captchaforge 0.2.36

/// Human behavior simulation — realistic mouse, keyboard, and scroll patterns.
///
/// Anti-bot detectors analyze:
///   - Mouse trajectory (bots move in straight lines)
///   - Typing cadence (bots type at constant speed)
///   - Scroll patterns (bots scroll uniformly)
///   - Idle time (bots never pause)
///
/// This module generates Bézier-curve mouse paths, variable typing delays,
/// and natural scroll increments. All async fns use SmallRng (Send-safe) so
/// futures remain Send-compatible for multi-threaded Tokio runtimes.
use chromiumoxide::cdp::browser_protocol::input::{
    DispatchKeyEventParams, DispatchKeyEventType, DispatchMouseEventParams, DispatchMouseEventType,
    MouseButton,
};
use chromiumoxide::Page;
use rand::{Rng, SeedableRng};
use std::time::Duration;

/// Move mouse along a Bézier curve from (x0,y0) to (x1,y1).
/// Generates 8-20 intermediate points with realistic timing.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::mouse_move_bezier;
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// mouse_move_bezier(page, 0.0, 0.0, 400.0, 300.0).await?;
/// # Ok(()) }
/// ```
pub async fn mouse_move_bezier(
    page: &Page,
    x0: f64,
    y0: f64,
    x1: f64,
    y1: f64,
) -> anyhow::Result<()> {
    let mut rng = rand::rngs::StdRng::from_entropy();
    let steps = rng.gen_range(8..=20);

    // Two random control points for the cubic Bézier
    let cx1 = x0 + (x1 - x0) * rng.gen_range(0.2..0.5) + rng.gen_range(-30.0..30.0);
    let cy1 = y0 + (y1 - y0) * rng.gen_range(0.1..0.4) + rng.gen_range(-20.0..20.0);
    let cx2 = x0 + (x1 - x0) * rng.gen_range(0.6..0.9) + rng.gen_range(-20.0..20.0);
    let cy2 = y0 + (y1 - y0) * rng.gen_range(0.5..0.8) + rng.gen_range(-15.0..15.0);

    for i in 0..=steps {
        let t = i as f64 / steps as f64;
        let u = 1.0 - t;

        // Cubic Bézier: B(t) = (1-t)³P0 + 3(1-t)²tP1 + 3(1-t)t²P2 + t³P3
        let x = u * u * u * x0 + 3.0 * u * u * t * cx1 + 3.0 * u * t * t * cx2 + t * t * t * x1;
        let y = u * u * u * y0 + 3.0 * u * u * t * cy1 + 3.0 * u * t * t * cy2 + t * t * t * y1;

        let params = DispatchMouseEventParams::builder()
            .r#type(DispatchMouseEventType::MouseMoved)
            .x(x)
            .y(y)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(params).await?;

        // Variable delay: faster in middle, slower at start/end (ease-in-out)
        let ease = (std::f64::consts::PI * t).sin(); // 0 at endpoints, 1 at midpoint
        let base_ms = rng.gen_range(8..25);
        let delay_ms = base_ms + ((1.0 - ease) * 15.0) as u64;
        tokio::time::sleep(Duration::from_millis(delay_ms)).await;
    }

    Ok(())
}

/// Move along a real-human recorded trajectory rather than a parametric
/// Bézier. Modern bot detectors (Akamai, DataDome, PerimeterX) train
/// classifiers on per-event features that distinguish parametric
/// curves from biomechanical motion — see [`crate::mouse_traces`] for
/// the full motivation.
///
/// Picks a random trace from the bundled library, rotates and scales
/// it onto the requested `(x0, y0) → (x1, y1)`, and dispatches one
/// mouse-event per trace point with the recorded inter-event delay
/// and ±1.5 px per-axis jitter.
///
/// Per-call cost depends on the picked trace — short-direct
/// (`direct_fast`, ~370ms) to long-careful (`slow_careful`, ~750ms).
/// Use [`mouse_move_bezier`] when you need a tight upper bound on
/// move time; use this when staying inside the detector envelope
/// matters more than ~hundreds-of-ms tail latency.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::mouse_move_human;
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// mouse_move_human(page, 0.0, 0.0, 400.0, 300.0).await?;
/// # Ok(()) }
/// ```
pub async fn mouse_move_human(
    page: &Page,
    x0: f64,
    y0: f64,
    x1: f64,
    y1: f64,
) -> anyhow::Result<()> {
    let mut rng = rand::rngs::StdRng::from_entropy();
    let trace = crate::mouse_traces::pick_trace(&mut rng);
    crate::mouse_traces::replay_trace(page, x0, y0, x1, y1, trace, 1.5).await
}

