Sketch Recognition, Fall 2006, Instructor: Tracy Hammond

Segmentation Homework Debugging Help

Code that created these values:

direction.m

curvature.m

dirtest.m

Direction & Curvature

Shape 1

Shape 1 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

3.1416,2.6779,2.1451,2.0647,1.8158,1.6296,1.5708,1.4382,1.2847,1.0041,0.7854,0.60554,0.49935,0.46365,0.13255,0.066568,0,-0.32175,-0.34556,-0.49394,-0.5071,-0.89606,-0.89606,-1.0517,-1.2723,-1.5708,-1.5708,-1.7682,-1.9196,-2.1294,-2.6345,-2.8198,-3.0585,3.1416,2.9764,2.8501,2.8501,2.6779,2.4981,2.2455,2.1588,2.1112,1.5708,1.5708,3.1416,0
2.6865,2.5927,2.1112,1.9333,1.7212,1.603,1.5019,1.3554,1.1659,0.89028,0.69045,0.5586,0.48089,0.28806,0.099669,0.035699,-0.19118,-0.33564,-0.39852,-0.49935,-0.6557,-0.89606,-0.98279,-1.1903,-1.3986,-1.5708,-1.6775,-1.8338,-2.0132,-2.3932,-2.7367,-2.9362,-3.1,3.0585,2.9181,2.8501,2.7828,2.6012,2.3562,2.2143,2.1294,1.9296,1.5708,2.0344,3.1416,NaN
2.6012,2.537,2.0169,1.826,1.6768,1.5491,1.4198,1.256,1.046,0.7854,0.63402,0.52807,0.35299,0.21109,0.069655,-0.10827,-0.26171,-0.37433,-0.4202,-0.57907,-0.72298,-0.95613,-1.1233,-1.3102,-1.4601,-1.6496,-1.7484,-1.9101,-2.2143,-2.5625,-2.8474,-3.0036,3.1138,2.9956,2.8966,2.8083,2.7187,2.4756,2.3086,2.1763,1.9974,1.8623,1.7682,2.0344,NaN,NaN
2.5454,2.4626,1.9208,1.7682,1.6191,1.4758,1.3299,1.1456,0.93071,0.72055,0.593,0.42367,0.27581,0.1622,-0.049141,-0.19469,-0.30865,-0.3937,-0.47146,-0.63275,-0.80865,-1.0808,-1.2405,-1.3869,-1.5512,-1.7127,-1.8208,-2.0647,-2.3907,-2.6992,-2.9229,-3.0792,3.0549,2.9617,2.8598,2.7611,2.6135,2.4228,2.2531,2.0832,1.938,1.9513,1.7682,NaN,NaN,NaN
2.4711,2.383,1.8611,1.7033,1.5455,1.3969,1.2268,1.0328,0.85599,0.67012,0.49589,0.34877,0.22348,0.041073,-0.13864,-0.24498,-0.33324,-0.43424,-0.51325,-0.7062,-0.95055,-1.1903,-1.3258,-1.4848,-1.6191,-1.7783,-1.9546,-2.2254,-2.5373,-2.796,-3.0022,3.1416,3.0172,2.925,2.8198,2.6779,2.5625,2.3562,2.1708,2.0344,2.0032,1.9513,NaN,NaN,NaN,NaN

Shape 1 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

3.1416,2.6779,2.1451,2.0647,1.8158,1.6296,1.5708,1.4382,1.2847,1.0041,0.7854,0.60554,0.49935,0.46365,0.13255,0.066568,0,-0.32175,-0.34556,-0.49394,-0.5071,-0.89606,-0.89606,-1.0517,-1.2723,-1.5708,-1.5708,-1.7682,-1.9196,-2.1294,-2.6345,-2.8198,-3.0585,-3.1416,-3.3067,-3.433,-3.433,-3.6052,-3.7851,-4.0376,-4.1244,-4.172,-4.7124,-4.7124,-3.1416,0
2.6865,2.5927,2.1112,1.9333,1.7212,1.603,1.5019,1.3554,1.1659,0.89028,0.69045,0.5586,0.48089,0.28806,0.099669,0.035699,-0.19118,-0.33564,-0.39852,-0.49935,-0.6557,-0.89606,-0.98279,-1.1903,-1.3986,-1.5708,-1.6775,-1.8338,-2.0132,-2.3932,-2.7367,-2.9362,-3.1,-3.2247,-3.3651,-3.433,-3.5004,-3.682,-3.927,-4.0689,-4.1538,-4.3536,-4.7124,-4.2487,-3.1416,NaN
2.6012,2.537,2.0169,1.826,1.6768,1.5491,1.4198,1.256,1.046,0.7854,0.63402,0.52807,0.35299,0.21109,0.069655,-0.10827,-0.26171,-0.37433,-0.4202,-0.57907,-0.72298,-0.95613,-1.1233,-1.3102,-1.4601,-1.6496,-1.7484,-1.9101,-2.2143,-2.5625,-2.8474,-3.0036,-3.1694,-3.2876,-3.3866,-3.4748,-3.5644,-3.8076,-3.9746,-4.1068,-4.2858,-4.4209,-4.515,-4.2487,NaN,NaN
2.5454,2.4626,1.9208,1.7682,1.6191,1.4758,1.3299,1.1456,0.93071,0.72055,0.593,0.42367,0.27581,0.1622,-0.049141,-0.19469,-0.30865,-0.3937,-0.47146,-0.63275,-0.80865,-1.0808,-1.2405,-1.3869,-1.5512,-1.7127,-1.8208,-2.0647,-2.3907,-2.6992,-2.9229,-3.0792,-3.2283,-3.3214,-3.4234,-3.5221,-3.6697,-3.8604,-4.0301,-4.2,-4.3452,-4.3319,-4.515,NaN,NaN,NaN
2.4711,2.383,1.8611,1.7033,1.5455,1.3969,1.2268,1.0328,0.85599,0.67012,0.49589,0.34877,0.22348,0.041073,-0.13864,-0.24498,-0.33324,-0.43424,-0.51325,-0.7062,-0.95055,-1.1903,-1.3258,-1.4848,-1.6191,-1.7783,-1.9546,-2.2254,-2.5373,-2.796,-3.0022,-3.1416,-3.2659,-3.3581,-3.4633,-3.6052,-3.7207,-3.927,-4.1123,-4.2487,-4.28,-4.3319,NaN,NaN,NaN,NaN

Shape 1 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.075956,0.055949,0.1721,0.17628,0.14964,0.14949,0.14739,0.11345,0.099947,0.088115,0.063107,0.055345,0.042223,0.023215,0.0066008,0.0091028,0.02087,0.025497,0.032577,0.075701,0.13769,0.22206,0.2226,0.17978,0.18702,0.21347,0.18583,0.21544,0.31617,0.38438,0.37101,0.36532,0.39543,0.4089,0.45001,0.50149,0.63116,0.97607,1.0477,1.2323,1.3786,1.5397,2.5133,2.618,NaN,NaN
0.084685,0.06694,0.13462,0.13677,0.12352,0.10844,0.10157,0.085253,0.068835,0.060481,0.044481,0.031071,0.02071,0.0060269,0.0075344,0.014878,0.022758,0.036321,0.054084,0.10154,0.14835,0.16498,0.16712,0.16196,0.15611,0.17917,0.20274,0.2412,0.28495,0.3103,0.31841,0.32257,0.35099,0.37561,0.44179,0.56136,0.66495,0.90825,0.99961,1.1549,1.4451,1.4148,NaN,NaN,NaN,NaN
0.08677,0.071966,0.12234,0.1136,0.102,0.091347,0.080006,0.068809,0.055105,0.042311,0.029664,0.017026,0.0056173,0.004881,0.014199,0.025323,0.038446,0.054095,0.075347,0.11234,0.14178,0.15705,0.15143,0.15744,0.17615,0.20669,0.21968,0.24462,0.27905,0.29924,0.31364,0.32691,0.37249,0.43596,0.50286,0.62423,0.73364,0.95421,1.1101,1.1401,NaN,NaN,NaN,NaN,NaN,NaN
0.087734,0.071621,0.10698,0.099729,0.086194,0.077731,0.067227,0.053711,0.041446,0.02886,0.015976,0.004648,0.0039115,0.014951,0.027138,0.03989,0.055367,0.07,0.089533,0.12149,0.13788,0.15478,0.16929,0.18313,0.19528,0.21831,0.23178,0.25329,0.2852,0.30807,0.33684,0.37597,0.42454,0.49487,0.57117,0.7003,0.83101,0.96253,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.083837,0.069356,0.09372,0.087361,0.075209,0.064077,0.053789,0.041104,0.028055,0.015198,0.0055511,0.0051228,0.015729,0.027497,0.041483,0.054757,0.069694,0.0835,0.098812,0.12851,0.15563,0.17782,0.18734,0.19759,0.20989,0.23066,0.24545,0.26831,0.30837,0.34974,0.38087,0.42554,0.48218,0.56173,0.64737,0.71942,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 1 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.075956,0.055949,0.1721,0.17628,0.14964,0.14949,0.14739,0.11345,0.099947,0.088115,0.063107,0.055345,0.042223,0.023215,0.0066008,0.0091028,0.02087,0.025497,0.032577,0.075701,0.13769,0.22206,0.2226,0.17978,0.18702,0.21347,0.18583,0.21544,0.31617,0.38438,0.37101,0.36532,0.39543,0.4089,0.45001,0.50149,0.63116,0.97607,1.0477,1.2323,1.3786,1.5397,2.5133,2.618,NaN,NaN
0.084685,0.06694,0.13462,0.13677,0.12352,0.10844,0.10157,0.085253,0.068835,0.060481,0.044481,0.031071,0.02071,0.0060269,0.0075344,0.014878,0.022758,0.036321,0.054084,0.10154,0.14835,0.16498,0.16712,0.16196,0.15611,0.17917,0.20274,0.2412,0.28495,0.3103,0.31841,0.32257,0.35099,0.37561,0.44179,0.56136,0.66495,0.90825,0.99961,1.1549,1.4451,1.4148,NaN,NaN,NaN,NaN
0.08677,0.071966,0.12234,0.1136,0.102,0.091347,0.080006,0.068809,0.055105,0.042311,0.029664,0.017026,0.0056173,0.004881,0.014199,0.025323,0.038446,0.054095,0.075347,0.11234,0.14178,0.15705,0.15143,0.15744,0.17615,0.20669,0.21968,0.24462,0.27905,0.29924,0.31364,0.32691,0.37249,0.43596,0.50286,0.62423,0.73364,0.95421,1.1101,1.1401,NaN,NaN,NaN,NaN,NaN,NaN
0.087734,0.071621,0.10698,0.099729,0.086194,0.077731,0.067227,0.053711,0.041446,0.02886,0.015976,0.004648,0.0039115,0.014951,0.027138,0.03989,0.055367,0.07,0.089533,0.12149,0.13788,0.15478,0.16929,0.18313,0.19528,0.21831,0.23178,0.25329,0.2852,0.30807,0.33684,0.37597,0.42454,0.49487,0.57117,0.7003,0.83101,0.96253,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.083837,0.069356,0.09372,0.087361,0.075209,0.064077,0.053789,0.041104,0.028055,0.015198,0.0055511,0.0051228,0.015729,0.027497,0.041483,0.054757,0.069694,0.0835,0.098812,0.12851,0.15563,0.17782,0.18734,0.19759,0.20989,0.23066,0.24545,0.26831,0.30837,0.34974,0.38087,0.42554,0.48218,0.56173,0.64737,0.71942,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 2

