1 files changed, 88 insertions, 0 deletions
diff --git a/apps/web/src/lib/animation/bezier.ts b/apps/web/src/lib/animation/bezier.ts
new file mode 100644
index 00000000..4dce027e
--- /dev/null
+++ b/apps/web/src/lib/animation/bezier.ts
@@ -0,0 +1,88 @@
+import type { ScalarAnimationKey } from "@/lib/animation/types";
+
+export function getBezierPoint({
+	progress,
+	p0,
+	p1,
+	p2,
+	p3,
+}: {
+	progress: number;
+	p0: number;
+	p1: number;
+	p2: number;
+	p3: number;
+}) {
+	const mt = 1 - progress;
+	return (
+		mt * mt * mt * p0 +
+		3 * mt * mt * progress * p1 +
+		3 * mt * progress * progress * p2 +
+		progress * progress * progress * p3
+	);
+}
+
+export function getDefaultRightHandle({
+	leftKey,
+	rightKey,
+}: {
+	leftKey: ScalarAnimationKey;
+	rightKey: ScalarAnimationKey;
+}) {
+	const span = rightKey.time - leftKey.time;
+	const valueDelta = rightKey.value - leftKey.value;
+	return {
+		dt: span / 3,
+		dv: valueDelta / 3,
+	};
+}
+
+export function getDefaultLeftHandle({
+	leftKey,
+	rightKey,
+}: {
+	leftKey: ScalarAnimationKey;
+	rightKey: ScalarAnimationKey;
+}) {
+	const span = rightKey.time - leftKey.time;
+	const valueDelta = rightKey.value - leftKey.value;
+	return {
+		dt: -span / 3,
+		dv: -valueDelta / 3,
+	};
+}
+
+export function solveBezierProgressForTime({
+	time,
+	leftKey,
+	rightKey,
+}: {
+	time: number;
+	leftKey: ScalarAnimationKey;
+	rightKey: ScalarAnimationKey;
+}) {
+	let lower = 0;
+	let upper = 1;
+	const rightHandle =
+		leftKey.rightHandle ?? getDefaultRightHandle({ leftKey, rightKey });
+	const leftHandle =
+		rightKey.leftHandle ?? getDefaultLeftHandle({ leftKey, rightKey });
+
+	for (let iteration = 0; iteration < 20; iteration++) {
+		const mid = (lower + upper) / 2;
+		const estimate = getBezierPoint({
+			progress: mid,
+			p0: leftKey.time,
+			p1: leftKey.time + rightHandle.dt,
+			p2: rightKey.time + leftHandle.dt,
+			p3: rightKey.time,
+		});
+		if (estimate < time) {
+			lower = mid;
+		} else {
+			upper = mid;
+		}
+	}
+
+	return (lower + upper) / 2;
+}