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I am new to Mathematica programming.

I have a question related to my work with this software.

I have the data points below:

{{128.011, 86.7748}, {128.011, 86.7748}, {128.167, 86.7663}, {128.19, 86.7649},
 {128.947, 86.7163}, {129.704, 86.6611}, {130.46, 86.5993}, {131.215, 86.5309},
 {131.97, 86.4559}, {132.724, 86.3743}, {133.478, 86.2862}, {134.23, 86.1915},
 {134.982, 86.0902}, {135.733, 85.9823}, {136.483, 85.868}, {137.231, 85.747},
 {137.979, 85.6196}, {138.726, 85.4856}, {139.471, 85.3451}, {140.215, 85.1981},
 {140.958, 85.0447}, {141.7, 84.8847}, {142.44, 84.7183}, {143.178, 84.5454},
 {143.915, 84.3661}, {144.651, 84.1804}, {145.384, 83.9883}, {146.116, 83.7897},
 {146.847, 83.5848}, {147.575, 83.3735}, {148.302, 83.1559}, {149.027, 82.9319},
 {149.749, 82.7016}, {150.47, 82.4651}, {151.189, 82.2222}, {151.905, 81.9731},
 {152.619, 81.7177}, {153.331, 81.4561}, {154.041, 81.1884}, {154.748, 80.9144},
 {155.453, 80.6343}, {156.156, 80.348}, {156.855, 80.0556}, {157.553, 79.7571},
 {158.247, 79.4525}, {158.939, 79.1419}, {159.629, 78.8253}, {160.315, 78.5026},
 {160.999, 78.174}, {161.68, 77.8394}, {162.357, 77.4989}, {163.032, 77.1525},
 {163.704, 76.8003}, {164.373, 76.4421}, {165.038, 76.0782}, {165.7, 75.7084},
 {166.359, 75.3329}, {167.015, 74.9517}, {167.668, 74.5647}, {168.317, 74.1721},
 {168.962, 73.7738}, {169.604, 73.3699}, {170.243, 72.9604}, {170.877, 72.5454},
 {171.509, 72.1248}, {172.136, 71.6988}, {172.76, 71.2672}, {173.38, 70.8303},
 {173.996, 70.388}, {174.609, 69.9402}, {175.217, 69.4872}, {175.821, 69.0289},
 {176.422, 68.5653}, {177.018, 68.0965}, {177.61, 67.6225}, {178.198, 67.1434},
 {178.782, 66.6592}, {179.362, 66.1698}, {179.937, 65.6755}, {180.508, 65.1761},
 {181.074, 64.6718}, {181.637, 64.1625}, {182.194, 63.6484}, {182.747, 63.1294},
 {183.296, 62.6056}, {183.84, 62.0771}, {184.38, 61.5438}, {184.914, 61.0058},
 {185.444, 60.4632}, {185.97, 59.916}, {186.49, 59.3642}, {187.006, 58.8079},
 {187.516, 58.2471}, {188.022, 57.6819}, {188.523, 57.1122}, {189.019, 56.5383},
 {189.51, 55.96}, {189.996, 55.3775}, {190.476, 54.7907}, {190.952, 54.1998},
 {191.422, 53.6048}, {191.888, 53.0056}, {192.347, 52.4025}, {192.802, 51.7953},
 {193.251, 51.1842}, {193.695, 50.5692}, {194.134, 49.9503}, {194.567, 49.3277},
 {194.995, 48.7013}, {195.417, 48.0712}, {195.834, 47.4374}, {196.245, 46.8},
 {196.651, 46.159}, {197.051, 45.5145}, {197.445, 44.8666}, {197.834, 44.2153},
 {198.217, 43.5605}, {198.594, 42.9025}, {198.966, 42.2412}, {199.331, 41.5767},
 {199.691, 40.909}, {200.045, 40.2382}, {200.393, 39.5643}, {200.736, 38.8874},