Shape 2 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

-1.5708,-2.2143,-2.1588,-2.415,-2.5749,-2.4859,-2.6477,-2.9305,3.1416,2.7092,2.2731,2.1708,2.0032,2.0055,1.9075,1.5708,1.3258,0.9273,0.7854,0.6288,0.18535,0.083141,0,-0.46365,-0.5586,-0.95055,-1.1903,-1.4464,-1.5708,-2.0899,-2.0344,-2.1588,-2.6224,-2.7828,-3.0309,3.1416,3.1416,0
-2.0344,-2.1731,-2.2753,-2.4981,-2.5253,-2.5625,-2.7869,-3.0349,2.9229,2.472,2.2143,2.0779,2.0044,1.9656,1.7798,1.4514,1.1071,0.86217,0.70449,0.38688,0.1419,0.047583,-0.23109,-0.51239,-0.74542,-1.0839,-1.2998,-1.5084,-1.8314,-2.0608,-2.0899,-2.4038,-2.705,-2.9105,-3.0828,3.1416,3.1416,NaN
-2.1193,-2.2655,-2.3744,-2.4933,-2.5662,-2.6779,-2.9024,3.0686,2.6779,2.3429,2.1263,2.0507,1.9789,1.8876,1.6595,1.2572,1.0041,0.7854,0.5071,0.2985,0.10769,-0.10308,-0.34556,-0.65108,-0.91291,-1.1903,-1.3808,-1.7005,-1.9055,-2.0899,-2.2655,-2.5415,-2.8198,-2.9829,-3.0916,3.1416,NaN,NaN
-2.2265,-2.3562,-2.4074,-2.5338,-2.6547,-2.7869,-3.0677,2.8431,2.5012,2.2242,2.0887,2.0215,1.9233,1.7996,1.4833,1.1425,0.90807,0.61814,0.41241,0.24498,0,-0.21294,-0.48996,-0.805,-1.0304,-1.2766,-1.5405,-1.7929,-1.9631,-2.2207,-2.4016,-2.6779,-2.8966,-2.9997,-3.0916,NaN,NaN,NaN
-2.325,-2.3915,-2.4579,-2.6135,-2.7479,-2.9356,3.004,2.6477,2.3483,2.1638,2.0568,1.9723,1.8558,1.6646,1.3618,1.0358,0.74195,0.5248,0.35299,0.1419,-0.094061,-0.34302,-0.65285,-0.91795,-1.1284,-1.4219,-1.6438,-1.8598,-2.0932,-2.338,-2.5393,-2.7707,-2.9169,-2.9997,NaN,NaN,NaN,NaN

Shape 2 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

-1.5708,-2.2143,-2.1588,-2.415,-2.5749,-2.4859,-2.6477,-2.9305,-3.1416,-3.574,-4.0101,-4.1123,-4.28,-4.2777,-4.3757,-4.7124,-4.9574,-5.3559,-5.4978,-5.6544,-6.0978,-6.2,-6.2832,-6.7468,-6.8418,-7.2337,-7.4735,-7.7296,-7.854,-8.3731,-8.3176,-8.442,-8.9056,-9.066,-9.3141,-9.4248,-9.4248,-6.2832
-2.0344,-2.1731,-2.2753,-2.4981,-2.5253,-2.5625,-2.7869,-3.0349,-3.3603,-3.8112,-4.0689,-4.2053,-4.2788,-4.3176,-4.5034,-4.8318,-5.176,-5.421,-5.5787,-5.8963,-6.1413,-6.2356,-6.5143,-6.7956,-7.0286,-7.3671,-7.583,-7.7916,-8.1146,-8.3439,-8.3731,-8.687,-8.9882,-9.1937,-9.366,-9.4248,-9.4248,NaN
-2.1193,-2.2655,-2.3744,-2.4933,-2.5662,-2.6779,-2.9024,-3.2146,-3.6052,-3.9403,-4.1569,-4.2324,-4.3042,-4.3956,-4.6237,-5.026,-5.2791,-5.4978,-5.7761,-5.9847,-6.1755,-6.3863,-6.6287,-6.9343,-7.1961,-7.4735,-7.664,-7.9837,-8.1887,-8.3731,-8.5487,-8.8247,-9.103,-9.2661,-9.3748,-9.4248,NaN,NaN
-2.2265,-2.3562,-2.4074,-2.5338,-2.6547,-2.7869,-3.0677,-3.4401,-3.7819,-4.059,-4.1945,-4.2617,-4.3599,-4.4836,-4.7999,-5.1407,-5.3751,-5.665,-5.8708,-6.0382,-6.2832,-6.4961,-6.7731,-7.0882,-7.3136,-7.5597,-7.8237,-8.0761,-8.2463,-8.5039,-8.6848,-8.9611,-9.1798,-9.2829,-9.3748,NaN,NaN,NaN
-2.325,-2.3915,-2.4579,-2.6135,-2.7479,-2.9356,-3.2792,-3.6355,-3.9349,-4.1194,-4.2264,-4.3109,-4.4274,-4.6185,-4.9214,-5.2473,-5.5412,-5.7584,-5.9302,-6.1413,-6.3772,-6.6262,-6.936,-7.2011,-7.4116,-7.7051,-7.927,-8.143,-8.3764,-8.6212,-8.8225,-9.0539,-9.2001,-9.2829,NaN,NaN,NaN,NaN

Shape 2 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.84913,0.3495,0.27013,0.29807,0.26184,0.25874,0.29983,0.34064,0.37876,0.37313,0.30967,0.24527,0.21735,0.25674,0.41081,0.59228,0.57769,0.59536,0.65516,0.60081,0.6561,0.91391,1.1074,1.133,1.1948,1.1582,1.2243,1.4915,1.5281,1.4778,1.5887,1.7294,1.6431,1.5799,1.6513,2.2848,NaN,NaN
0.32673,0.26625,0.2197,0.23208,0.23547,0.24846,0.28404,0.29781,0.27963,0.24401,0.21149,0.20978,0.24124,0.30581,0.40448,0.49302,0.51329,0.50003,0.54407,0.60843,0.69534,0.84489,0.96105,0.95429,1.0072,1.0911,1.1391,1.2313,1.3003,1.3353,1.3444,1.3736,1.3706,1.5215,NaN,NaN,NaN,NaN
0.25543,0.23031,0.21597,0.23378,0.24602,0.25214,0.25342,0.23649,0.21718,0.21725,0.22973,0.24845,0.27635,0.33123,0.41702,0.46369,0.48826,0.53193,0.59677,0.65018,0.72902,0.82508,0.91516,0.971,1.0169,1.0569,1.1184,1.214,1.2345,1.2399,1.2625,1.3872,NaN,NaN,NaN,NaN,NaN,NaN
0.24068,0.23217,0.22893,0.24063,0.23451,0.22079,0.21247,0.21676,0.23103,0.24718,0.25807,0.27563,0.30672,0.34901,0.42281,0.49516,0.53655,0.57624,0.64028,0.67959,0.75133,0.86482,0.94325,0.97448,1.0302,1.0839,1.1156,1.1742,1.201,1.2739,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.24707,0.23841,0.22386,0.21752,0.20607,0.20842,0.22506,0.24226,0.25494,0.27002,0.28452,0.29739,0.32833,0.38544,0.46755,0.53581,0.57917,0.61095,0.67249,0.7303,0.79793,0.88716,0.96749,1.0103,1.045,1.0799,1.1135,1.2105,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 2 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.84913,0.3495,0.27013,0.29807,0.26184,0.25874,0.29983,0.34064,0.37876,0.37313,0.30967,0.24527,0.21735,0.25674,0.41081,0.59228,0.57769,0.59536,0.65516,0.60081,0.6561,0.91391,1.1074,1.133,1.1948,1.1582,1.2243,1.4915,1.5281,1.4778,1.5887,1.7294,1.6431,1.5799,1.6513,2.2848,NaN,NaN
0.32673,0.26625,0.2197,0.23208,0.23547,0.24846,0.28404,0.29781,0.27963,0.24401,0.21149,0.20978,0.24124,0.30581,0.40448,0.49302,0.51329,0.50003,0.54407,0.60843,0.69534,0.84489,0.96105,0.95429,1.0072,1.0911,1.1391,1.2313,1.3003,1.3353,1.3444,1.3736,1.3706,1.5215,NaN,NaN,NaN,NaN
0.25543,0.23031,0.21597,0.23378,0.24602,0.25214,0.25342,0.23649,0.21718,0.21725,0.22973,0.24845,0.27635,0.33123,0.41702,0.46369,0.48826,0.53193,0.59677,0.65018,0.72902,0.82508,0.91516,0.971,1.0169,1.0569,1.1184,1.214,1.2345,1.2399,1.2625,1.3872,NaN,NaN,NaN,NaN,NaN,NaN
0.24068,0.23217,0.22893,0.24063,0.23451,0.22079,0.21247,0.21676,0.23103,0.24718,0.25807,0.27563,0.30672,0.34901,0.42281,0.49516,0.53655,0.57624,0.64028,0.67959,0.75133,0.86482,0.94325,0.97448,1.0302,1.0839,1.1156,1.1742,1.201,1.2739,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.24707,0.23841,0.22386,0.21752,0.20607,0.20842,0.22506,0.24226,0.25494,0.27002,0.28452,0.29739,0.32833,0.38544,0.46755,0.53581,0.57917,0.61095,0.67249,0.7303,0.79793,0.88716,0.96749,1.0103,1.045,1.0799,1.1135,1.2105,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 3

