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quadraticIn: Parabolic Acceleration

Squared intensity curve for smooth motion onset​

The quadraticIn function creates parabolic acceleration by squaring the input value. This mathematical relationship produces gentle acceleration that increases smoothly from zero.

f(t)=t2f(t) = t^2

The function transforms linear time progression into curved motion. Values near zero remain close to zero, while values approaching one accelerate toward the maximum.

Live Editor
const fragment = () => {
  const w = 0.01
  const t = iTime.fract()
  const y = quadraticIn(t)
  const Y = quadraticIn(uv.x)
  const a = vec3(0.2, 0.4, 0.9)
  const b = vec3(0.9, 0.7, 0.3)
  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)
}