{"cells":[{"cell_type":"markdown","metadata":{"id":"TfI3YO1uZgZa"},"source":["# **Functions to compute the dGLI coordinates**\n"]},{"cell_type":"markdown","source":["***Imports***"],"metadata":{"id":"0VsI6HxXbwTm"}},{"cell_type":"code","execution_count":1,"metadata":{"id":"A4Mc6LQtaJmQ","executionInfo":{"status":"ok","timestamp":1678795582822,"user_tz":-60,"elapsed":6,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"outputs":[],"source":["import numpy as np\n","from numpy.linalg import norm"]},{"cell_type":"markdown","metadata":{"id":"_Ij0sI19jsAC"},"source":["***dGLI functions***\n","\n","\n","\n","\n","\n","\n","\n"]},{"cell_type":"code","execution_count":2,"metadata":{"id":"Oj9xYUQcaBfw","executionInfo":{"status":"ok","timestamp":1678795582822,"user_tz":-60,"elapsed":5,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"outputs":[],"source":["# curve as the mesh border\n","def getdGLICoords(curve, sideSize):\n","    #corners = (0, 19, 38, 57)\n","    corners=[0, sideSize-1, 2*sideSize - 2, 3*sideSize - 3]\n","    subCurveEdges=selectedEdges(curve, corners)\n","    return dGLICoords(subCurveEdges)\n","\n","def selectedEdges(curve, cornersInd):\n","    selEdgesInd = []\n","    outCurve = []\n","    # If curve is not closed (ie, first and initisl point are not the same) we close it in order to consider also the last segment\n","    if curve[0] != curve[-1]:\n","        curve.append(curve[0])\n","   \n","    # for each corner we consider the two edges of both sides   \n","    for ind in cornersInd:\n","        selEdgesInd.append(subtractCircularBeg(len(curve), ind))\n","        selEdgesInd.append([ind+2, ind+3])\n","       \n","    #selEdgesInd = sorted(selEdgesInd)\n","    for e in selEdgesInd:\n","        outCurve.append([curve[e[0]], curve[e[1]]])\n","        \n","    return outCurve\n","   \n","\n","# This code defines what edges we take to compute the dGLI. Right now we take the edge before the last one in each side, as in the initial GLI paper\n","def subtractCircularBeg(total, ind):\n","    if ind == 0:\n","        return [total-3, total-2]\n","    else:\n","        return [ind-3, ind-2]\n","\n","\n","# edgesCurve1 contains a list of edges, that is, tuples {p1,p2} of 3D points\n","def dGLICoords(edgesCurve1):\n","    return dGLICoords2(edgesCurve1, edgesCurve1)\n","\n","def dGLICoords2(edgesCurve1, edgesCurve2):\n","    numP1 = len(edgesCurve1) # it has to be 8\n","    numP2 = len(edgesCurve2) # it has to be 8\n","\n","    # dGLIMatrix = []\n","    #dGLIMatrix = np.zeros((numP1, numP2), dtype = float)\n","    vector_res = []\n","\n","    for i in range(numP1):\n","      for j in range(i, numP2):\n","        if i!=j:\n","            dgli=dGLI(edgesCurve1[i][0], edgesCurve1[i][1], edgesCurve2[j][0], edgesCurve2[j][1])\n","            vector_res.append(dgli)\n","\n","    return vector_res\n","\n","\n","def dGLI(ap1, ap2, ap3, ap4):\n","    epsilon = 0.00001\n","    p1 = np.add(ap1 ,[0, 0, 0])\n","    p2 = np.add(ap2, [0, 0, epsilon])\n","    p3 = np.add(ap3, [0, 0, 0])\n","    p4 = np.add(ap4, [0, 0, epsilon])\n","# if we are evaluating the same segment\n","    if np.linalg.norm(np.subtract(ap1,ap3)) < 0.01 and np.linalg.norm(np.subtract(ap2,ap4)) < 0.01:\n","        ret = 0\n","    else:\n","        GLI = evalWritheTwoSegments(ap1, ap2, ap3, ap4)\n","        \n","        GLIPerturbed = evalWritheTwoSegments(p1, p2, p3, p4)\n","        \n","\n","        ret = (GLIPerturbed - GLI) / epsilon\n","\n","    if abs(ret) > 4.0:\n","        return np.sign(ret) * 4\n","    else:\n","        