/// Click at position with realistic mouse-down delay.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::click_realistic;
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// click_realistic(page, 200.0, 150.0).await?;
/// # Ok(()) }
/// ```
pub async fn click_realistic(page: &Page, x: f64, y: f64) -> anyhow::Result<()> {
    let mut rng = rand::rngs::StdRng::from_entropy();

    // Mouse down
    let down = DispatchMouseEventParams::builder()
        .r#type(DispatchMouseEventType::MousePressed)
        .x(x)
        .y(y)
        .button(MouseButton::Left)
        .click_count(1)
        .build()
        .map_err(anyhow::Error::msg)?;
    page.execute(down).await?;

    // Realistic hold time: 50-150ms
    tokio::time::sleep(Duration::from_millis(rng.gen_range(50..150))).await;

    // Mouse up
    let up = DispatchMouseEventParams::builder()
        .r#type(DispatchMouseEventType::MouseReleased)
        .x(x)
        .y(y)
        .button(MouseButton::Left)
        .click_count(1)
        .build()
        .map_err(anyhow::Error::msg)?;
    page.execute(up).await?;

    Ok(())
}

/// Type text with human-like cadence: variable inter-key delays, occasional pauses.
/// Average typing speed: ~200ms per character (60 WPM) with variance.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::type_realistic;
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// type_realistic(page, "hello world").await?;
/// # Ok(()) }
/// ```
pub async fn type_realistic(page: &Page, text: &str) -> anyhow::Result<()> {
    let mut rng = rand::rngs::StdRng::from_entropy();

    for (i, ch) in text.chars().enumerate() {
        let key_text = ch.to_string();

        // Key down
        let down = DispatchKeyEventParams::builder()
            .r#type(DispatchKeyEventType::KeyDown)
            .text(&key_text)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(down).await?;

        // Key press delay: 30-80ms
        tokio::time::sleep(Duration::from_millis(rng.gen_range(30..80))).await;

        // Key up
        let up = DispatchKeyEventParams::builder()
            .r#type(DispatchKeyEventType::KeyUp)
            .text(&key_text)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(up).await?;

        // Inter-key delay: 80-250ms with occasional longer pauses
        let base = rng.gen_range(80..250);
        let pause = if i > 0 && i % rng.gen_range(4..10) == 0 {
            rng.gen_range(200..600) // "thinking" pause every few characters
        } else {
            0
        };
        tokio::time::sleep(Duration::from_millis(base + pause)).await;
    }