 {201.072, 38.2076}, {201.403, 37.5248}, {201.727, 36.8392}, {202.046, 36.1508},
 {202.358, 35.4596}, {202.664, 34.7657}, {202.965, 34.0692}, {203.259, 33.3701},
 {203.547, 32.6684}, {203.829, 31.9643}, {204.105, 31.2577}, {204.375, 30.5488},
 {204.638, 29.8375}, {204.896, 29.1239}, {205.147, 28.4082}, {205.391, 27.6902},
 {205.63, 26.9702}, {205.862, 26.2481}, {206.088, 25.524}, {206.308, 24.7979},
 {206.521, 24.07}, {206.728, 23.3402}, {206.928, 22.6087}, {207.122, 21.8754},
 {207.31, 21.1405}, {207.491, 20.404}, {207.666, 19.6659}, {207.834, 18.9263},
 {207.996, 18.1853}, {208.152, 17.4428}, {208.301, 16.6991}, {208.443, 15.9541},
 {208.579, 15.2078}, {208.709, 14.4605}, {208.832, 13.712}, {208.948, 12.9624},
 {209.058, 12.2119}, {209.161, 11.4605}, {209.258, 10.7081}, {209.348, 9.95499},
 {209.432, 9.2011}, {209.509, 8.4465}, {209.579, 7.69125}, {209.643, 6.93543},
 {209.7, 6.17907}, {209.751, 5.42224}, {209.795, 4.665}, {209.832, 3.90741},
 {209.863, 3.14952}, {209.887, 2.39138}, {209.905, 1.63307}, {209.916, 0.874631},
 {209.92, 0.116125}, {209.918, -0.642389}, {209.909, -1.40085}, {209.893, -2.15921},
 {209.871, -2.91741}, {209.842, -3.67538}, {209.807, -4.43307}, {209.765, -5.19043},
 {209.716, -5.94738}, {209.661, -6.70389}, {209.599, -7.45989}, {209.531, -8.21531},
 {209.456, -8.97012}, {209.374, -9.72424}, {209.286, -10.4776}, {209.191, -11.2302},
 {209.09, -11.9819}, {208.982, -12.7327}, {208.868, -13.4826}, {208.747, -14.2314},
 {208.62, -14.9791}, {208.486, -15.7257}, {208.345, -16.4711}, {208.198, -17.2153},
 {208.045, -17.9581}, {207.885, -18.6995}, {207.718, -19.4396}, {207.545, -20.1781},
 {207.366, -20.9152}, {207.18, -21.6506}, {206.988, -22.3844}, {206.79, -23.1164},
 {206.585, -23.8468}, {206.374, -24.5752}, {206.156, -25.3019}, {205.932, -26.0266},
 {205.702, -26.7493}, {205.465, -27.47}, {205.222, -28.1886}, {204.973, -28.905},
 {204.718, -29.6192}, {204.456, -30.3312}, {204.188, -31.0409}, {203.914, -31.7482},
 {203.634, -32.4531}, {203.348, -33.1555}, {203.056, -33.8554}, {202.757, -34.5527},
 {202.453, -35.2474}, {202.142, -35.9394}, {201.825, -36.6287}, {201.503, -37.3152},
 {201.174, -37.9988}, {200.839, -38.6796}, {200.499, -39.3574}, {200.153, -40.0321},
 {199.8, -40.7039}, {199.442, -41.3725}, {199.078, -42.038}, {198.708, -42.7003},
 {198.333, -43.3594}, {197.952, -44.0151}, {197.565, -44.6675}, {197.172, -45.3165},
 {196.774, -45.9621}, {196.37, -46.6041}, {195.96, -47.2426}, {195.545, -47.8775},
 {195.125, -48.5087}, {194.699, -49.1363}, {194.267, -49.7601}, {193.83, -50.3801},
 {193.388, -50.9963}, {192.94, -51.6086}, {192.487, -52.217}, {192.029, -52.8214},
 {191.565, -53.4217}, {191.097, -54.018}, {190.623, -54.6102}, {190.143, -55.1983},
