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July 26th, 2019, 10:53 AM   #1
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Check whether two points are symmetrics/asymmetrics

I'm working on an Android app that lets a group of children draw whatever they want in a specific area. I need to check whether the lines and figure that they draw are symmetric. The problem is that since the app is designed to let them draw freehand, I don't know how to compare the lines by considering a certain flexibility. For example, I would consider symmetric these two "triangles" in the image: even if they have not the same inclination and the same length. Do you have any suggestion? These are the points of the two shapes, do you notice any constant or something similar I can use to find what I need?
Triangle on the top:
1303.9062, 245.88171
1306.9531, 239.48767
1309.055, 234.89392
1309.9219, 231.82782
1312.2241, 231.00659
1312.8906, 228.64291
1312.8906, 226.54477
1315.9375, 227.98535
1315.9375, 231.00659
1319.2817, 236.99414
1319.9219, 243.00916
1322.1042, 244.02539
1322.8906, 248.47485
1322.8906, 251.52356
1322.8906, 255.54462
1324.9263, 256.98926
1325.9375, 260.74615
1325.9375, 265.4226
1325.9375, 267.45148
1325.9375, 269.0193
1330.1698, 269.0193
1328.9062, 275.0343
1328.9062, 275.9956
1328.9062, 279.01685
1328.9062, 281.98315
1331.9531, 285.0044
1331.9531, 285.0044
Triangle in the bottom:
1133.9062, 950.9956
1133.9062, 955.37256
1136.1552, 959.9429
1136.9531, 965.0901
1138.6583, 968.71606
1139.9219, 972.3617
1142.586, 976.9783
1143.9062, 982.42285
1146.608, 985.6449
1146.9531, 990.5189
1149.9219, 999.83105
1149.9219, 1002.55286
1153.7056, 1005.82275
1152.8906, 1010.1306
1154.862, 1011.9697
1155.9375, 1016.5016
1155.9375, 1018.0122
1155.9375, 1020.9785
1155.9375, 1024.9885
1159.9219, 1024.9885
1163.43, 1017.47314
1162.8906, 1013.48035
1165.9375, 1008.792
1167.0302, 1000.8804
1168.9062, 995.6416
1171.9531, 990.8357
1175.2189, 986.532
1175.9375, 981.4552
1178.9062, 975.46765
1181.9531, 970.21094
1181.9531, 966.84827
1186.4062, 966.9807
1184.9219, 962.5906
1184.9219, 960.99316
1187.8906, 960.99316
1187.8906, 956.98315
1187.8906, 956.98315

Last edited by skipjack; July 27th, 2019 at 10:24 AM.
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July 28th, 2019, 08:17 AM   #2
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What does your input data look like?

This in general is a very difficult problem.
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July 28th, 2019, 09:48 AM   #3
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It does seem quite ambitious. On the other hand, touch screens have been around so long that there has to be a lot of work publicly available that can get you a large portion of the way without having to start from scratch. You might search AI forums or journals for shape recognition algorithms. My guess is there are already librairies for generating simple polylines, and from there it would be easier to define a "similarity" (or "discrepancy") function.
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