    Ok(())
}

/// Type text with bigram-aware human keystroke timing.
///
/// Uses [`crate::keystroke_timing::plan_keystrokes`] to produce a
/// schedule whose per-bigram inter-key gaps and per-character
/// hold-times match real-human envelopes (Dhakal et al. CHI 2018
/// envelope), then dispatches each keydown/keyup with the planned
/// timing.
///
/// Compared to [`type_realistic`] (which uses uniform 80–250ms gaps):
///
/// - Hot bigrams (`th`, `he`, `in`, ...) are typed at 60–110ms
///   intervals — over-trained motor programs are FAST.
/// - Cold bigrams (`qz`, `xj`, ...) are typed at 180–320ms intervals.
/// - Digit-pairs use a slower envelope because the number row is
///   not over-trained.
/// - Optional typo injection: at low probability (1.5% by default),
///   types a QWERTY-neighbour wrong character then a backspace then
///   the correct character — exactly the pattern detectors look for
///   to confirm a human typist.
/// - Optional thinking pauses (200–600ms) at the configured rate.
///
/// Backspaces (Unicode BS, `\u{0008}`) emitted by the planner are
/// dispatched as the `Backspace` named key via CDP.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::type_human;
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// type_human(page, "the quick brown fox").await?;
/// # Ok(()) }
/// ```
pub async fn type_human(page: &Page, text: &str) -> anyhow::Result<()> {
    use crate::keystroke_timing::{plan_keystrokes, TypingPlan};
    let mut rng = rand::rngs::StdRng::from_entropy();
    let plan = plan_keystrokes(text, TypingPlan::default(), &mut rng);
    for k in plan {
        if k.gap_ms_before > 0 {
            tokio::time::sleep(Duration::from_millis(k.gap_ms_before as u64)).await;
        }
        let down_builder = if k.ch == '\u{0008}' {
            DispatchKeyEventParams::builder()
                .r#type(DispatchKeyEventType::KeyDown)
                .key("Backspace")
                .windows_virtual_key_code(8)
        } else {
            let key_text = k.ch.to_string();
            DispatchKeyEventParams::builder()
                .r#type(DispatchKeyEventType::KeyDown)
                .text(key_text)
        };
        page.execute(down_builder.build().map_err(anyhow::Error::msg)?)
            .await?;
        tokio::time::sleep(Duration::from_millis(k.hold_ms as u64)).await;
        let up_builder = if k.ch == '\u{0008}' {
            DispatchKeyEventParams::builder()
                .r#type(DispatchKeyEventType::KeyUp)
                .key("Backspace")
                .windows_virtual_key_code(8)
        } else {
            let key_text = k.ch.to_string();
            DispatchKeyEventParams::builder()
                .r#type(DispatchKeyEventType::KeyUp)
                .text(key_text)
        };
        page.execute(up_builder.build().map_err(anyhow::Error::msg)?)
            .await?;
    }
    Ok(())
}

/// Scroll with human-like pattern: variable speed, direction micro-corrections.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::{scroll_realistic, ScrollDirection};
/// # async fn example(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// scroll_realistic(page, ScrollDirection::Down, 500).await?;
/// # Ok(()) }
/// ```
pub async fn scroll_realistic(
    page: &Page,
    direction: ScrollDirection,
    amount: u32,
) -> anyhow::Result<()> {
    let mut rng = rand::rngs::StdRng::from_entropy();
    let steps = rng.gen_range(3..=8).min(amount);
    let per_step = (amount as f64 / steps as f64) as i32;

    for _ in 0..steps {
        let delta = match direction {
            ScrollDirection::Down => per_step + rng.gen_range(-20..20),
            ScrollDirection::Up => -(per_step + rng.gen_range(-20..20)),
        };

        let js = format!("window.scrollBy(0, {})", delta);
        page.evaluate(js).await?;

        // Variable scroll delay: 100-400ms
        tokio::time::sleep(Duration::from_millis(rng.gen_range(100..400))).await;
    }

    Ok(())
}

/// Random idle pause — simulates reading/thinking time.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::idle_pause;
///
/// # async fn example() {
/// idle_pause().await;
/// # }
/// ```
pub async fn idle_pause() {
    let ms = rand::rngs::StdRng::from_entropy().gen_range(500..2000);
    tokio::time::sleep(Duration::from_millis(ms)).await;
}

/// Short micro-pause between actions (100-400ms).
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::micro_pause;
///
/// # async fn example() {
/// micro_pause().await;
/// # }
/// ```
pub async fn micro_pause() {
    let ms = rand::rngs::StdRng::from_entropy().gen_range(100..400);
    tokio::time::sleep(Duration::from_millis(ms)).await;
}

/// Pause for a uniformly-random duration in `[min_ms, max_ms]`.
///
/// General-purpose human-pacing primitive that complements
/// [`idle_pause`] (1-3s) and [`micro_pause`] (100-400ms) — pick this
/// when you need a specific window without doing the maths yourself.
/// Panics if `min_ms > max_ms`.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::random_pause;
/// # async fn run() {
/// random_pause(150, 600).await;
/// # }
/// ```
pub async fn random_pause(min_ms: u64, max_ms: u64) {
    assert!(
        min_ms <= max_ms,
        "random_pause: min_ms ({min_ms}) > max_ms ({max_ms})"
    );
    if min_ms == max_ms {
        tokio::time::sleep(Duration::from_millis(min_ms)).await;
        return;
    }
    let ms = rand::rngs::StdRng::from_entropy().gen_range(min_ms..=max_ms);
    tokio::time::sleep(Duration::from_millis(ms)).await;
}