 {189.659, -55.7821}, {189.17, -56.3617}, {188.675, -56.937}, {188.176, -57.5079},
 {187.672, -58.0745}, {187.163, -58.6366}, {186.648, -59.1943}, {186.129, -59.7475},
 {185.606, -60.2961}, {185.077, -60.8402}, {184.544, -61.3796}, {184.006, -61.9143},
 {183.463, -62.4443}, {182.916, -62.9695}, {182.364, -63.49}, {181.808, -64.0056},
 {181.247, -64.5164}, {180.682, -65.0222}, {180.112, -65.5231}, {179.538, -66.019},
 {178.96, -66.5099}, {178.377, -66.9957}, {177.791, -67.4764}, {177.2, -67.952},
 {176.605, -68.4223}, {176.006, -68.8875}, {175.402, -69.3475}, {174.795, -69.8021},
 {174.184, -70.2514}, {173.569, -70.6954}, {172.95, -71.134}, {172.328, -71.5672},
 {171.701, -71.9949}, {171.071, -72.4172}, {170.437, -72.8339}, {169.8, -73.2451},
 {169.159, -73.6507}, {168.515, -74.0507}, {167.867, -74.4451}, {167.215, -74.8338},
 {166.561, -75.2168}, {165.902, -75.5941}, {165.241, -75.9656}, {164.577, -76.3313},
 {163.909, -76.6912}, {163.238, -77.0453}, {162.564, -77.3935}, {161.887, -77.7358},
 {161.208, -78.0722}, {160.525, -78.4026}, {159.839, -78.7271}, {159.151, -79.0456},
 {158.46, -79.3581}, {157.766, -79.6645}, {157.069, -79.9648}, {156.37, -80.2591},
 {155.668, -80.5472}, {154.964, -80.8293}, {154.258, -81.1051}, {153.549, -81.3748},
 {152.837, -81.6383}, {152.124, -81.8956}, {151.408, -82.1466}, {150.69, -82.3914},
 {149.97, -82.6299}, {149.248, -82.8621}, {148.524, -83.088}, {147.798, -83.3076},
 {147.07, -83.5208}, {146.34, -83.7277}, {145.609, -83.9281}, {144.875, -84.1222},
 {144.141, -84.3099}, {143.404, -84.4912}, {142.666, -84.666}, {141.926, -84.8344},
 {141.185, -84.9964}, {140.443, -85.1518}, {139.699, -85.3008}, {138.954, -85.4433},
 {138.208, -85.5792}, {137.46, -85.7087}, {136.712, -85.8316}, {135.962, -85.948},
 {135.212, -86.0579}, {134.46, -86.1612}, {133.708, -86.2579}, {132.955, -86.348},
 {132.201, -86.4316}, {131.446, -86.5086}, {130.691, -86.579}, {129.935, -86.6429},
 {129.179, -86.7001}, {128.422, -86.7507}, {127.665, -86.7947}, {126.907, -86.8321},
 {126.15, -86.8629}, {125.391, -86.8871}, {124.633, -86.9047}, {123.875, -86.9156},
 {123.116, -86.9199}, {123.016, -86.9199}, {121.775, -86.7429}, {120.533, -86.5659},
 {119.292, -86.3888}, {118.05, -86.2118}, {116.809, -86.0348}, {115.567, -85.8578},
 {114.326, -85.6808}, {113.085, -85.5037}, {111.843, -85.3267}, {110.602, -85.1497},
 {109.36, -84.9727}, {108.119, -84.7957}, {106.878, -84.6187}, {105.636, -84.4416},
 {104.395, -84.2646}, {103.153, -84.0876}, {101.912, -83.9106}, {100.67, -83.7336},
 {99.429, -83.5565}, {98.1876, -83.3795}, {96.9462, -83.2025}, {95.7048, -83.0255},
