/** 行业常用缓动曲线（Duolingo / Material / 手游 Modal 规范） */

/** 入场：cubic-bezier(0, 0, 0.2, 1) — 快启慢收 */
export function easeEnter(t: number): number {
    return cubicBezierY(t, 0, 0, 0.2, 1);
}

/** 退场：cubic-bezier(0.4, 0, 1, 1) — 快出 */
export function easeExit(t: number): number {
    return cubicBezierY(t, 0.4, 0, 1, 1);
}

/** 庆祝 overshoot：cubic-bezier(0.34, 1.56, 0.64, 1) — Duolingo 奖励弹入 */
export function easeCelebrate(t: number): number {
    return cubicBezierY(t, 0.34, 1.56, 0.64, 1);
}

/** 标准双向往返：cubic-bezier(0.4, 0, 0.2, 1) */
export function easeStandard(t: number): number {
    return cubicBezierY(t, 0.4, 0, 0.2, 1);
}

function cubicBezierY(t: number, x1: number, y1: number, x2: number, y2: number): number {
    if (t <= 0) return 0;
    if (t >= 1) return 1;
    let lo = 0;
    let hi = 1;
    for (let i = 0; i < 10; i++) {
        const mid = (lo + hi) * 0.5;
        if (bezier(x1, x2, mid) < t) lo = mid;
        else hi = mid;
    }
    const u = (lo + hi) * 0.5;
    return bezier(y1, y2, u);
}

function bezier(a: number, b: number, t: number): number {
    const inv = 1 - t;
    return 3 * inv * inv * t * a + 3 * inv * t * t * b + t * t * t;
}