From 1a6b5bd27dcca793c92b7c0e8c68058f05378a62 Mon Sep 17 00:00:00 2001
From: Patrick Walton <pcwalton@mimiga.net>
Date: Sat, 29 Dec 2018 18:26:08 -0800
Subject: [PATCH] Optimize cubic Bezier sampling a bit

---
 utils/tile-svg/src/main.rs | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/utils/tile-svg/src/main.rs b/utils/tile-svg/src/main.rs
index afb5d0e3..00c002b9 100644
--- a/utils/tile-svg/src/main.rs
+++ b/utils/tile-svg/src/main.rs
@@ -1736,12 +1736,15 @@ impl CubicAxis {
 }
 impl SolveT for CubicAxis {
     fn sample(&self, t: f32) -> f32 {
-        // FIXME(pcwalton): Use Horner's method or something.
-        let p01 = lerp(self.from, self.ctrl0, t);
-        let p12 = lerp(self.ctrl0, self.ctrl1, t);
-        let p23 = lerp(self.ctrl1, self.to, t);
-        let (p012, p123) = (lerp(p01, p12, t), lerp(p12, p23, t));
-        lerp(p012, p123, t)
+        let t2 = t * t;
+        let t3 = t2 * t;
+
+        let c3 = self.to + 3.0 * (self.ctrl0 - self.ctrl1) - self.from;
+        let c2 = 3.0 * (self.from - 2.0 * self.ctrl0 + self.ctrl1);
+        let c1 = 3.0 * (self.ctrl0 - self.from);
+        let c0 = self.from;
+
+        c3 * t3 + c2 * t2 + c1 * t + c0
     }
     fn sample_deriv(&self, t: f32) -> f32 {
         let inv_t = 1.0 - t;