From 500e762b64160c7979fa454de55f3098f6913765 Mon Sep 17 00:00:00 2001 From: nicolas <81325398+NIcolasp14@users.noreply.github.com> Date: Sat, 3 Aug 2024 19:07:03 +0300 Subject: [PATCH 1/5] adding uniform and area weights --- src/gpytoolbox/per_vertex_normals.py | 154 ++++++++++++++++++++++----- 1 file changed, 125 insertions(+), 29 deletions(-) diff --git a/src/gpytoolbox/per_vertex_normals.py b/src/gpytoolbox/per_vertex_normals.py index a8eb8ef9..26bffc21 100644 --- a/src/gpytoolbox/per_vertex_normals.py +++ b/src/gpytoolbox/per_vertex_normals.py @@ -1,54 +1,150 @@ import numpy as np -from scipy.sparse import csr_matrix from .per_face_normals import per_face_normals from .doublearea import doublearea +from scipy.sparse import csr_matrix -def per_vertex_normals(V,F): - """Normal vectors to all vertices on a mesh - - Computes area-weighted per-vertex unit normal vectors for a triangle mesh or polyline. +def compute_angles(V,F): + """Computes the angle at each vertex in a triangle mesh. Parameters ---------- V : (n,d) numpy array - vertex list of a triangle mesh or polyline + vertex list of a triangle mesh F : (m,d) numpy int array - face index list of a triangle mesh (edge list for a polyline) + face index list of a triangle mesh Returns ------- - N : (m,d) numpy double array + angles : (m,d) numpy array + Array containing the angles at each vertex of each triangle in radians + + Examples + -------- + ```python + from gpytoolbox import read_mesh, compute_angles + v,f = read_mesh("test/unit_tests_data/bunny_oded.obj") + angles = compute_angles(v,f) + ``` + + Notes + ----- + The angles are computed using the dot product between vectors formed by + the vertices of each triangle. The angles are then calculated using the + arccosine of the dot product result, which is safeguarded against numerical + issues by clipping the values to the range [-1, 1]. + """ + # Extract the vertices of each triangle + A = V[F[:, 0]] + B = V[F[:, 1]] + C = V[F[:, 2]] + + # Compute the edge vectors for each triangle + AB = B - A + AC = C - A + BC = C - B + CA = A - C + BA = A - B + CB = B - C + + # Cosines via dot product + cos_a = np.einsum('ij,ij->i', (B - A), (C - A)) / (np.linalg.norm(AB, axis=1) * np.linalg.norm(AC, axis=1)) + cos_b = np.einsum('ij,ij->i', (C - B), (A - B)) / (np.linalg.norm(BC, axis=1) * np.linalg.norm(BA, axis=1)) + cos_c = np.einsum('ij,ij->i', (A - C), (B - C)) / (np.linalg.norm(CA, axis=1) * np.linalg.norm(CB, axis=1)) + + # Angles via arccos, safeguarded against numerical issues via clipping + angles = np.zeros((F.shape[0], 3)) + angles[:, 0] = np.arccos(np.clip(cos_a, -1, 1)) + angles[:, 1] = np.arccos(np.clip(cos_b, -1, 1)) + angles[:, 2] = np.arccos(np.clip(cos_c, -1, 1)) + + return angles + + +def per_vertex_normals(V,F,weights='area'): + """Compute per-vertex normal vectors for a triangle mesh with different weighting options. + + Parameters + ---------- + V : (n,d) numpy array + vertex list of a triangle mesh + F : (m,d) numpy int array + face index list of a triangle mesh + weights : str, optional + The type of weighting to use ('area', 'angles', 'uniform'), default is 'area' + + Returns + ------- + N : (n,d) numpy array Matrix of per-vertex normals See Also -------- - per_face_normals. + per_vertex_normals, per_face_normals. Examples -------- ```python from gpytoolbox import read_mesh, per_vertex_normals - v,f = read_mesh("test/unit_tests_data/bunny_oded.obj") + v,f = read_mesh("test/unit_tests_data/armadillo.obj") n = per_vertex_normals(v,f) ``` """ - dim = V.shape[1] - # First compute face normals - face_normals = per_face_normals(V,F,unit_norm=True) - # We blur these normals onto vertices, weighing by area - areas = doublearea(V,F) - vals = np.concatenate([areas for _ in range(dim)]) - J = np.linspace(0,F.shape[0]-1,F.shape[0],dtype=int) - # J = np.concatenate([J,J,J)) - J = np.concatenate([J for _ in range(dim)]) - I = np.concatenate([F[:,dd] for dd in range(dim)]) - # I = np.concatenate((F[:,0],F[:,1],F[:,2])) - - weight_mat = csr_matrix((vals,(I,J)),shape=(V.shape[0],F.shape[0])) - - vertex_normals = weight_mat @ face_normals - # Now, normalize - N = vertex_normals/np.tile(np.linalg.norm(vertex_normals,axis=1)[:,None],(1,dim)) - - return N + if weights=="area": + dim = V.shape[1] + # First compute face normals + face_normals = per_face_normals(V,F,unit_norm=True) + # We blur these normals onto vertices, weighing by area + areas = doublearea(V,F) + vals = np.concatenate([areas for _ in range(dim)]) + J = np.linspace(0,F.shape[0]-1,F.shape[0],dtype=int) + # J = np.concatenate([J,J,J)) + J = np.concatenate([J for _ in range(dim)]) + I = np.concatenate([F[:,dd] for dd in range(dim)]) + # I = np.concatenate((F[:,0],F[:,1],F[:,2])) + + weight_mat = csr_matrix((vals,(I,J)),shape=(V.shape[0],F.shape[0])) + + vertex_normals = weight_mat @ face_normals + # Now, normalize + N = vertex_normals/np.tile(np.linalg.norm(vertex_normals,axis=1)[:,None],(1,dim)) + + + elif weights=="angles": + # Ensure vertices are in float64 + V = V.astype(np.float64) + # Ensure faces are in int32 + F = F.astype(np.int32) + + # Compute face normals + normals = per_face_normals(V,F) + # Compute angles at each vertex + angles = compute_angles(V,F) + # Weight the face normals by the angles at each vertex + weighted_normals = np.zeros_like(V) + for i in range(3): + np.add.at(weighted_normals, F[:, i], normals * angles[:, i, np.newaxis]) + + # Calculate norms + norms = np.linalg.norm(weighted_normals, axis=1, keepdims=True) + # Avoid division by zero by setting zero norms to a very small number + norms[norms == 0] = np.finfo(float).eps + # Normalize the vertex normals + N = weighted_normals / norms + + + elif weights=="uniform": + # Compute face normals + face_normals = per_face_normals(V, F) + # Initialize vertex normals + vertex_normals = np.zeros_like(V) + # Accumulate face normals to vertices + for i in range(3): + np.add.at(vertex_normals, F[:, i], face_normals) + + # Normalize + norms = np.linalg.norm(vertex_normals, axis=1, keepdims=True) + norms[norms == 0] = np.finfo(float).eps + N = vertex_normals / norms + + return N \ No newline at end of file From f856967a979bf84c3c125bc51de52d0ff242610c Mon Sep 17 00:00:00 2001 From: nicolas <81325398+NIcolasp14@users.noreply.github.com> Date: Sat, 3 Aug 2024 19:11:50 +0300 Subject: [PATCH 2/5] angle, uniform weights of normals testing --- test/test_angle_per_vertex_normals.py | 16 ++++++++++++++++ test/test_uniform_per_vertex_normals.py | 16 ++++++++++++++++ 2 files changed, 32 insertions(+) create mode 100644 test/test_angle_per_vertex_normals.py create mode 100644 test/test_uniform_per_vertex_normals.py diff --git a/test/test_angle_per_vertex_normals.py b/test/test_angle_per_vertex_normals.py new file mode 100644 index 00000000..552a86d0 --- /dev/null +++ b/test/test_angle_per_vertex_normals.py @@ -0,0 +1,16 @@ +from .context import gpytoolbox +from .context import numpy as np +from .context import unittest + +class TestPerVertexNormals(unittest.TestCase): + # TODO WRITE THIS WITHOUT IGL + def test_armadillo(self): + self.assertTrue(True) + # Trying several meshes against the libigl per_vertex_normals + v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") + n = gpytoolbox.per_vertex_normals(v,f,weights="angles") + n_gt =np.array([[-0.58033928, -0.62497345, 0.52212499], [0.39674071, -0.34593286, 0.8502513], [-0.99620263, -0.015053311, -0.08575385], [-0.79294675, 0.26169193, -0.55022975], [0.27557666, -0.31001429, 0.90991683], [0.33176892, -0.44890485, 0.82970706], [-0.0066842995, -0.37620674, 0.92651163], [-0.40970709, -0.2662413, -0.87249966], [0.53076434, -0.035857551, 0.84676056], [-0.99200483, 0.091508844, 0.086905408], [-0.029785904, -0.31029757, -0.95017273], [0.36412627, -0.73037371, -0.57789818], [0.28666794, -0.39890851, -0.87103013], [-0.89675527, 0.091170699, 0.43303336], [-0.76812078, 0.58600323, -0.2580517], [0.88570172, 0.46408266, 0.012639472], [-0.23502894, -0.062670216, -0.9699659], [0.085361676, -0.11267902, -0.98995799], [-0.34517075, 0.7354364, -0.583087], [0.6558618, -0.17188735, -0.73505104], [0.20458527, -0.34227159, 0.91705781], [-0.30902205, -0.26784736, 0.91255858], [0.9128443, -0.32870305, -0.24221806], [-0.23094333, 0.35684463, -0.90516689], [0.28301127, 0.5045416, -0.81568523], [-0.015104128, -0.172324, 0.98492452], [0.72763293, 0.33621751, -0.59791981], [-0.27578193, -0.36739958, 0.88823526], [-0.35759652, 0.015582054, 0.93374618], [-0.2924019, -0.011228055, 0.9562296], [-0.35295824, -0.63392702, -0.68815479], [0.040764588, -0.90212123, -0.42955272], [0.0056669714, -0.66168968, -0.74975639], [0.56550948, -0.74144176, -0.36119682], [0.14234302, -0.26934469, 0.95246622], [-0.15764106, 0.5123459, -0.84418658], [-0.24673766, -0.40266457, 0.8814657], [0.93782264, -0.28021764, -0.20485792], [0.34463292, -0.43821266, 0.83017939], [-0.48265411, -0.4960362, -0.72179852], [-0.58067464, -0.12194169, -0.80495167], [-0.47108143, 0.18703044, -0.86203358], [0.55157075, -0.35291397, 0.75579193], [-0.79944921, -0.55235907, -0.23617879], [0.81396519, 0.52781467, -0.24263624], [0.45112291, 0.27607669, 0.84868709], [-0.44639737, -0.257198, 0.8570756], [-0.40792415, -0.32056147, 0.85489077], [-0.28979785, 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0.90744554], [0.43055171, -0.011199721, 0.90249642], [-0.54000377, 0.73598878, -0.40830925], [-0.76789645, 0.22175799, -0.60096459], [-0.49586239, 0.18156663, -0.84920789], [0.37833392, 0.1084091, -0.91929914], [-0.30243067, 0.8251814, -0.47708631], [-0.11953912, 0.92998174, -0.34762676], [-0.24028163, 0.71761232, -0.65367982], [-0.58751406, 0.6188037, -0.52144914], [-0.89327376, 0.40914812, 0.18617143], [-0.87109086, 0.38353431, 0.30676074], [0.77658599, -0.090876898, -0.62342249], [0.67525286, -0.32033953, -0.66439157], [0.67639496, -0.32988283, -0.65853411], [-0.25715745, 0.96617955, 0.019160484], [0.65821052, 0.0074913913, -0.75279664], [0.24709076, 0.73533317, -0.63105569], [-0.84041626, 0.31225933, 0.44293861], [-0.99632721, -0.071393184, 0.047276905], [-0.83974904, 0.3577234, 0.40847952], [-0.96834837, 0.17236397, 0.18053282], [-0.96358822, 0.082598789, 0.25431317], [-0.56586185, 0.73122562, 0.38093236], [-0.41790379, 0.76187537, 0.49487609], [-0.5110519, 0.62685168, 0.58811813], [0.51704851, -0.32708861, -0.7909955]]) + self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-4).all()) + +if __name__ == '__main__': + unittest.main() diff --git a/test/test_uniform_per_vertex_normals.py b/test/test_uniform_per_vertex_normals.py new file mode 100644 index 00000000..a42568ff --- /dev/null +++ b/test/test_uniform_per_vertex_normals.py @@ -0,0 +1,16 @@ +from .context import gpytoolbox +from .context import numpy as np +from .context import unittest + +class TestPerVertexNormals(unittest.TestCase): + # TODO WRITE THIS WITHOUT IGL + def test_armadillo(self): + self.assertTrue(True) + # Trying several meshes against the libigl per_vertex_normals + v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") + n = gpytoolbox.per_vertex_normals(v,f,weights="uniform") + n_gt = np.array([[-0.54375676, -0.67146189, 0.50345557], [0.3680567, -0.37012616, 0.85296007], [-0.99358704, -0.0026660158, -0.11303846], [-0.7896682, 0.26081942, -0.55533536], [0.32835029, -0.34572525, 0.87901089], [0.33364919, -0.45158064, 0.82749812], [-0.00036293698, -0.37755257, 0.92598808], [-0.40610072, -0.28467089, -0.86835746], [0.54936249, -0.013078096, 0.83548179], [-0.98992041, 0.10591697, 0.094016932], [-0.011413249, -0.33984804, -0.94041111], [0.32448913, -0.63140154, -0.70430029], [0.29646563, -0.37441852, -0.87858916], [-0.89869592, 0.10891412, 0.42483333], [-0.76679134, 0.58912991, -0.25486661], [0.88462245, 0.46403887, -0.045946068], [-0.21540011, -0.097693975, -0.97162682], [0.077551793, -0.079235238, -0.99383474], [-0.35510131, 0.75211151, -0.55518586], [0.58354626, -0.1950996, -0.78829557], [0.20717261, -0.3377013, 0.91817065], [-0.31077446, -0.26573299, 0.91258162], [0.91160641, -0.32978018, -0.24539517], [-0.22835277, 0.35600434, -0.90615447], [0.31152133, 0.52948317, -0.78905135], [0.0030362861, -0.19125379, 0.98153592], [0.77913082, 0.27269543, -0.56443988], [-0.27517267, -0.4097915, 0.86968438], [-0.36541973, 0.038007706, 0.93006657], [-0.31255374, 0.026384463, 0.94953358], [-0.32191263, -0.67594567, -0.66292512], [0.096742723, -0.91335926, -0.39549425], [-0.030491573, -0.70990128, -0.70364084], [0.53409376, -0.74738346, -0.39517315], [0.15552832, -0.26677097, 0.95112785], [-0.17270587, 0.50125053, -0.84789185], [-0.25335491, -0.36870035, 0.89435526], [0.97493157, -0.15335435, -0.16121685], [0.36044732, -0.4241274, 0.83077896], [-0.4923821, -0.49228556, -0.71778464], [-0.58553575, -0.14130194, -0.79823658], [-0.46939693, 0.18173872, -0.86408192], [0.54580289, -0.35794569, 0.75761078], [-0.78634098, -0.56892739, -0.24081008], [0.79866076, 0.55674462, -0.22842159], [0.44612571, 0.27442997, 0.85185682], [-0.42618095, -0.2848587, 0.85861826], [-0.39609577, -0.30863502, 0.86478469], [-0.29997235, 0.63699517, -0.71010826], [-0.013148917, 0.8114511, -0.58427239], [0.93589341, 0.11602893, 0.33262714], [-0.43977879, -0.49440049, -0.74977515], [0.20273161, 0.93150898, -0.30197833], [0.40272715, 0.86395394, -0.30231514], [-0.45518512, -0.58697512, -0.66952723], [0.70861544, 0.082394008, 0.70076771], [-0.14375127, -0.93695325, -0.31851874], [0.28003288, -0.95973529, 0.022130555], [0.57557108, -0.81515512, 0.065115834], [-0.54638747, -0.37979096, -0.7464714], [0.30914568, -0.1792306, 0.93397288], [0.568508, -0.58347144, -0.57996528], [0.77366015, -0.58090288, 0.2529858], [-0.61718779, 0.15344512, -0.77170838], [0.86451382, 0.0340458, -0.50145462], [0.9387553, 0.27688575, 0.20511647], [0.73581892, 0.16734975, -0.65617419], [0.49136486, -0.27549401, 0.82623461], [-0.37334631, 0.55753669, -0.74146165], [0.76482344, 0.63034747, 0.1330683], [-0.46594742, 0.53162178, -0.70729858], [0.66150809, 0.22397204, -0.71571194], [-0.98766929, -0.10667677, 0.11458374], [0.88993467, -0.3364169, -0.30796096], [-0.245268, -0.96134485, 0.1251387], [0.14095862, -0.19665832, 0.97028664], [0.050909939, -0.10800383, 0.99284609], [0.19082356, -0.80018439, -0.56858712], [-0.50759053, -0.61301994, -0.60544068], [-0.45302784, -0.68478921, -0.57081478], [-0.21833059, -0.89486544, -0.38929115], [0.18745937, -0.98180821, -0.030192966], [0.63856522, -0.71139942, 0.29350523], [0.1767559, 0.64163727, 0.74636383], [-0.6607177, -0.25627459, -0.70553204], [-0.42909042, -0.20173407, 0.88044578], [0.74015825, -0.49757241, 0.45231346], [0.89052325, -0.15720693, 0.42691256], [0.56287223, 0.75343656, 0.33986498], [-0.26257113, -0.95800672, 0.11523683], [0.61373713, -0.65542877, -0.44015891], [-0.4133999, 0.53361196, -0.73780675], [-0.35551565, 0.76928093, -0.53086295], [-0.20402969, -0.27412219, 0.93980259], [-0.16042032, 0.84230001, -0.51458334], [-0.12431783, 0.8394833, -0.52897341], [0.087415085, 0.95053449, -0.29806506], [0.43051317, 0.15566628, 0.88905929], [0.31151, 0.94567395, -0.093071493], [0.4982401, 0.86692417, 0.014116509], [0.024061978, 0.16349477, 0.98625072], [0.62982757, -0.10359607, 0.76979548], [-0.078211084, -0.96518947, -0.2495843], [0.63004808, -0.61876805, -0.46921798], [0.12898309, -0.9793178, -0.15588457], [-0.91177613, 0.26765075, 0.31149215], [-0.36587012, -0.8159349, -0.44764864], [-0.033199347, -0.73618142, 0.67596946], [0.55097816, -0.78141614, 0.29293664], [0.21717834, -0.64153095, 0.73571163], [-0.70728913, -0.031488571, -0.70622274], [0.023713546, -0.09182187, 0.99549305], [-0.98065942, -0.17300016, 0.091531696], [-0.28874203, -0.93573458, 0.20255574], [-0.037001756, -0.99922807, -0.013195707], [-0.2090905, 0.50190745, -0.83926758], [0.85673768, 0.22203241, 0.46551279], [-0.5992205, 0.41733224, -0.68320465], [0.77515173, 0.5370261, 0.33278035], [-0.56608015, -0.43509445, -0.70017575], [-0.04678766, 0.94936318, -0.31067743], [-0.42867959, -0.40113971, 0.80951884], [-0.36344934, 0.53764602, -0.76081623], [0.14694157, -0.98809727, -0.045518721], [0.47762273, -0.85907358, 0.18403562], [-0.60869539, -0.53025597, -0.59018517], [-0.37418343, -0.35426281, 0.85702078], [0.71251735, -0.55017096, 0.43546635], [0.63308141, -0.59306019, -0.49748119], [0.78412669, -0.44377133, -0.43383447], [-0.52763264, -0.54591388, 0.65083164], [0.78371023, -0.18696578, 0.59231923], [0.90156985, 0.27966052, 0.33009361], [-0.69614807, 0.20811886, -0.68706943], [-0.26349358, 0.024928874, 0.96433899], [-0.49751138, 0.62127466, -0.60539262], [0.4246987, 0.28119393, 0.86055853], [0.85553574, -0.46319114, -0.23132784], [0.92484898, -0.34130662, 0.16782182], [0.71685543, 0.20825198, -0.66539417], [-0.34990783, -0.49044958, 0.79813766], [0.2007819, 0.96942967, -0.14104162], [0.38569858, 0.92205969, 0.032288277], [-0.96215946, -0.25558011, -0.09448798], [-0.11735313, -0.44823032, -0.88618159], [-0.73009869, 0.66245561, -0.1676558], [0.26739221, -0.54622619, -0.79381254], [-0.67332328, 0.68369279, -0.28142484], [-0.29204346, -0.6692031, 0.68328458], [0.77850209, -0.094461496, 0.62049296], [-0.52435317, -0.0049150244, -0.8514867], [-0.24703749, 0.085044561, -0.96526675], [0.25295597, 0.038942545, -0.96669372], [-0.10467563, -0.65223323, 0.75075617], [-0.32565996, -0.12236606, 0.93753514], [0.72858795, -0.14361151, -0.6697278], [0.06597845, 0.53578363, -0.84177357], [-0.15029349, -0.24353985, 0.95817546], [0.66444855, 0.41073584, -0.62434301], [0.78765483, -0.41675377, -0.45377987], [-0.49789725, 0.21130772, 0.84109891], [-0.96630938, -0.24627701, -0.074791793], [-0.13875202, -0.95409336, -0.26543123], [0.11375818, -0.98914298, -0.09303356], [0.34096434, -0.025214127, 0.93973803], [-0.3960224, -0.81610295, -0.42088269], [0.73312805, -0.42129269, 0.53388737], [0.15601459, -0.54617983, 0.82301096], [-0.28037622, 0.84286149, 0.45931872], [-0.77078709, -0.18109073, -0.61081372], [-0.16031929, -0.37889783, 0.91144619], [0.32360878, -0.11631371, 0.93901463], [0.90098667, -0.37900841, -0.21112944], [-0.67307245, -0.49991774, -0.54502819], [0.027913034, -0.28636747, 0.95771318], [0.81393238, -0.16798687, 0.55614251], [-0.62636011, 0.49064137, -0.60575909], [-0.21826535, -0.25549067, 0.94185177], [-0.40330969, -0.55305586, 0.72902024], [0.609072, 0.76143433, 0.22192131], [0.69580945, 0.64702036, 0.31179138], [-0.96022424, -0.15712078, 0.23082994], [-0.29158563, -0.56198765, 0.77404632], [-0.13772961, 0.9242268, -0.35613954], [0.93584137, -0.35167995, -0.022850329], [0.41372352, 0.90859085, 0.057406662], [0.070966967, 0.97991008, -0.18638648], [-0.053696455, -0.270093, 0.96133577], [-0.028313478, -0.85642923, -0.51548746], [0.17159284, 0.13716939, 0.97557186], [0.5900357, -0.24126429, 0.77048648], [-0.16151373, 0.40548962, -0.89971744], [-0.48789438, -0.51081267, -0.70783437], [-0.35913753, -0.68471762, 0.63417821], [-0.84425233, -0.45895368, -0.27676619], [0.60360563, -0.7158963, -0.35093124], [0.96945601, -0.21666312, -0.11494404], [0.64350116, -0.64446861, -0.41299694], [0.98479046, 0.14146776, -0.10086931], [-0.39231718, 0.43480542, -0.81057479], [-0.66929763, 0.17932393, -0.72102955], [0.74696834, -0.35132565, 0.56445423], [0.11535416, -0.40016945, 0.90915226], [-0.19444246, 0.64961497, -0.7349779], [0.33732819, 0.1018807, 0.9358579], [0.43408803, 0.67968945, -0.59126122], [0.11117562, 0.73045683, -0.67384924], [-0.61007009, -0.19459571, 0.76808007], [0.133923, -0.77199662, 0.62135807], [0.37853218, -0.92185281, 0.083070978], [-0.84958904, 0.36047651, 0.38503916], [0.94466363, -0.25017008, 0.21219226], [0.7262006, -0.5976862, 0.33971148], [0.82794282, -0.27598433, 0.48820419], [0.71167574, -0.64028368, -0.28905787], [-0.63487458, 0.60089172, -0.48565771], [0.8422792, 0.52275356, -0.13150845], [0.76922001, 0.059533914, 0.6362046], [-0.7873084, -0.016306738, -0.61634372], [-0.77189687, 0.14148311, -0.61980461], [-0.9999654, -0.0016761409, 0.0081483448], [-0.78482687, -0.19985319, 0.58660505], [-0.67011031, 0.32944614, -0.66514466], [0.52906491, 0.35086226, 0.77264869], [0.81677054, 0.27018741, 0.50978883], [0.26034867, -0.45926723, 0.84928922], [-0.50841787, -0.055160222, 0.85934197], [0.16695472, -0.46597304, 0.86890463], [0.29725618, -0.27309138, 0.91490976], [0.085760291, -0.7493377, 0.65661114], [-0.39831984, 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-0.30207835], [0.041807485, 0.99558926, -0.083989036], [0.30920222, 0.90822411, -0.28199813], [0.28121991, 0.95964325, 0.00043768765], [0.50364377, -0.66880926, 0.54684288], [-0.6723316, 0.30988568, -0.67226564], [-0.73912898, 0.16754223, -0.65239401], [-0.66852928, -0.014500839, -0.74354444], [-0.56421479, -0.48603845, -0.66740415], [-0.18861115, 0.98204791, 0.0027808603], [-0.51316323, -0.28165167, -0.8107625], [-0.052302501, 0.99573112, -0.076052519], [0.095414984, 0.94365075, -0.31688997], [0.79083885, -0.60807609, -0.069407395], [0.97770552, -0.12449165, 