monotonicsteffen.lua

function monotonicSteffen(y0, y1, y2, y3, x0, x1, x2, x3, x)
  local x1x0, x2x1, x3x2 = x1-x0, x2-x1, x3-x2
  local delta0, delta1, delta2 = (y1-y0) / (x1x0 + 1e-30), (y2-y1) / (x2x1 + 1e-30), (y3-y2) / (x3x2 + 1e-30)
  local m1 = (sign(delta0)+sign(delta1)) * min(abs(delta0),abs(delta1), 0.5*abs((x2x1*delta0 + x1x0*delta1) / (x2-x0 + 1e-30)))
  local m2 = (sign(delta1)+sign(delta2)) * min(abs(delta1),abs(delta2), 0.5*abs((x3x2*delta1 + x2x1*delta2) / (x3-x1 + 1e-30)))
  local xx1 = x - x1
  local xrel = xx1 / max(x2x1, 1e-30)
  return y1 + xx1*(m1 + xrel*(delta1 - m1 + (xrel - 1)*(m1 + m2 - 2*delta1)))
end