Shape 3 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

1.5708,1.5708,1.837,1.8805,1.904,1.9642,2.0989,2.1886,2.2865,2.5797,2.7886,3.1416,-2.8198,-2.2974,-2.2455,-1.7359,-1.5708,-1.2978,-1.0406,-0.83536,-0.49935,-0.30288,0,0.1566,0.3097,0.30805,0.23685,0.2606,0.1297,0.071307,0,-0.24498,-0.48448,-0.82538,-0.91795,-1.1659,-1.3045,-1.2793,-1.5708,-1.5708,-2.0701,-2.3127,-2.3562,-2.5213,-2.6012,-2.6779,3.1416,3.1416,3.1416,0
1.5708,1.7682,1.8673,1.8964,1.9348,2.0305,2.1398,2.2273,2.4365,2.6607,2.9326,-2.9709,-2.5948,-2.2707,-1.9974,-1.6421,-1.4017,-1.1526,-0.94677,-0.67771,-0.42066,-0.15991,0.088007,0.24498,0.30893,0.26791,0.24896,0.20464,0.097727,0.042528,-0.11379,-0.38051,-0.63832,-0.87606,-1.0209,-1.2252,-1.2925,-1.4142,-1.5708,-1.837,-2.2073,-2.3329,-2.4186,-2.5536,-2.6224,-2.8198,3.1416,3.1416,3.1416,NaN
1.7561,1.8392,1.8891,1.9245,1.989,2.0767,2.1735,2.3299,2.5228,2.7611,3.1,-2.7799,-2.4828,-2.0969,-1.8281,-1.4767,-1.2405,-1.0502,-0.81872,-0.588,-0.31039,-0.039979,0.18432,0.26625,0.28177,0.26521,0.21608,0.15914,0.071307,-0.031735,-0.25367,-0.52143,-0.73782,-0.95703,-1.0883,-1.2405,-1.3734,-1.4711,-1.762,-2.0344,-2.2565,-2.3744,-2.4559,-2.5703,-2.6779,-2.9442,3.1416,3.1416,NaN,NaN
1.8329,1.8762,1.9179,1.9743,2.0323,2.1103,2.2513,2.4011,2.6104,2.8935,-3.0172,-2.6516,-2.3127,-1.9365,-1.6184,-1.3087,-1.1294,-0.92914,-0.73579,-0.48562,-0.19205,0.07983,0.21867,0.25732,0.27581,0.23591,0.17985,0.12928,0.011627,-0.14531,-0.38832,-0.63275,-0.82384,-1.0171,-1.1227,-1.3045,-1.4255,-1.6438,-1.9473,-2.1212,-2.3007,-2.4038,-2.472,-2.6012,-2.7611,-3.0172,3.1416,NaN,NaN,NaN
1.8731,1.909,1.9667,2.0158,2.0639,2.1766,2.309,2.4703,2.7253,3.0217,-2.882,-2.488,-2.1363,-1.7224,-1.4198,-1.192,-1.0078,-0.8489,-0.6453,-0.36717,-0.061777,0.13323,0.22348,0.25811,0.25044,0.20176,0.15381,0.077431,-0.085505,-0.25994,-0.50817,-0.72097,-0.88674,-1.0533,-1.1818,-1.356,-1.5708,-1.829,-2.042,-2.1774,-2.3312,-2.4167,-2.4917,-2.6547,-2.8431,-3.0172,NaN,NaN,NaN,NaN

Shape 3 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

1.5708,1.5708,1.837,1.8805,1.904,1.9642,2.0989,2.1886,2.2865,2.5797,2.7886,3.1416,3.4633,3.9857,4.0376,4.5472,4.7124,4.9854,5.2426,5.4478,5.7838,5.9803,6.2832,6.4398,6.5929,6.5912,6.52,6.5438,6.4129,6.3545,6.2832,6.0382,5.7987,5.4578,5.3652,5.1173,4.9786,5.0038,4.7124,4.7124,4.213,3.9704,3.927,3.7618,3.682,3.6052,3.1416,3.1416,3.1416,0
1.5708,1.7682,1.8673,1.8964,1.9348,2.0305,2.1398,2.2273,2.4365,2.6607,2.9326,3.3123,3.6884,4.0125,4.2858,4.6411,4.8815,5.1306,5.3364,5.6055,5.8625,6.1233,6.3712,6.5282,6.5921,6.5511,6.5321,6.4878,6.3809,6.3257,6.1694,5.9027,5.6449,5.4071,5.2622,5.0579,4.9907,4.869,4.7124,4.4461,4.0759,3.9502,3.8646,3.7296,3.6607,3.4633,3.1416,3.1416,3.1416,NaN
1.7561,1.8392,1.8891,1.9245,1.989,2.0767,2.1735,2.3299,2.5228,2.7611,3.1,3.5033,3.8004,4.1863,4.4551,4.8065,5.0427,5.233,5.4645,5.6952,5.9728,6.2432,6.4675,6.5494,6.565,6.5484,6.4993,6.4423,6.3545,6.2514,6.0295,5.7618,5.5454,5.3262,5.1949,5.0427,4.9098,4.8121,4.5212,4.2487,4.0267,3.9088,3.8273,3.7129,3.6052,3.339,3.1416,3.1416,NaN,NaN
1.8329,1.8762,1.9179,1.9743,2.0323,2.1103,2.2513,2.4011,2.6104,2.8935,3.2659,3.6315,3.9704,4.3466,4.6648,4.9745,5.1538,5.354,5.5474,5.7976,6.0911,6.363,6.5019,6.5405,6.559,6.5191,6.463,6.4125,6.2948,6.1379,5.8949,5.6504,5.4593,5.2661,5.1605,4.9786,4.8577,4.6393,4.3359,4.162,3.9825,3.8794,3.8112,3.682,3.5221,3.2659,3.1416,NaN,NaN,NaN
1.8731,1.909,1.9667,2.0158,2.0639,2.1766,2.309,2.4703,2.7253,3.0217,3.4012,3.7952,4.1469,4.5608,4.8634,5.0912,5.2753,5.4343,5.6379,5.916,6.2214,6.4164,6.5067,6.5413,6.5336,6.4849,6.437,6.3606,6.1977,6.0232,5.775,5.5622,5.3964,5.2299,5.1013,4.9272,4.7124,4.4541,4.2412,4.1058,3.952,3.8665,3.7915,3.6285,3.4401,3.2659,NaN,NaN,NaN,NaN

Shape 3 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.99573,0.34336,0.14931,0.070732,0.053083,0.055347,0.064334,0.091507,0.1227,0.16317,0.27428,0.35526,0.41241,0.5059,0.53249,0.50576,0.35605,0.26312,0.26599,0.32245,0.43152,0.58884,0.56421,0.43144,0.39939,0.37141,0.31991,0.35601,0.3716,0.39676,0.51053,0.45556,0.42443,0.40776,0.42206,0.56695,0.67278,0.7422,0.68189,0.54806,0.42037,0.38326,0.49994,0.76553,1.2928,3.0557,3.1416,1.2566,NaN,NaN
0.20546,0.094713,0.064538,0.051672,0.04866,0.0585,0.072566,0.10046,0.14756,0.1947,0.28046,0.35082,0.39274,0.42005,0.35147,0.28419,0.2519,0.24293,0.27697,0.35159,0.40863,0.4128,0.38802,0.33218,0.29633,0.30255,0.28636,0.31222,0.35602,0.352,0.38769,0.36048,0.3525,0.39441,0.43057,0.53229,0.56451,0.52623,0.44122,0.38155,0.3793,0.4224,0.58802,0.98092,1.5101,1.5821,NaN,NaN,NaN,NaN
0.082717,0.064132,0.056134,0.054925,0.057081,0.070387,0.093287,0.12847,0.179,0.22978,0.30637,0.34861,0.32678,0.29273,0.26971,0.26006,0.26376,0.27752,0.3027,0.33009,0.35242,0.34534,0.31418,0.29778,0.28052,0.2901,0.29769,0.30794,0.33124,0.32559,0.35079,0.36416,0.37316,0.41504,0.43457,0.46992,0.44611,0.41287,0.405,0.40758,0.44114,0.52463,0.72167,0.90315,NaN,NaN,NaN,NaN,NaN,NaN
0.067256,0.06386,0.062066,0.064402,0.072022,0.090058,0.11722,0.15779,0.21105,0.25368,0.286,0.27783,0.26931,0.26946,0.27547,0.28587,0.28601,0.28047,0.29297,0.3061,0.30679,0.31299,0.29645,0.28929,0.29006,0.29137,0.29322,0.29922,0.3187,0.33429,0.36622,0.38321,0.38559,0.40048,0.39149,0.40387,0.41717,0.42799,0.4487,0.47689,0.52035,0.5344,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.070924,0.071531,0.074905,0.080052,0.089768,0.11144,0.14238,0.18256,0.21821,0.23095,0.25206,0.26217,0.27434,0.29052,0.29305,0.2867,0.28165,0.27316,0.27331,0.28996,0.29378,0.30257,0.30214,0.29044,0.28779,0.28744,0.29033,0.30904,0.33364,0.35148,0.37668,0.37753,0.36366,0.36818,0.38026,0.41661,0.4505,0.48178,0.50846,0.48677,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 3 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.99573,0.34336,0.14931,0.070732,0.053083,0.055347,0.064334,0.091507,0.1227,0.16317,0.27428,0.35526,0.41241,0.5059,0.53249,0.50576,0.35605,0.26312,0.26599,0.32245,0.43152,0.58884,0.56421,0.43144,0.39939,0.37141,0.31991,0.35601,0.3716,0.39676,0.51053,0.45556,0.42443,0.40776,0.42206,0.56695,0.67278,0.7422,0.68189,0.54806,0.42037,0.38326,0.49994,0.76553,1.2928,3.0557,3.1416,1.2566,NaN,NaN
0.20546,0.094713,0.064538,0.051672,0.04866,0.0585,0.072566,0.10046,0.14756,0.1947,0.28046,0.35082,0.39274,0.42005,0.35147,0.28419,0.2519,0.24293,0.27697,0.35159,0.40863,0.4128,0.38802,0.33218,0.29633,0.30255,0.28636,0.31222,0.35602,0.352,0.38769,0.36048,0.3525,0.39441,0.43057,0.53229,0.56451,0.52623,0.44122,0.38155,0.3793,0.4224,0.58802,0.98092,1.5101,1.5821,NaN,NaN,NaN,NaN
0.082717,0.064132,0.056134,0.054925,0.057081,0.070387,0.093287,0.12847,0.179,0.22978,0.30637,0.34861,0.32678,0.29273,0.26971,0.26006,0.26376,0.27752,0.3027,0.33009,0.35242,0.34534,0.31418,0.29778,0.28052,0.2901,0.29769,0.30794,0.33124,0.32559,0.35079,0.36416,0.37316,0.41504,0.43457,0.46992,0.44611,0.41287,0.405,0.40758,0.44114,0.52463,0.72167,0.90315,NaN,NaN,NaN,NaN,NaN,NaN
0.067256,0.06386,0.062066,0.064402,0.072022,0.090058,0.11722,0.15779,0.21105,0.25368,0.286,0.27783,0.26931,0.26946,0.27547,0.28587,0.28601,0.28047,0.29297,0.3061,0.30679,0.31299,0.29645,0.28929,0.29006,0.29137,0.29322,0.29922,0.3187,0.33429,0.36622,0.38321,0.38559,0.40048,0.39149,0.40387,0.41717,0.42799,0.4487,0.47689,0.52035,0.5344,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.070924,0.071531,0.074905,0.080052,0.089768,0.11144,0.14238,0.18256,0.21821,0.23095,0.25206,0.26217,0.27434,0.29052,0.29305,0.2867,0.28165,0.27316,0.27331,0.28996,0.29378,0.30257,0.30214,0.29044,0.28779,0.28744,0.29033,0.30904,0.33364,0.35148,0.37668,0.37753,0.36366,0.36818,0.38026,0.41661,0.4505,0.48178,0.50846,0.48677,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 4