0.16909683], [-0.2118618, -0.74183414, 0.63623634], [-0.78794939, -0.21988395, 0.57514069], [0.63970757, -0.16766617, 0.75010817], [0.20145588, -0.89797077, 0.39123398], [-0.27954583, -0.92541694, 0.25584687], [0.39160928, -0.91679254, 0.078317342], [0.46869754, -0.88333239, -0.0068194618], [0.32845401, -0.23171868, 0.91565518], [0.4285271, -0.025665699, 0.90316432], [-0.50362936, 0.73669553, -0.45126174], [-0.74165772, 0.43092477, -0.51405025], [-0.51051569, 0.211249, -0.8335152], [0.39836961, 0.21196311, -0.8923975], [-0.31501456, 0.81454908, -0.48710946], [-0.1146738, 0.92459792, -0.36327484], [-0.22775985, 0.71760246, -0.65815816], [-0.53358136, 0.6619505, -0.52641472], [-0.88695368, 0.42457916, 0.18178477], [-0.86319528, 0.39682742, 0.31212482], [0.76660627, -0.090021804, -0.63577583], [0.66628998, -0.35209205, -0.65733466], [0.6683207, -0.36135897, -0.65020545], [-0.29699971, 0.95211886, 0.072531684], [0.64185276, 0.038512792, -0.76586017], [0.2165585, 0.74526232, -0.63062388], [-0.82783928, 0.31324463, 0.46536], [-0.99592267, -0.075792588, 0.048923601], [-0.90076341, 0.30096651, 0.31312048], [-0.97124676, 0.17086994, 0.16578053], [-0.96062776, 0.10681973, 0.25648362], [-0.52152828, 0.77576501, 0.35524204], [-0.40730574, 0.77145274, 0.48883812], [-0.56947973, 0.60664495, 0.55468436], [0.49529499, -0.31280809, -0.81045295]]) + self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-5).all()) + +if __name__ == '__main__': + unittest.main() From 97c230e1f6834999dfad3921a594bd55627547f3 Mon Sep 17 00:00:00 2001 From: nicolas <81325398+NIcolasp14@users.noreply.github.com> Date: Sun, 4 Aug 2024 11:39:12 +0300 Subject: [PATCH 3/5] unified per vertex normal testing --- test/test_per_vertex_normals.py | 22 +++++++++++++++++++++- 1 file changed, 21 insertions(+), 1 deletion(-) diff --git a/test/test_per_vertex_normals.py b/test/test_per_vertex_normals.py index e91cdd7e..74a2700e 100644 --- a/test/test_per_vertex_normals.py +++ b/test/test_per_vertex_normals.py @@ -4,7 +4,7 @@ class TestPerVertexNormals(unittest.TestCase): # TODO WRITE THIS WITHOUT IGL - def test_bunny(self): + def test_area_weights(self): self.assertTrue(True) # Trying several meshes against the libigl per_vertex_normals v,f = gpytoolbox.read_mesh("test/unit_tests_data/bunny_oded.obj") @@ -18,5 +18,25 @@ def test_bunny(self): n = gpytoolbox.per_vertex_normals(v,f) self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-4).all()) + + def test_uniform_weights(self): + self.assertTrue(True) + # Trying several meshes against the libigl per_vertex_normals + v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") + n = gpytoolbox.per_vertex_normals(v,f,weights="uniform") + n_gt = np.array([[-0.54375676, -0.67146189, 0.50345557], [0.3680567, -0.37012616, 0.85296007], [-0.99358704, -0.0026660158, -0.11303846], [-0.7896682, 0.26081942, -0.55533536], [0.32835029, -0.34572525, 0.87901089], [0.33364919, -0.45158064, 0.82749812], [-0.00036293698, -0.37755257, 0.92598808], [-0.40610072, -0.28467089, -0.86835746], [0.54936249, -0.013078096, 0.83548179], [-0.98992041, 0.10591697, 0.094016932], [-0.011413249, -0.33984804, -0.94041111], [0.32448913, -0.63140154, -0.70430029], [0.29646563, -0.37441852, -0.87858916], [-0.89869592, 0.10891412, 0.42483333], [-0.76679134, 0.58912991, -0.25486661], [0.88462245, 0.46403887, -0.045946068], [-0.21540011, -0.097693975, -0.97162682], [0.077551793, -0.079235238, -0.99383474], [-0.35510131, 0.75211151, -0.55518586], [0.58354626, -0.1950996, -0.78829557], [0.20717261, -0.3377013, 0.91817065], [-0.31077446, -0.26573299, 0.91258162], [0.91160641, -0.32978018, -0.24539517], [-0.22835277, 0.35600434, -0.90615447], [0.31152133, 0.52948317, -0.78905135], [0.0030362861, -0.19125379, 0.98153592], [0.77913082, 0.27269543, -0.56443988], [-0.27517267, -0.4097915, 0.86968438], [-0.36541973, 0.038007706, 0.93006657], [-0.31255374, 0.026384463, 0.94953358], [-0.32191263, -0.67594567, -0.66292512], [0.096742723, -0.91335926, -0.39549425], [-0.030491573, -0.70990128, -0.70364084], [0.53409376, -0.74738346, -0.39517315], [0.15552832, -0.26677097, 0.95112785], [-0.17270587, 0.50125053, -0.84789185], [-0.25335491, -0.36870035, 0.89435526], [0.97493157, -0.15335435, -0.16121685], [0.36044732, -0.4241274, 0.83077896], [-0.4923821, -0.49228556, -0.71778464], [-0.58553575, -0.14130194, -0.79823658], [-0.46939693, 0.18173872, -0.86408192], [0.54580289, -0.35794569, 0.75761078], [-0.78634098, -0.56892739, -0.24081008], [0.79866076, 0.55674462, -0.22842159], [0.44612571, 0.27442997, 0.85185682], [-0.42618095, -0.2848587, 0.85861826], [-0.39609577, -0.30863502, 0.86478469], [-0.29997235, 0.63699517, -0.71010826], [-0.013148917, 0.8114511, -0.58427239], [0.93589341, 0.11602893, 0.33262714], [-0.43977879, -0.49440049, -0.74977515], [0.20273161, 0.93150898, -0.30197833], [0.40272715, 0.86395394, -0.30231514], [-0.45518512, -0.58697512, -0.66952723], [0.70861544, 0.082394008, 0.70076771], [-0.14375127, -0.93695325, -0.31851874], [0.28003288, -0.95973529, 0.022130555], [0.57557108, -0.81515512, 0.065115834], [-0.54638747, -0.37979096, -0.7464714], [0.30914568, -0.1792306, 0.93397288], [0.568508, -0.58347144, -0.57996528], [0.77366015, -0.58090288, 0.2529858], [-0.61718779, 0.15344512, -0.77170838], [0.86451382, 0.0340458, -0.50145462], [0.9387553, 0.27688575, 0.20511647], [0.73581892, 0.16734975, -0.65617419], [0.49136486, -0.27549401, 0.82623461], [-0.37334631, 0.55753669, -0.74146165], [0.76482344, 0.63034747, 0.1330683], [-0.46594742, 0.53162178, -0.70729858], [0.66150809, 0.22397204, -0.71571194], [-0.98766929, -0.10667677, 0.11458374], [0.88993467, -0.3364169, -0.30796096], [-0.245268, -0.96134485, 0.1251387], [0.14095862, -0.19665832, 0.97028664], [0.050909939, -0.10800383, 0.99284609], [0.19082356, -0.80018439, -0.56858712], [-0.50759053, -0.61301994, -0.60544068], [-0.45302784, -0.68478921, -0.57081478], [-0.21833059, -0.89486544, -0.38929115], [0.18745937, -0.98180821, -0.030192966], [0.63856522, -0.71139942, 0.29350523], [0.1767559, 0.64163727, 0.74636383], [-0.6607177, -0.25627459, -0.70553204], [-0.42909042, -0.20173407, 0.88044578], [0.74015825, -0.49757241, 0.45231346], [0.89052325, -0.15720693, 0.42691256], [0.56287223, 0.75343656, 0.33986498], [-0.26257113, -0.95800672, 0.11523683], [0.61373713, -0.65542877, -0.44015891], [-0.4133999, 0.53361196, -0.73780675], [-0.35551565, 0.76928093, -0.53086295], [-0.20402969, -0.27412219, 0.93980259], [-0.16042032, 0.84230001, -0.51458334], [-0.12431783, 0.8394833, -0.52897341], [0.087415085, 0.95053449, -0.29806506], [0.43051317, 0.15566628, 0.88905929], [0.31151, 0.94567395, -0.093071493], [0.4982401, 0.86692417, 0.014116509], [0.024061978, 0.16349477, 0.98625072], [0.62982757, -0.10359607, 0.76979548], [-0.078211084, -0.96518947, -0.2495843], [0.63004808, -0.61876805, -0.46921798], [0.12898309, -0.9793178, -0.15588457], [-0.91177613, 0.26765075, 0.31149215], [-0.36587012, -0.8159349, -0.44764864], [-0.033199347, -0.73618142, 0.67596946], [0.55097816, -0.78141614, 0.29293664], [0.21717834, -0.64153095, 0.73571163], [-0.70728913, -0.031488571, -0.70622274], [0.023713546, -0.09182187, 0.99549305], [-0.98065942, -0.17300016, 0.091531696], [-0.28874203, -0.93573458, 0.20255574], [-0.037001756, -0.99922807, -0.013195707], [-0.2090905, 0.50190745, -0.83926758], [0.85673768, 0.22203241, 0.46551279], [-0.5992205, 0.41733224, -0.68320465], [0.77515173, 0.5370261, 0.33278035], [-0.56608015, -0.43509445, -0.70017575], [-0.04678766, 0.94936318, -0.31067743], [-0.42867959, -0.40113971, 0.80951884], [-0.36344934, 0.53764602, -0.76081623], [0.14694157, -0.98809727, -0.045518721], [0.47762273, -0.85907358, 0.18403562], [-0.60869539, -0.53025597, -0.59018517], [-0.37418343, -0.35426281, 0.85702078], [0.71251735, -0.55017096, 0.43546635], [0.63308141, -0.59306019, -0.49748119], [0.78412669, -0.44377133, -0.43383447], [-0.52763264, -0.54591388, 0.65083164], [0.78371023, -0.18696578, 0.59231923], [0.90156985, 0.27966052, 0.33009361], [-0.69614807, 0.20811886, -0.68706943], [-0.26349358, 0.024928874, 0.96433899], [-0.49751138, 0.62127466, -0.60539262], [0.4246987, 0.28119393, 0.86055853], [0.85553574, -0.46319114, -0.23132784], [0.92484898, -0.34130662, 0.16782182], [0.71685543, 0.20825198, -0.66539417], [-0.34990783, -0.49044958, 0.79813766], [0.2007819, 0.96942967, -0.14104162], [0.38569858, 0.92205969, 0.032288277], [-0.96215946, -0.25558011, -0.09448798], [-0.11735313, -0.44823032, -0.88618159], [-0.73009869, 0.66245561, -0.1676558], [0.26739221, -0.54622619, -0.79381254], [-0.67332328, 0.68369279, -0.28142484], [-0.29204346, -0.6692031, 0.68328458], [0.77850209, -0.094461496, 0.62049296], [-0.52435317, -0.0049150244, -0.8514867], [-0.24703749, 0.085044561, -0.96526675], [0.25295597, 0.038942545, -0.96669372], [-0.10467563, -0.65223323, 0.75075617], [-0.32565996, -0.12236606, 0.93753514], [0.72858795, -0.14361151, -0.6697278], [0.06597845, 0.53578363, -0.84177357], [-0.15029349, -0.24353985, 0.95817546], [0.66444855, 0.41073584, -0.62434301], [0.78765483, -0.41675377, -0.45377987], [-0.49789725, 0.21130772, 0.84109891], [-0.96630938, -0.24627701, -0.074791793], [-0.13875202, -0.95409336, -0.26543123], [0.11375818, -0.98914298, -0.09303356], [0.34096434, -0.025214127, 0.93973803], [-0.3960224, -0.81610295, -0.42088269], [0.73312805, -0.42129269, 0.53388737], [0.15601459, -0.54617983, 0.82301096], [-0.28037622, 0.84286149, 0.45931872], [-0.77078709, -0.18109073, -0.61081372], [-0.16031929, -0.37889783, 0.91144619], [0.32360878, -0.11631371, 0.93901463], [0.90098667, -0.37900841, -0.21112944], [-0.67307245, -0.49991774, -0.54502819], [0.027913034, -0.28636747, 0.95771318], [0.81393238, -0.16798687, 0.55614251], [-0.62636011, 0.49064137, -0.60575909], [-0.21826535, -0.25549067, 0.94185177], [-0.40330969, -0.55305586, 0.72902024], [0.609072, 0.76143433, 0.22192131], [0.69580945, 0.64702036, 0.31179138], [-0.96022424, -0.15712078, 0.23082994], [-0.29158563, -0.56198765, 0.77404632], [-0.13772961, 0.9242268, -0.35613954], [0.93584137, -0.35167995, -0.022850329], [0.41372352, 0.90859085, 0.057406662], [0.070966967, 0.97991008, -0.18638648], [-0.053696455, -0.270093, 0.96133577], [-0.028313478, -0.85642923, -0.51548746], [0.17159284, 0.13716939, 0.97557186], [0.5900357, -0.24126429, 0.77048648], [-0.16151373, 0.40548962, -0.89971744], [-0.48789438, -0.51081267, -0.70783437], [-0.35913753, -0.68471762, 