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skills/slack-gif-creator/core/easing.py

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+#!/usr/bin/env python3
+"""
+Easing Functions - Timing functions for smooth animations.
+
+Provides various easing functions for natural motion and timing.
+All functions take a value t (0.0 to 1.0) and return eased value (0.0 to 1.0).
+"""
+
+import math
+
+
+def linear(t: float) -> float:
+    """Linear interpolation (no easing)."""
+    return t
+
+
+def ease_in_quad(t: float) -> float:
+    """Quadratic ease-in (slow start, accelerating)."""
+    return t * t
+
+
+def ease_out_quad(t: float) -> float:
+    """Quadratic ease-out (fast start, decelerating)."""
+    return t * (2 - t)
+
+
+def ease_in_out_quad(t: float) -> float:
+    """Quadratic ease-in-out (slow start and end)."""
+    if t < 0.5:
+        return 2 * t * t
+    return -1 + (4 - 2 * t) * t
+
+
+def ease_in_cubic(t: float) -> float:
+    """Cubic ease-in (slow start)."""
+    return t * t * t
+
+
+def ease_out_cubic(t: float) -> float:
+    """Cubic ease-out (fast start)."""
+    return (t - 1) * (t - 1) * (t - 1) + 1
+
+
+def ease_in_out_cubic(t: float) -> float:
+    """Cubic ease-in-out."""
+    if t < 0.5:
+        return 4 * t * t * t
+    return (t - 1) * (2 * t - 2) * (2 * t - 2) + 1
+
+
+def ease_in_bounce(t: float) -> float:
+    """Bounce ease-in (bouncy start)."""
+    return 1 - ease_out_bounce(1 - t)
+
+
+def ease_out_bounce(t: float) -> float:
+    """Bounce ease-out (bouncy end)."""
+    if t < 1 / 2.75:
+        return 7.5625 * t * t
+    elif t < 2 / 2.75:
+        t -= 1.5 / 2.75
+        return 7.5625 * t * t + 0.75
+    elif t < 2.5 / 2.75:
+        t -= 2.25 / 2.75
+        return 7.5625 * t * t + 0.9375
+    else:
+        t -= 2.625 / 2.75
+        return 7.5625 * t * t + 0.984375
+
+
+def ease_in_out_bounce(t: float) -> float:
+    """Bounce ease-in-out."""
+    if t < 0.5:
+        return ease_in_bounce(t * 2) * 0.5
+    return ease_out_bounce(t * 2 - 1) * 0.5 + 0.5
+
+
+def ease_in_elastic(t: float) -> float:
+    """Elastic ease-in (spring effect)."""
+    if t == 0 or t == 1:
+        return t
+    return -math.pow(2, 10 * (t - 1)) * math.sin((t - 1.1) * 5 * math.pi)
+
+
+def ease_out_elastic(t: float) -> float:
+    """Elastic ease-out (spring effect)."""
+    if t == 0 or t == 1:
+        return t
+    return math.pow(2, -10 * t) * math.sin((t - 0.1) * 5 * math.pi) + 1
+
+
+def ease_in_out_elastic(t: float) -> float:
+    """Elastic ease-in-out."""
+    if t == 0 or t == 1:
+        return t
+    t = t * 2 - 1
+    if t < 0:
+        return -0.5 * math.pow(2, 10 * t) * math.sin((t - 0.1) * 5 * math.pi)
+    return math.pow(2, -10 * t) * math.sin((t - 0.1) * 5 * math.pi) * 0.5 + 1
+
+
+# Convenience mapping
+EASING_FUNCTIONS = {
+    'linear': linear,
+    'ease_in': ease_in_quad,
+    'ease_out': ease_out_quad,
+    'ease_in_out': ease_in_out_quad,
+    'bounce_in': ease_in_bounce,
+    'bounce_out': ease_out_bounce,
+    'bounce': ease_in_out_bounce,
+    'elastic_in': ease_in_elastic,
+    'elastic_out': ease_out_elastic,
+    'elastic': ease_in_out_elastic,
+}
+
+
+def get_easing(name: str = 'linear'):
+    """Get easing function by name."""
