Shift time series where readings are offset - pandas

Question

I want to get readings every 15 minutes starting on the hour given a set of readings that are made hourly but at offset minutes from the hour.
My first approach was to use resample to 15 mins but I did not get expected results:
So if readings are on the hour, resampling works fine:
left_key = pd.to_datetime(['2020-12-01 00:00',
'2020-12-01 01:00',
'2020-12-01 02:00',
'2020-12-01 03:00',
'2020-12-01 04:00',
'2020-12-01 05:00'])
left_data = pd.Series([12,12,13,15,16,15], index=left_key, name='master')
resampled = left_data.resample('15min')
resampled.interpolate(method='spline', order=2)
Yields just what I need:
2020-12-01 00:00:00 12.000000
2020-12-01 00:15:00 11.777455
2020-12-01 00:30:00 12.079464
2020-12-01 00:45:00 12.370313
2020-12-01 01:00:00 12.000000
2020-12-01 01:15:00 12.918527
2020-12-01 01:30:00 13.175893
But if the readings are offset from the hour:
left_key = pd.to_datetime(['2020-12-01 00:06',
'2020-12-01 01:06',
'2020-12-01 02:06',
'2020-12-01 03:06',
'2020-12-01 04:06',
'2020-12-01 05:06'])
left_data = pd.Series([12,12,13,15,16,15], index=left_key, name='master')
resampled = left_data.resample('15min')
resampled.interpolate(method='spline', order=2)
Now I get no data
2020-12-01 00:00:00 NaN
2020-12-01 00:15:00 NaN
2020-12-01 00:30:00 NaN
2020-12-01 00:45:00 NaN
2020-12-01 01:00:00 NaN
And if I resample hourly, it simply shifts the readings back
resampled = left_data.resample('H')
resampled.interpolate(method='spline', order=2)
2020-12-01 00:00:00 12
2020-12-01 01:00:00 12
2020-12-01 02:00:00 13
2020-12-01 03:00:00 15
2020-12-01 04:00:00 16
2020-12-01 05:00:00 15
Is there a way to get resample to interpolate readings so I have the correct value on the hour?
(and is there a better title for this question!)
Update
While the solutions works it is not suitable for larger volumes of data. 1000 rows was too much for my machine! Even reducing the initial resample size required large amounts of memory and time to complete.
Here is another solution from this question: Interpolate one time series onto custom time series
# create a new index for the ranges of datetimes required
starts = df.index.min()
starts = datetime(starts.year, starts.month, starts.day, starts.hour,15*(starts.minute // 15))
master = pd.date_range(starts, df.index.max(), freq="15min")
# will need this to identify original data rows later
df['tag'] = True
# merge with original data and interpolate missing rows
idx = df.index.union(master)
df2 = df.reindex(idx).interpolate('index')
# now remove the things we don't want
df2.drop(df2.index[0], inplace=True) # first value will be NaN (unless has real data)
# use the tag column to remove the original data and then drop that column
df2 = df2[df2['tag'].isna()]
df2.drop(columns=['tag',], inplace=True)
This is much much faster!

Answer 1

OK. This is not the most beautiful of all solutions, but it has worked for me in the past. It's a trick consisting of resampling twice with a negligeable time interval befor applying the one you want. First of all, you need to set your index on time (Dates).
left_key = pd.to_datetime(['2020-12-01 00:06',
'2020-12-01 01:06',
'2020-12-01 02:06',
'2020-12-01 03:06',
'2020-12-01 04:06',
'2020-12-01 05:06'])
left_data = pd.Series([12,12,13,15,16,15])
df = pd.DataFrame({'Dates':left_key , 'Values':left_data})
df.set_index('Dates', inplace=True)
df1 = df.resample('1ms').interpolate(method='spline', order=2).resample('15min').first()
which gives
Values
Dates
2020-12-01 00:00:00 12.000000
2020-12-01 00:15:00 11.653527
2020-12-01 00:30:00 11.960000
2020-12-01 00:45:00 12.255313
2020-12-01 01:00:00 12.539464
2020-12-01 01:15:00 12.812455
2020-12-01 01:30:00 13.074286
2020-12-01 01:45:00 13.324955
2020-12-01 02:00:00 13.564464
2020-12-01 02:15:00 13.792813
2020-12-01 02:30:00 14.010000
2020-12-01 02:45:00 14.216027
2020-12-01 03:00:00 14.410893
2020-12-01 03:15:00 14.594598
2020-12-01 03:30:00 14.767143
2020-12-01 03:45:00 14.928527
2020-12-01 04:00:00 15.078750
2020-12-01 04:15:00 15.217812
2020-12-01 04:30:00 15.345714
2020-12-01 04:45:00 15.462455
2020-12-01 05:00:00 15.568036
Then, you concatenate with your original df
frames = [df, df1]
df2 = pd.concat(frames)
df2.sort_values('Dates')
which returns
Values
Dates
2020-12-01 00:00:00 12.000000
2020-12-01 00:06:00 12.000000
2020-12-01 00:15:00 11.653527
2020-12-01 00:30:00 11.960000
2020-12-01 00:45:00 12.255313
2020-12-01 01:00:00 12.539464
2020-12-01 01:06:00 12.000000
2020-12-01 01:15:00 12.812455
2020-12-01 01:30:00 13.074286
2020-12-01 01:45:00 13.324955
2020-12-01 02:00:00 13.564464
2020-12-01 02:06:00 13.000000
2020-12-01 02:15:00 13.792813
2020-12-01 02:30:00 14.010000
2020-12-01 02:45:00 14.216027
2020-12-01 03:00:00 14.410893
2020-12-01 03:06:00 15.000000
2020-12-01 03:15:00 14.594598
2020-12-01 03:30:00 14.767143
2020-12-01 03:45:00 14.928527
2020-12-01 04:00:00 15.078750
2020-12-01 04:06:00 16.000000
2020-12-01 04:15:00 15.217812
2020-12-01 04:30:00 15.345714
2020-12-01 04:45:00 15.462455
2020-12-01 05:00:00 15.568036
2020-12-01 05:06:00 15.000000