/// Triple-click at `(x, y)` to select all text in an input/textarea.
///
/// Shortcut for "select-all-then-type" patterns common when filling
/// captcha answer fields that pre-populate with placeholder text.
/// Three real CDP `MousePressed`/`MouseReleased` pairs at the same
/// coordinate with the click counter incrementing each time — that's
/// what chromium uses to detect a triple-click and apply line-select.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::triple_click;
/// # async fn run(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// triple_click(page, 320.0, 200.0).await?;
/// # Ok(()) }
/// ```
pub async fn triple_click(page: &Page, x: f64, y: f64) -> anyhow::Result<()> {
    use chromiumoxide::cdp::browser_protocol::input::DispatchMouseEventParams;
    for click_count in 1i64..=3 {
        let down = DispatchMouseEventParams::builder()
            .r#type(DispatchMouseEventType::MousePressed)
            .x(x)
            .y(y)
            .button(MouseButton::Left)
            .click_count(click_count)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(down).await?;
        let up = DispatchMouseEventParams::builder()
            .r#type(DispatchMouseEventType::MouseReleased)
            .x(x)
            .y(y)
            .button(MouseButton::Left)
            .click_count(click_count)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(up).await?;
        // Real triple-clicks land within ~80-120ms of each other;
        // anything beyond ~250ms triggers a click + double-click +
        // single-click rather than the line-select gesture.
        tokio::time::sleep(Duration::from_millis(60)).await;
    }
    Ok(())
}

/// Hover the mouse over a viewport coordinate WITHOUT clicking, then
/// dwell for 200-700ms — triggers `mouseenter` / `mouseover` listeners
/// that anti-bot widgets watch for to confirm the visitor's pointer
/// is actually traversing the page (real users rest the cursor on
/// elements; bots warp to coordinates and click).
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::hover_dwell;
/// # async fn run(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// hover_dwell(page, 320.0, 240.0).await?;
/// # Ok(()) }
/// ```
pub async fn hover_dwell(page: &Page, x: f64, y: f64) -> anyhow::Result<()> {
    use chromiumoxide::cdp::browser_protocol::input::DispatchMouseEventParams;
    let mv = DispatchMouseEventParams::builder()
        .r#type(DispatchMouseEventType::MouseMoved)
        .x(x)
        .y(y)
        .build()
        .map_err(anyhow::Error::msg)?;
    page.execute(mv).await?;
    let ms = rand::rngs::StdRng::from_entropy().gen_range(200..700);
    tokio::time::sleep(Duration::from_millis(ms)).await;
    Ok(())
}