 {94.4634, -82.8485}, {93.222, -82.6714}, {91.9805, -82.4944}, {90.7391, -82.3174},
 {89.4977, -82.1404}, {88.2563, -81.9634}, {87.0149, -81.7863}, {85.7734, -81.6093},
 {84.532, -81.4323}, {83.2906, -81.2553}, {82.0492, -81.0783}, {80.8078, -80.9012},
 {79.5664, -80.7242}, {78.3249, -80.5472}, {77.0835, -80.3702}, {75.8421, -80.1932},
 {74.6007, -80.0162}, {73.3593, -79.8391}, {72.1178, -79.6621}, {70.8764, -79.4851},
 {69.635, -79.3081}, {68.3936, -79.1311}, {67.1522, -78.954}, {65.9107, -78.777},
 {64.6693, -78.6}, {63.4279, -78.423}, {62.1865, -78.246}, {60.9451, -78.0689},
 {59.7037, -77.8919}, {58.4622, -77.7149}, {57.2208, -77.5379}, {55.9794, -77.3609},
 {54.738, -77.1838}, {53.4966, -77.0068}, {52.2551, -76.8298}, {51.0137, -76.6528},
 {49.7723, -76.4758}, {48.5309, -76.2987}, {47.2895, -76.1217}, {46.0481, -75.9447},
 {44.8066, -75.7677}, {43.5652, -75.5907},{42.3238, -75.4137}, {41.0824, -75.2366},
 {39.841, -75.0596}, {38.5995, -74.8826}, {37.3581, -74.7056}, {36.1167, -74.5286},
 {34.8753, -74.3515}, {33.6339, -74.1745}, {32.3924, -73.9975}, {31.151, -73.8205},
 {29.9096, -73.6435}, {28.6682, -73.4664}, {27.4268, -73.2894}, {26.1854, -73.1124},
 {24.9439, -72.9354}, {23.7025, -72.7584}, {22.4611, -72.5813}, {21.2197, -72.4043},
 {19.9783, -72.2273}, {18.7368, -72.0503}, {17.4954, -71.8733},{16.254, -71.6962},
 {15.0126, -71.5192}, {13.7712, -71.3422}, {12.5297, -71.1652}, {11.2883, -70.9882},
 {10.0469, -70.8112}, {8.80549, -70.634},{7.56408, -70.4571}, {6.32266, -70.2801},
 {5.08124, -70.1031}, {3.83982, -69.9261}, {2.5984, -69.749}, {1.35698, -69.572},
 {0.115564, -69.395}, {0.015564, -69.495}, {-0.590887, -69.4925}, {-1.19729, -69.4847},
 {-1.80361, -69.4716}, {-2.40979, -69.4532}, {-3.01578, -69.4295}, {-3.62154, -69.4006},
 {-4.22703, -69.3663}, {-4.8322, -69.3268}, {-5.437, -69.282}, {-6.04138, -69.2319},
 {-6.64531, -69.1765}, {-7.24873, -69.1159}, {-7.85159, -69.05}, {-8.45386, -68.9789},
 {-9.05549, -68.9025}, {-9.65642, -68.8208}, {-10.2566, -68.734}, {-10.856, -68.6418},
 {-11.4546, -68.5445}, {-12.0524, -68.4419}, {-12.6492, -68.3341}, {-13.245, -68.2211},
 {-13.8398, -68.103}, {-14.4336, -67.9796}, {-15.0263, -67.8511}, {-15.6178, -67.7173},
 {-16.2082, -67.5785},{-16.7973, -67.4345}, {-17.3851, -67.2853}, {-17.9716, -67.131},
 {-18.5567, -66.9717}, {-19.1405, -66.8072}, {-19.7227, -66.6376}, {-20.3035, -66.4629},
 {-20.8827, -66.2832}, {-21.4603, -66.0985}, {-22.0363, -65.9087}, {-22.6106, -65.7139},
 {-23.1832, -65.5141}, {-23.7541, -65.3093}, {-24.3231, -65.0995}, {-24.8902, -64.8847},
 {-25.4555, -64.6651}, {-26.0189, -64.4405}, {-26.5802, -64.211}, {-27.1395, -63.9766},
 {-27.6968, -63.7373}, {-28.2519, -63.4932}, {-28.8049, -63.2442}, {-29.3557, -62.9904},