Shape 4 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

1.5708,1.6815,1.7234,1.743,1.7079,1.5708,1.6421,1.5708,1.5708,1.2925,1.5708,0.7854,0.588,0,0,-0.24498,-0.30288,-0.2268,-0.11711,-0.11488,-0.11711,-0.076772,0,-0.17985,0,0,0,0,-2.1421,-2.191,-2.0344,-1.9513,-1.8925,-1.8491,-2.0344,-1.8158,-1.7682,-2.3562,-2.3562,3.1416,3.1416,3.1416,2.9229,2.9442,2.9764,2.9997,3.0172,3.1416,3.1416,-2.4981,-2.6779,0
1.6615,1.7063,1.7359,1.7234,1.6352,1.6036,1.6133,1.5708,1.4537,1.4056,1.4056,0.6435,0.2783,0,-0.16515,-0.2783,-0.26917,-0.16515,-0.11576,-0.11576,-0.099669,-0.039979,-0.086738,-0.11066,0,0,0,-2.0899,-2.167,-2.1025,-1.9996,-1.9296,-1.8737,-1.9196,-1.9296,-1.7895,-1.9757,-2.3562,-2.8966,3.1416,3.1416,3.009,2.9305,2.9617,2.9889,3.009,3.0792,3.1416,-2.8501,-2.583,-2.6779,NaN
1.6952,1.7251,1.7234,1.6646,1.6374,1.5958,1.6059,1.5153,1.4801,1.344,1.1071,0.35877,0.15265,-0.13553,-0.23109,-0.26212,-0.21406,-0.1419,-0.11614,-0.10674,-0.071307,-0.083141,-0.066568,-0.094952,0,0,-1.9757,-2.1421,-2.1143,-2.0586,-1.9784,-1.9118,-1.9075,-1.8925,-1.8693,-1.9196,-2.0344,-2.6779,-3.0509,3.1416,3.0509,2.9927,2.9442,2.9764,2.9997,3.0549,3.0962,-2.9764,-2.7986,-2.583,NaN,NaN
1.7186,1.7184,1.6725,1.6591,1.6258,1.593,1.5708,1.5221,1.4411,1.1903,0.7854,0.21109,-0.039979,-0.2075,-0.2299,-0.22049,-0.17863,-0.13614,-0.10915,-0.088007,-0.094061,-0.069655,-0.060532,-0.086738,0,-1.7819,-2.0899,-2.0989,-2.0779,-2.0344,-1.9614,-1.9264,-1.8925,-1.8623,-1.9513,-1.9656,-2.2896,-2.9148,-3.0828,3.0618,3.0309,2.9889,2.9585,2.9889,3.0385,3.0727,-3.0648,-2.9181,-2.7986,NaN,NaN,NaN
1.7145,1.6732,1.6657,1.6464,1.6212,1.5708,1.5708,1.4995,1.3353,0.98279,0.51915,0,-0.14531,-0.21243,-0.2004,-0.18822,-0.16697,-0.12722,-0.093841,-0.10092,-0.083141,-0.065125,-0.057081,-0.083141,-1.2925,-2.0055,-2.0672,-2.0657,-2.0564,-2.0158,-1.9669,-1.9154,-1.8717,-1.9196,-1.9832,-2.1588,-2.6224,-2.985,3.1032,3.0419,3.021,2.9912,2.9718,3.0245,3.0561,-3.1113,-3.009,-2.9181,NaN,NaN,NaN,NaN

Shape 4 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

1.5708,1.6815,1.7234,1.743,1.7079,1.5708,1.6421,1.5708,1.5708,1.2925,1.5708,0.7854,0.588,0,0,-0.24498,-0.30288,-0.2268,-0.11711,-0.11488,-0.11711,-0.076772,0,-0.17985,0,0,0,0,-2.1421,-2.191,-2.0344,-1.9513,-1.8925,-1.8491,-2.0344,-1.8158,-1.7682,-2.3562,-2.3562,-3.1416,-3.1416,-3.1416,-3.3603,-3.339,-3.3067,-3.2835,-3.2659,-3.1416,-3.1416,-2.4981,-2.6779,0
1.6615,1.7063,1.7359,1.7234,1.6352,1.6036,1.6133,1.5708,1.4537,1.4056,1.4056,0.6435,0.2783,0,-0.16515,-0.2783,-0.26917,-0.16515,-0.11576,-0.11576,-0.099669,-0.039979,-0.086738,-0.11066,0,0,0,-2.0899,-2.167,-2.1025,-1.9996,-1.9296,-1.8737,-1.9196,-1.9296,-1.7895,-1.9757,-2.3562,-2.8966,-3.1416,-3.1416,-3.2741,-3.3527,-3.3214,-3.2942,-3.2741,-3.204,-3.1416,-2.8501,-2.583,-2.6779,NaN
1.6952,1.7251,1.7234,1.6646,1.6374,1.5958,1.6059,1.5153,1.4801,1.344,1.1071,0.35877,0.15265,-0.13553,-0.23109,-0.26212,-0.21406,-0.1419,-0.11614,-0.10674,-0.071307,-0.083141,-0.066568,-0.094952,0,0,-1.9757,-2.1421,-2.1143,-2.0586,-1.9784,-1.9118,-1.9075,-1.8925,-1.8693,-1.9196,-2.0344,-2.6779,-3.0509,-3.1416,-3.2323,-3.2905,-3.339,-3.3067,-3.2835,-3.2283,-3.187,-2.9764,-2.7986,-2.583,NaN,NaN
1.7186,1.7184,1.6725,1.6591,1.6258,1.593,1.5708,1.5221,1.4411,1.1903,0.7854,0.21109,-0.039979,-0.2075,-0.2299,-0.22049,-0.17863,-0.13614,-0.10915,-0.088007,-0.094061,-0.069655,-0.060532,-0.086738,0,-1.7819,-2.0899,-2.0989,-2.0779,-2.0344,-1.9614,-1.9264,-1.8925,-1.8623,-1.9513,-1.9656,-2.2896,-2.9148,-3.0828,-3.2214,-3.2522,-3.2942,-3.3247,-3.2942,-3.2447,-3.2104,-3.0648,-2.9181,-2.7986,NaN,NaN,NaN
1.7145,1.6732,1.6657,1.6464,1.6212,1.5708,1.5708,1.4995,1.3353,0.98279,0.51915,0,-0.14531,-0.21243,-0.2004,-0.18822,-0.16697,-0.12722,-0.093841,-0.10092,-0.083141,-0.065125,-0.057081,-0.083141,-1.2925,-2.0055,-2.0672,-2.0657,-2.0564,-2.0158,-1.9669,-1.9154,-1.8717,-1.9196,-1.9832,-2.1588,-2.6224,-2.985,-3.18,-3.2413,-3.2622,-3.292,-3.3114,-3.2587,-3.2271,-3.1113,-3.009,-2.9181,NaN,NaN,NaN,NaN

Shape 4 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.45007,0.2318,0.14177,0.095433,0.079017,0.07833,0.10163,0.1529,0.2566,0.29712,0.45901,0.2736,0.077312,0.024498,0.029825,0.026591,0.021485,0.015062,0.0080641,0.0071323,0.0064293,0.010249,0.0077589,0.0098927,0,0,0.71404,0.2456,0.18812,0.15612,0.15262,0.22201,0.34449,0.48496,0.65367,0.64412,0.81749,1.8512,1.9572,0.94248,0.7418,0.64659,0.69881,0.88798,0.7493,0.64038,0.59451,0.62723,0.75615,0.54645,NaN,NaN
0.1772,0.11261,0.084914,0.072429,0.073733,0.084899,0.11883,0.16449,0.2451,0.2449,0.21,0.075129,0.0015453,0.019796,0.018397,0.016893,0.011973,0.0088499,0.0057984,0.0071509,0.0070072,0.0059378,0.0054205,0.0077589,0.16478,0.19137,0.17281,0.14541,0.14111,0.15211,0.17658,0.2552,0.36906,0.46837,0.62525,0.84947,1.0342,0.99259,0.86948,0.63935,0.59627,0.62236,0.60262,0.62081,0.55241,0.52623,0.54412,0.48821,NaN,NaN,NaN,NaN
0.10598,0.085647,0.079049,0.077775,0.086283,0.097734,0.12747,0.15936,0.18554,0.14622,0.073986,0.013561,0.0054167,0.014465,0.012246,0.011669,0.0092279,0.0084274,0.0062687,0.0056481,0.0059008,0.0053221,0.064178,0.11055,0.13592,0.13373,0.1355,0.14557,0.15814,0.17891,0.20893,0.29319,0.42273,0.60759,0.79353,0.75522,0.76024,0.70723,0.68658,0.624,0.5643,0.54987,0.52461,0.54512,0.53002,0.46648,NaN,NaN,NaN,NaN,NaN,NaN
0.094207,0.087949,0.088228,0.086816,0.092446,0.098641,0.1151,0.1267,0.10589,0.061348,0.032842,0.0049155,0.0053915,0.010635,0.0098469,0.010791,0.0089592,0.0071175,0.0056808,0.0053395,0.037926,0.069688,0.093498,0.10572,0.11962,0.13728,0.15299,0.16818,0.1809,0.20762,0.25149,0.37683,0.53988,0.61347,0.68114,0.63127,0.65333,0.6748,0.63129,0.56509,0.51511,0.5128,0.5137,0.49519,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.1013,0.095152,0.092991,0.087768,0.087447,0.088149,0.08758,0.077297,0.061621,0.037173,0.017209,0.0014663,0.004729,0.010009,0.0095133,0.0094482,0.008304,0.0068257,0.025066,0.044175,0.06729,0.081341,0.095733,0.11544,0.13801,0.15974,0.17551,0.19297,0.21193,0.25868,0.31936,0.41815,0.52969,0.56118,0.61675,0.62188,0.61462,0.60659,0.56801,0.53043,0.50786,0.47928,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 4 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.45007,0.2318,0.14177,0.095433,0.079017,0.07833,0.10163,0.1529,0.2566,0.29712,0.45901,0.2736,0.077312,0.024498,0.029825,0.026591,0.021485,0.015062,0.0080641,0.0071323,0.0064293,0.010249,0.0077589,0.0098927,0,0,0.71404,0.2456,0.18812,0.15612,0.15262,0.22201,0.34449,0.48496,0.65367,0.64412,0.81749,1.8512,1.9572,0.94248,0.7418,0.64659,0.69881,0.88798,0.7493,0.64038,0.59451,0.62723,0.75615,0.54645,NaN,NaN
0.1772,0.11261,0.084914,0.072429,0.073733,0.084899,0.11883,0.16449,0.2451,0.2449,0.21,0.075129,0.0015453,0.019796,0.018397,0.016893,0.011973,0.0088499,0.0057984,0.0071509,0.0070072,0.0059378,0.0054205,0.0077589,0.16478,0.19137,0.17281,0.14541,0.14111,0.15211,0.17658,0.2552,0.36906,0.46837,0.62525,0.84947,1.0342,0.99259,0.86948,0.63935,0.59627,0.62236,0.60262,0.62081,0.55241,0.52623,0.54412,0.48821,NaN,NaN,NaN,NaN
0.10598,0.085647,0.079049,0.077775,0.086283,0.097734,0.12747,0.15936,0.18554,0.14622,0.073986,0.013561,0.0054167,0.014465,0.012246,0.011669,0.0092279,0.0084274,0.0062687,0.0056481,0.0059008,0.0053221,0.064178,0.11055,0.13592,0.13373,0.1355,0.14557,0.15814,0.17891,0.20893,0.29319,0.42273,0.60759,0.79353,0.75522,0.76024,0.70723,0.68658,0.624,0.5643,0.54987,0.52461,0.54512,0.53002,0.46648,NaN,NaN,NaN,NaN,NaN,NaN
0.094207,0.087949,0.088228,0.086816,0.092446,0.098641,0.1151,0.1267,0.10589,0.061348,0.032842,0.0049155,0.0053915,0.010635,0.0098469,0.010791,0.0089592,0.0071175,0.0056808,0.0053395,0.037926,0.069688,0.093498,0.10572,0.11962,0.13728,0.15299,0.16818,0.1809,0.20762,0.25149,0.37683,0.53988,0.61347,0.68114,0.63127,0.65333,0.6748,0.63129,0.56509,0.51511,0.5128,0.5137,0.49519,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.1013,0.095152,0.092991,0.087768,0.087447,0.088149,0.08758,0.077297,0.061621,0.037173,0.017209,0.0014663,0.004729,0.010009,0.0095133,0.0094482,0.008304,0.0068257,0.025066,0.044175,0.06729,0.081341,0.095733,0.11544,0.13801,0.15974,0.17551,0.19297,0.21193,0.25868,0.31936,0.41815,0.52969,0.56118,0.61675,0.62188,0.61462,0.60659,0.56801,0.53043,0.50786,0.47928,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 5

