How to Convert Number Ranges While Preserving Ratios?

Converting Number Ranges While Preserving Ratios

Given a range of values that need to be transformed to another range, maintaining their relative ratios, we present a general algorithm and its Python implementation.

Algorithm:

To convert a value from an old range (OldMin, OldMax) to a new range (NewMin, NewMax) while maintaining the ratio:

``
NewValue = (((OldValue - OldMin) * (NewMax - NewMin)) / (OldMax - OldMin)) NewMin
``

Or more readably:

``
OldRange = (OldMax - OldMin)
NewRange = (NewMax - NewMin)
NewValue = (((OldValue - OldMin) * NewRange) / OldRange) NewMin
``

If the old range has a zero span (OldMin = OldMax), the calculation is modified to:

``
OldRange = (OldMax - OldMin)
if (OldRange == 0)

NewValue = NewMin

else
{

NewRange = (NewMax - NewMin)
NewValue = (((OldValue - OldMin) * NewRange) / OldRange) + NewMin

}
``

In this scenario, NewMin is the default choice for the new value, but other options like NewMax or their average might also be contextually appropriate.

Python Implementation:

``
def convert_range(old_value, old_min, old_max, new_min, new_max):
"""Converts a value from one range to another while preserving ratio."""
old_range = old_max - old_min
if old_range == 0:

return new_min

new_range = new_max - new_min
return (((old_value - old_min) * new_range) / old_range) new_min
``

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