return ret\n","\n","def evalWritheTwoSegments(p1, p2, p3, p4):\n","    n1 = np.cross(np.subtract(p3,p1), np.subtract(p4,p1)) / norm(np.cross(np.subtract(p3,p1), np.subtract(p4,p1)))\n","    n2 = np.cross(np.subtract(p4,p1), np.subtract(p4,p2)) / norm(np.cross(np.subtract(p4,p1), np.subtract(p4,p2)))\n","    n3 = np.cross(np.subtract(p4,p2), np.subtract(p3,p2)) / norm(np.cross(np.subtract(p4,p2), np.subtract(p3,p2)))\n","    n4 = np.cross(np.subtract(p3,p2), np.subtract(p3,p1)) / norm(np.cross(np.subtract(p3,p2), np.subtract(p3,p1)))\n","    sgn = np.sign(np.dot(np.cross(np.subtract(p4,p3),np.subtract(p2,p1)), np.subtract(p3,p1)))\n","    ret = np.arcsin(np.dot(n1,n2)) + np.arcsin(np.dot(n2,n3)) + np.arcsin(np.dot(n3,n4)) + np.arcsin(np.dot(n4,n1))\n","    return sgn*ret\n"]},{"cell_type":"markdown","metadata":{"id":"NHtPwimfaGFi"},"source":["***Validation test***"]},{"cell_type":"code","execution_count":3,"metadata":{"id":"mt8H7ym2aGFi","executionInfo":{"status":"ok","timestamp":1678795582823,"user_tz":-60,"elapsed":6,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"outputs":[],"source":["curve1=[[-0.275117, -1.22472, 0.782454], [-0.275234, -1.25103, 0.781838], [-0.275101, -1.27738, 0.781222], [-0.275021, -1.30368, 0.780606], [-0.274939, -1.32991, 0.779992], [-0.275092, -1.35622, 0.779376], [-0.275112, -1.38247, 0.778763], [-0.274996, -1.40869, 0.778149], [-0.274911, -1.43499, 0.777533], [-0.27483, -1.46128, 0.776918], [-0.274693, -1.48758, 0.776383], [-0.274582, -1.51387, 0.775688], [-0.274454, -1.54017, 0.775142], [-0.274411, -1.56646, 0.774458], [-0.274332, -1.59275, 0.773842], [-0.274237, -1.61917, 0.773224], [-0.273913, -1.64545, 0.772608], [-0.273668, -1.67197, 0.771988], [-0.27352, -1.69833, 0.771372], [-0.273452, -1.72462, 0.770811], [-0.247152, -1.72457, 0.770776], [-0.220774, -1.72464, 0.770792], [-0.194233, -1.72479, 0.770807], [-0.167959, -1.72517, 0.770816], [-0.141366, -1.72521, 0.770833], [-0.115029, -1.72532, 0.770849], [-0.0887752, -1.72523, 0.770869], [-0.0624425, -1.7252, 0.770888], [-0.0362156, -1.72511, 0.770907], [-0.00989175, -1.72516, 0.770926], [0.0163153, -1.72522, 0.770942], [0.0425979, -1.72504, 0.770964], [0.0688676, -1.725, 0.770983], [0.0951935, -1.7252, 0.770996], [0.121492, -1.72535, 0.771011], [0.147809, -1.7254, 0.771028], [0.174208, -1.72534, 0.771047], [0.200562, -1.72534, 0.771065], [0.22688, -1.72538, 0.771083], [0.227004, -1.69907, 0.771698], [0.226941, -1.67272, 0.772315], [0.227182, -1.64638, 0.772932], [0.227149, -1.62007, 0.773547], [0.227037, -1.59369, 0.774164], [0.227106, -1.56743, 0.77478], [0.227092, -1.54114, 0.775394], [0.22705, -1.51486, 0.776009], [0.226998, -1.48857, 0.776624], [0.226921, -1.46228, 0.77724], [0.226857, -1.43599, 0.777855], [0.226784, -1.40969, 0.77849], [0.226746, -1.38343, 0.779139], [0.226794, -1.35713, 0.7797], [0.226663, -1.33091, 0.780314], [0.226626, -1.30455, 0.78093], [0.226133, -1.27801, 0.781551], [0.225905, -1.25163, 0.782169], [0.225697, -1.22534, 0.782803], [0.19938, -1.2255, 0.782762], [0.173024, -1.22548, 0.782744], [0.146611, -1.22504, 0.782736], [0.120292, -1.22486, 0.782722], [0.0936924, -1.22471, 0.782707], [0.0673476, -1.22475, 0.782688], [0.0409484, -1.22486, 0.782668], [0.0146931, -1.22499, 0.782647], [-0.0116226, -1.22515, 0.782626], [-0.0379447, -1.2251, 0.782608], [-0.0642397, -1.225, 0.782592], [-0.0905873, -1.22497, 0.782575], [-0.117038, -1.22487, 0.782559], [-0.143311, -1.22465, 0.782546], [-0.169638, -1.2245, 0.782531], [-0.195966, -1.22439, 0.782516], [-0.22255, -1.22456, 