Shape 5 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

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-1.0339,-1.045,-1.0535,-1.0226,-1.0019,-0.9273,-0.80235,-0.66243,-0.47212,-0.34162,-0.1974,-0.073041,0.1974,0.48996,0.73091,0.81569,0.86418,0.86026,0.8394,0.72664,0.5224,0.30288,-0.062419,-0.6435,-0.98889,-1.2387,-1.355,-1.4162,-1.4406,-1.4724,-1.5015,-1.5232,-1.593,-1.6673,-1.7943,-2.0344,-2.2318,-2.5309,-2.8198,-2.9764,3.089,2.8653,2.7572,2.6779,2.6488,2.6438,2.6576,2.715,2.6779,2.6189,2.5755,2.5266,2.5062,2.5203,2.5291,2.5399,2.5727,2.5984,2.705,3.0845,-2.6224,-2.012,-1.7648,-1.6688,-1.6025,-1.5541,-1.4169,-1.2747,-1.1635,-1.0783,-0.9545,-0.89606,NaN,NaN,NaN
-1.0412,-1.0552,-1.0335,-0.99844,-0.96211,-0.89729,-0.7551,-0.588,-0.41507,-0.2831,-0.1364,0.083141,0.32175,0.588,0.75838,0.85197,0.84914,0.83911,0.75093,0.65457,0.43395,0.10221,-0.44237,-0.85774,-1.121,-1.2875,-1.3796,-1.4219,-1.4623,-1.485,-1.5106,-1.5414,-1.6332,-1.7168,-1.826,-2.0899,-2.4469,-2.7018,-2.9442,3.1416,2.8966,2.792,2.715,2.6779,2.6591,2.6521,2.6779,2.6779,2.6353,2.5904,2.559,2.5213,2.5229,2.5232,2.5256,2.5536,2.6032,2.6585,2.8872,-2.8906,-2.2896,-1.8979,-1.7289,-1.6506,-1.5576,-1.4813,-1.3258,-1.2444,-1.1372,-1.0698,-0.9545,NaN,NaN,NaN,NaN

