musicmouse/espmusicmouse/lib/ledtl/helpers/BellCurve.h

#pragma once

#include <cstdint>

static inline float bellCurveApproximation(float x, float inverseWidth)
{
  if (x < 0)
    x = -x;

  const auto nx = x * inverseWidth * 4;
  if (nx > 2)
    return 0.0f;

  const auto x2 = nx * nx;
  const auto x3 = x2 * nx;
  const auto res = 1.0f + 0.27606958941084f * x3 - 0.80213917882168f * x2;

  return res < 0.0f ? 0.0f : res;
}

// Function start at 0 (x=0) and goes smoothly up to 1 and arrives 1 at x=width
// inverse width has to be 1 / width (should be cached outside)
static inline float stepFunction(float x, float width, float inverseWidth)
{
  if (x < 0.0f)
    return 0.0f;
  if (x >= width)
    return 1.0f;

  auto bellInvWidth = inverseWidth * 0.5f;
  auto nx = (-x + width) * bellInvWidth * 4;
  auto x2 = nx * nx;
  auto x3 = x2 * nx;
  return 1 + 0.2760695894 * x3 - 0.8021391 * x2;
}