first commit - hilbert 2d poly
This commit is contained in:
commit
ac732863d3
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.gitignore
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.gitignore
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/target
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331
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331
Cargo.lock
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9
Cargo.toml
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9
Cargo.toml
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@ -0,0 +1,9 @@
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[package]
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name = "hilbert"
|
||||
version = "0.1.0"
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edition = "2021"
|
||||
|
||||
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
|
||||
|
||||
[dependencies]
|
||||
image = "0.23.14"
|
||||
141
src/main.rs
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141
src/main.rs
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|
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use image::{ImageBuffer, Rgb, RgbImage};
|
||||
|
||||
trait Distance<const N: usize> {
|
||||
fn dist(&self, a: [f64; N], b: [f64; N]) -> Result<f64, &'static str>;
|
||||
}
|
||||
|
||||
struct HilbertPoly {
|
||||
vertices: Vec<[f64; 2]>
|
||||
}
|
||||
|
||||
#[allow(dead_code)]
|
||||
struct Euclidean<const N: usize>();
|
||||
|
||||
impl<const N: usize> Distance<N> for Euclidean<N> {
|
||||
fn dist(&self, a: [f64; N], b: [f64; N]) -> Result<f64, &'static str> {
|
||||
Ok(a.iter().zip(b.iter()).map(|x| (x.1 - x.0) * (x.1 - x.0)).sum::<f64>().sqrt())
|
||||
}
|
||||
}
|
||||
|
||||
#[allow(dead_code)]
|
||||
struct Manhattan<const N: usize>();
|
||||
|
||||
impl<const N: usize> Distance<N> for Manhattan<N> {
|
||||
fn dist(&self, a: [f64; N], b: [f64; N]) -> Result<f64, &'static str> {
|
||||
Ok(a.iter().zip(b.iter()).map(|x| f64::abs(x.1 - x.0)).sum::<f64>())
|
||||
}
|
||||
}
|
||||
|
||||
impl<const N: usize> Distance<N> for HilbertPoly {
|
||||
fn dist(&self, a: [f64; N], b: [f64; N]) -> Result<f64, &'static str> {
|
||||
|
||||
// 2d Hilbert Convex Polygon, 3d is slightly different as it will be to a side (edge of
|
||||
// convex set )
|
||||
if N != 2 {
|
||||
return Err("Dim != 2");
|
||||
};
|
||||
|
||||
// Get edges.
|
||||
let mut edges = self.vertices.windows(2).map(|x| [x[0], x[1]]).collect::<Vec<[[f64; 2]; 2]>>();
|
||||
edges.push([self.vertices[0], self.vertices[self.vertices.len() - 1]]);
|
||||
|
||||
// Assert that the Hilbert convex set is convex.
|
||||
let mut prev = 0.0;
|
||||
let mut curr;
|
||||
for i in 0..N {
|
||||
let edge_one = edges[i];
|
||||
let edge_two = edges[(i + 1) % N];
|
||||
curr = (edge_one[1][0] - edge_one[0][0]) * (edge_two[1][1] - edge_one[0][1]) -
|
||||
(edge_one[1][1] - edge_one[0][1]) * (edge_two[1][0] - edge_one[0][0]);
|
||||
if curr != 0.0 {
|
||||
if curr * prev < 0.0 {
|
||||
return Err("Not convex.");
|
||||
} else {
|
||||
prev = curr;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Check if points are both inside the set