Shape 5 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

-0.7854,-1.1071,-1.1903,-0.98279,-1.049,-1.0769,-0.94677,-0.84415,-0.62025,-0.61073,-0.38051,-0.2268,-0.16515,0,0.32175,0.7854,0.7854,0.83798,0.83798,0.95055,0.7854,0.70863,0.29146,0.1419,0,-0.70863,-1.212,-1.3258,-1.4219,-1.4289,-1.4711,-1.4411,-1.5708,-1.5708,-1.5708,-1.7682,-2.1588,-2.1588,-2.3562,-2.3562,-2.9442,-2.9997,-3.1416,-3.3866,-3.5814,-3.6458,-3.7296,-3.6052,-3.5598,-3.5782,-3.5221,-3.7035,-3.7523,-3.7743,-3.7995,-3.7944,-3.6664,-3.7439,-3.7743,-3.6409,-3.4904,-3.1416,-2.1294,-1.8925,-1.5708,-1.6705,-1.5708,-1.5708,-1.344,-1.249,-0.99946,-0.98279,-0.7854,-0.7854,0
-1.0304,-1.1659,-1.0344,-1.0216,-1.0626,-1.0235,-0.90175,-0.75093,-0.6163,-0.50284,-0.29544,-0.1974,-0.09066,0.12435,0.60554,0.7854,0.81569,0.83798,0.90116,0.88035,0.75315,0.4869,0.23109,0.066568,-0.38051,-1.0371,-1.2679,-1.3787,-1.4255,-1.4494,-1.455,-1.4959,-1.5708,-1.5708,-1.6332,-1.9296,-2.1588,-2.2143,-2.3562,-2.7367,-2.9764,-3.0828,-3.2942,-3.5221,-3.6116,-3.682,-3.6655,-3.586,-3.5682,-3.5465,-3.6304,-3.7296,-3.7634,-3.7851,-3.7973,-3.7296,-3.7028,-3.7588,-3.7207,-3.5682,-3.3491,-2.5899,-1.9937,-1.7127,-1.6263,-1.6313,-1.5708,-1.4601,-1.2882,-1.1325,-0.99442,-0.90975,-0.7854,-0.7854,NaN
-1.1342,-1.0412,-1.0419,-1.0415,-1.0332,-0.97998,-0.83486,-0.71883,-0.55329,-0.40123,-0.25169,-0.1419,0,0.37299,0.67474,0.80667,0.82384,0.88187,0.86718,0.83989,0.60554,0.39479,0.15866,-0.22348,-0.80865,-1.1501,-1.3258,-1.3971,-1.4404,-1.4464,-1.4877,-1.5132,-1.5708,-1.6065,-1.7274,-1.9974,-2.191,-2.2655,-2.6779,-2.8633,-3.0509,-3.2323,-3.4633,-3.5692,-3.6426,-3.6578,-3.6365,-3.584,-3.551,-3.6181,-3.6801,-3.7453,-3.7733,-3.7874,-3.7569,-3.734,-3.725,-3.7296,-3.6578,-3.4633,-2.9764,-2.2753,-1.8158,-1.6952,-1.6116,-1.6133,-1.4959,-1.3734,-1.1903,-1.1071,-0.96299,-0.89606,-0.7854,NaN,NaN
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Shape 5 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.52373,0.2152,0.074549,0.039554,0.033975,0.038186,0.043928,0.05026,0.054791,0.053011,0.032036,0.015366,0.0070651,0.067821,0.11665,0.12166,0.1054,0.097613,0.083955,0.081669,0.081352,0.058087,0.024747,0.037604,0.11154,0.1234,0.11792,0.11375,0.1043,0.10508,0.10355,0.11401,0.1625,0.21347,0.3415,0.69915,0.92549,1.3688,1.8047,1.047,0.74654,0.55813,0.3816,0.1963,0.15498,0.18815,0.20922,0.23089,0.29407,0.28361,0.2054,0.16388,0.15343,0.17488,0.22885,0.25844,0.27035,0.29353,0.35031,0.42389,0.44463,0.41089,0.25326,0.1792,0.1333,0.14538,0.16613,0.15229,0.11117,0.090724,0.11602,0.22295,0.27768,NaN,NaN
0.10415,0.057613,0.039248,0.031879,0.03122,0.035216,0.040361,0.04174,0.037431,0.028529,0.0097391,0.017097,0.044997,0.075589,0.090166,0.089866,0.077711,0.072494,0.06794,0.058032,0.048845,0.012477,0.042823,0.075028,0.091897,0.096746,0.091442,0.090849,0.086554,0.091804,0.10547,0.12535,0.19156,0.29104,0.42955,0.78679,1.0454,0.98979,0.84068,0.59317,0.41522,0.23552,0.1799,0.15964,0.14761,0.17274,0.20374,0.21234,0.20197,0.17192,0.14577,0.14097,0.15271,0.1733,0.20733,0.22882,0.25263,0.28579,0.31821,0.34306,0.29254,0.22578,0.15183,0.13402,0.12245,0.12252,0.11353,0.097621,0.095437,0.10202,0.1204,NaN,NaN,NaN,NaN
0.051155,0.042602,0.035589,0.031442,0.031638,0.033768,0.034999,0.03172,0.022218,0.0042592,0.017921,0.037945,0.055122,0.071696,0.075524,0.074262,0.068424,0.059528,0.052996,0.033548,0.00011868,0.034478,0.061996,0.076258,0.082054,0.08635,0.083438,0.086534,0.092107,0.10355,0.13068,0.17023,0.25147,0.37958,0.55578,0.77324,0.76683,0.64438,0.484,0.27894,0.21424,0.18602,0.16515,0.15782,0.15861,0.17725,0.17952,0.16647,0.15711,0.15105,0.1474,0.14831,0.16001,0.17895,0.21289,0.23911,0.2558,0.27374,0.26934,0.24938,0.19857,0.17108,0.13792,0.12199,0.10455,0.097725,0.10223,0.1037,0.099409,NaN,NaN,NaN,NaN,NaN,NaN
0.044245,0.040091,0.035334,0.030914,0.029772,0.029545,0.026594,0.016404,0.0012064,0.015925,0.032567,0.046614,0.05562,0.064682,0.068392,0.063601,0.057123,0.041992,0.020556,0.0040512,0.030368,0.050691,0.065013,0.074263,0.078065,0.084072,0.088338,0.096084,0.11093,0.13372,0.16805,0.22038,0.32633,0.44531,0.5401,0.60094,0.50051,0.31599,0.24772,0.21386,0.18952,0.1774,0.17115,0.16398,0.1538,0.15541,0.15318,0.15168,0.15584,0.15506,0.15392,0.15658,0.17101,0.1924,0.2205,0.23792,0.23668,0.23127,0.20988,0.19994,0.17524,0.15151,0.11913,0.10305,0.098462,0.10192,0.10456,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.04286,0.038745,0.033434,0.028353,0.025331,0.020773,0.012955,0.00092978,0.013578,0.028121,0.038897,0.047448,0.05369,0.057239,0.058767,0.048631,0.030885,0.011091,0.007877,0.025213,0.042834,0.056573,0.066301,0.075244,0.0834,0.092461,0.10367,0.1193,0.13804,0.1679,0.214,0.26985,0.3579,0.42791,0.42924,0.32866,0.26867,0.23802,0.21311,0.19857,0.19068,0.17959,0.16407,0.15001,0.1406,0.14634,0.15289,0.15487,0.16005,0.16107,0.16332,0.16844,0.17984,0.19595,0.2119,0.21435,0.20142,0.19936,0.18965,0.17797,0.15036,0.12749,0.11153,0.10591,0.10029,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 5 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.52373,0.2152,0.074549,0.039554,0.033975,0.038186,0.043928,0.05026,0.054791,0.053011,0.032036,0.015366,0.0070651,0.067821,0.11665,0.12166,0.1054,0.097613,0.083955,0.081669,0.081352,0.058087,0.024747,0.037604,0.11154,0.1234,0.11792,0.11375,0.1043,0.10508,0.10355,0.11401,0.1625,0.21347,0.3415,0.69915,0.92549,1.3688,1.8047,1.047,0.74654,0.55813,0.3816,0.1963,0.15498,0.18815,0.20922,0.23089,0.29407,0.28361,0.2054,0.16388,0.15343,0.17488,0.22885,0.25844,0.27035,0.29353,0.35031,0.42389,0.44463,0.41089,0.25326,0.1792,0.1333,0.14538,0.16613,0.15229,0.11117,0.090724,0.11602,0.22295,0.27768,NaN,NaN
0.10415,0.057613,0.039248,0.031879,0.03122,0.035216,0.040361,0.04174,0.037431,0.028529,0.0097391,0.017097,0.044997,0.075589,0.090166,0.089866,0.077711,0.072494,0.06794,0.058032,0.048845,0.012477,0.042823,0.075028,0.091897,0.096746,0.091442,0.090849,0.086554,0.091804,0.10547,0.12535,0.19156,0.29104,0.42955,0.78679,1.0454,0.98979,0.84068,0.59317,0.41522,0.23552,0.1799,0.15964,0.14761,0.17274,0.20374,0.21234,0.20197,0.17192,0.14577,0.14097,0.15271,0.1733,0.20733,0.22882,0.25263,0.28579,0.31821,0.34306,0.29254,0.22578,0.15183,0.13402,0.12245,0.12252,0.11353,0.097621,0.095437,0.10202,0.1204,NaN,NaN,NaN,NaN
0.051155,0.042602,0.035589,0.031442,0.031638,0.033768,0.034999,0.03172,0.022218,0.0042592,0.017921,0.037945,0.055122,0.071696,0.075524,0.074262,0.068424,0.059528,0.052996,0.033548,0.00011868,0.034478,0.061996,0.076258,0.082054,0.08635,0.083438,0.086534,0.092107,0.10355,0.13068,0.17023,0.25147,0.37958,0.55578,0.77324,0.76683,0.64438,0.484,0.27894,0.21424,0.18602,0.16515,0.15782,0.15861,0.17725,0.17952,0.16647,0.15711,0.15105,0.1474,0.14831,0.16001,0.17895,0.21289,0.23911,0.2558,0.27374,0.26934,0.24938,0.19857,0.17108,0.13792,0.12199,0.10455,0.097725,0.10223,0.1037,0.099409,NaN,NaN,NaN,NaN,NaN,NaN
0.044245,0.040091,0.035334,0.030914,0.029772,0.029545,0.026594,0.016404,0.0012064,0.015925,0.032567,0.046614,0.05562,0.064682,0.068392,0.063601,0.057123,0.041992,0.020556,0.0040512,0.030368,0.050691,0.065013,0.074263,0.078065,0.084072,0.088338,0.096084,0.11093,0.13372,0.16805,0.22038,0.32633,0.44531,0.5401,0.60094,0.50051,0.31599,0.24772,0.21386,0.18952,0.1774,0.17115,0.16398,0.1538,0.15541,0.15318,0.15168,0.15584,0.15506,0.15392,0.15658,0.17101,0.1924,0.2205,0.23792,0.23668,0.23127,0.20988,0.19994,0.17524,0.15151,0.11913,0.10305,0.098462,0.10192,0.10456,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.04286,0.038745,0.033434,0.028353,0.025331,0.020773,0.012955,0.00092978,0.013578,0.028121,0.038897,0.047448,0.05369,0.057239,0.058767,0.048631,0.030885,0.011091,0.007877,0.025213,0.042834,0.056573,0.066301,0.075244,0.0834,0.092461,0.10367,0.1193,0.13804,0.1679,0.214,0.26985,0.3579,0.42791,0.42924,0.32866,0.26867,0.23802,0.21311,0.19857,0.19068,0.17959,0.16407,0.15001,0.1406,0.14634,0.15289,0.15487,0.16005,0.16107,0.16332,0.16844,0.17984,0.19595,0.2119,0.21435,0.20142,0.19936,0.18965,0.17797,0.15036,0.12749,0.11153,0.10591,0.10029,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 6

Shape 6 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

1.8925,1.9784,2.0899,2.184,2.2249,2.1527,2.2655,2.3562,2.3108,2.3907,2.6477,2.8633,2.9997,3.1416,3.1416,3.1416,3.1416,0,-0.38051,-0.29146,-0.40489,-0.51445,-0.39234,-0.43467,-0.34877,-0.41241,-0.47647,-0.47647,-0.42142,-0.36933,-0.39061,-0.46365,-0.588,0,-1.5708,1.5708,1.5708,2.3562,2.0344,2.0779,2.0533,2.0779,1.9451,1.9591,1.9055,1.8737,1.8158,1.8491,1.7682,2.3562,1.5708,-0.7854,-0.69474,-0.68232,-0.73997,-0.69866,-0.70226,-0.72664,-0.72664,-0.62025,-0.67474,-0.46365,0,-0.7854,0
1.9731,2.0158,2.1442,2.2058,2.1855,2.21,2.3121,2.3387,2.3425,2.4981,2.7187,2.9305,3.0585,3.1416,3.1416,3.1416,0,-0.24498,-0.32175,-0.35877,-0.4744,-0.44814,-0.41333,-0.38896,-0.38051,-0.44442,-0.47647,-0.45023,-0.39479,-0.37691,-0.41822,-0.49394,-0.46365,-0.7854,0,1.5708,2.0344,2.1588,2.0701,2.0608,2.0672,2.0124,1.9513,1.932,1.8925,1.8491,1.8281,1.8158,1.8925,2.0344,-0.588,-0.72664,-0.68573,-0.71701,-0.71883,-0.7005,-0.71236,-0.72664,-0.68232,-0.6435,-0.62025,-0.32175,-0.46365,-0.7854,NaN
2.0106,2.0686,2.1763,2.185,2.2143,2.261,2.3118,2.3492,2.4099,2.5602,2.7869,2.985,3.075,3.1416,3.1416,3.1416,-0.32175,-0.27095,-0.36254,-0.43779,-0.43911,-0.44345,-0.39005,-0.39708,-0.41241,-0.4551,-0.45924,-0.42331,-0.39387,-0.39234,-0.43663,-0.46365,-0.6435,0,1.5708,1.8925,2.0344,2.0989,2.0591,2.0689,2.0239,1.9974,1.9371,1.9169,1.8748,1.8491,1.8158,1.8693,1.8491,-0.46365,-0.66104,-0.69866,-0.71409,-0.70991,-0.71306,-0.70743,-0.71481,-0.7062,-0.68052,-0.62025,-0.5586,-0.46365,-0.46365,NaN,NaN
2.0635,2.11,2.1687,2.2082,2.2534,2.27,2.3227,2.3869,2.4539,2.6224,2.8387,3.0061,3.0828,3.1416,3.1416,-0.46365,-0.30288,-0.3311,-0.43241,-0.42066,-0.43779,-0.41658,-0.39595,-0.41748,-0.42841,-0.44726,-0.43708,-0.41822,-0.40211,-0.40291,-0.42419,-0.51915,-0.46365,0.7854,2.0344,1.9513,2.0647,2.0701,2.0678,2.0297,2.0097,1.9769,1.9259,1.9007,1.8717,1.8392,1.8438,1.8491,1.3258,-0.6435,-0.67474,-0.71883,-0.70863,-0.70771,-0.71574,-0.70968,-0.70449,-0.70226,-0.66405,-0.588,-0.588,-0.46365,NaN,NaN,NaN
2.1053,2.1204,2.1929,2.2426,2.2619,2.2828,2.3518,2.4143,2.5006,2.6695,2.8633,3.0172,3.089,3.1416,-1.1071,-0.34302,-0.35144,-0.41146,-0.41822,-0.42445,-0.4153,-0.41566,-0.41275,-0.42954,-0.42711,-0.432,-0.43149,-0.42215,-0.40891,-0.39708,-0.45066,-0.46365,-0.24498,1.5708,2.0344,2.0344,2.0577,2.0736,2.0298,2.0156,1.9906,1.9631,1.9132,1.8963,1.8637,1.8555,1.8338,1.6615,-0.1419,-0.66964,-0.70691,-0.712,-0.70691,-0.71091,-0.71672,-0.70278,-0.70226,-0.69233,-0.6435,-0.60229,-0.588,NaN,NaN,NaN,NaN

