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quadraticInOut: Symmetric Acceleration Curve

Mirrored quadratic motion with acceleration followed by deceleration​

The quadraticInOut function combines acceleration and deceleration through piecewise quadratic curves. The first half accelerates while the second half mirrors this motion in reverse.

f(t)={2t2if t<0.5−2t2+4t−1if t≥0.5f(t) = \begin{cases} 2t^2 & \text{if } t < 0.5 \\ -2t^2 + 4t - 1 & \text{if } t \geq 0.5 \end{cases}

The mathematical relationship creates smooth transitions at the midpoint while maintaining quadratic curvature throughout both phases.

Live Editor
const fragment = () => {
  const w = 0.01
  const t = iTime.fract()
  const y = quadraticInOut(t)
  const Y = quadraticInOut(uv.x)
  const a = vec3(0.9, 0.2, 0.4)
  const b = vec3(0.3, 0.8, 0.9)
  const c = a.mix(b, y).mul(uv.x.step(t))
  const lines = mmin2(smoothstep(0, w, uv.mod(0.1).min(uv.sub(vec2(t, y)).abs())))
  const curve = stroke(uv.y.sub(Y), 0, w).mul(c)
  const color = lines.oneMinus().mul(0.2).add(curve)
  return vec4(color, 1)
}