 {-29.9043, -62.7319}, {-30.4506, -62.4685}, {-30.9946, -62.2004}, {-31.5362, -61.9276},
 {-32.0754, -61.65}, {-32.6122, -61.3677}, {-33.1465, -61.0808}, {-33.6782, -60.7892},
 {-34.2074, -60.493}, {-34.734, -60.1922}, {-35.258, -59.8868}, {-35.7792, -59.5769},
 {-36.2978, -59.2624}, {-36.8135, -58.9433}, {-37.3265, -58.6198}, {-37.8366, -58.2919},
 {-38.3439, -57.9595}, {-38.8482, -57.6227}, {-39.3496, -57.2815},{-39.8479, -56.9359},
 {-40.3433, -56.586}, {-40.8355, -56.2318}, {-41.3247, -55.8733}, {-41.8107, -55.5105},
 {-42.2935, -55.1436}, {-42.7731, -54.7724}, {-43.2495, -54.397}, {-43.7225, -54.0176},
 {-44.1922, -53.6339}, {-44.6586, -53.2463}, {-45.1216, -52.8545}, {-45.5811, -52.4588},
 {-46.0371, -52.059}, {-46.4897, -51.6553}, {-46.9387, -51.2476}, {-47.3841, -50.836},
 {-47.8259, -50.4206}, {-48.2641, -50.0013}, {-48.6986, -49.5782}, {-49.1294, -49.1514},
 {-49.5564, -48.7208}, {-49.9797, -48.2865}, {-50.3992, -47.8485}, {-50.8148, -47.4069},
 {-51.2266, -46.9616}, {-51.6344, -46.5128}, {-52.0384, -46.0604}, {-52.4383, -45.6046},
 {-52.8343, -45.1452}, {-53.2263, -44.6824}, {-53.6141, -44.2163}, {-53.998, -43.7467},
 {-54.3777, -43.2738}, {-54.7532, -42.7977}, {-55.1246, -42.3182}, {-55.4918, -41.8356},
 {-55.8548, -41.3497}, {-56.2135, -40.8607}, {-56.5679, -40.3686}, {-56.918, -39.8734},
 {-57.2638, -39.3752},{-57.6053, -38.874}, {-57.9423, -38.3698}, {-58.2749, -37.8627},
 {-58.6031, -37.3528}, {-58.9269, -36.8399}, {-59.2461, -36.3243}, {-59.5608, -35.8059},
 {-59.871, -35.2848}, {-60.1767, -34.761}, {-60.4777, -34.2345}, {-60.7741, -33.7055},
 {-61.066, -33.1738}, {-61.3531, -32.6397}, {-61.6356, -32.103}, {-61.9134, -31.5639},
 {-62.1865, -31.0224}, {-62.4549, -30.4786}, {-62.7185, -29.9324}, {-62.9773, -29.384},
 {-63.2313, -28.8333}, {-63.4805, -28.2804},{-63.7249, -27.7253}, {-63.9644, -27.1682},
 {-64.1991, -26.609}, {-64.4288, -26.0477}, {-64.6537, -25.4845}, {-64.8736, -24.9193},
 {-65.0886, -24.3522}, {-65.2986, -23.7833}, {-65.5037, -23.2126}, {-65.7037, -22.6401},
 {-65.8988, -22.0658}, {-66.0889, -21.4899}, {-66.2739, -20.9124}, {-66.4538, -20.3333},
 {-66.6288, -19.7526}, {-66.7986, -19.1704}, {-66.9633, -18.5867}, {-67.123, -18.0017},
 {-67.2775, -17.4152}, {-67.4269, -16.8275}, {-67.5712, -16.2384},{-67.7103, -15.6481},
 {-67.8443, -15.0567}, {-67.9731, -14.464}, {-68.0968, -13.8703}, {-68.2152, -13.2755},
 {-68.3285, -12.6798}, {-68.4365, -12.083}, {-68.5393, -11.4853}, {-68.637, -10.8868},
 {-68.7294, -10.2874}, {-68.8165, -9.68725}, {-68.8984, -9.08635}, {-68.9751, -8.48476},
 {-69.0465, -7.88252}, {-69.1127, -7.27968}, {-69.1736, -6.67629}, {-69.2292, -6.07239},