0.782494], [-0.248787, -1.22467, 0.782473]]\n","curve2=[[-0.274013, -1.22362, 0.78248], [-0.274121, -1.24992, 0.781865], [-0.274277, -1.27628, 0.781248], [-0.274351, -1.30274, 0.780629], [-0.274399, -1.32903, 0.780013], [-0.274337, -1.3554, 0.779396], [-0.274296, -1.38176, 0.778779], [-0.274306, -1.40811, 0.778163], [-0.274257, -1.43443, 0.777547], [-0.274275, -1.46103, 0.776924], [-0.274277, -1.48735, 0.776308], [-0.274324, -1.51409, 0.775683], [-0.274294, -1.54041, 0.775067], [-0.274309, -1.56723, 0.774439], [-0.274228, -1.59355, 0.773823], [-0.274117, -1.6202, 0.773199], [-0.273742, -1.64651, 0.772584], [-0.27357, -1.67271, 0.771971], [-0.273591, -1.69908, 0.771354], [-0.273632, -1.72538, 0.770806], [-0.247339, -1.72536, 0.770757], [-0.220982, -1.72539, 0.770774], [-0.194607, -1.72555, 0.770789], [-0.168338, -1.72585, 0.7708], [-0.142027, -1.72584, 0.770818], [-0.115805, -1.72574, 0.770838], [-0.0895951, -1.72558, 0.77086], [-0.0633502, -1.72518, 0.770888], [-0.0371641, -1.72516, 0.770906], [-0.0108621, -1.72512, 0.770925], [0.0152077, -1.72523, 0.770941], [0.0414956, -1.72539, 0.770955], [0.0677782, -1.72545, 0.770971], [0.0940687, -1.72578, 0.770982], [0.120372, -1.72601, 0.770994], [0.146707, -1.72618, 0.771009], [0.173125, -1.72623, 0.771026], [0.199464, -1.72638, 0.771089], [0.225781, -1.72648, 0.771071], [0.225978, -1.70017, 0.771672], [0.225929, -1.67375, 0.77229], [0.226257, -1.64747, 0.772905], [0.22641, -1.62113, 0.773522], [0.226279, -1.59449, 0.774145], [0.226448, -1.56816, 0.774761], [0.226117, -1.54107, 0.775395], [0.225976, -1.51482, 0.778409], [0.22322, -1.48897, 0.787774], [0.217795, -1.46586, 0.799501], [0.203239, -1.44877, 0.814823], [0.179907, -1.44302, 0.825737], [0.160577, -1.45034, 0.809227], [0.136648, -1.44792, 0.798528], [0.112715, -1.45821, 0.802008], [0.0878899, -1.46119, 0.809629], [0.0622547, -1.46364, 0.814631], [0.0405122, -1.45877, 0.828698], [0.0212286, -1.44561, 0.84084], [0.00901499, -1.44389, 0.817439], [0.00570795, -1.42479, 0.79966], [0.00233644, -1.39887, 0.798553], [-0.00219762, -1.37313, 0.801654], [-0.00672734, -1.34741, 0.803741], [-0.0067696, -1.32132, 0.804368], [-0.0153184, -1.30246, 0.82066], [-0.0186663, -1.27743, 0.827653], [-0.0211709, -1.25201, 0.82139], [-0.0422448, -1.24106, 0.810026], [-0.0631711, -1.22996, 0.797863], [-0.0886693, -1.2263, 0.790357], [-0.115376, -1.225, 0.78659], [-0.141338, -1.22437, 0.782554], [-0.168229, -1.22403, 0.782544], [-0.194488, -1.22379, 0.782531], [-0.221338, -1.22369, 0.782515], [-0.247714, -1.22365, 0.782498]]"]},{"cell_type":"code","execution_count":4,"metadata":{"id":"4jckWYFqaGFj","executionInfo":{"status":"ok","timestamp":1678795582823,"user_tz":-60,"elapsed":5,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"outputs":[],"source":["coordsdGLI1=[4, 0.157887, 0.21199, 0.110153, 0.0993557, 0.156534, 0.00452688, 0.00122104, 0.156315, 0.0982562, 0.109479, 0.210012, 0.157283, 4, 0.156497, 0.210565, 0.112167, 0.100889, 0.00163678, 0.156106,0.101049, 0.111878, 4, 0.158544, 0.210827, 0.00543083, 0.156991, 4]\n","coordsdGLI2=[4, 0.157766, 0.211115, 0.110596, 0.0995439, -0.00844612, 0.43422,0.00180441, 0.154916, 0.0986447, 0.109765, 0.0663872, 0.501821, 4, 0.155185, 0.20997, 0.205149, 0.295824, 0.000790318, 0.156102, 0.222728, 0.272104, 4, 0.632962, 0.122105, 0.592691, 0.0267658, -4]"]},{"cell_type":"code","execution_count":5,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"8CHe-p66aGFk","executionInfo":{"status":"ok","timestamp":1678795582823,"user_tz":-60,"elapsed":5,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}},"outputId":"74fd263f-63d8-4052-f737-944a4274b26e"},"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 