logisticCurve

fn logisticCurve(x: f32, midpoint: f32, steepness: f32, minValue: f32, maxValue: f32) -> vec2<f32> {
  // Scale factor for steepness
  let k = max(0.001, steepness);
  
  // Shift x relative to midpoint
  let z = -k * (x - midpoint);
  
  // Calculate the exponent
  let expTerm = exp(z);
  
  // Calculate the logistic function value
  let logistic = 1.0 / (1.0 + expTerm);
  
  // Scale to min-max range
  let range = maxValue - minValue;
  let value = minValue + range * logistic;
  
  // Calculate the derivative
  let derivative = range * k * expTerm / ((1.0 + expTerm) * (1.0 + expTerm));
  
  return vec2<f32>(value, derivative);
}