#!/usr/bin/python | |

''' | |

Copyright 2013 Google Inc. | |

Use of this source code is governed by a BSD-style license that can be | |

found in the LICENSE file. | |

''' | |

import math | |

import pprint | |

def withinStdDev(n): | |

"""Returns the percent of samples within n std deviations of the normal.""" | |

return math.erf(n / math.sqrt(2)) | |

def withinStdDevRange(a, b): | |

"""Returns the percent of samples within the std deviation range a, b""" | |

if b < a: | |

return 0; | |

if a < 0: | |

if b < 0: | |

return (withinStdDev(-a) - withinStdDev(-b)) / 2; | |

else: | |

return (withinStdDev(-a) + withinStdDev(b)) / 2; | |

else: | |

return (withinStdDev(b) - withinStdDev(a)) / 2; | |

#We have a bunch of smudged samples which represent the average coverage of a range. | |

#We have a 'center' which may not line up with those samples. | |

#From the 'center' we want to make a normal approximation where '5' sample width out we're at '3' std deviations. | |

#The first and last samples may not be fully covered. | |

#This is the sub-sample shift for each set of FIR coefficients (the centers of the lcds in the samples) | |

#Each subpxl takes up 1/3 of a pixel, so they are centered at x=(i/n+1/2n), or 1/6, 3/6, 5/6 of a pixel. | |

#Each sample takes up 1/4 of a pixel, so the results fall at (x*4)%1, or 2/3, 0, 1/3 of a sample. | |

samples_per_pixel = 4 | |

subpxls_per_pixel = 3 | |

#sample_offsets is (frac, int) in sample units. | |

sample_offsets = [math.modf((float(subpxl_index)/subpxls_per_pixel + 1.0/(2.0*subpxls_per_pixel))*samples_per_pixel) for subpxl_index in range(subpxls_per_pixel)] | |

#How many samples to consider to the left and right of the subpxl center. | |

sample_units_width = 5 | |

#The std deviation at sample_units_width. | |

std_dev_max = 3 | |

#The target sum is in some fixed point representation. | |

#Values larger the 1 in fixed point simulate ink spread. | |

target_sum = 0x110 | |

for sample_offset, sample_align in sample_offsets: | |

coeffs = [] | |

coeffs_rounded = [] | |

#We start at sample_offset - sample_units_width | |

current_sample_left = sample_offset - sample_units_width | |

current_std_dev_left = -std_dev_max | |

done = False | |

while not done: | |

current_sample_right = math.floor(current_sample_left + 1) | |

if current_sample_right > sample_offset + sample_units_width: | |

done = True | |

current_sample_right = sample_offset + sample_units_width | |

current_std_dev_right = current_std_dev_left + ((current_sample_right - current_sample_left) / sample_units_width) * std_dev_max | |

coverage = withinStdDevRange(current_std_dev_left, current_std_dev_right) | |

coeffs.append(coverage * target_sum) | |

coeffs_rounded.append(int(round(coverage * target_sum))) | |

current_sample_left = current_sample_right | |

current_std_dev_left = current_std_dev_right | |

# Now we have the numbers we want, but our rounding needs to add up to target_sum. | |

delta = 0 | |

coeffs_rounded_sum = sum(coeffs_rounded) | |

if coeffs_rounded_sum > target_sum: | |

# The coeffs add up to too much. Subtract 1 from the ones which were rounded up the most. | |

delta = -1 | |

if coeffs_rounded_sum < target_sum: | |

# The coeffs add up to too little. Add 1 to the ones which were rounded down the most. | |

delta = 1 | |

if delta: | |

print "Initial sum is 0x%0.2X, adjusting." % (coeffs_rounded_sum,) | |

coeff_diff = [(coeff_rounded - coeff) * delta | |

for coeff, coeff_rounded in zip(coeffs, coeffs_rounded)] | |

class IndexTracker: | |

def __init__(self, index, item): | |

self.index = index | |

self.item = item | |

def __lt__(self, other): | |

return self.item < other.item | |

def __repr__(self): | |

return "arr[%d] == %s" % (self.index, repr(self.item)) | |

coeff_pkg = [IndexTracker(i, diff) for i, diff in enumerate(coeff_diff)] | |

coeff_pkg.sort() | |

# num_elements_to_force_round had better be < (2 * sample_units_width + 1) or | |

# * our math was wildy wrong | |

# * an awful lot of the curve is out side our sample | |

# either is pretty bad, and probably means the results will not be useful. | |

num_elements_to_force_round = abs(coeffs_rounded_sum - target_sum) | |

for i in xrange(num_elements_to_force_round): | |

print "Adding %d to index %d to force round %f." % (delta, coeff_pkg[i].index, coeffs[coeff_pkg[i].index]) | |

coeffs_rounded[coeff_pkg[i].index] += delta | |

print "Prepending %d 0x00 for allignment." % (sample_align,) | |

coeffs_rounded_aligned = ([0] * int(sample_align)) + coeffs_rounded | |

print ', '.join(["0x%0.2X" % coeff_rounded for coeff_rounded in coeffs_rounded_aligned]) | |

print sum(coeffs), hex(sum(coeffs_rounded)) | |