From ac732863d3cda11e01fd4e506a6c00f8bbe8114c Mon Sep 17 00:00:00 2001
From: EvilMuffinHa <hkailadka88@gmail.com>
Date: Thu, 16 Jun 2022 17:10:32 -0400
Subject: [PATCH] first commit - hilbert 2d poly

---
 .gitignore  |   1 +
 Cargo.lock  | 331 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 Cargo.toml  |   9 ++
 src/main.rs | 141 ++++++++++++++++++++++
 4 files changed, 482 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 Cargo.lock
 create mode 100644 Cargo.toml
 create mode 100644 src/main.rs

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ea8c4bf
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+/target
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..f051aa0
--- /dev/null
+++ b/Cargo.lock
@@ -0,0 +1,331 @@
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diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..beda60c
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,9 @@
+[package]
+name = "hilbert"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+image = "0.23.14"
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..b34ac53
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,141 @@
+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());
+}