 {-69.2795, -5.46803}, {-69.3246, -4.86325}, {-69.3644, -4.2581}, {-69.3989, -3.65263},
 {-69.4282, -3.04688}, {-69.4521, -2.44089}, {-69.4708, -1.83473}, {-69.4841, -1.22842},
 {-69.4922, -0.622014}, {-69.495, -0.015564}, {-69.4925, 0.590887}, {-69.4847, 1.19729},
 {-69.4716, 1.80361}, {-69.4532, 2.40979}, {-69.4295, 3.01578}, {-69.4006, 3.62154},
 {-69.3663, 4.22703}, {-69.3268, 4.8322}, {-69.282, 5.437}, {-69.2319, 6.04138},
 {-69.1765, 6.64531}, {-69.1159, 7.24873}, {-69.05, 7.85159}, {-68.9789, 8.45386},
 {-68.9025, 9.05549}, {-68.8208, 9.65642}, {-68.734, 10.2566}, {-68.6418, 10.856},
 {-68.5445, 11.4546}, {-68.4419, 12.0524}, {-68.3341, 12.6492}, {-68.2211, 13.245},
 {-68.103, 13.8398}, {-67.9796, 14.4336}, {-67.8511, 15.0263}, {-67.7173, 15.6178},
 {-67.5785, 16.2082}, {-67.4345, 16.7973}, {-67.2853, 17.3851}, {-67.131, 17.9716},
 {-66.9717, 18.5567}, {-66.8072, 19.1405}, {-66.6376, 19.7227}, {-66.4629, 20.3035},
 {-66.2832, 20.8827}, {-66.0985, 21.4603}, {-65.9087, 22.0363}, {-65.7139, 22.6106},
 {-65.5141, 23.1832}, {-65.3093, 23.7541}, {-65.0995, 24.3231}, {-64.8847, 24.8902},
 {-64.6651, 25.4555}, {-64.4405, 26.0189}, {-64.211, 26.5802}, {-63.9766, 27.1395},
 {-63.7373, 27.6968}, {-63.4932, 28.2519}, {-63.2442, 28.8049}, {-62.9904, 29.3557},
 {-62.7319, 29.9043}, {-62.4685, 30.4506}, {-62.2004, 30.9946}, {-61.9276, 31.5362},
 {-61.65, 32.0754}, {-61.3677, 32.6122}, {-61.0808, 33.1465}, {-60.7892, 33.6782},
 {-60.493, 34.2074}, {-60.1922, 34.734}, {-59.8868, 35.258}, {-59.5769, 35.7792},
 {-59.2624, 36.2978}, {-58.9433, 36.8135}, {-58.6198, 37.3265},{-58.2919, 37.8366},
 {-57.9595, 38.3439}, {-57.6227, 38.8482}, {-57.2815, 39.3496}, {-56.9359, 39.8479},
 {-56.586, 40.3433}, {-56.2318, 40.8355}, {-55.8733, 41.3247}, {-55.5105, 41.8107},
 {-55.1436, 42.2935}, {-54.7724, 42.7731}, {-54.397, 43.2495}, {-54.0176, 43.7225},
 {-53.6339, 44.1922},{-53.2463, 44.6586}, {-52.8545, 45.1216}, {-52.4588, 45.5811},
 {-52.059, 46.0371}, {-51.6553, 46.4897}, {-51.2476, 46.9387}, {-50.836, 47.3841},
 {-50.4206, 47.8259}, {-50.0013, 48.2641}, {-49.5782, 48.6986}, {-49.1514, 49.1294},
 {-48.7208, 49.5564}, {-48.2865, 49.9797}, {-47.8485, 50.3992}, {-47.4069, 50.8148},
 {-46.9616, 51.2266}, {-46.5128, 51.6344}, {-46.0604, 52.0384}, {-45.6046, 52.4383},
 {-45.1452, 52.8343}, {-44.6824, 53.2263},{-44.2163, 53.6141}, {-43.7467, 53.998},
 {-43.2738, 54.3777}, {-42.7977, 54.7532}, {-42.3182, 55.1246}, {-41.8356, 55.4918},
 {-41.3497, 55.8548}, {-40.8607, 56.2135}, {-40.3686, 56.5679}, {-39.8734, 56.918},
 {-39.3752, 57.2638}, {-38.874, 57.6053}, {-38.3698, 57.9423}, {-37.8627, 58.2749},
 {-37.3528, 58.6031}, {-36.8399, 58.9269}, {-36.3243, 59.2461}, {-35.8059, 59.5608},
