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[bug #59324] Erroneous values of rotation and scaling for some quads


From: Sachin Kumar Singh
Subject: [bug #59324] Erroneous values of rotation and scaling for some quads
Date: Sat, 24 Oct 2020 13:17:13 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:81.0) Gecko/20100101 Firefox/81.0

Follow-up Comment #2, bug #59324 (project gnuastro):

The calculation of theta and scale value is added and can be found in this
commit
<https://gitlab.com/sachinkumarsingh092/gnuastro-matching-fits-nohealpix/-/commit/adc88715448f29064e3d8dbc473a06f713547d6d>.

The output is as shown below

        theta=-1.52537, scale=-1264.99
        theta=1.53104, scale=1252.12
        theta=-1.53929, scale=-1268.35
        ===============================
        theta=-1.52537, scale=-1264.99
        theta=1.53104, scale=1252.12
        theta=-1.54225, scale=-1267.78
        ===============================
        theta=-1.52537, scale=-1264.99
        theta=1.53104, scale=1252.12
        theta=-1.49836, scale=-1239.92
        ===============================
        theta=-1.52537, scale=-1264.99
        theta=1.53104, scale=1252.12
        theta=-1.54144, scale=-1267.4
        ===============================
        theta=-1.54927, scale=-1267.97
        theta=-1.54759, scale=-1267.98
        theta=-1.53598, scale=-1264.07
        ===============================
        theta=-1.53591, scale=-1266.92
        theta=-1.52105, scale=-1258.33
        theta=-1.53271, scale=-1265.06
        ===============================
        theta=-1.53591, scale=-1266.92
        theta=-1.52105, scale=-1258.33
        theta=-1.51485, scale=-1253.24
        ===============================
        theta=-1.53591, scale=-1266.92
        theta=-1.52105, scale=-1258.33
        theta=-1.55731, scale=-1269.17
        ===============================
        theta=-1.53591, scale=-1266.92
        theta=-1.52105, scale=-1258.33
        theta=-1.55451, scale=-1268.47
        ===============================
        theta=-1.53591, scale=-1266.92
        theta=-1.52105, scale=-1258.33
        theta=-1.5483, scale=-1267.51
        ===============================
        theta=-1.55175, scale=-1273.39
        theta=-1.55325, scale=-1269.28
        theta=-1.55473, scale=-1271.6
        ===============================
        theta=-1.55175, scale=-1273.39
        theta=-1.53732, scale=-1266.36
        theta=-1.55473, scale=-1271.6
        ===============================
        theta=-1.56394, scale=-1272.94
        theta=-1.52942, scale=-1262.56
        theta=1.5668, scale=1270.71


As seen, many quads have the correct and approximately equal values which can
be used by averaging out. But some values are just the opposite sign from the
rest of the values. 

The three values are produced because we subtract the first coordinate of the
quad from all the values and essentially bring it to origin, from where the
calculations are easy. Then we compare each corresponding coordinate of query
and reference and hence have three values.

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