From e0eb1e28c5a4d1d304cf06363bce1e42f55e47f6 Mon Sep 17 00:00:00 2001
From: matt <matt@dont-ping.me>
Date: Mon, 23 Oct 2023 17:03:35 -0700
Subject: [PATCH] feat: add Lagrange interpolation

- added only as 3 buffer interpolation
---
 packages/maath/src/buffer.ts | 20 +++++++++++++++++++-
 packages/maath/src/misc.ts   | 16 ++++++++++++++++
 2 files changed, 35 insertions(+), 1 deletion(-)

diff --git a/packages/maath/src/buffer.ts b/packages/maath/src/buffer.ts
index b36d6e8..0fc6ea9 100644
--- a/packages/maath/src/buffer.ts
+++ b/packages/maath/src/buffer.ts
@@ -6,7 +6,7 @@
 
 import { Quaternion, Vector3 } from "three";
 import type { TypedArray, MyVector2, MyVector3 } from "./ctypes";
-import { lerp as _lerp } from "./misc";
+import { lerp as _lerp, lpi3 as _lpi3 } from "./misc";
 import * as v2 from "./vector2";
 import * as v3 from "./vector3";
 
@@ -84,6 +84,24 @@ export function lerp(
   }
 }
 
+/**
+ *
+ * Interpolates using Lagrane Interpolation between three buffers, passed in as array into final
+ *
+ * @param buffers array of three buffers: bufferA, bufferB, bufferC
+ * @param final interpolation buffer (output)
+ * @param t time, reccomended
+ */
+export function lpi3(
+  buffers: [TypedArray, TypedArray, TypedArray],
+  final: TypedArray,
+  t: number
+) {
+  for (let i = 0; i < buffers[0].length; i++) {
+    final[i] = _lpi3([buffers[0][i], buffers[1][i], buffers[2][i]], t);
+  }
+}
+
 // TODO add stride
 // TODO Fix types & vectors
 /**
diff --git a/packages/maath/src/misc.ts b/packages/maath/src/misc.ts
index 9d050f5..b973cc2 100644
--- a/packages/maath/src/misc.ts
+++ b/packages/maath/src/misc.ts
@@ -174,6 +174,22 @@ export function fade(t: number) {
   return t * t * t * (t * (t * 6 - 15) + 10);
 }
 
+/**
+ *
+ * Returns the result of lagrange polynomial interpolation between A, B, and C by the time of t
+ *
+ * @param v array of three numbers to interpolate between
+ * @param t time
+ * @returns 3-point interpolation given pos of t
+ */
+export function lpi3(v: [number, number, number], t: number) {
+  return (
+    2 * (t - 1) * (t - 0.5) * v[0] -
+    4 * (t - 1) * t * v[1] +
+    2 * (t - 0.5) * t * v[2]
+  );
+}
+
 /**
  *
  * Returns the result of linearly interpolating between input A and input B by input T.