0.63417821], [-0.84425233, -0.45895368, -0.27676619], [0.60360563, -0.7158963, -0.35093124], [0.96945601, -0.21666312, -0.11494404], [0.64350116, -0.64446861, -0.41299694], [0.98479046, 0.14146776, -0.10086931], [-0.39231718, 0.43480542, -0.81057479], [-0.66929763, 0.17932393, -0.72102955], [0.74696834, -0.35132565, 0.56445423], [0.11535416, -0.40016945, 0.90915226], [-0.19444246, 0.64961497, -0.7349779], [0.33732819, 0.1018807, 0.9358579], [0.43408803, 0.67968945, -0.59126122], [0.11117562, 0.73045683, -0.67384924], [-0.61007009, -0.19459571, 0.76808007], [0.133923, -0.77199662, 0.62135807], [0.37853218, -0.92185281, 0.083070978], [-0.84958904, 0.36047651, 0.38503916], [0.94466363, -0.25017008, 0.21219226], [0.7262006, -0.5976862, 0.33971148], [0.82794282, -0.27598433, 0.48820419], [0.71167574, -0.64028368, -0.28905787], [-0.63487458, 0.60089172, -0.48565771], [0.8422792, 0.52275356, -0.13150845], [0.76922001, 0.059533914, 0.6362046], [-0.7873084, -0.016306738, -0.61634372], [-0.77189687, 0.14148311, -0.61980461], [-0.9999654, -0.0016761409, 0.0081483448], [-0.78482687, -0.19985319, 0.58660505], [-0.67011031, 0.32944614, -0.66514466], [0.52906491, 0.35086226, 0.77264869], [0.81677054, 0.27018741, 0.50978883], [0.26034867, -0.45926723, 0.84928922], [-0.50841787, -0.055160222, 0.85934197], [0.16695472, -0.46597304, 0.86890463], [0.29725618, -0.27309138, 0.91490976], [0.085760291, -0.7493377, 0.65661114], [-0.39831984, 0.75326175, -0.52339091], [0.94253189, -0.33244078, -0.03341809], [-0.82381685, 0.56485406, -0.04759925], [0.42255516, 0.88343344, 0.20246603], [0.026523145, 0.59167524, -0.80573999], [-0.06218543, 0.95451177, -0.29161661], [0.27943478, 0.95931503, -0.040384109], [0.71191834, -0.10076565, 0.69499537], [0.016555475, -0.51614156, -0.85634328], [-0.64957602, 0.031077128, 0.75966125], [-0.52180302, -0.40041583, 0.75325213], [0.26149108, -0.53907143, -0.80064], [-0.093891907, -0.15475136, -0.98348174], [0.18913486, -0.19052202, 0.9632909], [-0.70976819, 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[0.96131279, -0.26464831, 0.076413348], [-0.73160006, -0.66693628, -0.14127049], [0.82115672, -0.56422419, -0.085747846], [-0.72827517, -0.68028561, -0.082624289], [-0.96737671, -0.24743781, 0.054376713], [0.76551017, -0.62724409, -0.14338423], [-0.89503205, -0.44250481, -0.055741569], [-0.6634624, -0.728893, 0.16891607], [0.030496984, 0.35867862, 0.9329628], [-0.88499455, -0.30740318, 0.34969692], [-0.84097206, -0.48918092, -0.23123154], [-0.060103281, -0.96953663, 0.23745806], [0.26704629, -0.89409047, 0.3595671], [0.62453184, -0.29748782, 0.72212255], [-0.81868211, -0.3105199, 0.48304967], [0.62463836, -0.7153769, 0.31314983], [0.94502, -0.32111371, -0.061831879], [0.66918594, -0.64992053, 0.36026863], [-0.12646089, -0.87172311, 0.47339883], [0.87006168, 0.48948157, 0.058313591], [-0.04922358, -0.88233605, 0.46803861], [0.50597631, 0.70994772, -0.48985938], [0.49647198, -0.72169388, 0.48236243], [-0.28951137, -0.85867971, 0.42290935], [0.42035245, -0.73800785, 0.52787142], 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0.2711765], [-0.93101805, -0.32658244, 0.16293958], [-0.48107526, 0.18738014, 0.85642004], [-0.46359381, 0.83184956, 0.30513454], [-0.83649895, -0.41141794, -0.36194584], [0.056078624, 0.39824749, 0.91556219], [-0.47880718, 0.87791973, 0.0007906129], [-0.61408392, 0.75503592, 0.2298297], [-0.59963278, 0.77426583, 0.20236833], [-0.93492969, -0.1593429, 0.31704308], [-0.92263502, 0.385673, -0.00097363314], [-0.77352815, 0.41914921, -0.47536106], [-0.89988138, -0.31225338, -0.30448536], [-0.79431738, 0.54400614, -0.27040196], [0.42701574, -0.075768431, 0.9010642], [-0.40244272, 0.40180603, 0.82255199], [-0.46027317, 0.84143411, -0.28308523], [-0.71074256, 0.59102304, -0.38149283], [0.92819215, 0.15295287, -0.33921196], [0.34057909, 0.26556952, 0.90193055], [0.55660595, 0.3920257, 0.73246547], [-0.44130486, 0.87886152, -0.18125243], [-0.87970818, 0.15765268, 0.44861917], [-0.86004011, 0.42548632, 0.28158905], [-0.99324558, -0.095850997, 0.06538965], [-0.32994769, -0.87673701, -0.34995247], [0.81577855, -0.19650504, 0.54395875], [0.017400961, -0.98165707, 0.18985945], [0.78558038, -0.10206391, 0.61028389], [0.65455157, -0.6862462, 0.3172198], [0.73695821, 0.076924061, 0.67154693], [0.84426108, 0.096123054, 0.52724149], [-0.93934786, 0.029860396, -0.34166352], [-0.098041026, 0.63567863, -0.76570271], [0.6766203, 0.69637263, -0.23926998], [0.41877891, 0.79067867, -0.44659989], [0.82546011, 0.21620699, 0.52141169], [0.10032548, 0.7409567, -0.66401654], [0.77811188, -0.027810393, -0.62750975], [0.91514877, 0.23037172, 0.33080447], [-0.11706924, 0.92204862, -0.36894598], [0.66270164, 0.14992195, 0.73372334], [-0.30529557, 0.5854731, -0.7510099], [-0.8347346, 0.5494739, 0.036008084], [0.25151444, -0.78219175, -0.57001452], [0.15702583, 0.61615387, -0.77181429], [-0.1301096, 0.70608636, -0.69607007], [0.027401079, 0.78222248, -0.62239632], [0.91365854, 0.33083883, -0.23616466], [0.67649641, 0.70303228, -0.21931305], [-0.25268498, 0.9673379, 0.020191254], [0.2689837, 0.66259786, 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-0.63766559], [-0.1118036, -0.46947314, -0.87583956], [-0.31302664, -0.39388715, -0.86421481], [-0.32160263, -0.62294248, -0.71310197], [-0.63073772, -0.20425196, -0.7486328], [-0.21373702, -0.14989481, -0.96532276], [-0.012601179, -0.37564714, -0.92667709], [0.62295048, -0.52908891, -0.57619236], [-0.61918357, 0.1117391, -0.77725548], [-0.54340758, -0.44760692, -0.71018043], [0.5781796, -0.46162314, -0.67276477], [-0.15981583, -0.49722453, -0.85277586], [0.14252315, -0.38417328, -0.91219408], [-0.42951298, -0.67225846, -0.60298189], [0.74673358, -0.40666241, -0.5263218], [-0.84898958, -0.018175289, -0.52809692], [-0.39612639, -0.17387461, -0.90158278], [-0.14389773, -0.1303985, -0.98096365], [0.10351026, -0.16587207, -0.98069979], [0.11040873, -0.31597111, -0.94232275], [0.4713473, -0.62823588, -0.61899225], [-0.065302858, -0.10822244, -0.99197956], [0.80315928, -0.26187413, -0.53512346], [0.18298332, -0.20635936, 0.96121429], [0.94711954, -0.036874133, -0.3187552], [-0.38544661, 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[-0.023228978, 0.3842967, 0.92291737], [-0.94374156, 0.15297052, 0.29317552], [-0.5748158, 0.81276116, 0.094900482], [-0.13583662, -0.90217094, -0.40943376], [-0.79066933, -0.091016124, 0.6054404], [-0.52399162, 0.8517163, 0.0034823385], [0.42821648, -0.640481, 0.63750665], [0.66871438, 0.74347348, 0.0082621876], [-0.43931163, 0.89792457, 0.027143405], [0.35185311, 0.89808849, -0.26388722], [-0.34350275, 0.92422741, -0.16676198], [0.24812949, 0.92042405, -0.30207835], [0.041807485, 0.99558926, -0.083989036], [0.30920222, 0.90822411, -0.28199813], [0.28121991, 0.95964325, 0.00043768765], [0.50364377, -0.66880926, 0.54684288], [-0.6723316, 0.30988568, -0.67226564], [-0.73912898, 0.16754223, -0.65239401], [-0.66852928, -0.014500839, -0.74354444], [-0.56421479, -0.48603845, -0.66740415], [-0.18861115, 0.98204791, 0.0027808603], [-0.51316323, -0.28165167, -0.8107625], [-0.052302501, 0.99573112, -0.076052519], [0.095414984, 0.94365075, -0.31688997], [0.79083885, -0.60807609, -0.069407395], [0.97770552, -0.12449165, 0.16909683], [-0.2118618, -0.74183414, 0.63623634], [-0.78794939, -0.21988395, 0.57514069], [0.63970757, -0.16766617, 0.75010817], [0.20145588, -0.89797077, 0.39123398], [-0.27954583, -0.92541694, 0.25584687], [0.39160928, -0.91679254, 0.078317342], [0.46869754, -0.88333239, -0.0068194618], [0.32845401, -0.23171868, 0.91565518], [0.4285271, -0.025665699, 0.90316432], [-0.50362936, 0.73669553, -0.45126174], [-0.74165772, 0.43092477, -0.51405025], [-0.51051569, 0.211249, -0.8335152], [0.39836961, 0.21196311, -0.8923975], [-0.31501456, 0.81454908, -0.48710946], [-0.1146738, 0.92459792, -0.36327484], [-0.22775985, 0.71760246, -0.65815816], [-0.53358136, 0.6619505, -0.52641472], [-0.88695368, 0.42457916, 0.18178477], [-0.86319528, 0.39682742, 0.31212482], [0.76660627, -0.090021804, -0.63577583], [0.66628998, -0.35209205, -0.65733466], [0.6683207, -0.36135897, -0.65020545], [-0.29699971, 0.95211886, 0.072531684], [0.64185276, 0.038512792, -0.76586017], [0.2165585, 0.74526232, -0.63062388], [-0.82783928, 0.31324463, 0.46536], [-0.99592267, -0.075792588, 0.048923601], [-0.90076341, 0.30096651, 0.31312048], [-0.97124676, 0.17086994, 0.16578053], [-0.96062776, 0.10681973, 0.25648362], [-0.52152828, 0.77576501, 0.35524204], [-0.40730574, 0.77145274, 0.48883812], [-0.56947973, 0.60664495, 0.55468436], [0.49529499, -0.31280809, -0.81045295]]) + self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-5).all()) + + + # TODO WRITE THIS WITHOUT IGL + def test_angle_weights(self): + self.assertTrue(True) + # Trying several meshes against the libigl per_vertex_normals + v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") + n = gpytoolbox.per_vertex_normals(v,f,weights="angles") + n_gt =np.array([[-0.58033928, -0.62497345, 0.52212499], [0.39674071, -0.34593286, 0.8502513], [-0.99620263, -0.015053311, -0.08575385], [-0.79294675, 0.26169193, -0.55022975], [0.27557666, -0.31001429, 0.90991683], [0.33176892, -0.44890485, 0.82970706], [-0.0066842995, -0.37620674, 0.92651163], [-0.40970709, -0.2662413, -0.87249966], [0.53076434, -0.035857551, 0.84676056], [-0.99200483, 0.091508844, 0.086905408], [-0.029785904, -0.31029757, -0.95017273], [0.36412627, -0.73037371, -0.57789818], [0.28666794, -0.39890851, -0.87103013], [-0.89675527, 0.091170699, 0.43303336], [-0.76812078, 0.58600323, -0.2580517], [0.88570172, 0.46408266, 0.012639472], [-0.23502894, -0.062670216, -0.9699659], [0.085361676, -0.11267902, -0.98995799], [-0.34517075, 0.7354364, -0.583087], [0.6558618, -0.17188735, -0.73505104], [0.20458527, -0.34227159, 0.91705781], [-0.30902205, -0.26784736, 0.91255858], [0.9128443, -0.32870305, -0.24221806], [-0.23094333, 0.35684463, -0.90516689], [0.28301127, 0.5045416, -0.81568523], [-0.015104128, -0.172324, 0.98492452], [0.72763293, 0.33621751, -0.59791981], [-0.27578193, -0.36739958, 0.88823526], [-0.35759652, 0.015582054, 0.93374618], [-0.2924019, -0.011228055, 0.9562296], [-0.35295824, -0.63392702, -0.68815479], [0.040764588, -0.90212123, -0.42955272], [0.0056669714, -0.66168968, -0.74975639], [0.56550948, -0.74144176, -0.36119682], [0.14234302, -0.26934469, 0.95246622], [-0.15764106, 0.5123459, -0.84418658], [-0.24673766, -0.40266457, 