0.00000000e+00, -7.42077762e-03, -2.86392515e-03, -8.98584216e-03,\n","       -6.70087500e-03, -1.44530528e-03, -6.01598058e-02,  2.58584185e-06,\n","        6.19962443e-06,  1.67558940e-05,  3.11568586e-06,  4.31539510e-05,\n","       -1.72805118e-05,  0.00000000e+00,  5.34579329e-05,  1.67061345e-05,\n","        4.84554496e-05,  2.96485786e-06,  2.80903744e-05, -1.94972331e-05,\n","        1.02811748e-05, -2.40118605e-05,  0.00000000e+00,  1.05625642e-05,\n","        4.27202940e-05, -5.77448635e-05,  2.53460572e-05,  0.00000000e+00])"]},"metadata":{},"execution_count":5}],"source":["np.subtract(getdGLICoords(curve2,20),coordsdGLI2)"]},{"cell_type":"code","execution_count":6,"metadata":{"id":"e21FDhr9aGFl","outputId":"fa9e01a4-6486-4dbb-d381-d0fde1b0e1bb","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1678795582823,"user_tz":-60,"elapsed":4,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 0.00000000e+00, -6.70909851e-03, -2.28528248e-03, -8.80553778e-03,\n","       -6.57200450e-03, -1.84706875e-02, -9.96671119e-04, -4.19067314e-06,\n","        1.02640890e-05, -5.36111307e-06,  1.05842879e-05, -1.40534791e-05,\n","        4.17421837e-06,  0.00000000e+00, -2.18635520e-05,  8.42880493e-06,\n","       -1.37615926e-05, -2.50930516e-06, -8.42548915e-05, -2.61306155e-05,\n","       -2.40078060e-05, -1.20327106e-05,  0.00000000e+00, -1.51643627e-06,\n","        2.47290196e-06,  2.04432819e-06,  2.23256957e-06,  0.00000000e+00])"]},"metadata":{},"execution_count":6}],"source":["np.subtract(getdGLICoords(curve1,20),coordsdGLI1)"]},{"cell_type":"code","source":["#Function to obtain the cloth border given a mesh of the cloth from the VR simulator.\n","def getSquaredBorder(mesh, sideSize):\n","    s1 = list(range(0, sideSize-1))\n","    s2 = [(i+1)*sideSize-1 for i in range(0, sideSize-1)]\n","    s3 = [sideSize*sideSize-i-1 for i in range(0, sideSize-1)]\n","    s4 = list(reversed([(i+1)*sideSize for i in range(0, sideSize-1)]))\n","    borderInd = s1 + s2 + s3 + s4\n","    return [mesh[i] for i in borderInd]"],"metadata":{"id":"PcBixUKHA_nI","executionInfo":{"status":"ok","timestamp":1678796074331,"user_tz":-60,"elapsed":234,"user":{"displayName":"Júlia Borràs Sol","userId":"01088779723042130478"}}},"execution_count":12,"outputs":[]},{"cell_type":"code","source":["testMesh=[[-0.273914, -1.22369, 0.782479], [-0.274051, -1.25, 0.781863], [-0.274196, -1.27633, 0.781247], [-0.274297, -1.30279, 0.780627], [-0.274317, -1.32902, 0.780014], [-0.274223, -1.35539, 0.779397], [-0.274104, -1.3817, 0.778781], [-0.274083, -1.40807, 0.778164], [-0.273951, -1.43438, 0.777548], [-0.273931, -1.46098, 0.776926], [-0.273853, -1.4873, 0.77631], [-0.273808, -1.51399, 0.775685], [-0.273758, -1.54031, 0.775069], [-0.273698, -1.56705, 0.774444], [-0.273633, -1.59337, 0.773828], [-0.273478, -1.6201, 0.773202], [-0.273043, -1.64641, 0.772587], [-0.272816, -1.67277, 0.77197], [-0.272773, -1.69908, 0.771373], [-0.272628, -1.72538, 0.770739], [-0.247594, -1.22367, 0.782497], [-0.247719, -1.24998, 0.781882], [-0.247882, -1.27631, 0.781265], [-0.24797, -1.30269, 0.780648], [-0.248002, -1.329, 0.780032], [-0.247797, -1.35529, 0.779417], [-0.247784, -1.38161, 0.778801], [-0.247623, -1.40812, 0.778181], [-0.24763, -1.43449, 0.777564], [-0.2475, -1.46109, 0.776941], [-0.247533, -1.48746, 0.776324], [-0.247409, -1.51405, 0.775702], [-0.247438, -1.54044, 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