Twigs date_modify filter accepts every string, which is supported by phps strtotime().
These strings are called Relative Formats.
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Examples:
In the original post you used:
{% set day = date('m/d/Y') %}
{% set nextDay = day|date_modify('+1 day') %}
but with Relative Formats you can also do something like this:
{% set var = day|date_modify('now') %}
{% set var = day|date_modify('10 September 2000') %}
{% set var = day|date_modify('+1 week') %}
{% set var = day|date_modify('+1 week 2 days 4 hours 2 seconds') %}
{% set var = day|date_modify('next Thursday') %}
{% set var = day|date_modify('last Monday') %}
{% set var = day|date_modify('next month') %}
(These are equivalents of the php-doc examples )
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So this weekend would be:
{% set var = day|date_modify('next Friday') %}
Or Saturday, personally I start my weekends on Thursday, so it's hard to give a good example ;)
Next weekend:
{% set var = day|date_modify('next Friday +7 days') %}
Next weekend in one year, half an hour ago:
{% set var = day|date_modify('next Friday +1 year -30 minutes') %}