/// Touch-style swipe gesture between two viewport coordinates.
///
/// Unlike a desktop drag, mobile swipes have higher initial velocity
/// and a brief decelerating tail. Useful for slider widgets in mobile
/// stealth profiles ([`crate::stealth_profiles::StealthProfile::SafariIphone`],
/// [`crate::stealth_profiles::StealthProfile::ChromeAndroid`]).
///
/// `duration_ms` controls the total swipe time (typical 250-500ms for
/// a fast gesture, 700-1200ms for a deliberate one). 25 sub-steps
/// gives a smooth-enough trajectory without spamming events.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::touch_swipe;
/// # async fn run(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// // Swipe a slider knob 280px to the right.
/// touch_swipe(page, 40.0, 200.0, 320.0, 200.0, 350).await?;
/// # Ok(()) }
/// ```
pub async fn touch_swipe(
    page: &Page,
    x0: f64,
    y0: f64,
    x1: f64,
    y1: f64,
    duration_ms: u64,
) -> anyhow::Result<()> {
    use chromiumoxide::cdp::browser_protocol::input::DispatchMouseEventParams;
    let down = DispatchMouseEventParams::builder()
        .r#type(DispatchMouseEventType::MousePressed)
        .x(x0)
        .y(y0)
        .button(MouseButton::Left)
        .click_count(1)
        .build()
        .map_err(anyhow::Error::msg)?;
    page.execute(down).await?;
    let steps = 25;
    let step_ms = (duration_ms / steps as u64).max(8);
    for s in 1..=steps {
        // Ease-out: faster at start, slower at end.
        let t = s as f64 / steps as f64;
        let eased = 1.0 - (1.0 - t).powi(2);
        let x = x0 + (x1 - x0) * eased;
        let y = y0 + (y1 - y0) * eased;
        let mv = DispatchMouseEventParams::builder()
            .r#type(DispatchMouseEventType::MouseMoved)
            .x(x)
            .y(y)
            .build()
            .map_err(anyhow::Error::msg)?;
        page.execute(mv).await?;
        tokio::time::sleep(Duration::from_millis(step_ms)).await;
    }
    let up = DispatchMouseEventParams::builder()
        .r#type(DispatchMouseEventType::MouseReleased)
        .x(x1)
        .y(y1)
        .button(MouseButton::Left)
        .click_count(1)
        .build()
        .map_err(anyhow::Error::msg)?;
    page.execute(up).await?;
    Ok(())
}

/// Scrub the mouse along a sinusoidal jitter path while standing
/// still — simulates the imperceptible micro-tremor of a real
/// pointing device that anti-bot heuristics use as a humanity signal.
///
/// `cycles` of ±2-4px around the centroid over `cycle_ms` each.
/// 3 cycles × 80ms is a good default; longer dwells benefit from 5-8
/// cycles. Runs synchronously from the CDP perspective but yields
/// to the runtime between events so the page can process them.
///
/// # Example
///
/// ```rust,no_run
/// use captchaforge::behavior::pointer_jitter;
/// # async fn run(page: &chromiumoxide::Page) -> anyhow::Result<()> {
/// pointer_jitter(page, 400.0, 300.0, 5, 80).await?;
/// # Ok(()) }
/// ```
#[cfg(test)]
mod random_pause_tests {
    use super::*;
    use std::time::Instant;

    #[tokio::test]
    async fn random_pause_returns_within_window() {
        let start = Instant::now();
        random_pause(50, 80).await;
        let elapsed_ms = start.elapsed().as_millis() as u64;
        // Allow a generous +50ms scheduler tolerance — tokio sleeps
        // are "at least", not "exactly".
        assert!(
            (50..=130).contains(&elapsed_ms),
            "random_pause(50, 80) elapsed {elapsed_ms}ms (expected 50..=130)"
        );
    }

    #[tokio::test]
    async fn random_pause_with_equal_bounds_does_not_panic() {
        let start = Instant::now();
        random_pause(40, 40).await;
        let elapsed_ms = start.elapsed().as_millis() as u64;
        assert!(elapsed_ms >= 40);
    }

    #[tokio::test]
    #[should_panic(expected = "random_pause: min_ms")]
    async fn random_pause_panics_when_min_exceeds_max() {
        random_pause(200, 100).await;
    }
}

pub async fn pointer_jitter(
    page: &Page,
    cx: f64,
    cy: f64,
    cycles: u32,
    cycle_ms: u64,
) -> anyhow::Result<()> {
    use chromiumoxide::cdp::browser_protocol::input::DispatchMouseEventParams;
    let mut rng = rand::rngs::StdRng::from_entropy();
    for c in 0..cycles {
        let amp_x: f64 = rng.gen_range(2.0..4.5);
        let amp_y: f64 = rng.gen_range(2.0..4.5);
        let phase: f64 = rng.gen_range(0.0..std::f64::consts::TAU);
        let steps = 8u64;
        for s in 0..steps {
            let theta = phase + (c as f64 + s as f64 / steps as f64) * std::f64::consts::TAU;
            let x = cx + amp_x * theta.sin();
            let y = cy + amp_y * (theta * 1.7).cos();
            let mv = DispatchMouseEventParams::builder()
                .r#type(DispatchMouseEventType::MouseMoved)
                .x(x)
                .y(y)
                .build()
                .map_err(anyhow::Error::msg)?;
            page.execute(mv).await?;
            tokio::time::sleep(Duration::from_millis(cycle_ms / steps)).await;
        }
    }
    Ok(())
}

/// Direction for realistic scroll simulation.
///
/// # Example
///
/// ```
/// use captchaforge::behavior::ScrollDirection;
///
/// let down = ScrollDirection::Down;
/// let up = ScrollDirection::Up;
/// assert_ne!(down, up);
/// ```
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum ScrollDirection {
    Up,
    Down,
}

#[cfg(test)]
mod tests {
    #[test]
    fn bezier_control_points_within_range() {
        let (x0, _y0) = (100.0, 200.0);
        let (x1, _y1) = (500.0, 400.0);
        let t0 = 0.0_f64;
        let t1 = 1.0_f64;
        let u0 = 1.0 - t0;
        let u1 = 1.0 - t1;
        let bx0 = u0.powi(3) * x0 + t0.powi(3) * x1;
        let bx1 = u1.powi(3) * x0 + t1.powi(3) * x1;
        assert!((bx0 - x0).abs() < 0.001);
        assert!((bx1 - x1).abs() < 0.001);
    }

    use super::*;

    #[test]
    fn scroll_direction_clone_copy() {
        let d = ScrollDirection::Down;
        let d2 = d;
        assert_eq!(d, d2);
    }

    #[test]
    fn scroll_direction_debug() {
        let d = ScrollDirection::Up;
        assert!(format!("{:?}", d).contains("Up"));
    }

    #[test]
    fn bezier_midpoint_t_0_5() {
        let x0 = 0.0;
        let y0 = 0.0;
        let x1 = 100.0;
        let y1 = 0.0;
        let cx1 = 25.0;
        let cy1 = 50.0;
        let cx2 = 75.0;
        let cy2 = 50.0;
        let t = 0.5;
        let u = 1.0 - t;
        let x = u * u * u * x0 + 3.0 * u * u * t * cx1 + 3.0 * u * t * t * cx2 + t * t * t * x1;
        let y = u * u * u * y0 + 3.0 * u * u * t * cy1 + 3.0 * u * t * t * cy2 + t * t * t * y1;
        assert!((x - 50.0_f64).abs() < 1.0);
        assert!((y - 37.5_f64).abs() < 1.0);
    }

    #[test]
    fn bezier_is_linear_when_control_points_on_line() {
        let x0 = 0.0;
        let x1 = 100.0;
        let cx1 = 33.0;
        let cx2 = 66.0;
        for i in 0..=10 {
            let t = i as f64 / 10.0;
            let u = 1.0 - t;
            let x = u * u * u * x0 + 3.0 * u * u * t * cx1 + 3.0 * u * t * t * cx2 + t * t * t * x1;
            assert!((x - (t * 100.0)).abs() < 1.0, "t={} x={}", t, x);
        }
    }

    #[test]
    fn ease_function_zero_at_endpoints() {
        let ease_0 = (std::f64::consts::PI * 0.0).sin();
        let ease_1 = (std::f64::consts::PI * 1.0).sin();
        assert!((ease_0).abs() < 0.001);
        assert!((ease_1).abs() < 0.001);
    }

    #[test]
    fn ease_function_max_at_midpoint() {
        let ease = (std::f64::consts::PI * 0.5).sin();
        assert!((ease - 1.0).abs() < 0.001);
    }

    #[test]
    fn bezier_formula_degenerate_case_same_point() {
        let x0 = 50.0;
        let x1 = 50.0;
        let cx1 = 50.0;
        let cx2 = 50.0;
        for i in 0..=10 {
            let t = i as f64 / 10.0;
            let u = 1.0 - t;
            let x = u * u * u * x0 + 3.0 * u * u * t * cx1 + 3.0 * u * t * t * cx2 + t * t * t * x1;
            assert!((x - 50.0).abs() < 0.001);
        }
    }
}