From 38810f749c3443fcd685a077f57b4870ac15c868 Mon Sep 17 00:00:00 2001
From: Emi Simpson <emi@alchemi.dev>
Date: Wed, 17 Nov 2021 23:43:31 -0500
Subject: [PATCH] Replace circumcenter algorithm with a faster one

---
 src/main.rs | 39 +++++++++++++++++++++++----------------
 1 file changed, 23 insertions(+), 16 deletions(-)

diff --git a/src/main.rs b/src/main.rs
index c66e0ba..8c9aac8 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,5 +1,6 @@
 pub mod util;
 
+use macroquad::prelude::DMat3;
 use smallvec::SmallVec;
 use smallvec::smallvec;
 use std::collections::HashSet;
@@ -337,25 +338,31 @@ impl Triangle {
 	}
 
 	fn calc_circumcenter(a: DVec2, b: DVec2, c: DVec2) -> (DVec2, f64) {
-		let len_a = b.distance(c);
-		let len_b = c.distance(a);
-		let len_c = a.distance(b);
 
-		let cos_a = (len_b.powf(2.0) + len_c.powf(2.0) - len_a.powf(2.0)) / (2.0 * len_b * len_c );
-		let cos_b = (len_c.powf(2.0) + len_a.powf(2.0) - len_b.powf(2.0)) / (2.0 * len_c * len_a );
+		let mag_a2 = a.powf(2.).dot(DVec2::ONE);
+		let mag_b2 = b.powf(2.).dot(DVec2::ONE);
+		let mag_c2 = c.powf(2.).dot(DVec2::ONE);
 
-		let ang_a = f64::acos(cos_a);
-		let ang_b = f64::acos(cos_b);
-		let ang_c = PI - ang_a - ang_b;
-
-		let sin_2a = f64::sin(2.0 * ang_a);
-		let sin_2b = f64::sin(2.0 * ang_b);
-		let sin_2c = f64::sin(2.0 * ang_c);
-
-		let circumcenter = DVec2::new(
-			(a.x * sin_2a + b.x * sin_2b + c.x * sin_2c) / (sin_2a + sin_2b + sin_2c),
-			(a.y * sin_2a + b.y * sin_2b + c.y * sin_2c) / (sin_2a + sin_2b + sin_2c),
+		let s = DVec2::new(
+			DMat3::from_cols_array(&[
+				mag_a2, a.y, 1.,
+				mag_b2, b.y, 1.,
+				mag_c2, c.y, 1.,
+			]).determinant() * 0.5,
+			DMat3::from_cols_array(&[
+				a.x, mag_a2, 1.,
+				b.x, mag_b2, 1.,
+				c.x, mag_c2, 1.,
+			]).determinant() * 0.5,
 		);
+
+		let little_a = DMat3::from_cols_array(&[
+			a.x, a.y, 1.,
+			b.x, b.y, 1.,
+			c.x, c.y, 1.,
+		]).determinant();
+
+		let circumcenter = s / little_a;
 		let radius = circumcenter.distance(a);
 
 		(circumcenter, radius)