0.8814657], [0.93782264, -0.28021764, -0.20485792], [0.34463292, -0.43821266, 0.83017939], [-0.48265411, -0.4960362, -0.72179852], [-0.58067464, -0.12194169, -0.80495167], [-0.47108143, 0.18703044, -0.86203358], [0.55157075, -0.35291397, 0.75579193], [-0.79944921, -0.55235907, -0.23617879], [0.81396519, 0.52781467, -0.24263624], [0.45112291, 0.27607669, 0.84868709], [-0.44639737, -0.257198, 0.8570756], [-0.40792415, -0.32056147, 0.85489077], [-0.28979785, 0.66158642, -0.69160727], [-0.029014915, 0.77097308, -0.63620644], [0.93492148, 0.12848221, 0.33077811], [-0.44096226, -0.48922993, -0.75246685], [0.15914652, 0.92401612, -0.34765873], [0.41048816, 0.8657862, -0.28620573], [-0.47219524, -0.59189974, -0.65321233], [0.67513604, 0.080322872, 0.73330727], [-0.13527499, -0.94173623, -0.30795056], [0.27987602, -0.95999247, -0.0091576935], [0.54672177, -0.83639077, 0.039316451], [-0.5517589, -0.31271952, -0.77315498], [0.30688327, -0.21337311, 0.92752066], [0.57330916, -0.58219693, -0.57650962], [0.79190689, -0.54637084, 0.27269468], [-0.62600537, 0.11078992, -0.77190859], [0.86518166, 0.024905301, -0.50083971], [0.92846291, 0.28884755, 0.23350314], [0.73511043, 0.16955303, -0.65640264], [0.50153791, -0.26293576, 0.82421144], [-0.40030564, 0.54227872, -0.73870778], [0.74348956, 0.66162515, 0.097341853], [-0.46538989, 0.49966729, -0.73057844], [0.65246343, 0.23032603, -0.72197049], [-0.98723794, -0.11997452, 0.10472514], [0.88095122, -0.34927665, -0.31926598], [-0.22825835, -0.96567115, 0.12400546], [0.1534336, -0.1777133, 0.97204738], [0.072694551, -0.10523675, 0.99178664], [0.16700977, -0.79747114, -0.57978231], [-0.51078299, -0.57298217, -0.6409307], [-0.42788697, -0.72889514, -0.53443861], [-0.22446364, -0.88815314, -0.40099884], [0.17681294, -0.98407029, -0.018516086], [0.67477535, -0.67132401, 0.30659794], [0.16522656, 0.65326624, 0.73887983], [-0.65616532, -0.2667515, -0.70589709], [-0.41589156, -0.20282043, 0.88650893], [0.72814917, -0.48438486, 0.4849434], [0.90727437, -0.14195558, 0.39585583], [0.56020201, 0.75534542, 0.34003971], [-0.26620126, -0.95592924, 0.12383936], [0.60800008, -0.66656712, -0.43130519], [-0.42594904, 0.5499208, -0.71843895], [-0.35085051, 0.77504425, -0.52555716], [-0.1949318, -0.30134023, 0.93337863], [-0.15252214, 0.85125194, -0.50210271], [-0.093404695, 0.85242558, -0.51443774], [0.091737568, 0.95386805, -0.28586704], [0.44473174, 0.15650695, 0.88188392], [0.27725697, 0.95289057, -0.12299649], [0.51532129, 0.85584856, 0.044353205], [-0.010014084, 0.17444378, 0.98461621], [0.61817135, -0.10436694, 0.7790839], [-0.071647316, -0.95628429, -0.28352603], [0.6293333, -0.61294256, -0.47774576], [0.16099833, -0.98026192, -0.11474361], [-0.9145539, 0.26563585, 0.30500615], [-0.38064292, -0.80141942, -0.46134356], [-0.025002852, -0.72669931, 0.68650052], [0.57007855, -0.7750442, 0.27261132], [0.20133219, -0.63399051, 0.74667354], [-0.70490422, -0.038268442, -0.70826942], [0.010066079, -0.079392931, 0.99679257], [-0.9809107, -0.17215927, 0.090417876], [-0.29376762, -0.93193103, 0.21261499], [-0.035785264, -0.99933853, -0.0064737759], [-0.21244194, 0.4796895, -0.85133214], [0.85880817, 0.17873233, 0.48010757], [-0.59482011, 0.41980946, -0.6855283], [0.79318984, 0.50559619, 0.33944421], [-0.55083244, -0.41216926, -0.72574108], [-0.040750938, 0.95069893, -0.30742626], [-0.4180161, -0.42135144, 0.80481396], [-0.29958462, 0.54655893, -0.78199897], [0.10645242, -0.99197996, -0.068144223], [0.47076718, -0.86380149, 0.17951393], [-0.61836729, -0.50098289, -0.60550644], [-0.38662001, -0.31616659, 0.86635077], [0.7170811, -0.52768689, 0.45534739], [0.64053819, -0.60238187, -0.47628449], [0.76765547, -0.44919828, -0.45708422], [-0.54349876, -0.52408247, 0.65570318], [0.78235193, -0.15782309, 0.60250919], [0.90875626, 0.26819749, 0.31973766], [-0.6968758, 0.20464193, -0.68737602], [-0.26379234, 0.01759738, 0.96441896], [-0.52162399, 0.61673949, -0.58952591], [0.4315633, 0.28825547, 0.85478764], [0.87157142, -0.42589113, -0.24285801], [0.92652648, -0.34548935, 0.14894893], [0.70528492, 0.20654253, -0.67816913], [-0.35256832, -0.48518061, 0.80018457], [0.19851857, 0.96792664, -0.15397531], [0.4190958, 0.90535857, 0.068443866], [-0.95587237, -0.27854145, -0.093395312], [-0.16637326, -0.46125705, -0.87152847], [-0.73416491, 0.64556795, -0.21034237], [0.24661242, -0.56832659, -0.78497592], [-0.65833779, 0.69682352, -0.28465476], [-0.28208106, -0.69253441, 0.66394756], [0.78572637, -0.060551268, 0.61560346], [-0.47737459, -0.019207291, -0.87848994], [-0.21719755, 0.10631406, -0.97032085], [0.26617148, 0.074003023, -0.9610808], [-0.10410151, -0.65303954, 0.75013481], [-0.32202476, -0.11608344, 0.93958751], [0.69482637, -0.14491645, -0.70442568], [0.076520082, 0.51662441, 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[-0.82532288, 0.56466046, -0.00083935077], [0.40304776, 0.89397494, 0.19586044], [0.031174984, 0.56352323, -0.82551177], [-0.06852356, 0.95499256, -0.28860653], [0.25569899, 0.96581182, -0.042726541], [0.7133403, -0.11114061, 0.69194898], [-0.021012155, -0.52292416, -0.85212018], [-0.6721231, 0.036779586, 0.73952539], [-0.4741546, -0.41124405, 0.77849582], [0.31101569, -0.48100654, -0.81969625], [-0.039287885, -0.13942869, -0.98945242], [0.18386735, -0.18123818, 0.96609809], [-0.70055591, 0.21639944, 0.67999464], [0.43955236, -0.093766816, -0.8933093], [0.38289442, 0.80946324, -0.44515293], [-0.62427768, -0.70388979, -0.3388459], [-0.2951844, 0.24782709, -0.92273935], [0.12216118, 0.28144496, -0.9517696], [0.61914703, 0.38312955, -0.68546969], [0.49287224, -0.35629841, 0.79380627], [0.20425943, 0.6299011, -0.74933483], [0.31108834, 0.90798517, -0.28069017], [-0.27865904, -0.88477286, -0.37353195], [0.41981221, -0.54511478, 0.72567733], [0.2403483, -0.9699219, 0.038525433], [0.97299768, 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0.16754103, -0.64465803], [-0.66864856, -0.018116332, -0.74335785], [-0.52913975, -0.47844481, -0.70078647], [-0.18980607, 0.98171466, 0.014490533], [-0.62709108, -0.24677082, -0.73882402], [-0.054084117, 0.99653499, -0.063189618], [0.089175188, 0.94055008, -0.32773973], [0.82221022, -0.56467045, -0.071537685], [0.97996405, -0.079775832, 0.18250008], [-0.15737603, -0.72004694, 0.67584406], [-0.7913352, -0.2132642, 0.57298079], [0.61451769, -0.20432134, 0.76198477], [0.21694857, -0.8986707, 0.38121424], [-0.17173499, -0.94746013, 0.26986364], [0.38255606, -0.92236384, 0.053812734], [0.4628648, -0.88346938, -0.072374233], [0.34934804, -0.23344923, 0.90744554], [0.43055171, -0.011199721, 0.90249642], [-0.54000377, 0.73598878, -0.40830925], [-0.76789645, 0.22175799, -0.60096459], [-0.49586239, 0.18156663, -0.84920789], [0.37833392, 0.1084091, -0.91929914], [-0.30243067, 0.8251814, -0.47708631], [-0.11953912, 0.92998174, -0.34762676], [-0.24028163, 0.71761232, -0.65367982], [-0.58751406, 0.6188037, -0.52144914], [-0.89327376, 0.40914812, 0.18617143], [-0.87109086, 0.38353431, 0.30676074], [0.77658599, -0.090876898, -0.62342249], [0.67525286, -0.32033953, -0.66439157], [0.67639496, -0.32988283, -0.65853411], [-0.25715745, 0.96617955, 0.019160484], [0.65821052, 0.0074913913, -0.75279664], [0.24709076, 0.73533317, -0.63105569], [-0.84041626, 0.31225933, 0.44293861], [-0.99632721, -0.071393184, 0.047276905], [-0.83974904, 0.3577234, 0.40847952], [-0.96834837, 0.17236397, 0.18053282], [-0.96358822, 0.082598789, 0.25431317], [-0.56586185, 0.73122562, 0.38093236], [-0.41790379, 0.76187537, 0.49487609], [-0.5110519, 0.62685168, 0.58811813], [0.51704851, -0.32708861, -0.7909955]]) + self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-4).all()) + + if __name__ == '__main__': unittest.main() \ No newline at end of file From 35ebcb9a1865e57cb9e658931e4244c8bf395a0a Mon Sep 17 00:00:00 2001 From: nicolas <81325398+NIcolasp14@users.noreply.github.com> Date: Sun, 4 Aug 2024 11:40:38 +0300 Subject: [PATCH 4/5] unified per_vertex_normal testing --- test/test_angle_per_vertex_normals.py | 16 ---------------- test/test_uniform_per_vertex_normals.py | 16 ---------------- 2 files changed, 32 deletions(-) delete mode 100644 test/test_angle_per_vertex_normals.py delete mode 100644 test/test_uniform_per_vertex_normals.py diff --git a/test/test_angle_per_vertex_normals.py b/test/test_angle_per_vertex_normals.py deleted file mode 100644 index 552a86d0..00000000 --- a/test/test_angle_per_vertex_normals.py +++ /dev/null @@ -1,16 +0,0 @@ -from .context import gpytoolbox -from .context import numpy as np -from .context import unittest - -class TestPerVertexNormals(unittest.TestCase): - # TODO WRITE THIS WITHOUT IGL - def test_armadillo(self): - self.assertTrue(True) - # Trying several meshes against the libigl per_vertex_normals - v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") - n = gpytoolbox.per_vertex_normals(v,f,weights="angles") - n_gt =np.array([[-0.58033928, -0.62497345, 0.52212499], [0.39674071, -0.34593286, 0.8502513], [-0.99620263, -0.015053311, -0.08575385], [-0.79294675, 0.26169193, -0.55022975], [0.27557666, -0.31001429, 0.90991683], [0.33176892, -0.44890485, 0.82970706], [-0.0066842995, -0.37620674, 0.92651163], [-0.40970709, -0.2662413, -0.87249966], [0.53076434, -0.035857551, 0.84676056], [-0.99200483, 0.091508844, 0.086905408], [-0.029785904, -0.31029757, -0.95017273], [0.36412627, -0.73037371, -0.57789818], [0.28666794, -0.39890851, -0.87103013], [-0.89675527, 0.091170699, 0.43303336], [-0.76812078, 0.58600323, -0.2580517], [0.88570172, 0.46408266, 0.012639472], [-0.23502894, -0.062670216, -0.9699659], [0.085361676, -0.11267902, -0.98995799], [-0.34517075, 0.7354364, -0.583087], [0.6558618, -0.17188735, -0.73505104], [0.20458527, -0.34227159, 0.91705781], [-0.30902205, -0.26784736, 0.91255858], [0.9128443, -0.32870305, -0.24221806], [-0.23094333, 0.35684463, -0.90516689], [0.28301127, 0.5045416, -0.81568523], [-0.015104128, 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0.17111695, -0.39624571], [0.78220753, 0.60659989, -0.14208431], [0.70097962, 0.67745956, 0.22288141], [0.65881465, 0.7155332, -0.23232629], [0.66148699, 0.74818667, 0.05149436], [0.35338818, 0.2692039, 0.89590516], [0.61425147, -0.0035025205, 0.78910257], [-0.89771389, -0.15358699, -0.41294166], [-0.89714159, 0.15197875, -0.41477635], [-0.81705002, -0.40952684, -0.40585346], [0.59979579, 0.70002171, -0.3875753], [0.70878481, -0.12185504, 0.69482044], [0.92005028, -0.38979183, -0.03962101], [-0.49447277, 0.26341036, 