Make bilinear patch splitting a little smarter.

This way it doesn't just keep splitting on the same axis
repeatedly, creating narrow, long patches..

src/lerp.rs

@@ -3,7 +3,7 @@
 use math3d::{Matrix4x4, Normal, Point, Vector};
 
 /// Trait for allowing a type to be linearly interpolated.
-pub trait Lerp {
+pub trait Lerp: Copy {
     fn lerp(self, other: Self, alpha: f32) -> Self;
 }
 
@@ -17,7 +17,7 @@ pub fn lerp<T: Lerp>(a: T, b: T, alpha: f32) -> T {
 
 /// Interpolates a slice of data as if each adjecent pair of elements
 /// represent a linear segment.
-pub fn lerp_slice<T: Lerp + Copy>(s: &[T], alpha: f32) -> T {
+pub fn lerp_slice<T: Lerp>(s: &[T], alpha: f32) -> T {
     debug_assert!(!s.is_empty());
     debug_assert!(alpha >= 0.0);
     debug_assert!(alpha <= 1.0);
@@ -73,6 +73,33 @@ impl<T: Lerp> Lerp for (T, T) {
     }
 }
 
+impl<T: Lerp> Lerp for [T; 2] {
+    fn lerp(self, other: Self, alpha: f32) -> Self {
+        [self[0].lerp(other[0], alpha), self[1].lerp(other[1], alpha)]
+    }
+}
+
+impl<T: Lerp> Lerp for [T; 3] {
+    fn lerp(self, other: Self, alpha: f32) -> Self {
+        [
+            self[0].lerp(other[0], alpha),
+            self[1].lerp(other[1], alpha),
+            self[2].lerp(other[2], alpha),
+        ]
+    }
+}
+
+impl<T: Lerp> Lerp for [T; 4] {
+    fn lerp(self, other: Self, alpha: f32) -> Self {
+        [
+            self[0].lerp(other[0], alpha),
+            self[1].lerp(other[1], alpha),
+            self[2].lerp(other[2], alpha),
+            self[3].lerp(other[3], alpha),
+        ]
+    }
+}
+
 impl Lerp for glam::Vec4 {
     fn lerp(self, other: glam::Vec4, alpha: f32) -> glam::Vec4 {
         (self * (1.0 - alpha)) + (other * alpha)

src/surface/bilinear_patch.rs

@@ -1,5 +1,8 @@
 use super::{point_order, PointOrder, Splitable, MAX_EDGE_DICE};
-use crate::{lerp::lerp, math::Point};
+use crate::{
+    lerp::{lerp, lerp_slice},
+    math::Point,
+};
 
 #[derive(Debug, Copy, Clone)]
 pub struct BilinearPatch<'a> {
@@ -41,8 +44,8 @@ impl<'a> Splitable for BilinearSubPatch<'a> {
     where
         F: Fn(Point, Point) -> f32,
     {
-        // Get the points of the sub-patch.
-        let patch = self.original.control_points[0];
+        // Get the points of the sub-patch at time 0.5.
+        let patch = lerp_slice(self.original.control_points, 0.5);
         let points = [
             bilerp_point(patch, self.clip[0]),
             bilerp_point(patch, self.clip[1]),
@@ -58,9 +61,38 @@ impl<'a> Splitable for BilinearSubPatch<'a> {
             metric(points[3], points[0]),
         ];
 
-        // Do the split, if needed.
-        for i in 0..4 {
-            if self.must_split[i] || edge_metric[i] > MAX_EDGE_DICE as f32 {
+        // Find an edge to split, if any.
+        let split_edge_index = {
+            // Find the "longest" edge in terms of the metric.
+            let (edge_i, m) = edge_metric
+                .iter()
+                .enumerate()
+                .max_by(|a, b| {
+                    if a.1 > b.1 {
+                        std::cmp::Ordering::Greater
+                    } else {
+                        std::cmp::Ordering::Less
+                    }
+                })
+                .unwrap();
+
+            // Return an edge to split, if a split is needed.
+            if *m > MAX_EDGE_DICE as f32 {
+                // Split needed because of over-long edge.
+                Some(edge_i)
+            } else {
+                // Return the the first edge with "must_split" set, if any.
+                // Otherwise returns `None`.
+                self.must_split
+                    .iter()
+                    .enumerate()
+                    .find(|a| *a.1)
+                    .map(|a| a.0)
+            }
+        };
+
+        // Do the split if needed
+        if let Some(i) = split_edge_index {
             let edge_1 = (i, (i + 1) % 4);
             let edge_2 = ((i + 2) % 4, (i + 3) % 4);
             let new_must_split = {
@@ -72,9 +104,8 @@ impl<'a> Splitable for BilinearSubPatch<'a> {
 
             let midpoint_1 = lerp(self.clip[edge_1.0], self.clip[edge_1.1], 0.5);
             let midpoint_2 = {
-                    let alpha = if self.must_split[edge_2.0]
-                        || edge_metric[edge_2.0] > MAX_EDGE_DICE as f32
-                    {
+                let alpha =
+                    if self.must_split[edge_2.0] || edge_metric[edge_2.0] > MAX_EDGE_DICE as f32 {
                         0.5
                     } else {
                         let edge_2_dice_rate = edge_metric[edge_2.0].ceil();
@@ -99,11 +130,10 @@ impl<'a> Splitable for BilinearSubPatch<'a> {
             patch_2.clip[edge_1.0] = midpoint_1;
             patch_2.clip[edge_2.1] = midpoint_2;
 
-                return Some((patch_1, patch_2));
-            }
-        }
-
-        // No splitting needed to be done.
+            Some((patch_1, patch_2))
+        } else {
+            // No split
             None
         }
     }
+}