core/math: add basic Bézier interpolations on Float

Signed-off-by: Jean Privat <jean@pryen.org>

diff --git a/lib/core/math.nit b/lib/core/math.nit
index 50b36e9..c08c735 100644 (file)
--- 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)