0.82831858], [-0.84492722, 0.47849783, 0.23903518], [-0.98794662, 0.15151819, 0.03168155], [-0.97801528, 0.059496379, 0.19986569], [-0.035408815, 0.39396213, 0.91844437], [-0.94223149, 0.18833351, 0.27700238], [-0.57582991, 0.81046874, 0.10751898], [-0.18840472, -0.89381496, -0.40693794], [-0.79523565, -0.093401045, 0.59906302], [-0.52876735, 0.84797327, 0.036693535], [0.4515211, -0.62646644, 0.63534911], [0.65633409, 0.75418081, -0.020901355], [-0.43366667, 0.90107337, -4.6054118e-05], [0.35653642, 0.8927784, -0.27536977], [-0.35541126, 0.92493994, -0.13479224], [0.24816706, 0.91942654, -0.30507039], [0.015000708, 0.99434233, -0.10515851], [0.32202641, 0.90490349, -0.27829601], [0.29859657, 0.95437625, 0.0024624711], [0.52027672, -0.66805851, 0.53198681], [-0.67341106, 0.32795508, -0.66254284], [-0.74588607, 0.16754103, -0.64465803], [-0.66864856, -0.018116332, -0.74335785], [-0.52913975, -0.47844481, -0.70078647], [-0.18980607, 0.98171466, 0.014490533], [-0.62709108, -0.24677082, -0.73882402], [-0.054084117, 0.99653499, -0.063189618], [0.089175188, 0.94055008, -0.32773973], [0.82221022, -0.56467045, -0.071537685], [0.97996405, -0.079775832, 0.18250008], [-0.15737603, -0.72004694, 0.67584406], [-0.7913352, -0.2132642, 0.57298079], [0.61451769, -0.20432134, 0.76198477], [0.21694857, -0.8986707, 0.38121424], [-0.17173499, -0.94746013, 0.26986364], [0.38255606, -0.92236384, 0.053812734], [0.4628648, -0.88346938, -0.072374233], [0.34934804, -0.23344923, 0.90744554], [0.43055171, -0.011199721, 0.90249642], [-0.54000377, 0.73598878, -0.40830925], [-0.76789645, 0.22175799, -0.60096459], [-0.49586239, 0.18156663, -0.84920789], [0.37833392, 0.1084091, -0.91929914], [-0.30243067, 0.8251814, -0.47708631], [-0.11953912, 0.92998174, -0.34762676], [-0.24028163, 0.71761232, -0.65367982], [-0.58751406, 0.6188037, -0.52144914], [-0.89327376, 0.40914812, 0.18617143], [-0.87109086, 0.38353431, 0.30676074], [0.77658599, -0.090876898, -0.62342249], [0.67525286, -0.32033953, -0.66439157], [0.67639496, -0.32988283, -0.65853411], [-0.25715745, 0.96617955, 0.019160484], [0.65821052, 0.0074913913, -0.75279664], [0.24709076, 0.73533317, -0.63105569], [-0.84041626, 0.31225933, 0.44293861], [-0.99632721, -0.071393184, 0.047276905], [-0.83974904, 0.3577234, 0.40847952], [-0.96834837, 0.17236397, 0.18053282], [-0.96358822, 0.082598789, 0.25431317], [-0.56586185, 0.73122562, 0.38093236], [-0.41790379, 0.76187537, 0.49487609], [-0.5110519, 0.62685168, 0.58811813], [0.51704851, -0.32708861, -0.7909955]]) - self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-4).all()) - -if __name__ == '__main__': - unittest.main() diff --git a/test/test_uniform_per_vertex_normals.py b/test/test_uniform_per_vertex_normals.py deleted file mode 100644 index a42568ff..00000000 --- a/test/test_uniform_per_vertex_normals.py +++ /dev/null @@ -1,16 +0,0 @@ -from .context import gpytoolbox -from .context import numpy as np -from .context import unittest - -class TestPerVertexNormals(unittest.TestCase): - # TODO WRITE THIS WITHOUT IGL - def test_armadillo(self): - self.assertTrue(True) - # Trying several meshes against the libigl per_vertex_normals - v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") - n = gpytoolbox.per_vertex_normals(v,f,weights="uniform") - n_gt = np.array([[-0.54375676, -0.67146189, 0.50345557], [0.3680567, -0.37012616, 0.85296007], [-0.99358704, -0.0026660158, -0.11303846], [-0.7896682, 0.26081942, -0.55533536], [0.32835029, 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[0.26704629, -0.89409047, 0.3595671], [0.62453184, -0.29748782, 0.72212255], [-0.81868211, -0.3105199, 0.48304967], [0.62463836, -0.7153769, 0.31314983], [0.94502, -0.32111371, -0.061831879], [0.66918594, -0.64992053, 0.36026863], [-0.12646089, -0.87172311, 0.47339883], [0.87006168, 0.48948157, 0.058313591], [-0.04922358, -0.88233605, 0.46803861], [0.50597631, 0.70994772, -0.48985938], [0.49647198, -0.72169388, 0.48236243], [-0.28951137, -0.85867971, 0.42290935], [0.42035245, -0.73800785, 0.52787142], [-0.42195952, -0.77938135, 0.46315751], [0.37454295, -0.10051259, 0.92174552], [-0.47145111, -0.56711514, 0.67536232], [0.74320894, -0.35384794, 0.56783105], [0.67722524, -0.33520078, 0.65498581], [0.71472783, -0.17628025, 0.67682302], [0.4303834, -0.19964743, 0.88029031], [0.26845736, -0.23755905, 0.93353968], [0.6519508, -0.22064013, 0.72545026], [-0.81887943, -0.39460372, 0.41680257], [0.51783219, -0.30113078, 0.80073096], [-0.8711411, -0.27224064, 0.40865414], [0.28555463, -0.2530165, 0.92435989], [0.075379046, 0.04509714, 0.99613465], [-0.85800701, -0.21131931, 0.46815396], [0.30670093, 0.17175619, 0.93618073], [0.3253084, 0.28979307, 0.90010801], [-0.80385979, 0.2725279, 0.52871352], [-0.27406181, -0.45759659, -0.84586967], [-0.22897911, -0.83605316, 0.49858167], [-0.79280429, 0.41958476, 0.44205202], [0.41500043, 0.75842145, 0.50256496], [0.27654971, -0.15681178, 0.94811936], [-0.55386454, 0.47945718, 0.68070176], [0.63728753, 0.72855127, 0.25115265], [0.6471799, 0.7124756, 0.2711765], [-0.93101805, -0.32658244, 0.16293958], [-0.48107526, 0.18738014, 0.85642004], [-0.46359381, 0.83184956, 0.30513454], [-0.83649895, -0.41141794, -0.36194584], [0.056078624, 0.39824749, 0.91556219], [-0.47880718, 0.87791973, 0.0007906129], [-0.61408392, 0.75503592, 0.2298297], [-0.59963278, 0.77426583, 0.20236833], [-0.93492969, -0.1593429, 0.31704308], [-0.92263502, 0.385673, -0.00097363314], [-0.77352815, 0.41914921, -0.47536106], [-0.89988138, -0.31225338, -0.30448536], [-0.79431738, 0.54400614, -0.27040196], [0.42701574, -0.075768431, 0.9010642], [-0.40244272, 0.40180603, 0.82255199], [-0.46027317, 0.84143411, -0.28308523], [-0.71074256, 0.59102304, -0.38149283], [0.92819215, 0.15295287, -0.33921196], [0.34057909, 0.26556952, 0.90193055], [0.55660595, 0.3920257, 0.73246547], [-0.44130486, 0.87886152, -0.18125243], [-0.87970818, 0.15765268, 0.44861917], [-0.86004011, 0.42548632, 0.28158905], [-0.99324558, -0.095850997, 0.06538965], [-0.32994769, -0.87673701, -0.34995247], [0.81577855, -0.19650504, 0.54395875], [0.017400961, -0.98165707, 0.18985945], [0.78558038, -0.10206391, 0.61028389], [0.65455157, -0.6862462, 0.3172198], [0.73695821, 0.076924061, 0.67154693], [0.84426108, 0.096123054, 0.52724149], [-0.93934786, 0.029860396, -0.34166352], [-0.098041026, 0.63567863, -0.76570271], [0.6766203, 0.69637263, -0.23926998], [0.41877891, 0.79067867, -0.44659989], [0.82546011, 0.21620699, 0.52141169], [0.10032548, 0.7409567, -0.66401654], [0.77811188, -0.027810393, -0.62750975], [0.91514877, 0.23037172, 0.33080447], [-0.11706924, 0.92204862, -0.36894598], [0.66270164, 0.14992195, 0.73372334], [-0.30529557, 0.5854731, -0.7510099], [-0.8347346, 0.5494739, 0.036008084], [0.25151444, -0.78219175, -0.57001452], [0.15702583, 0.61615387, -0.77181429], [-0.1301096, 0.70608636, -0.69607007], [0.027401079, 0.78222248, -0.62239632], [0.91365854, 0.33083883, -0.23616466], [0.67649641, 0.70303228, -0.21931305], [-0.25268498, 0.9673379, 0.020191254], [0.2689837, 0.66259786, -0.69900776], [0.073515903, 0.66053782, -0.74718485], [0.15938244, -0.33212853, -0.92967084], [-0.3788843, 0.11610496, -0.91813197], [-0.61101591, 0.027154976, -0.79115243], [0.081273356, 0.064725634, -0.99458797], [0.40883833, -0.17348553, -0.8959654], [-0.1884156, -0.65905426, -0.72811197], [-0.047834914, -0.56038576, -0.82684921], [0.24496529, -0.60687817, -0.75610244], [-0.32508243, -0.55416502, -0.76630447], [-0.83308191, 0.5307622, 0.15577552], [-0.33745514, -0.35440588, -0.87207826], [-0.31966446, 0.23634878, 0.91758045], [-0.21163, -0.30947132, -0.92706], [-0.26699721, -0.44309411, -0.85579209], [0.077684299, -0.37984168, -0.92178384], [-0.35415105, -0.40362413, -0.84360215], [-0.21326901, -0.240059, -0.94704171], [-0.06226961, -0.37439618, -0.92517566], [0.47872878, -0.53464775, -0.69639826], [-0.52137708, -0.079414726, -0.849623], [-0.69498364, 0.034453292, -0.71819963], [-0.46832077, 0.016962521, -0.88339568], [0.68653614, 0.42198593, 0.59211148], [-0.51317535, -0.57448555, -0.63766559], [-0.1118036, -0.46947314, -0.87583956], [-0.31302664, -0.39388715, -0.86421481], [-0.32160263, -0.62294248, -0.71310197], [-0.63073772, -0.20425196, -0.7486328], [-0.21373702, -0.14989481, -0.96532276], [-0.012601179, -0.37564714, -0.92667709], [0.62295048, -0.52908891, -0.57619236], [-0.61918357, 0.1117391, -0.77725548], [-0.54340758, -0.44760692, -0.71018043], [0.5781796, -0.46162314, -0.67276477], [-0.15981583, -0.49722453, -0.85277586], [0.14252315, -0.38417328, -0.91219408], [-0.42951298, -0.67225846, -0.60298189], [0.74673358, -0.40666241, -0.5263218], [-0.84898958, -0.018175289, -0.52809692], [-0.39612639, -0.17387461, -0.90158278], [-0.14389773, -0.1303985, -0.98096365], [0.10351026, -0.16587207, -0.98069979], [0.11040873, -0.31597111, -0.94232275], [0.4713473, -0.62823588, -0.61899225], [-0.065302858, -0.10822244, -0.99197956], [0.80315928, -0.26187413, -0.53512346], [0.18298332, -0.20635936, 0.96121429], [0.94711954, -0.036874133, -0.3187552], [-0.38544661, -0.20168554, -0.90041871], [0.74403546, 0.51401743, 0.42684577], [-0.77135602, -0.0066061238, -0.63636958], [0.92537023, 0.037788506, -0.37717631], [-0.78863488, 0.15221176, -0.5957236], [0.268477, 0.3162098, 0.90990739], [0.87212998, 0.37528762, -0.31392435], [0.81050079, 0.19843098, -0.55110218], [0.77584367, 0.16385219, -0.60927749], [0.8829576, 0.20071713, -0.42438014], [0.78347185, 0.60518082, -0.14116669], [0.65744676, 0.70267507, 0.27205057], [0.67271915, 0.70871389, -0.21254074], [0.66098381, 0.74936022, 0.039492536], [0.31897685, 0.27130942, 0.90809965], [0.59092948, 0.024655124, 0.80634637], [-0.91742976, -0.1164594, -0.38047319], [-0.89612005, 0.13589105, -0.42249554], [-0.81567103, -0.4033456, -0.4147205], [0.61555811, 0.68176575, -0.39532731], [0.70548621, -0.11650985, 0.6990813], [0.91990787, -0.39120365, -0.027004209], [-0.50689185, 0.22141654, 0.83308785], [-0.84230608, 0.49561185, 0.2118711], [-0.98921204, 0.14366366, 0.028640808], [-0.97433388, 0.055380944, 0.218189], [-0.023228978, 0.3842967, 0.92291737], [-0.94374156, 0.15297052, 0.29317552], [-0.5748158, 0.81276116, 0.094900482], [-0.13583662, -0.90217094, -0.40943376], [-0.79066933, -0.091016124, 0.6054404], [-0.52399162, 0.8517163, 0.0034823385], [0.42821648, -0.640481, 0.63750665], [0.66871438, 0.74347348, 0.0082621876], [-0.43931163, 0.89792457, 0.027143405], [0.35185311, 0.89808849, -0.26388722], [-0.34350275, 