fix cubic_hermite coefficients & powers

src/interpolate.rs

@@ -127,15 +127,16 @@ macro_rules! impl_Interpolate {
         let three_t = t * 3.;
         let t2 = t * t;
         let t3 = t2 * t;
-        let two_t3 = t3 * two_t;
+        let two_t3 = t2 * two_t;
-        let three_t2 = t2 * three_t;
+        let two_t2 = t * two_t;
+        let three_t2 = t * three_t;
 
         // tangents
         let m0 = (b.1 - x.1) / (b.0 - x.0);
         let m1 = (y.1 - a.1) / (y.0 - a.0);
 
         a.1 * (two_t3 - three_t2 + 1.)
-          + m0 * (t3 - t2 * two_t + t)
+          + m0 * (t3 - two_t2 + t)
           + b.1 * (three_t2 - two_t3)
           + m1 * (t3 - t2)
       }
@@ -192,15 +193,16 @@ macro_rules! impl_InterpolateT {
         let three_t = t * 3.;
         let t2 = t * t;
         let t3 = t2 * t;
-        let two_t3 = t3 * two_t;
+        let two_t3 = t2 * two_t;
-        let three_t2 = t2 * three_t;
+        let two_t2 = t * two_t;
+        let three_t2 = t * three_t;
 
         // tangents
         let m0 = (b.1 - x.1) / (Self::from(b.0 - x.0));
         let m1 = (y.1 - a.1) / (Self::from(y.0 - a.0));
 
         a.1 * (two_t3 - three_t2 + 1.)
-          + m0 * (t3 - t2 * two_t + t)
+          + m0 * (t3 - two_t2 + t)
           + b.1 * (three_t2 - two_t3)
           + m1 * (t3 - t2)
       }

tests/integ.rs

@@ -131,6 +131,12 @@ fn linear_interpolation_several_keys() {
   assert_eq!(spline.clamped_sample(11.), Some(4.));
 }
 
+#[test]
+fn cubic_interpolation() {
+  let start = Key::new(0., 0., Interpolation::CatmullRom);
+  let end = Key::new(1., 10., Interpolation::default());
+}
+
 #[test]
 fn several_interpolations_several_keys() {
   let start = Key::new(0., 0., Interpolation::Step(0.5));