buildvrt: add "common" value to "-resolution" argument

[dbaston]

Feature description

I am using gdalbuildvrt to mosaic several tiles from the Copernicus 30m global DEM. The horizontal resolution of this dataset varies by tile. When using gdalbuildvrt to mosaic adjacent tiles with 3-second and 5-second horizontal resolutions, I need to use a horizontal resolution of 1 second, but none of the automatic options available with -resolution can return this value.

I am thinking of implementing -resolution=common, which would attempt to calculate a resolution that can be multiplied by an integer to arrive at both of the input resolutions. An example implementation in Python:

import pytest
import fractions
import math

def common_res(a, b):
    frac_a = fractions.Fraction(a).limit_denominator(10000)
    frac_b = fractions.Fraction(b).limit_denominator(10000)

    common_denom = math.lcm(frac_a.denominator, frac_b.denominator)

    num_a = frac_a.numerator * int(common_denom / frac_a.denominator)
    num_b = frac_b.numerator * int(common_denom / frac_b.denominator)

    common_num = math.gcd(num_a, num_b)

    return common_num / common_denom

@pytest.mark.parametrize("a,b,expected", [
    (5/3600, 3/3600, 1/3600),
    (5, 3, 1),
    (5/3600, 2.5/3600, 2.5/3600),
    (1/10, 1, 1/10),
    (1/10, 1/3, 1/30),
    (1/17, 1/13, 1/221), 
    (1/17, 1/3600, 1/61200),
    ])
def test_common_res(a, b, expected):
    assert common_res(a, b) == expected

The key piece here is the Fraction.limit_denominator method. This could be adapted from CPython or other implementations such as this one.

If this seems like an appropriate addition, I can go ahead and implement it. We would probably want some guardrails to prevent disaggregation by more than a factor of N. This also fails to consider rasters whose resolutions may be "compatible" but whose origin points make them not so.

Additional context

No response

[rouault]

sounds like a good idea

[jratike80]

Agreed, good idea. The GDIWG elevation and orthophoto products also change the horizontal resolution at some latitudes.