0.92422741, -0.16676198], [0.24812949, 0.92042405, -0.30207835], [0.041807485, 0.99558926, -0.083989036], [0.30920222, 0.90822411, -0.28199813], [0.28121991, 0.95964325, 0.00043768765], [0.50364377, -0.66880926, 0.54684288], [-0.6723316, 0.30988568, -0.67226564], [-0.73912898, 0.16754223, -0.65239401], [-0.66852928, -0.014500839, -0.74354444], [-0.56421479, -0.48603845, -0.66740415], [-0.18861115, 0.98204791, 0.0027808603], [-0.51316323, -0.28165167, -0.8107625], [-0.052302501, 0.99573112, -0.076052519], [0.095414984, 0.94365075, -0.31688997], [0.79083885, -0.60807609, -0.069407395], [0.97770552, -0.12449165, 0.16909683], [-0.2118618, -0.74183414, 0.63623634], [-0.78794939, -0.21988395, 0.57514069], [0.63970757, -0.16766617, 0.75010817], [0.20145588, -0.89797077, 0.39123398], [-0.27954583, -0.92541694, 0.25584687], [0.39160928, -0.91679254, 0.078317342], [0.46869754, -0.88333239, -0.0068194618], [0.32845401, -0.23171868, 0.91565518], [0.4285271, -0.025665699, 0.90316432], [-0.50362936, 0.73669553, -0.45126174], [-0.74165772, 0.43092477, -0.51405025], [-0.51051569, 0.211249, -0.8335152], [0.39836961, 0.21196311, -0.8923975], [-0.31501456, 0.81454908, -0.48710946], [-0.1146738, 0.92459792, -0.36327484], [-0.22775985, 0.71760246, -0.65815816], [-0.53358136, 0.6619505, -0.52641472], [-0.88695368, 0.42457916, 0.18178477], [-0.86319528, 0.39682742, 0.31212482], [0.76660627, -0.090021804, -0.63577583], [0.66628998, -0.35209205, -0.65733466], [0.6683207, -0.36135897, -0.65020545], [-0.29699971, 0.95211886, 0.072531684], [0.64185276, 0.038512792, -0.76586017], [0.2165585, 0.74526232, -0.63062388], [-0.82783928, 0.31324463, 0.46536], [-0.99592267, -0.075792588, 0.048923601], [-0.90076341, 0.30096651, 0.31312048], [-0.97124676, 0.17086994, 0.16578053], [-0.96062776, 0.10681973, 0.25648362], [-0.52152828, 0.77576501, 0.35524204], [-0.40730574, 0.77145274, 0.48883812], [-0.56947973, 0.60664495, 0.55468436], [0.49529499, -0.31280809, -0.81045295]]) - self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-5).all()) - -if __name__ == '__main__': - unittest.main() From 0ada47cdda5df2dfab9a9223c340cd56b4225da2 Mon Sep 17 00:00:00 2001 From: nicolas <81325398+NIcolasp14@users.noreply.github.com> Date: Sun, 4 Aug 2024 15:55:15 +0300 Subject: [PATCH 5/5] per_vertex_normal contribution adjusted --- src/gpytoolbox/per_vertex_normals.py | 114 +++++++++++++++++---------- test/test_per_vertex_normals.py | 2 +- 2 files changed, 74 insertions(+), 42 deletions(-) diff --git a/src/gpytoolbox/per_vertex_normals.py b/src/gpytoolbox/per_vertex_normals.py index 26bffc21..2e8cf83e 100644 --- a/src/gpytoolbox/per_vertex_normals.py +++ b/src/gpytoolbox/per_vertex_normals.py @@ -2,9 +2,10 @@ from .per_face_normals import per_face_normals from .doublearea import doublearea from scipy.sparse import csr_matrix +from scipy.spatial import KDTree -def compute_angles(V,F): +def compute_angles(V, F): """Computes the angle at each vertex in a triangle mesh. Parameters @@ -61,8 +62,9 @@ def compute_angles(V,F): return angles -def per_vertex_normals(V,F,weights='area'): - """Compute per-vertex normal vectors for a triangle mesh with different weighting options. +def per_vertex_normals(V, F, weights='area', correct_invalid_normals=True): + """Compute per-vertex normal vectors for a triangle mesh with different weighting options, + with an option to correct invalid normals (True) or omit them (False). Parameters ---------- @@ -71,16 +73,20 @@ def per_vertex_normals(V,F,weights='area'): F : (m,d) numpy int array face index list of a triangle mesh weights : str, optional - The type of weighting to use ('area', 'angles', 'uniform'), default is 'area' + the type of weighting to use ('area', 'angle', 'uniform'), default is 'area' + correct_invalid_normals : bool, optional + if True, invalid normals (NaN, inf, zero vectors) will be corrected, either by calculating + them based on nearby valid normals, or -in extreme cases- replacing them with a default normal vector + if False, the invalid normals are omitted Returns ------- N : (n,d) numpy array - Matrix of per-vertex normals + matrix of per-vertex normals See Also -------- - per_vertex_normals, per_face_normals. + per_face_normals Examples -------- @@ -90,10 +96,16 @@ def per_vertex_normals(V,F,weights='area'): n = per_vertex_normals(v,f) ``` """ + # Ensure vertices are in float64 + V = V.astype(np.float64) + # Ensure faces are in int32 + F = F.astype(np.int32) + + # Compute face normals + face_normals = per_face_normals(V, F, unit_norm=True) + if weights=="area": dim = V.shape[1] - # First compute face normals - face_normals = per_face_normals(V,F,unit_norm=True) # We blur these normals onto vertices, weighing by area areas = doublearea(V,F) vals = np.concatenate([areas for _ in range(dim)]) @@ -104,47 +116,67 @@ def per_vertex_normals(V,F,weights='area'): # I = np.concatenate((F[:,0],F[:,1],F[:,2])) weight_mat = csr_matrix((vals,(I,J)),shape=(V.shape[0],F.shape[0])) - - vertex_normals = weight_mat @ face_normals - # Now, normalize - N = vertex_normals/np.tile(np.linalg.norm(vertex_normals,axis=1)[:,None],(1,dim)) - - - elif weights=="angles": - # Ensure vertices are in float64 - V = V.astype(np.float64) - # Ensure faces are in int32 - F = F.astype(np.int32) - - # Compute face normals - normals = per_face_normals(V,F) + weighted_normals = weight_mat @ face_normals + + elif weights=="angle": # Compute angles at each vertex angles = compute_angles(V,F) # Weight the face normals by the angles at each vertex weighted_normals = np.zeros_like(V) for i in range(3): - np.add.at(weighted_normals, F[:, i], normals * angles[:, i, np.newaxis]) - - # Calculate norms - norms = np.linalg.norm(weighted_normals, axis=1, keepdims=True) - # Avoid division by zero by setting zero norms to a very small number - norms[norms == 0] = np.finfo(float).eps - # Normalize the vertex normals - N = weighted_normals / norms - - + np.add.at(weighted_normals, F[:, i], face_normals * angles[:, i, np.newaxis]) + elif weights=="uniform": - # Compute face normals - face_normals = per_face_normals(V, F) - # Initialize vertex normals - vertex_normals = np.zeros_like(V) + # Compute (non-)weighted normals uniformly + weighted_normals = np.zeros_like(V) # Accumulate face normals to vertices for i in range(3): - np.add.at(vertex_normals, F[:, i], face_normals) + np.add.at(weighted_normals, F[:, i], face_normals) + + # Calculate norms + norms = np.linalg.norm(weighted_normals, axis=1, keepdims=True) + # Identify indices with problematic normals (nan, inf, negative norms) + problematic_indices = np.where(np.isnan(norms) | np.isinf(norms) | (norms <= 0))[0] + # Identify indices with valid normals + valid_indices = np.where(np.isfinite(norms) & (norms > 0))[0] + + # Normalize valid normals + N = np.where(norms > 0, weighted_normals / norms, np.zeros_like(weighted_normals)) + + # Ensure all normals are unit vectors (handling edge cases) + if problematic_indices.size > 0 and correct_invalid_normals: + print("Handling problematic indices") - # Normalize - norms = np.linalg.norm(vertex_normals, axis=1, keepdims=True) - norms[norms == 0] = np.finfo(float).eps - N = vertex_normals / norms + # Build KDTree using only valid vertices + if valid_indices.size > 0: + valid_tree = KDTree(V[valid_indices]) + + for idx in problematic_indices: + print(f"Handling vertex {idx}") + + # Use nearest valid normal for invalid normals + if valid_indices.size > 0: + # Query the nearest valid normal + dist, pos = valid_tree.query(V[idx], k=1) + nearest_valid_idx = valid_indices[pos] + # Assign the nearest valid normal to the current problematic normal + if np.isfinite(dist) and dist > 0: + N[idx] = N[nearest_valid_idx] + norms[idx] = np.linalg.norm(N[nearest_valid_idx], keepdims=True) + print(f"Updated normal for vertex {idx} from valid neighbor.") + # Else assign a default normal + else: + N[idx] = np.array([1, 0, 0]) + norms[idx] = 1.0 + print(f"Assigned default normal due to lack of valid neighbors.") + + # Else assign a default normal + else: + N[idx] = np.array([1, 0, 0]) + norms[idx] = 1.0 + print(f"No valid vertices available, default normal assigned.") + + # Normalize only the previously problematic normals + N[problematic_indices] = N[problematic_indices] / np.maximum(norms[problematic_indices], np.finfo(float).eps) return N \ No newline at end of file diff --git a/test/test_per_vertex_normals.py b/test/test_per_vertex_normals.py index 74a2700e..d622ed63 100644 --- a/test/test_per_vertex_normals.py +++ b/test/test_per_vertex_normals.py @@ -33,7 +33,7 @@ def test_angle_weights(self): self.assertTrue(True) # Trying several meshes against the libigl per_vertex_normals v,f = gpytoolbox.read_mesh("test/unit_tests_data/armadillo.obj") - n = gpytoolbox.per_vertex_normals(v,f,weights="angles") + n = gpytoolbox.per_vertex_normals(v,f,weights="angle") n_gt =np.array([[-0.58033928, -0.62497345, 0.52212499], [0.39674071, -0.34593286, 0.8502513], [-0.99620263, -0.015053311, -0.08575385], [-0.79294675, 0.26169193, -0.55022975], [0.27557666, -0.31001429, 0.90991683], [0.33176892, -0.44890485, 0.82970706], [-0.0066842995, -0.37620674, 0.92651163], [-0.40970709, -0.2662413, -0.87249966], [0.53076434, -0.035857551, 0.84676056], [-0.99200483, 0.091508844, 0.086905408], [-0.029785904, -0.31029757, -0.95017273], [0.36412627, -0.73037371, -0.57789818], [0.28666794, -0.39890851, -0.87103013], [-0.89675527, 0.091170699, 0.43303336], [-0.76812078, 0.58600323, -0.2580517], [0.88570172, 0.46408266, 0.012639472], [-0.23502894, -0.062670216, -0.9699659], [0.085361676, -0.11267902, -0.98995799], [-0.34517075, 0.7354364, -0.583087], [0.6558618, -0.17188735, -0.73505104], [0.20458527, -0.34227159, 0.91705781], [-0.30902205, -0.26784736, 0.91255858], [0.9128443, -0.32870305, -0.24221806], [-0.23094333, 0.35684463, -0.90516689], [0.28301127, 0.5045416, -0.81568523], [-0.015104128, -0.172324, 0.98492452], [0.72763293, 0.33621751, -0.59791981], [-0.27578193, -0.36739958, 0.88823526], [-0.35759652, 0.015582054, 0.93374618], [-0.2924019, -0.011228055, 0.9562296], [-0.35295824, -0.63392702, -0.68815479], [0.040764588, -0.90212123, -0.42955272], [0.0056669714, -0.66168968, -0.74975639], [0.56550948, -0.74144176, -0.36119682], [0.14234302, -0.26934469, 0.95246622], [-0.15764106, 0.5123459, -0.84418658], [-0.24673766, -0.40266457, 0.8814657], [0.93782264, -0.28021764, -0.20485792], [0.34463292, -0.43821266, 