Implement "hilbert spiral" bucket rendering order.

src/renderer.rs

@@ -118,18 +118,32 @@ impl<'a> Renderer<'a> {
             let _ = io::stdout().flush();
 
             // Populate job queue
-            let bucket_n = {
-                let bucket_count_x = (width / bucket_size) + 1;
-                let bucket_count_y = (height / bucket_size) + 1;
+            let hilbert_count = (thread_count as f32).sqrt() as u32;
+            let (middle_bucket, bucket_n) = {
+                let bucket_count_x =
+                    (width / bucket_size) + if (width % bucket_size) != 0 { 1 } else { 0 };
+                let bucket_count_y =
+                    (height / bucket_size) + if (height % bucket_size) != 0 { 1 } else { 0 };
                 let larger = cmp::max(bucket_count_x, bucket_count_y);
                 let pow2 = upper_power_of_two(larger);
-                pow2 * pow2
+                let buffer = hilbert_count; // For hilbert spiral.
+                (
+                    (bucket_count_x / 2, bucket_count_y / 2),
+                    (pow2 + buffer) * (pow2 + buffer),
+                )
             };
-            for hilbert_d in 0..bucket_n {
-                let (bx, by) = hilbert::decode(hilbert_d);
+            for hilbert_spiral_i in 0..bucket_n {
+                let (bx, by) =
+                    crate::space_fill::hilbert_spiral::decode(hilbert_spiral_i, hilbert_count);
 
-                let x = bx * bucket_size;
-                let y = by * bucket_size;
+                let bx = middle_bucket.0 as i32 + bx;
+                let by = middle_bucket.1 as i32 + by;
+                if bx < 0 || by < 0 {
+                    continue;
+                }
+
+                let x = bx as u32 * bucket_size;
+                let y = by as u32 * bucket_size;
                 let w = if width >= x {
                     min(bucket_size, width - x)
                 } else {

src/space_fill.rs

@@ -11,13 +11,13 @@ pub mod hilbert {
     /// y: The y coordinate.  Must be no greater than 2^16-1.
     ///
     /// Returns the hilbert curve index corresponding to the (x,y) coordinates given.
-    pub fn encode(x: u32, y: u32) -> u32 {
+    pub fn encode(x: u32, y: u32, n: u32) -> u32 {
         assert!(x < N);
         assert!(y < N);
 
         let (mut x, mut y) = (x, y);
         let mut d = 0;
-        let mut s = N >> 1;
+        let mut s = n >> 1;
         while s > 0 {
             let rx = if (x & s) > 0 { 1 } else { 0 };
             let ry = if (y & s) > 0 { 1 } else { 0 };
@@ -35,11 +35,11 @@ pub mod hilbert {
     /// d: The hilbert curve index.
     ///
     /// Returns the (x, y) coords at the given index.
-    pub fn decode(d: u32) -> (u32, u32) {
+    pub fn decode(d: u32, n: u32) -> (u32, u32) {
         let (mut x, mut y) = (0, 0);
         let mut s = 1;
         let mut t = d;
-        while s < N {
+        while s < n {
             let rx = 1 & (t >> 1);
             let ry = 1 & (t ^ rx);
             (x, y) = hilbert_rotate(s, rx, ry, x, y);
@@ -118,6 +118,76 @@ pub mod morton {
     }
 }
 
+/// Yields coordinates in outward spiral, but incorporating a Hilbert
+/// curve at the smaller scales.
+pub mod hilbert_spiral {
+    /// Convert from hilbert-spiral index to (x,y).
+    ///
+    /// Note: this returns both negative and positive coordinates.
+    /// It starts at 0,0 and spirals outwards.
+    ///
+    /// i: The hilbert-spiral index.
+    /// hilbert_size: the size of the hulbert blocks on a side.  Will be
+    ///               rounded down to the nearest power of two.
+    ///
+    /// Returns the (x, y) coords at the given index.
+    pub fn decode(i: u32, hilbert_size: u32) -> (i32, i32) {
+        assert!(hilbert_size > 0);
+        let hilbert_size = 1 << (31 - u32::leading_zeros(hilbert_size));
+
+        let hilbert_cells = hilbert_size * hilbert_size;
+
+        let hilbert_i = i % hilbert_cells;
+        let spiral_i = i / hilbert_cells;
+
+        let (mut sx, mut sy, section) = decode_spiral(spiral_i);
+        sx = (sx * hilbert_size as i32) - (hilbert_size / 2) as i32;
+        sy = (sy * hilbert_size as i32) - (hilbert_size / 2) as i32;
+
+        let (hx, hy) = {
+            let (hx, hy) = super::hilbert::decode(hilbert_i, hilbert_size);
+            let a = hilbert_size - 1;
+            match section {
+                0 => (hx, a - hy),
+                1 => (a - hy, hx),
+                2 => (a - hx, hy),
+                3 => (hy, a - hx),
+                _ => unreachable!(),
+            }
+        };
+
+        (sx + hx as i32, sy + hy as i32)
+    }
+
+    pub fn decode_spiral(i: u32) -> (i32, i32, u32) {
+        if i == 0 {
+            return (0, 0, 3);
+        }
+
+        // 0 = first ring outside of center, 1 = second, and so on.
+        let ring = (((i as f64).sqrt() - 1.0) / 2.0) as u32;
+
+        // The size of the ring along one side.
+        let size = 1 + ((ring + 1) * 2);
+
+        let n = i - ((size - 2) * (size - 2)); // The zero-indexed cell of the ring.
+        let arm = n / (size - 1); // The arm of the ring.
+        let arm_n = n % (size - 1); // The index within the arm of the ring.
+
+        // The two coordinates.  They just need to be flipped around depending on the arm.
+        let radius = ring as i32 + 1;
+        let d = -(size as i32 / 2) + 1 + arm_n as i32;
+
+        match arm {
+            0 => (d, -radius, 0),
+            1 => (radius, d, if arm_n == (size - 2) { 2 } else { 1 }),
+            2 => (-d, radius, 2),
+            3 => (-radius, -d, 3),
+            _ => unreachable!(),
+        }
+    }
+}
+
 //-------------------------------------------------------------
 
 #[cfg(test)]