 {-35.2848, 59.871}, {-34.761, 60.1767}, {-34.2345, 60.4777},{-33.7055, 60.7741},
 {-33.1738, 61.066}, {-32.6397, 61.3531}, {-32.103, 61.6356}, {-31.5639, 61.9134},
 {-31.0224, 62.1865}, {-30.4786, 62.4549}, {-29.9324, 62.7185}, {-29.384, 62.9773},
 {-28.8333, 63.2313}, {-28.2804, 63.4805}, {-27.7253, 63.7249}, {-27.1682, 63.9644},
 {-26.609, 64.1991}, {-26.0477, 64.4288}, {-25.4845, 64.6537}, {-24.9193, 64.8736},
 {-24.3522, 65.0886}, {-23.7833, 65.2986}, {-23.2126, 65.5037}, {-22.6401, 65.7037},
 {-22.0658, 65.8988}, {-21.4899, 66.0889}, {-20.9124, 66.2739}, {-20.3333, 66.4538},
 {-19.7526, 66.6288}, {-19.1704, 66.7986}, {-18.5867, 66.9633}, {-18.0017, 67.123},
 {-17.4152, 67.2775}, {-16.8275, 67.4269}, {-16.2384, 67.5712}, {-15.6481, 67.7103},
 {-15.0567, 67.8443}, {-14.464, 67.9731}, {-13.8703, 68.0968}, {-13.2755, 68.2152},
 {-12.6798, 68.3285}, {-12.083, 68.4365},{-11.8937, 68.4697}, {-11.87, 68.4738},
 {-11.8463, 68.4779}, {-11.8227, 68.4819}, {-11.799, 68.486}, {-11.7753, 68.4901},
 {-11.7516, 68.4942}, {-11.7279, 68.4983}, {-11.7042, 68.5023}, {-11.6805, 68.5064},
 {-11.6569, 68.5104}, {-11.6332, 68.5144}, {-11.5976, 68.5204}, {-11.5739, 68.5244},
 {-11.5502, 68.5284}, {-11.5265, 68.5324}, {-11.5028, 68.5365}, {-11.479, 68.5404},
 {-11.4554, 68.5443}, {-11.4316, 68.5483}, {-11.408, 68.5522},{-11.3842, 68.5562},
 {-11.3605, 68.5601}, {-11.325, 68.566}, {-11.3012, 68.57}, {-11.2538, 68.5778},
 {-11.2182, 68.5835}, {-11.1708, 68.5913}, {-11.1352, 68.5971}, {-11.0878, 68.6047},
 {-11.0522, 68.6105}, {-11.0165, 68.6162}, {-10.9928, 68.62}, {-10.9572, 68.6257},
 {-10.9335, 68.6295}, {-10.9098, 68.6333}, {-10.886, 68.6371}, {-10.8504, 68.6428},
 {-10.8148, 68.6484},{-10.7555, 68.6577}, {-10.7317, 68.6614}, {-10.6723, 68.6706},
 {-10.6129, 68.6798}, {-10.5654, 68.6872}, {-10.5417, 68.6908}, {-10.5179, 68.6944},
 {-10.4823, 68.6999}, {-10.4466, 68.7053}, {-10.4228, 68.709}, {-10.3992, 68.7126},
 {-10.3754, 68.7161}, {-10.3516, 68.7197}, {-10.3278, 68.7233}, {-10.304, 68.7269},
 {-10.2803, 68.7305}, {-10.2566, 68.7339}, {-10.2328, 68.7375}, {-10.209, 68.7411},
 {-10.1852, 68.7446}, {-10.1614, 68.7481},{-10.1377, 68.7516}, {-10.1139, 68.7551},
 {-10.0782, 68.7604}, {-10.0544, 68.7639}, {-10.0187, 68.7691}, {-9.995, 68.7725},
 {-9.9593, 68.7777}, {-9.92361, 68.7829}, {-9.89977, 68.7862}, {-9.87601, 68.7897},
 {-9.85226, 68.7931}, {-9.82842, 68.7964}, {-9.80466, 68.7999}, {-9.78082, 68.8033},
 {-9.75708, 68.8067}, {-9.73324, 68.81}, {-9.70949, 68.8134}, {-9.68565, 68.8168},
 {-9.66181, 68.8201}, {-9.63809, 68.8234}, {-9.61425, 68.8268}, {-9.59041, 68.8301},
 {-9.55478, 68.835}, {-9.53094, 68.8384}, {-9.46748, 68.8466}