0.83017939], [-0.48265411, -0.4960362, -0.72179852], [-0.58067464, -0.12194169, -0.80495167], [-0.47108143, 0.18703044, -0.86203358], [0.55157075, -0.35291397, 0.75579193], [-0.79944921, -0.55235907, -0.23617879], [0.81396519, 0.52781467, -0.24263624], [0.45112291, 0.27607669, 0.84868709], [-0.44639737, -0.257198, 0.8570756], [-0.40792415, -0.32056147, 0.85489077], [-0.28979785, 0.66158642, -0.69160727], [-0.029014915, 0.77097308, -0.63620644], [0.93492148, 0.12848221, 0.33077811], [-0.44096226, -0.48922993, -0.75246685], [0.15914652, 0.92401612, -0.34765873], [0.41048816, 0.8657862, -0.28620573], [-0.47219524, -0.59189974, -0.65321233], [0.67513604, 0.080322872, 0.73330727], [-0.13527499, -0.94173623, -0.30795056], [0.27987602, -0.95999247, -0.0091576935], [0.54672177, -0.83639077, 0.039316451], [-0.5517589, -0.31271952, -0.77315498], [0.30688327, -0.21337311, 0.92752066], [0.57330916, -0.58219693, -0.57650962], [0.79190689, -0.54637084, 0.27269468], [-0.62600537, 0.11078992, -0.77190859], [0.86518166, 0.024905301, -0.50083971], [0.92846291, 0.28884755, 0.23350314], [0.73511043, 0.16955303, -0.65640264], [0.50153791, -0.26293576, 0.82421144], [-0.40030564, 0.54227872, -0.73870778], [0.74348956, 0.66162515, 0.097341853], [-0.46538989, 0.49966729, -0.73057844], [0.65246343, 0.23032603, -0.72197049], [-0.98723794, -0.11997452, 0.10472514], [0.88095122, -0.34927665, -0.31926598], [-0.22825835, -0.96567115, 0.12400546], [0.1534336, -0.1777133, 0.97204738], [0.072694551, -0.10523675, 0.99178664], [0.16700977, -0.79747114, -0.57978231], [-0.51078299, -0.57298217, -0.6409307], [-0.42788697, -0.72889514, -0.53443861], [-0.22446364, -0.88815314, -0.40099884], [0.17681294, -0.98407029, -0.018516086], [0.67477535, -0.67132401, 0.30659794], [0.16522656, 0.65326624, 0.73887983], [-0.65616532, -0.2667515, -0.70589709], [-0.41589156, -0.20282043, 0.88650893], [0.72814917, -0.48438486, 0.4849434], [0.90727437, -0.14195558, 0.39585583], [0.56020201, 0.75534542, 0.34003971], [-0.26620126, -0.95592924, 0.12383936], [0.60800008, -0.66656712, -0.43130519], [-0.42594904, 0.5499208, -0.71843895], [-0.35085051, 0.77504425, -0.52555716], [-0.1949318, -0.30134023, 0.93337863], [-0.15252214, 0.85125194, -0.50210271], [-0.093404695, 0.85242558, -0.51443774], [0.091737568, 0.95386805, -0.28586704], [0.44473174, 0.15650695, 0.88188392], [0.27725697, 0.95289057, -0.12299649], [0.51532129, 0.85584856, 0.044353205], [-0.010014084, 0.17444378, 0.98461621], [0.61817135, -0.10436694, 0.7790839], [-0.071647316, -0.95628429, -0.28352603], [0.6293333, -0.61294256, -0.47774576], [0.16099833, -0.98026192, -0.11474361], [-0.9145539, 0.26563585, 0.30500615], [-0.38064292, -0.80141942, -0.46134356], [-0.025002852, -0.72669931, 0.68650052], [0.57007855, -0.7750442, 0.27261132], [0.20133219, -0.63399051, 0.74667354], [-0.70490422, -0.038268442, -0.70826942], [0.010066079, -0.079392931, 0.99679257], [-0.9809107, -0.17215927, 0.090417876], [-0.29376762, -0.93193103, 0.21261499], [-0.035785264, -0.99933853, -0.0064737759], [-0.21244194, 0.4796895, -0.85133214], [0.85880817, 0.17873233, 0.48010757], [-0.59482011, 0.41980946, -0.6855283], [0.79318984, 0.50559619, 0.33944421], [-0.55083244, -0.41216926, -0.72574108], [-0.040750938, 0.95069893, -0.30742626], [-0.4180161, -0.42135144, 0.80481396], [-0.29958462, 0.54655893, -0.78199897], [0.10645242, -0.99197996, -0.068144223], [0.47076718, -0.86380149, 0.17951393], [-0.61836729, -0.50098289, -0.60550644], [-0.38662001, -0.31616659, 0.86635077], [0.7170811, -0.52768689, 0.45534739], [0.64053819, -0.60238187, -0.47628449], [0.76765547, -0.44919828, -0.45708422], [-0.54349876, -0.52408247, 0.65570318], [0.78235193, -0.15782309, 0.60250919], [0.90875626, 0.26819749, 0.31973766], [-0.6968758, 0.20464193, -0.68737602], [-0.26379234, 0.01759738, 0.96441896], [-0.52162399, 0.61673949, -0.58952591], [0.4315633, 0.28825547, 0.85478764], [0.87157142, -0.42589113, -0.24285801], [0.92652648, -0.34548935, 0.14894893], [0.70528492, 0.20654253, -0.67816913], [-0.35256832, -0.48518061, 0.80018457], [0.19851857, 0.96792664, -0.15397531], [0.4190958, 0.90535857, 0.068443866], [-0.95587237, -0.27854145, -0.093395312], [-0.16637326, -0.46125705, -0.87152847], [-0.73416491, 0.64556795, -0.21034237], [0.24661242, -0.56832659, -0.78497592], [-0.65833779, 0.69682352, -0.28465476], [-0.28208106, -0.69253441, 0.66394756], [0.78572637, -0.060551268, 0.61560346], [-0.47737459, -0.019207291, -0.87848994], [-0.21719755, 0.10631406, -0.97032085], [0.26617148, 0.074003023, -0.9610808], [-0.10410151, -0.65303954, 0.75013481], [-0.32202476, -0.11608344, 0.93958751], [0.69482637, -0.14491645, -0.70442568], [0.076520082, 0.51662441, -0.85278596], [-0.14452623, -0.24160227, 0.95955225], [0.67406967, 0.39448107, -0.62451162], [0.81356185, -0.41931662, -0.40285319], [-0.50131007, 0.21506491, 0.83811413], [-0.96494537, -0.26190816, -0.016868811], [-0.14026898, -0.95317757, -0.26791254], [0.12732851, -0.98769885, -0.090765811], [0.32635462, 0.063794508, 0.94309221], [-0.40688064, -0.80455746, -0.43259154], [0.7186177, -0.48787314, 0.49554858], [0.14684306, -0.53158805, 0.83417699], [-0.27158447, 0.84525409, 0.46020364], [-0.76552541, -0.21838409, -0.60521008], [-0.12874701, -0.40414392, 0.90558925], [0.32780659, -0.16815803, 0.92965892], [0.90710382, -0.37117389, -0.19847569], [-0.67726453, -0.50623849, -0.53388701], [0.059569282, -0.29455454, 0.95377624], [0.82621967, -0.15728174, 0.54094687], [-0.64338066, 0.496107, -0.58304302], [-0.22549635, -0.2266259, 0.94751892], [-0.41725154, -0.54637667, 0.72620499], [0.61754532, 0.75354739, 0.22539765], [0.69883643, 0.64201674, 0.31534448], [-0.96341256, -0.16163045, 0.21380325], [-0.29482156, -0.57056413, 0.7665095], [-0.15686148, 0.91602101, -0.36918829], [0.93737552, -0.34745601, -0.024524384], [0.40121129, 0.91502778, 0.041876769], [0.060291605, 0.97902065, -0.1946368], [-0.03727974, -0.30895764, 0.95034488], [0.018841554, -0.88274082, -0.46948231], [0.16204971, 0.13845477, 0.97702107], [0.57681935, -0.24525064, 0.77918648], [-0.19189905, 0.35908169, -0.91336471], [-0.49427205, -0.4807956, -0.72424495], [-0.36842473, -0.69411006, 0.61844519], [-0.86308962, -0.44036974, -0.24728687], [0.64299273, -0.70292423, -0.30406886], [0.96119606, -0.21624518, -0.17128971], [0.66681249, -0.60423089, -0.43619507], [0.97632515, 0.16936053, -0.13455933], [-0.39931788, 0.41151011, -0.81927081], [-0.67863081, 0.17790217, -0.71260862], [0.75213999, -0.33711832, 0.56624789], [0.099099449, -0.39642499, 0.91270287], [-0.21498929, 0.63270209, -0.74395408], [0.31671673, 0.095075574, 0.94374316], [0.47730679, 0.66050711, -0.57957621], [0.088485463, 0.73292266, -0.67453294], [-0.64410038, -0.17852955, 0.74381577], [0.14233159, -0.77008559, 0.62186003], [0.38981976, -0.91571348, 0.097516043], [-0.86234675, 0.35129523, 0.36462275], [0.94136916, -0.2573331, 0.2181829], [0.72684343, -0.60324114, 0.32832721], [0.81320239, -0.26165505, 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[-0.64694824, -0.22228291, 0.7294164], [-0.72622591, -0.33638614, -0.59953339], [0.79982626, 0.53294063, -0.27613808], [-0.5361802, 0.43308404, -0.72453365], [-0.35926579, 0.82375873, 0.43857684], [-0.31141786, 0.64076881, -0.70173659], [-0.19040658, -0.43282688, 0.88113917], [-0.20978026, -0.43765823, 0.87432689], [0.91115507, -0.33983193, -0.23304655], [-0.69888094, -0.68865937, -0.19316757], [-0.18084515, -0.71030181, 0.68026934], [-0.14457087, -0.57130344, 0.80790571], [0.47241341, -0.87699933, 0.087736768], [-0.32182725, 0.18980425, 0.92757834], [-0.59544813, -0.64868218, -0.47397569], [-0.9992611, -0.0067033935, -0.037846073], [0.85200106, -0.22836117, -0.47111078], [0.84855709, -0.21567542, 0.48315109], [0.64443832, 0.21093014, -0.73498825], [-0.99901972, 0.018668876, 0.040138167], [-0.58422636, 0.40763782, -0.70179126], [0.88102777, 0.077586321, 0.4666588], [0.82934341, 0.42170795, 0.36654047], [-0.13528495, -0.51990084, 0.84344597], [-0.57570296, 0.65595356, -0.48815062], 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[-0.7919351, 0.16553519, -0.5877388], [0.22924308, 0.32026463, 0.91917255], [0.87199871, 0.36969668, -0.3208467], [0.80780442, 0.20304851, -0.55337449], [0.81834846, 0.1815087, -0.54530761], [0.90205783, 0.17111695, -0.39624571], [0.78220753, 0.60659989, -0.14208431], [0.70097962, 0.67745956, 0.22288141], [0.65881465, 0.7155332, -0.23232629], [0.66148699, 0.74818667, 0.05149436], [0.35338818, 0.2692039, 0.89590516], [0.61425147, -0.0035025205, 0.78910257], [-0.89771389, -0.15358699, -0.41294166], [-0.89714159, 0.15197875, -0.41477635], [-0.81705002, -0.40952684, -0.40585346], [0.59979579, 0.70002171, -0.3875753], [0.70878481, -0.12185504, 0.69482044], [0.92005028, -0.38979183, -0.03962101], [-0.49447277, 0.26341036, 0.82831858], [-0.84492722, 0.47849783, 0.23903518], [-0.98794662, 0.15151819, 0.03168155], [-0.97801528, 0.059496379, 0.19986569], [-0.035408815, 0.39396213, 0.91844437], [-0.94223149, 0.18833351, 0.27700238], [-0.57582991, 0.81046874, 0.10751898], [-0.18840472, 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[0.61451769, -0.20432134, 0.76198477], [0.21694857, -0.8986707, 0.38121424], [-0.17173499, -0.94746013, 0.26986364], [0.38255606, -0.92236384, 0.053812734], [0.4628648, -0.88346938, -0.072374233], [0.34934804, -0.23344923, 0.90744554], [0.43055171, -0.011199721, 0.90249642], [-0.54000377, 0.73598878, -0.40830925], [-0.76789645, 0.22175799, -0.60096459], [-0.49586239, 0.18156663, -0.84920789], [0.37833392, 0.1084091, -0.91929914], [-0.30243067, 0.8251814, -0.47708631], [-0.11953912, 0.92998174, -0.34762676], [-0.24028163, 0.71761232, -0.65367982], [-0.58751406, 0.6188037, -0.52144914], [-0.89327376, 0.40914812, 0.18617143], [-0.87109086, 0.38353431, 0.30676074], [0.77658599, -0.090876898, -0.62342249], [0.67525286, -0.32033953, -0.66439157], [0.67639496, -0.32988283, -0.65853411], [-0.25715745, 0.96617955, 0.019160484], [0.65821052, 0.0074913913, -0.75279664], [0.24709076, 0.73533317, -0.63105569], [-0.84041626, 0.31225933, 0.44293861], [-0.99632721, -0.071393184, 0.047276905], [-0.83974904, 0.3577234, 0.40847952], [-0.96834837, 0.17236397, 0.18053282], [-0.96358822, 0.082598789, 0.25431317], [-0.56586185, 0.73122562, 0.38093236], [-0.41790379, 0.76187537, 0.49487609], [-0.5110519, 0.62685168, 0.58811813], [0.51704851, -0.32708861, -0.7909955]]) self.assertTrue(np.isclose(n-n_gt,0.0,atol=1e-4).all())