# Geodesic Regression on Sphere Manifold # Manifolds import manifolds import numpy as np import StatsModel as sm import matplotlib.pyplot as plt # Visualization import vtk # Parameters nDimManifold = 3 # Ground Truth p_interp = manifolds.sphere(nDimManifold) v_slope = manifolds.sphere_tVec(nDimManifold) p_interp.SetPoint([0.0, 0.0, 1.0]) v_slope.SetTangentVector([0, np.pi * 0.25, 0]) # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2.0 # Generate a random point on the manifold nData = 500 dim = nDimManifold sigma = 0.1 pt_list = []
##################################################### # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold # Parameters nDimManifold = 3 nData = 200 dim = nDimManifold sigma = 0.15 # Ground Truth p_interp = manifolds.sphere(nDimManifold) v_slope = manifolds.sphere_tVec(nDimManifold) p_interp.SetPoint([0.0, 0.0, 1.0]) v_slope.SetTangentVector([0, np.pi * 0.25, 0]) # Point List # Base Function ( Geodesic ) pt_list = [] # Projected sin on the base point function at time t pt_list_proj_sin = [] # Time List t_list = []
arrow_transform = vtk.vtkTransform()
arrow_transform.Translate(start_point)
arrow_transform.Concatenate(tVec_at_b0_mat)
arrow_transform.Scale(length, length, length)
arrow_transform.Update()
transformPD = vtk.vtkTransformPolyDataFilter()
transformPD.SetInputData(arrowBase.GetOutput())
transformPD.SetTransform(arrow_transform)
transformPD.Update()
return transformPD.GetOutput()
# Base Intercept Point
beta0 = manifolds.sphere(nDimManifold)
beta0.SetPoint([1, 0, 0])
gamma1 = manifolds.sphere_tVec(nDimManifold)
gamma1.SetTangentVector([0.0, -0.3, 0.0])
tVec_to_f_i = manifolds.sphere_tVec(nDimManifold)
tVec_to_f_i.SetTangentVector([0.0, -1.0, 0.0])
f_i = beta0.ExponentialMap(tVec_to_f_i)
# f_i.SetPoint( [ 0, 1, 0 ] )
gamma1_f_i = beta0.ParallelTranslateAtoB(beta0, f_i, gamma1)
pt_sigma = 0.15
# Set CM-Rep Abstract Point
cmrep_ij = manifolds.cmrep_abstract(nAtoms)
# Center
center_ij = manifolds.euclidean(3)
# print( "Center Of Mass " )
center_ij.SetPoint(cenOfMass)
# Scale
scale_ij = manifolds.pos_real(1)
# print( "Scale" )
scale_ij.SetPoint(length_HX)
# Abstract Position
pos_ij = manifolds.sphere(3 * (nAtoms - 1))
# print( "Abstract Position" )
# print( np.array( Z_H_flatten ).flatten().shape )
# print( 3 * ( nAtoms - 1 ) )
pos_ij.SetPoint(np.array(Z_H_flatten).flatten())
# Radius
rad_ij = manifolds.pos_real(nAtoms)
# print( "Radius" )
rad_ij.SetPoint(rad_arr)
# CM-Rep Point
pt_abs = [center_ij, scale_ij, pos_ij, rad_ij]
# print( "CMRep Abstract Point" )
# Data Generation # ##################################################### # Generating sphere manifolds. distributed over time perturbed by Gaussian random # Time t0 = 0 t1 = 2 # Generate a random point on the manifold # Parameters nDimManifold = 3 nData = 200 dim = nDimManifold sigma = 0.15 # Population Bias p_bias = manifolds.sphere(nDimManifold) v_bias = manifolds.sphere_tVec(nDimManifold) p_bias.SetPoint([0.0, 0.0, 1.0]) v_bias.SetTangentVector([0, np.pi * 0.1, 0]) bias_param_t0 = 0.0 bias_param_t1 = 3.0 nSubj = 10 bias_step = (bias_param_t1 - bias_param_t0) / float(nSubj - 1) # Subject-wise Ground Truth subj_t0 = -0.5 subj_t1 = 0.5
print( eucl_pt_r.Type ) # Sphere sphere_tVec = manifolds.sphere_tVec( 3 ) sphere_tVec.SetTangentVector( [ 0, 0.8192, 0 ] ) sphere_tVec.Write( "sphere_tVec.tvec" ) sphere_tVec_r = manifolds.sphere_tVec( 3 ) sphere_tVec_r.Read( "sphere_tVec.tvec" ) print( sphere_tVec_r.tVector ) print( sphere_tVec_r.nDim ) print( sphere_tVec_r.Type ) sphere_pt = manifolds.sphere( 3 ) sphere_pt.SetPoint( [ 0.0, 1.0, 0.0 ] ) sphere_pt.Write( "sphere.rpt" ) sphere_pt_r = manifolds.sphere( 3 ) sphere_pt_r.Read( "sphere.rpt" ) print( sphere_pt_r.pt ) print( sphere_pt_r.nDim ) print( sphere_pt_r.Type ) # Pos Real pos_real_tVec = manifolds.pos_real_tVec( 1 ) pos_real_tVec.SetTangentVector( 2 ) pos_real_tVec.Write( "pos_real_tVec.tvec" )
normal2_arr = []
for k in range(nAtoms):
pos = polyData.GetPoint(k)
pos_cen = np.subtract(pos, cenOfMass)
polyData_cen.GetPoints().SetPoint(k, pos_cen)
pos_centered_arr.append(pos_cen)
spoke1 = polyData.GetPointData().GetArray("Spoke1").GetTuple(k)
spoke1 = np.divide(spoke1, np.linalg.norm(spoke1))
spoke2 = polyData.GetPointData().GetArray("Spoke2").GetTuple(k)
spoke2 = np.divide(spoke2, np.linalg.norm(spoke2))
normal1_k = manifolds.sphere(3)
normal2_k = manifolds.sphere(3)
normal1_k.SetPoint(spoke1)
normal2_k.SetPoint(spoke2)
normal1_arr.append(normal1_k)
normal2_arr.append(normal2_k)
rad = polyData.GetPointData().GetArray(
"Radius Function").GetValue(k)
rad_arr.append(rad)
pos_centered_arr_flatten = np.matrix(pos_centered_arr).flatten()
print(pos_centered_arr_flatten.shape)