I plotted these data points in Mathematica:

my points

I want the curve offset of 4 mm as shown below. How can I write a program in Mathematica to do that?

curve and offset

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14
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Letting pts be the points in the OP (after removing the duplicated first point), here is how to use Interpolation[] along with Lee's centripetal parametrization scheme to plot a parallel curve:

parametrizeCurve[pts_ /; MatrixQ[pts, NumericQ], a : (_?NumericQ) : 1/2] := 
                          FoldList[Plus, 0, Normalize[(Norm /@ Differences[pts])^a, Total]]

tvals = parametrizeCurve[pts];
{xf, yf} = Interpolation[Transpose[{tvals, #}]] & /@ Transpose[pts];

With[{h = 4}, 
     ParametricPlot[{{xf[t], yf[t]},
                     {xf[t], yf[t]} + h Normalize[{-yf'[t], xf'[t]}]}, {t, 0, 1}]]

parallel of an interpolated curve

A related approach would be to use B-splines, as in this answer.

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  • $\begingroup$ #1. I see that on the intersection between "circle and line" (left side) there is any "excess line". Is it possible to remove it? #2. If I want to take a "new curve" only, what should I do? $\endgroup$ – Mukidi Lee Jul 27 '17 at 2:19
  • $\begingroup$ It's a problem with your points, then; you might want to adjust the points in the original curve near the kink you describe. Note that I'm plotting two parametric curves in the list, and the second one is the parallel. $\endgroup$ – J. M. will be back soon Jul 27 '17 at 3:58
  • $\begingroup$ OK, I undestand. For second one curve, is it possible to export its coordinate in *txt file? I have tried it following the program: datanew={} For[i = 1, i < Length[dp] + 1, i++, {xi, yi, zi} = {Take[dp[[i, 1]]], dp[[i, 2]], 0}; AppendTo[datanew, {xi, yi, zi}]; ]; Export["DaPo.txt", datanew]; and unsuccessfully $\endgroup$ – Mukidi Lee Jul 28 '17 at 19:36
  • $\begingroup$ Using the same data as above: Export["mydata.txt", Table[{xf[t], yf[t]} + h Normalize[{-yf'[t], xf'[t]}], {t, tvals}]]. $\endgroup$ – J. M. will be back soon Jul 30 '17 at 2:33
7
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Here is a simple numeric approach. Starting with your data as curve:

ppfn[d_][p : {a_, b_}] := Mean[p] + d Normalize[Cross[a - b]]  (* thanks J. M. ! *)

curve2 = DeleteDuplicatesBy[curve, Round[#, 2] &];
curve2 = BlockMap[ppfn[-15], curve2, 2, 1];

Graphics[{Thick, Red, Line@curve, Blue, Line@curve2}]

enter image description here

  • Use Developer`PartitionMap in place of BlockMap for version 10.1 and earlier.
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  • 1
    $\begingroup$ Out of votes today, but let me offer a simplification: ppfn[d_][p : {a_, b_}] := Mean[p] + d Normalize[Cross[a - b]] $\endgroup$ – J. M. will be back soon Jul 30 '17 at 7:53
  • $\begingroup$ @J.M. Thanks! I have this funny feeling you've offered me that same simplification before. I'm not sure I'll ever learn. $\endgroup$ – Mr.Wizard Jul 30 '17 at 8:34

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