|
||||
let (mut i, mut j, mut c) = (0, self.vertices.len() - 1, false);
|
||||
loop {
|
||||
if i >= self.vertices.len() {
|
||||
break;
|
||||
}
|
||||
|
||||
|
||||
if ((self.vertices[i][1] > a[1]) != (self.vertices[j][1] > a[1])) && (a[0] < (self.vertices[j][0] - self.vertices[i][0]) * (a[1] - self.vertices[i][1]) / (self.vertices[j][1] - self.vertices[i][1]) + self.vertices[i][0]) {
|
||||
c = !c;
|
||||
}
|
||||
j = i;
|
||||
i += 1;
|
||||
}
|
||||
|
||||
if !c {
|
||||
return Err("First point not in set.");
|
||||
}
|
||||
|
||||
|
||||
let (mut i, mut j, mut c) = (0, self.vertices.len() - 1, false);
|
||||
loop {
|
||||
if i >= self.vertices.len() {
|
||||
break;
|
||||
}
|
||||
|
||||
|
||||
if ((self.vertices[i][1] > b[1]) != (self.vertices[j][1] > b[1])) && (b[0] < (self.vertices[j][0] - self.vertices[i][0]) * (b[1] - self.vertices[i][1]) / (self.vertices[j][1] - self.vertices[i][1]) + self.vertices[i][0]) {
|
||||
c = !c;
|
||||
}
|
||||
j = i;
|
||||
i += 1;
|
||||
}
|
||||
|
||||
if !c {
|
||||
return Err("Second point not in set.");
|
||||
}
|
||||
|
||||
// Intersect the line with each polygon side
|
||||
let slope = (b[1] - a[1]) / (b[0] - a[0]);
|
||||
let p_intersect = edges.into_iter().map(|p| {
|
||||
let edge_slope = (p[1][1] - p[0][1]) / (p[1][0] - p[0][0]);
|
||||
let d = edge_slope - slope;
|
||||
if d == 0.0 {
|
||||
None
|
||||
} else {
|
||||
Some([((edge_slope * p[0][0] - p[0][1]) - (slope * a[0] - a[1])) / d, ((slope * (edge_slope * p[0][0] - p[0][1])) - (edge_slope * (slope * a[0] - a[1]))) / d])
|
||||
}
|
||||
}).filter(|x| x.is_some()).map(|x| x.map_or([0.0, 0.0], |x| x)).collect::<Vec<[f64; 2]>>();
|
||||
|
||||
// Find the closest distance
|
||||
let a_closest = p_intersect.clone().into_iter().map(|p| (p, (p[0] - a[0]) * (p[0] - a[0]) + (p[1] - a[1]) * (p[1] - a[1]))).min_by(|a, b| a.1.partial_cmp(&b.1).unwrap()).unwrap();
|
||||
let b_closest = p_intersect.into_iter().map(|p| (p, (p[0] - b[0]) * (p[0] - b[0]) + (p[1] - b[1]) * (p[1] - b[1]))).min_by(|a, b| a.1.partial_cmp(&b.1).unwrap()).unwrap();
|
||||
|
||||
let pb = f64::sqrt((a_closest.0[0] - b[0]) * (a_closest.0[0] - b[0]) + (a_closest.0[1] - b[1]) * (a_closest.0[1] - b[1]));
|
||||
let pa = f64::sqrt(a_closest.1);
|
||||
let aq = f64::sqrt((b_closest.0[0] - a[0]) * (b_closest.0[0] - a[0]) + (b_closest.0[1] - a[1]) * (b_closest.0[1] - a[1]));
|
||||
let bq = f64::sqrt(b_closest.1);
|
||||
|
||||
Ok(f64::ln((pb * aq) / (pa * bq)))
|
||||
}
|
||||
}
|
||||
|
||||
fn naive_voronoi_2d(metric: &mut dyn Distance<2>, w: u32, h: u32, points: Vec<(u32, u32)>) {
|
||||
let mut image: RgbImage = ImageBuffer::new(w, h);
|
||||
// All points must be in the width / height
|
||||
for p in points {
|
||||
assert!(p.0 <= w);
|
||||
assert!(p.1 <= h);
|
||||
}
|
||||
|
||||
for i in 0..w {
|
||||
for j in 0..h {
|
||||
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fn main() {
|
||||
|
||||
let triangle = HilbertPoly { vertices: vec![[-8.0, 0.0], [8.0, 0.0], [0.0, 8.0]] };
|
||||
println!("{}", triangle.dist([-2.0, 2.0], [2.0, 2.0]).unwrap());
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user