feat: implement index section 2

Co-authored-by: Sylvanysc <Sylvanysc@users.noreply.github.com>
Co-authored-by: xudeyu444 <xudeyu444@users.noreply.github.com>
Co-authored-by: 奕 <a18355849597@outlook.com>

utils/index.ts

@@ -0,0 +1,41 @@
+export function range(start: number, end: number, x: number): number {
+  return Math.min(end, Math.max(start, x));
+}
+
+export function getCubicBezier(x1: number, y1: number, x2: number, y2: number) {
+  return (t: number) => {
+    const oneMinusT = 1 - t;
+    const oneMinusTSquared = oneMinusT * oneMinusT; // (1-t)^2
+    const oneMinusTCubed = oneMinusTSquared * oneMinusT; // (1-t)^3
+
+    const tSquared = t * t; // t^2
+    const tCubed = tSquared * t; // t^3
+
+    // Y(t) = P0y*(1-t)^3 + 3*P1y*t*(1-t)^2 + 3*P2y*t^2*(1-t) + P3y*t^3
+    const y =
+      0 * oneMinusTCubed +
+      3 * y2 * t * oneMinusTSquared +
+      3 * y1 * tSquared * oneMinusT +
+      1 * tCubed;
+
+    return y;
+  };
+}
+
+export function mergeTimingFunctions(
+  fn1: (t: number) => number,
+  fn2: (t: number) => number
+): (t: number) => number {
+  return (t: number) => {
+    if (t < 0.5) {
+      return fn1(t * 2) / 2; // Scale down for first half
+    }
+    return fn2((t - 0.5) * 2) / 2 + 0.5; // Scale down for second half and offset
+  };
+}
+
+export const eieo = getCubicBezier(0.5, 0.0, 0.5, 1.0);
+
+export const eieo2 = mergeTimingFunctions(eieo, eieo);
+
+export const riro = getCubicBezier(0.0, 0.5, 1.0, 0.5);