C[omp]ute

From: andrew cooke <andrew@...>

Date: Wed, 28 Jul 2010 10:16:53 -0400

There's a nice algorithm for auto-scaling axes, called the "nice number
algorithm", written by Paul Heckbert and published in "Graphics Gems" -
http://books.google.com/books?id=fvA7zLEFWZgC&pg=PA61&lpg=PA61&dq=nice+numbers+graphics+gems&source=bl&ots=7LdCq3nI-j&sig=L8qoZ8l_a95KAtHmMjagJ8cC0U0&hl=en&ei=KDhQTKLwGcT48AbTsvnEAQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBYQ6AEwAQ#v=onepage&q&f=false

The routines below implement this, but are parameterised over the number base
used, so can also be used for axes based on units that repeat over multiples
of 12, 60, or any other value.


from calendar import timegm
from math import floor, log, log10, ceil
from time import gmtime

# These allow the use with base 10, 12 and 60:
LIM10 = (10, [(1.5, 1), (3, 2), (7, 5)], [1, 2, 5])
LIM12 = (12, [(1.5, 1), (3, 2), (8, 6)], [1, 2, 6])
LIM60 = (60, [(1.5, 1), (20, 15), (40, 30)], [1, 15, 40])

def heckbert_d(lo, hi, ntick=5, limits=None):
    '''
    Calculate the step size.
    '''
    if limits is None:
        limits = LIM10
    (base, rfs, fs) = limits
    def nicenum(x, round):
        step = base ** floor(log(x)/log(base))
        f = float(x) / step
        nf = base
        if round:
            for (a, b) in rfs:
                if f < a:
                    nf = b
                    break
        else:
            for a in fs:
                if f <= a:
                    nf = a
                    break
        return nf * step
    delta = nicenum(hi-lo, False)
    return nicenum(delta / (ntick-1), True)

def heckbert(lo, hi, ntick=5, limits=None):
    '''
    Calculate the axes lables.
    '''
    def _heckbert():
        d = heckbert_d(lo, hi, ntick=ntick, limits=limits)
        graphlo = floor(lo / d) * d
        graphhi = ceil(hi / d) * d
        fmt = '%' + '.%df' %  max(-floor(log10(d)), 0)
        value = graphlo
        while value < graphhi + 0.5*d:
            yield fmt % value
            value += d
    return list(_heckbert())


This can then be used with a range of seconds as follows:


def autoscale_time(start, end):
    '''
    Yields a sequence of epochs that are nicely spaced.

    start and end are Unix epochs.
    '''
    time_chunks = [('days', 3 * 24 * 60 * 60, 24 * 60 * 60, 2, None),
                   ('hours', 3 * 60 * 60, 60 * 60, 3, LIM12),
                   ('minutes', 3 * 60, 60, 4, LIM60),
                   ('seconds', 0, 1, 5, LIM60)]
    for (name, limit, secs, sindex, limits) in self.time_chunks:
	if (end - start) > limit:
	    break
    d = heckbert_d(start / secs, end / secs, limits=limits)

    # zero out lower steps, so that we get a starting date that's an
    # integral number of units
    stime = list(gmtime(start))
    for i in range(sindex, 9):
	stime[i] = 0

    # generate a sequence of epochs (cannot use the usual heckbert routine 
    # because formatting will be different)
    value = timegm(stime)
    while value <= end:
	if value >= start:
            yield value
	value += d * secs


This could be extended further by:

- having different formats in the time_chunks parameter, so that different
  intervals are formatted differently

- adding months etc.  This would require changing the "secs" increment to be a
  timedelta and working with datetime instances rather than epochs (because
  months are not all equally sized).


NOTE: The code above is cut + pasted from some working code and is not tested
in its existing form; I may have introduced a bug somewhere, but hopefully
this illustrates the idea.

Andrew