Shape 6 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

1.8925,1.9784,2.0899,2.184,2.2249,2.1527,2.2655,2.3562,2.3108,2.3907,2.6477,2.8633,2.9997,3.1416,3.1416,3.1416,3.1416,0,-0.38051,-0.29146,-0.40489,-0.51445,-0.39234,-0.43467,-0.34877,-0.41241,-0.47647,-0.47647,-0.42142,-0.36933,-0.39061,-0.46365,-0.588,0,-1.5708,1.5708,1.5708,2.3562,2.0344,2.0779,2.0533,2.0779,1.9451,1.9591,1.9055,1.8737,1.8158,1.8491,1.7682,2.3562,1.5708,-0.7854,-0.69474,-0.68232,-0.73997,-0.69866,-0.70226,-0.72664,-0.72664,-0.62025,-0.67474,-0.46365,0,-0.7854,0
1.9731,2.0158,2.1442,2.2058,2.1855,2.21,2.3121,2.3387,2.3425,2.4981,2.7187,2.9305,3.0585,3.1416,3.1416,3.1416,0,-0.24498,-0.32175,-0.35877,-0.4744,-0.44814,-0.41333,-0.38896,-0.38051,-0.44442,-0.47647,-0.45023,-0.39479,-0.37691,-0.41822,-0.49394,-0.46365,-0.7854,0,1.5708,2.0344,2.1588,2.0701,2.0608,2.0672,2.0124,1.9513,1.932,1.8925,1.8491,1.8281,1.8158,1.8925,2.0344,-0.588,-0.72664,-0.68573,-0.71701,-0.71883,-0.7005,-0.71236,-0.72664,-0.68232,-0.6435,-0.62025,-0.32175,-0.46365,-0.7854,NaN
2.0106,2.0686,2.1763,2.185,2.2143,2.261,2.3118,2.3492,2.4099,2.5602,2.7869,2.985,3.075,3.1416,3.1416,3.1416,5.9614,6.0122,5.9206,5.8454,5.8441,5.8397,5.8931,5.8861,5.8708,5.8281,5.8239,5.8599,5.8893,5.8908,5.8466,5.8195,5.6397,6.2832,7.854,8.1757,8.3176,8.3821,8.3423,8.3521,8.307,8.2806,8.2202,8.2001,8.158,8.1323,8.099,8.1525,8.1323,5.8195,5.6221,5.5845,5.5691,5.5733,5.5701,5.5758,5.5684,5.577,5.6027,5.6629,5.7246,5.8195,5.8195,NaN,NaN
2.0635,2.11,2.1687,2.2082,2.2534,2.27,2.3227,2.3869,2.4539,2.6224,2.8387,3.0061,3.0828,3.1416,3.1416,5.8195,5.9803,5.9521,5.8508,5.8625,5.8454,5.8666,5.8872,5.8657,5.8548,5.8359,5.8461,5.865,5.8811,5.8803,5.859,5.764,5.8195,7.0686,8.3176,8.2345,8.3479,8.3533,8.351,8.3129,8.2928,8.2601,8.2091,8.1839,8.1549,8.1223,8.127,8.1323,7.609,5.6397,5.6084,5.5644,5.5746,5.5755,5.5674,5.5735,5.5787,5.5809,5.6191,5.6952,5.6952,5.8195,NaN,NaN,NaN
2.1053,2.1204,2.1929,2.2426,2.2619,2.2828,2.3518,2.4143,2.5006,2.6695,2.8633,3.0172,3.089,3.1416,5.176,5.9402,5.9317,5.8717,5.865,5.8587,5.8679,5.8675,5.8704,5.8536,5.8561,5.8512,5.8517,5.861,5.8743,5.8861,5.8325,5.8195,6.0382,7.854,8.3176,8.3176,8.3409,8.3568,8.313,8.2988,8.2737,8.2463,8.1964,8.1795,8.1469,8.1387,8.117,7.9446,6.1413,5.6135,5.5763,5.5712,5.5763,5.5723,5.5665,5.5804,5.5809,5.5909,5.6397,5.6809,5.6952,NaN,NaN,NaN,NaN

Shape 6 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.11668,0.086701,0.11361,0.092655,0.07976,0.073358,0.071945,0.087518,0.14225,0.22395,0.38606,0.62745,0.76902,1.1781,1.885,1.5708,0.55222,0.080137,0.068046,0.047164,0.031492,0.023207,0.018886,0.018123,0.01767,0.019557,0.019698,0.019008,0.018169,0.023701,0.048782,0.071125,0.46874,0,0.7854,2.7489,2.4693,1.7721,0.492,0.18261,0.1113,0.098116,0.10788,0.11925,0.13608,0.19012,0.2765,0.48254,0.8744,1.3013,0.017293,0.17941,0.074476,0.040976,0.033559,0.031893,0.037074,0.057399,0.097929,0.1172,0.13177,0.38598,0.32532,NaN,NaN
0.095758,0.074371,0.077707,0.06854,0.062957,0.066338,0.080872,0.10842,0.17925,0.28293,0.43363,0.68398,0.91184,1.0472,0.90443,0.45306,0.099145,0.046725,0.034512,0.024412,0.020164,0.016986,0.015606,0.015823,0.015274,0.015798,0.015834,0.017934,0.023608,0.027278,0.088177,0.062651,0.14878,0.98175,1.3505,1.7008,0.67528,0.28152,0.15179,0.10649,0.091667,0.089479,0.10003,0.12172,0.15161,0.23278,0.35776,0.45689,0.35855,0.12197,0.039551,0.056432,0.038147,0.029964,0.029476,0.033787,0.043796,0.062818,0.084871,0.13946,0.17404,NaN,NaN,NaN,NaN
0.07719,0.064824,0.065797,0.065153,0.070677,0.08156,0.10486,0.14362,0.22727,0.35267,0.53883,0.69938,0.68803,0.58348,0.32324,0.12329,0.018534,0.026326,0.023111,0.018727,0.017154,0.015783,0.014661,0.014519,0.014136,0.016003,0.019384,0.02036,0.038348,0.026481,0.0035537,0.15306,0.59574,1.0509,0.59558,0.34654,0.20299,0.14707,0.11616,0.097087,0.091136,0.097134,0.11444,0.15092,0.1953,0.23786,0.25091,0.20047,0.069503,0.004921,0.028037,0.038538,0.033062,0.031675,0.034291,0.039145,0.044772,0.073526,0.10318,NaN,NaN,NaN,NaN,NaN,NaN
0.067566,0.063159,0.071478,0.076662,0.087669,0.10389,0.13241,0.18075,0.28397,0.38076,0.46914,0.51121,0.38234,0.23829,0.11028,0.040317,0.0030025,0.020143,0.019265,0.017111,0.015928,0.014778,0.013937,0.014931,0.016839,0.017735,0.028152,0.020059,0.0065441,0.030043,0.11712,0.31145,0.44102,0.29219,0.19731,0.17536,0.14572,0.12459,0.10946,0.10194,0.10193,0.11654,0.1407,0.1555,0.16077,0.16205,0.10793,0.050164,0.013386,0.0082972,0.0269,0.038266,0.036643,0.035585,0.035398,0.044586,0.052311,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.072124,0.072505,0.085283,0.093841,0.10735,0.12753,0.16245,0.19775,0.26517,0.32556,0.33366,0.27874,0.17075,0.097708,0.051319,0.019177,0.0026409,0.018152,0.017545,0.015887,0.015035,0.015071,0.016093,0.016297,0.023087,0.017562,0.0094473,0.0088819,0.035986,0.084088,0.16923,0.19701,0.17766,0.15664,0.14339,0.14404,0.13173,0.12479,0.11753,0.11745,0.1205,0.11983,0.12315,0.12426,0.10141,0.070844,0.040903,0.017302,0.00037902,0.014491,0.031097,0.041372,0.037462,0.039463,0.039954,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 6 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.11668,0.086701,0.11361,0.092655,0.07976,0.073358,0.071945,0.087518,0.14225,0.22395,0.38606,0.62745,0.76902,1.1781,1.885,1.5708,0.55222,0.080137,0.068046,0.047164,0.031492,0.023207,0.018886,0.018123,0.01767,0.019557,0.019698,0.019008,0.018169,0.023701,0.048782,0.071125,0.46874,0,0.7854,2.7489,2.4693,1.7721,0.492,0.18261,0.1113,0.098116,0.10788,0.11925,0.13608,0.19012,0.2765,0.48254,0.8744,1.3013,0.017293,0.17941,0.074476,0.040976,0.033559,0.031893,0.037074,0.057399,0.097929,0.1172,0.13177,0.38598,0.32532,NaN,NaN
0.095758,0.074371,0.077707,0.06854,0.062957,0.066338,0.080872,0.10842,0.17925,0.28293,0.43363,0.68398,0.91184,1.0472,0.90443,0.45306,0.099145,0.046725,0.034512,0.024412,0.020164,0.016986,0.015606,0.015823,0.015274,0.015798,0.015834,0.017934,0.023608,0.027278,0.088177,0.062651,0.14878,0.98175,1.3505,1.7008,0.67528,0.28152,0.15179,0.10649,0.091667,0.089479,0.10003,0.12172,0.15161,0.23278,0.35776,0.45689,0.35855,0.12197,0.039551,0.056432,0.038147,0.029964,0.029476,0.033787,0.043796,0.062818,0.084871,0.13946,0.17404,NaN,NaN,NaN,NaN
0.07719,0.064824,0.065797,0.065153,0.070677,0.08156,0.10486,0.14362,0.22727,0.35267,0.53883,0.69938,0.68803,0.58348,0.32324,0.12329,0.018534,0.026326,0.023111,0.018727,0.017154,0.015783,0.014661,0.014519,0.014136,0.016003,0.019384,0.02036,0.038348,0.026481,0.0035537,0.15306,0.59574,1.0509,0.59558,0.34654,0.20299,0.14707,0.11616,0.097087,0.091136,0.097134,0.11444,0.15092,0.1953,0.23786,0.25091,0.20047,0.069503,0.004921,0.028037,0.038538,0.033062,0.031675,0.034291,0.039145,0.044772,0.073526,0.10318,NaN,NaN,NaN,NaN,NaN,NaN
0.067566,0.063159,0.071478,0.076662,0.087669,0.10389,0.13241,0.18075,0.28397,0.38076,0.46914,0.51121,0.38234,0.23829,0.11028,0.040317,0.0030025,0.020143,0.019265,0.017111,0.015928,0.014778,0.013937,0.014931,0.016839,0.017735,0.028152,0.020059,0.0065441,0.030043,0.11712,0.31145,0.44102,0.29219,0.19731,0.17536,0.14572,0.12459,0.10946,0.10194,0.10193,0.11654,0.1407,0.1555,0.16077,0.16205,0.10793,0.050164,0.013386,0.0082972,0.0269,0.038266,0.036643,0.035585,0.035398,0.044586,0.052311,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.072124,0.072505,0.085283,0.093841,0.10735,0.12753,0.16245,0.19775,0.26517,0.32556,0.33366,0.27874,0.17075,0.097708,0.051319,0.019177,0.0026409,0.018152,0.017545,0.015887,0.015035,0.015071,0.016093,0.016297,0.023087,0.017562,0.0094473,0.0088819,0.035986,0.084088,0.16923,0.19701,0.17766,0.15664,0.14339,0.14404,0.13173,0.12479,0.11753,0.11745,0.1205,0.11983,0.12315,0.12426,0.10141,0.070844,0.040903,0.017302,0.00037902,0.014491,0.031097,0.041372,0.037462,0.039463,0.039954,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 7