+    return EASING_FUNCTIONS.get(name, linear)
+
+
+def interpolate(start: float, end: float, t: float, easing: str = 'linear') -> float:
+    """
+    Interpolate between two values with easing.
+
+    Args:
+        start: Start value
+        end: End value
+        t: Progress from 0.0 to 1.0
+        easing: Name of easing function
+
+    Returns:
+        Interpolated value
+    """
+    ease_func = get_easing(easing)
+    eased_t = ease_func(t)
+    return start + (end - start) * eased_t
+
+
+def ease_back_in(t: float) -> float:
+    """Back ease-in (slight overshoot backward before forward motion)."""
+    c1 = 1.70158
+    c3 = c1 + 1
+    return c3 * t * t * t - c1 * t * t
+
+
+def ease_back_out(t: float) -> float:
+    """Back ease-out (overshoot forward then settle back)."""
+    c1 = 1.70158
+    c3 = c1 + 1
+    return 1 + c3 * pow(t - 1, 3) + c1 * pow(t - 1, 2)
+
+
+def ease_back_in_out(t: float) -> float:
+    """Back ease-in-out (overshoot at both ends)."""
+    c1 = 1.70158
+    c2 = c1 * 1.525
+    if t < 0.5:
+        return (pow(2 * t, 2) * ((c2 + 1) * 2 * t - c2)) / 2
+    return (pow(2 * t - 2, 2) * ((c2 + 1) * (t * 2 - 2) + c2) + 2) / 2
+
+
+def apply_squash_stretch(base_scale: tuple[float, float], intensity: float,
+                         direction: str = 'vertical') -> tuple[float, float]:
+    """
+    Calculate squash and stretch scales for more dynamic animation.
+
+    Args:
+        base_scale: (width_scale, height_scale) base scales
+        intensity: Squash/stretch intensity (0.0-1.0)
+        direction: 'vertical', 'horizontal', or 'both'
+
+    Returns:
+        (width_scale, height_scale) with squash/stretch applied
+    """
+    width_scale, height_scale = base_scale
+
+    if direction == 'vertical':
+        # Compress vertically, expand horizontally (preserve volume)
+        height_scale *= (1 - intensity * 0.5)
+        width_scale *= (1 + intensity * 0.5)
+    elif direction == 'horizontal':
+        # Compress horizontally, expand vertically
+        width_scale *= (1 - intensity * 0.5)
+        height_scale *= (1 + intensity * 0.5)
+    elif direction == 'both':
+        # General squash (both dimensions)
+        width_scale *= (1 - intensity * 0.3)
+        height_scale *= (1 - intensity * 0.3)
+
+    return (width_scale, height_scale)
+
+
+def calculate_arc_motion(start: tuple[float, float], end: tuple[float, float],
+                        height: float, t: float) -> tuple[float, float]:
+    """
+    Calculate position along a parabolic arc (natural motion path).
+
+    Args:
+        start: (x, y) starting position
+        end: (x, y) ending position
+        height: Arc height at midpoint (positive = upward)
+        t: Progress (0.0-1.0)
+
+    Returns:
+        (x, y) position along arc
+    """
+    x1, y1 = start
+    x2, y2 = end
+
+    # Linear interpolation for x
+    x = x1 + (x2 - x1) * t
+
+    # Parabolic interpolation for y
+    # y = start + progress * (end - start) + arc_offset
+    # Arc offset peaks at t=0.5
+    arc_offset = 4 * height * t * (1 - t)
+    y = y1 + (y2 - y1) * t - arc_offset
+
+    return (x, y)
+
+
+# Add new easing functions to the convenience mapping
+EASING_FUNCTIONS.update({
+    'back_in': ease_back_in,
+    'back_out': ease_back_out,
+    'back_in_out': ease_back_in_out,
+    'anticipate': ease_back_in,     # Alias
+    'overshoot': ease_back_out,     # Alias
+})