From bbdad2d96ae5da4ad07ff18de87b8b596ffb9218 Mon Sep 17 00:00:00 2001
From: Jean Privat <jean@pryen.org>
Date: Mon, 21 Sep 2015 15:22:14 -0400
Subject: [PATCH] =?utf8?q?core/math:=20add=20basic=20B=C3=A9zier=20interpola?=
 =?utf8?q?tions=20on=20Float?=
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Signed-off-by: Jean Privat <jean@pryen.org>
---
 lib/core/math.nit |   39 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 39 insertions(+)

diff --git a/lib/core/math.nit b/lib/core/math.nit
index 50b36e9..c08c735 100644
--- a/lib/core/math.nit
+++ b/lib/core/math.nit
@@ -333,6 +333,45 @@ redef class Float
 	# assert -0.5.lerp(0.0, 128.0) == -64.0
 	# ~~~
 	fun lerp(a, b: Float): Float do return (1.0 - self) * a + self * b
+
+	# Quadratic Bézier interpolation between `a` and `b` with an `handle` using `self` as weight
+	#
+	# ~~~
+	# assert  0.00.qerp(0.0, 32.0, 128.0) == 0.0
+	# assert  0.25.qerp(0.0, 32.0, 128.0) == 20.0
+	# assert  0.50.qerp(0.0, 32.0, 128.0) == 48.0
+	# assert  0.75.qerp(0.0, 32.0, 128.0) == 84.0
+	# assert  1.00.qerp(0.0, 32.0, 128.0) == 128.0
+	# ~~~
+	fun qerp(a, handle, b: Float): Float do
+		var p = self
+		var i = 1.0 - p
+		var r =     i*i * a +
+			2.0*i*p * handle +
+			    p*p * b
+		return r
+	end
+
+	# Cubic Bézier interpolation between `a` and `b` with two handles using `self` as weight
+	#
+	# The Cubic Bézier interpolation is the most common one and use two control points.
+	#
+	# ~~~
+	# assert  0.00.cerp(0.0, 32.0, 128.0, 64.0) == 0.0
+	# assert  0.25.cerp(0.0, 32.0, 128.0, 64.0) == 32.5
+	# assert  0.50.cerp(0.0, 32.0, 128.0, 64.0) == 68.0
+	# assert  0.75.cerp(0.0, 32.0, 128.0, 64.0) == 85.5
+	# assert  1.00.cerp(0.0, 32.0, 128.0, 64.0) == 64.0
+	# ~~~
+	fun cerp(a, a_handle, b_handle, b: Float): Float do
+		var p = self
+		var i = 1.0 - p
+		var r =     i*i*i  * a +
+			3.0*i*i*p * a_handle +
+			3.0*i*p*p * b_handle +
+			    p*p*p * b
+		return r
+	end
 end
 
 # Positive float infinite (IEEE 754)
-- 
1.7.9.5