Shape 7 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

1.5708,1.8491,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5351,1.5708,1.494,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,0
1.8158,1.6879,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5519,1.5508,1.5422,1.5308,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN
1.6815,1.6352,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5583,1.5575,1.5391,1.5495,1.5396,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN
1.6332,1.6116,1.5708,1.5708,1.5708,1.5708,1.5708,1.561,1.561,1.5481,1.5441,1.5523,1.5422,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN,NaN
1.6108,1.6016,1.5708,1.5708,1.5708,1.5708,1.5627,1.5627,1.5534,1.5508,1.5464,1.5533,1.543,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN,NaN,NaN

Shape 7 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

1.5708,1.8491,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5351,1.5708,1.494,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,0
1.8158,1.6879,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5519,1.5508,1.5422,1.5308,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN
1.6815,1.6352,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5583,1.5575,1.5391,1.5495,1.5396,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN
1.6332,1.6116,1.5708,1.5708,1.5708,1.5708,1.5708,1.561,1.561,1.5481,1.5441,1.5523,1.5422,1.5708,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN,NaN
1.6108,1.6016,1.5708,1.5708,1.5708,1.5708,1.5627,1.5627,1.5534,1.5508,1.5464,1.5533,1.543,1.5708,1.5708,1.5708,1.5708,1.5708,NaN,NaN,NaN,NaN

Shape 7 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.60273,0.28881,0.19635,0.14726,0.1386,0.12401,0.1071,0.096171,0.089936,0.08821,0.091966,0.1323,0.18514,0.24802,0.47124,1.1781,1.1781,0.94248,1.5708,1.5708,NaN,NaN
0.25193,0.16502,0.13541,0.1122,0.10069,0.090276,0.08144,0.076636,0.075884,0.087916,0.10314,0.14392,0.22196,0.34148,0.561,0.87266,1.122,0.8976,NaN,NaN,NaN,NaN
0.17009,0.12917,0.1078,0.0924,0.084307,0.078275,0.074533,0.079406,0.085656,0.10166,0.12795,0.18813,0.27969,0.3927,0.6468,0.8568,NaN,NaN,NaN,NaN,NaN,NaN
0.13072,0.10578,0.091568,0.081977,0.077907,0.080115,0.081989,0.089869,0.10233,0.12628,0.15748,0.22304,0.33447,0.41888,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.10797,0.09256,0.084141,0.082906,0.083715,0.08846,0.094812,0.10725,0.1217,0.14791,0.18648,0.24034,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 7 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.60273,0.28881,0.19635,0.14726,0.1386,0.12401,0.1071,0.096171,0.089936,0.08821,0.091966,0.1323,0.18514,0.24802,0.47124,1.1781,1.1781,0.94248,1.5708,1.5708,NaN,NaN
0.25193,0.16502,0.13541,0.1122,0.10069,0.090276,0.08144,0.076636,0.075884,0.087916,0.10314,0.14392,0.22196,0.34148,0.561,0.87266,1.122,0.8976,NaN,NaN,NaN,NaN
0.17009,0.12917,0.1078,0.0924,0.084307,0.078275,0.074533,0.079406,0.085656,0.10166,0.12795,0.18813,0.27969,0.3927,0.6468,0.8568,NaN,NaN,NaN,NaN,NaN,NaN
0.13072,0.10578,0.091568,0.081977,0.077907,0.080115,0.081989,0.089869,0.10233,0.12628,0.15748,0.22304,0.33447,0.41888,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.10797,0.09256,0.084141,0.082906,0.083715,0.08846,0.094812,0.10725,0.1217,0.14791,0.18648,0.24034,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 8

Shape 8 Direction without 2pi smoothing (neighborhoods, 1,2,3,4,5)

Values:

0,0.7854,0.7854,0.1974,0.16515,0.1419,0.1974,0.24498,0.1419,0,0.076772,0.062419,0,0.055499,0,0,0,0,0,0,0,0,0,0,0.46365,0,0,1.5708,0,0,0,0,0
0.46365,0.7854,0.32175,0.17985,0.15265,0.16515,0.21867,0.17985,0.055499,0.041643,0.068856,0.02631,0.024995,0.034469,0,0,0,0,0,0,0,0,0,0.1974,0.24498,0,0.7854,0.46365,0,0,0,0,NaN
0.588,0.40489,0.24498,0.16515,0.16515,0.18535,0.18535,0.09066,0.064427,0.049958,0.039196,0.035699,0.019605,0.022723,0,0,0,0,0,0,0,0,0.083141,0.1419,0.1974,0.32175,0.32175,0.24498,0,0,0,NaN,NaN
0.35877,0.2985,0.2075,0.17219,0.17985,0.17219,0.11066,0.085505,0.063743,0.032247,0.043451,0.029842,0.01515,0.016948,0,0,0,0,0,0,0,0.047583,0.071307,0.12435,0.38051,0.1974,0.1974,0.16515,0,0,NaN,NaN,NaN
0.2783,0.24498,0.2054,0.18311,0.17074,0.11711,0.099669,0.078271,0.043451,0.037482,0.037482,0.024385,0.012345,0.013888,0,0,0,0,0,0,0.028564,0.043451,0.066568,0.24498,0.2783,0.1419,0.1419,0.1419,0,NaN,NaN,NaN,NaN

Shape 8 Direction with 2pi smoothing (neighborhoods 1,2,3,4,5)

Values:

0,0.7854,0.7854,0.1974,0.16515,0.1419,0.1974,0.24498,0.1419,0,0.076772,0.062419,0,0.055499,0,0,0,0,0,0,0,0,0,0,0.46365,0,0,1.5708,0,0,0,0,0
0.46365,0.7854,0.32175,0.17985,0.15265,0.16515,0.21867,0.17985,0.055499,0.041643,0.068856,0.02631,0.024995,0.034469,0,0,0,0,0,0,0,0,0,0.1974,0.24498,0,0.7854,0.46365,0,0,0,0,NaN
0.588,0.40489,0.24498,0.16515,0.16515,0.18535,0.18535,0.09066,0.064427,0.049958,0.039196,0.035699,0.019605,0.022723,0,0,0,0,0,0,0,0,0.083141,0.1419,0.1974,0.32175,0.32175,0.24498,0,0,0,NaN,NaN
0.35877,0.2985,0.2075,0.17219,0.17985,0.17219,0.11066,0.085505,0.063743,0.032247,0.043451,0.029842,0.01515,0.016948,0,0,0,0,0,0,0,0.047583,0.071307,0.12435,0.38051,0.1974,0.1974,0.16515,0,0,NaN,NaN,NaN
0.2783,0.24498,0.2054,0.18311,0.17074,0.11711,0.099669,0.078271,0.043451,0.037482,0.037482,0.024385,0.012345,0.013888,0,0,0,0,0,0,0.028564,0.043451,0.066568,0.24498,0.2783,0.1419,0.1419,0.1419,0,NaN,NaN,NaN,NaN

Shape 8 Curvature using the absolute value as in Yu (neighborhoods 3,5,7,9,11)

Values:

0.65065,0.62515,0.17625,0.045113,0.038349,0.048009,0.063355,0.03456,0.0121,0.0057903,0.0047882,0.0031005,0.0013865,0.0019119,0,0,0,0,0,0,0,0,0.046365,0.088549,0.10945,0.5236,0.7854,0.5236,0,0,0,NaN,NaN
0.21656,0.14812,0.075621,0.040546,0.039834,0.03108,0.02422,0.014931,0.0059627,0.0031366,0.0028176,0.0017584,0.00084053,0.00094021,0,0,0,0,0,0,0.01405,0.021833,0.032569,0.24702,0.32624,0.2618,0.2618,0.2244,0,NaN,NaN,NaN,NaN
0.10292,0.096164,0.064872,0.031515,0.023935,0.018255,0.012836,0.007938,0.0038613,0.0021372,0.0020473,0.0012149,0.00059024,0.00064512,0,0,0,0,0.0073595,0.0090492,0.012452,0.083943,0.1253,0.18106,0.19875,0.15708,0.17453,NaN,NaN,NaN,NaN,NaN,NaN
0.084959,0.071158,0.041543,0.02096,0.014824,0.010779,0.0080813,0.0056854,0.0029742,0.0016077,0.0015816,0.00095049,0.00044747,0.00047832,0,0,0.005095,0.0059263,0.0068958,0.037511,0.051851,0.074697,0.10054,0.13353,0.1537,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.055419,0.045572,0.02648,0.013284,0.0099138,0.0080451,0.0063645,0.0043961,0.0023843,0.0013146,0.0012717,0.0007654,0.00037747,0.00042035,0.0039628,0.0042837,0.0048684,0.025044,0.029384,0.035545,0.047054,0.065131,0.087555,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN

Shape 8 Curvature simply summing the values (neighborhoods 3,5,7,9,11)

Values:

0.65065,0.62515,0.17625,0.045113,0.038349,0.048009,0.063355,0.03456,0.0121,0.0057903,0.0047882,0.0031005,0.0013865,0.0019119,0,0,0,0,0,0,0,0,0.046365,0.088549,0.10945,0.5236,0.7854,0.5236,0,0,0,NaN,NaN
0.21656,0.14812,0.075621,0.040546,0.039834,0.03108,0.02422,0.014931,0.0059627,0.0031366,0.0028176,0.0017584,0.00084053,0.00094021,0,0,0,0,0,0,0.01405,0.021833,0.032569,0.24702,0.32624,0.2618,0.2618,0.2244,0,NaN,NaN,NaN,NaN
0.10292,0.096164,0.064872,0.031515,0.023935,0.018255,0.012836,0.007938,0.0038613,0.0021372,0.0020473,0.0012149,0.00059024,0.00064512,0,0,0,0,0.0073595,0.0090492,0.012452,0.083943,0.1253,0.18106,0.19875,0.15708,0.17453,NaN,NaN,NaN,NaN,NaN,NaN
0.084959,0.071158,0.041543,0.02096,0.014824,0.010779,0.0080813,0.0056854,0.0029742,0.0016077,0.0015816,0.00095049,0.00044747,0.00047832,0,0,0.005095,0.0059263,0.0068958,0.037511,0.051851,0.074697,0.10054,0.13353,0.1537,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
0.055419,0.045572,0.02648,0.013284,0.0099138,0.0080451,0.0063645,0.0043961,0.0023843,0.0013146,0.0012717,0.0007654,0.00037747,0.00042035,0.0039628,0.0042837,0.0048684,0.025044,0.029384,0.035545,0.047054,0.065131,0.087555,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN