),
None => 1_f64,
}
})
.collect()
}
pub struct BlueNoiseIterator {
dimensions: Vec<f64>,
min_distance: f64,
k_abort: usize,
samples: Vec<Vec<f64>>,
bggrid: BackgroundGrid,
active: Vec<usize>,
active_idx: usize,
next_active: Vec<usize>,
}
impl BlueNoiseIterator {
fn new(dimensions: Vec<f64>, min_distance: f64, k_abort: usize) -> BlueNoiseIterator {
BlueNoiseIterator {
dimensions: dimensions.clone(),
min_distance: min_distance,
k_abort: k_abort,
samples: Vec::new(),
bggrid: BackgroundGrid::new(dimensions, min_distance),
active: Vec::new(),
active_idx: 0,
next_active: Vec::new(),
}
}
}
impl Iterator for BlueNoiseIterator {
type Item = Vec<f64>;
fn next(&mut self) -> Option<Vec<f64>> {
let dimension = self.dimensions.len();
let mut rng = rand::thread_rng();
if self.samples.is_empty() {
let initial_sample: Vec<f64> = self.dimensions
.iter()
.map(|x| rng.gen_range::<f64>(0_f64, *x))
.collect();
let initial_sample_id = self.bggrid
.insert(initial_sample.clone(), &mut self.samples)
.unwrap();
debug_assert_eq!(initial_sample_id, 1);
self.active.push(initial_sample_id);
return Some(initial_sample);
}
if self.active_idx >= self.active.len() {
self.active_idx = 0;
self.active = self.next_active.clone();
self.next_active = Vec::new();
}
if self.active.is_empty() {
return None;
}
let current_id = self.active[self.active_idx];
let current_samp = self.samples[current_id - 1].clone();
for _ in 0..self.k_abort {
let radius = rng.gen_range::<f64>(self.min_distance, 2_f64 * self.min_distance);
let angles = (0..dimension - 1)
.map(|_| rng.gen_range::<f64>(0_f64, 2_f64 * std::f64::consts::PI))
.collect();
let samp_offs = polar_to_cartesian(radius, angles);
debug_assert_eq!(samp_offs.len(), dimension);
let samp = samp_offs.into_iter()
.zip(current_samp.iter())
.map(|(offs, x)| x + offs)
.collect();
match self.bggrid.insert(samp, &mut self.samples) {
Ok(new_samp_id) => {
self.next_active.push(current_id);
self.next_active.push(new_samp_id);
self.active_idx += 1;
return Some(self.samples[new_samp_id - 1].clone());
}
Err(_) => {
}
}
}
self.active_idx += 1;
self.next()
}
}
pub fn blue_noise(dimensions: Vec<f64>, min_distance: f64, k_abort: usize) -> Vec<Vec<f64>> {
let mut it = BlueNoiseIterator::new(dimensions, min_distance, k_abort);
while let Some(_) = it.next() {}
it.samples
}
pub fn blue_noise_iter(dimensions: Vec<f64>,
min_distance: f64,
k_abort: usize)
-> BlueNoiseIterator {
BlueNoiseIterator::new(dimensions, min_distance, k_abort)
}
#[test]
fn grid_corners() {
let mut grid = BackgroundGrid::new(vec![35_f64, 9_f64], 4.0);
let mut samples = Vec::new();
assert_eq!(grid.cell_count.len(), 2);
assert_eq!(grid.insert(vec![0., 9.], &mut samples), Err(()));
assert_eq!(samples.len(), 0);
assert_eq!(grid.insert(vec![0., 0.], &mut samples), Ok(1));
assert_eq!(samples.len(), 1);
assert_eq!(grid.insert(vec![34., 0.], &mut samples), Ok(2));
assert_eq!(samples.len(), 2);
assert_eq!(grid.insert(vec![0., 8.], &mut samples), Ok(3));
assert_eq!(samples.len(), 3);
assert_eq!(grid.insert(vec![34., 8.], &mut samples), Ok(4));
assert_eq!(samples.len(), 4);
}
#[cfg(test)]
mod tests {
use super::*;
extern crate rand;
use rand::Rng;
use std::f64;
#[test]
fn sanity_3d() {
sanity_nd(3, 15., 25.);
}
#[test]
#[ignore]
fn sanity_6d() {
sanity_nd(6, 6., 6.5);
}
fn sanity_nd(dimension: usize, minr: f64, maxr: f64) {
let mut rng = rand::thread_rng();
let radius = 3.;
let mut dimensions: Vec<f64> = Vec::new();
for _ in 0..dimension {
dimensions.push(rng.gen_range::<f64>(minr, maxr));
}
assert_eq!(dimensions.len(), dimension);
let samples = blue_noise(dimensions, radius, 30);
println!("there are {} samples.", samples.len());
for s1 in samples.iter() {
let mut mindst = f64::INFINITY;
for s2 in samples.iter() {
if s1 == s2 {
continue;
}
let dst = super::BackgroundGrid::dst_sqr(s1, s2).sqrt();
if dst < mindst {
mindst = dst;
}
}
assert!(mindst >= radius);
assert!(mindst < 2_f64 * radius);
}
}
fn get_image(radius: f64, size: usize) -> Vec<Vec<bool>> {
let samples = blue_noise(vec![size as f64, size as f64], radius, 30);
let mut image = vec![vec![false; size]; size];
for s in samples {
image[s[1] as usize][s[0] as usize] = true;
}
image
}
#[test]
fn sanity_2d() {
let size: isize = 128;
let radius: isize = 8;
let image = get_image(radius as f64, size as usize);
for y in 0..size {
for x in 0..size {
if image[y as usize][x as usize] {
for dy in 0..radius {
for dx in 0..radius {
if dx == 0 && dy == 0 {
continue;
}
image.get((y + dy) as usize).map(|line| {
match line.get((x + dx) as usize) {
Some(&true) => {
assert!(dx * dx + dy * dy >= (radius - 1) * (radius - 1));
}
_ => {}
}
});
}
}
}
}
}
}
}