#! /usr/bin/python3
# Last edited on 2020-11-15 12:48:52 by jstolfi

# Generates a grayscale ".pgm" image whose samples are defined by a quadratic 
# equation with given coefficients.

import sys
from math import floor

def gen_quadr_samples(NX,NY,CX,CY,FXX,FXY,FYY):
  """Genereates and array (list of lists) of float samples
  with {NX} columns and {NY} rows, where sample on column {ix}  and
  row {iy} has value {(FXX/2)*x^2 + FXY*x*y + (FYY/2)*y^2},
  where {x = ix + 0.5 - CX} and {y = iy + 0.5 - CY}."""
  
  sys.stderr.write("creating image\n")
  sys.stderr.write("size = %d %d\n" % (NX, NY))
  sys.stderr.write("center = (%.2f %.2f)\n" % (CX, CY))
  sys.stderr.write("derivatives = (%.3f %.3f %.3f)\n" % (FXX, FXY, FYY)) 
  
  img = []
  for iy in range(NY):
    y = iy + 0.5 - CY
    row = []
    for ix in range(NX):
      x = ix + 0.5 - CX
      v = 0.5*FXX*x*x + FXY*x*y + 0.5*FYY*y*y
      row.append(v)
    img.append(row)
  return img
  
def write_image(img):
  """Writes the array of samples {img} to standard output 
  as a PGM file, after affnely normalizing them so that their range
  is {0..65535}."""
  
  # Array dimensions:
  NY = len(img)
  NX = len(img[0])
  
  # Find the max and min samples:
  vmin = +1.0e100
  vmax = -1.0e100
  for row in img:
   for v in row:
     vmin = min(v, vmin)
     vmax = max(v, vmax)
 
  sys.stderr.write("raw range = [%.6f %.6f]\n" % (vmin, vmax))

  # Write the PGM header:
  sys.stdout.write("P2\n")
  sys.stdout.write("%d %d\n" % (NX, NY))
  sys.stdout.write("65535\n")
  
  # Write the samples, normalized:
  for row in img:
   for v in row:
     vn = (v - vmin)/(vmax - vmin)
     ivn = int(floor(65535*vn + 0.5))
     sys.stdout.write(" %d" % ivn)
   sys.stdout.write("\n")
  
  sys.stdout.flush()
  
  
# Main program:

NX = int(sys.argv[1])
NY = int(sys.argv[2])
CX = float(sys.argv[3])
CY = float(sys.argv[4])
FXX = float(sys.argv[5])
FXY = float(sys.argv[6])
FYY = float(sys.argv[7])

img = gen_quadr_samples(NX,NY,CX,CY,FXX,FXY,FYY)
write_image(img)