Python numpy.cross方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def set_by_3pts(self,origin, pt1, pt2):
        """
        origin: tuple 3
        pt1: tuple 3
        pt2: tuple 3
        """
        self.origin=origin    
        vec1 = np.array([pt1[0] - origin[0] , pt1[1] - origin[1] , pt1[2] - origin[2]])
        vec2 = np.array([pt2[0] - origin[0] , pt2[1] - origin[1] , pt2[2] - origin[2]])
        cos = np.dot(vec1, vec2)/np.linalg.norm(vec1)/np.linalg.norm(vec2)
        if  cos == 1 or cos == -1:
            raise Exception("Three points should not in a line!!")        
        self.x = vec1/np.linalg.norm(vec1)
        z = np.cross(vec1, vec2)
        self.z = z/np.linalg.norm(z)
        self.y = np.cross(self.z, self.x) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def __init__(self,origin, pt1, pt2, name=None):
        """
        origin: 3x1 vector
        pt1: 3x1 vector
        pt2: 3x1 vector
        """
        self.__origin=origin    
        vec1 = np.array([pt1[0] - origin[0] , pt1[1] - origin[1] , pt1[2] - origin[2]])
        vec2 = np.array([pt2[0] - origin[0] , pt2[1] - origin[1] , pt2[2] - origin[2]])
        cos = np.dot(vec1, vec2)/np.linalg.norm(vec1)/np.linalg.norm(vec2)
        if  cos == 1 or cos == -1:
            raise Exception("Three points should not in a line!!")        
        self.__x = vec1/np.linalg.norm(vec1)
        z = np.cross(vec1, vec2)
        self.__z = z/np.linalg.norm(z)
        self.__y = np.cross(self.z, self.x)
        self.__name=uuid.uuid1() if name==None else name 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def vector_angle(u, v, direction=None):
    '''
    vector_angle(u, v) yields the angle between the two vectors u and v. The optional argument 
    direction is by default None, which specifies that the smallest possible angle between the
    vectors be reported; if the vectors u and v are 2D vectors and direction parameters True and
    False specify the clockwise or counter-clockwise directions, respectively; if the vectors are
    3D vectors, then direction may be a 3D point that is not in the plane containing u, v, and the
    origin, and it specifies around which direction (u x v or v x u) the the counter-clockwise angle
    from u to v should be reported (the cross product vector that has a positive dot product with
    the direction argument is used as the rotation axis).
    '''
    if direction is None:
        return np.arccos(vector_angle_cos(u, v))
    elif direction is True:
        return np.arctan2(v[1], v[0]) - np.arctan2(u[1], u[0])
    elif direction is False:
        return np.arctan2(u[1], u[0]) - np.arctan2(v[1], v[0])
    else:
        axis1 = normalize(u)
        axis2 = normalize(np.cross(u, v))
        if np.dot(axis2, direction) < 0:
            axis2 = -axis2
        return np.arctan2(np.dot(axis2, v), np.dot(axis1, v)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def _retinotopic_field_sign_triangles(m, retinotopy):
    t = m.tess if isinstance(m, geo.Mesh) or isinstance(m, geo.Topology) else m
    # get the polar angle and eccen data as a complex number in degrees
    if pimms.is_str(retinotopy):
        (x,y) = as_retinotopy(retinotopy_data(m, retinotopy), 'geographical')
    elif retinotopy is Ellipsis:
        (x,y) = as_retinotopy(retinotopy_data(m, 'any'),      'geographical')
    else:
        (x,y) = as_retinotopy(retinotopy,                     'geographical')
    # Okay, now we want to make some coordinates...
    coords = np.asarray([x, y])
    us = coords[:, t.indexed_faces[1]] - coords[:, t.indexed_faces[0]]
    vs = coords[:, t.indexed_faces[2]] - coords[:, t.indexed_faces[0]]
    (us,vs) = [np.concatenate((xs, np.full((1, t.face_count), 0.0))) for xs in [us,vs]]
    xs = np.cross(us, vs, axis=0)[2]
    xs[np.isclose(xs, 0)] = 0
    return np.sign(xs) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def rotate_camera_to_point_at(up_from, lookat_from, up_to, lookat_to):
  inputs = [up_from, lookat_from, up_to, lookat_to]
  for i in range(4):
    inputs[i] = normalize(np.array(inputs[i]).reshape((-1,)))
  up_from, lookat_from, up_to, lookat_to = inputs
  r1 = r_between(lookat_from, lookat_to)

  new_x = np.dot(r1, np.array([1, 0, 0]).reshape((-1, 1))).reshape((-1))
  to_x = normalize(np.cross(lookat_to, up_to))
  angle = np.arccos(np.dot(new_x, to_x))
  if angle > ANGLE_EPS:
    if angle < np.pi - ANGLE_EPS:
      ax = normalize(np.cross(new_x, to_x))
      flip = np.dot(lookat_to, ax)
      if flip > 0:
        r2 = get_r_matrix(lookat_to, angle)
      elif flip < 0:
        r2 = get_r_matrix(lookat_to, -1. * angle)
    else:
      # Angle of rotation is too close to 180 degrees, direction of rotation
      # does not matter.
      r2 = get_r_matrix(lookat_to, angle)
  else:
    r2 = np.eye(3)
  return np.dot(r2, r1) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def calculate_camera_variables(eye, lookat, up, fov, aspect_ratio, fov_is_vertical=False):
    import numpy as np
    import math

    W = np.array(lookat) - np.array(eye)
    wlen = np.linalg.norm(W)
    U = np.cross(W, np.array(up))
    U /= np.linalg.norm(U)
    V = np.cross(U, W)
    V /= np.linalg.norm(V)

    if fov_is_vertical:
        vlen = wlen * math.tan(0.5 * fov * math.pi / 180.0)
        V *= vlen
        ulen = vlen * aspect_ratio
        U *= ulen
    else:
        ulen = wlen * math.tan(0.5 * fov * math.pi / 180.0)
        U *= ulen
        vlen = ulen * aspect_ratio
        V *= vlen

    return U, V, W 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def update_normals(self):
        v0 = self.vectors[:, 0, :3]
        v1 = self.vectors[:, 1, :3]
        v2 = self.vectors[:, 2, :3]
        _normals = numpy.cross(v1 - v0, v2 - v0)

        for i in range(len(_normals)):
            norm = numpy.linalg.norm(_normals[i])
            if norm != 0:
                _normals[i] /= numpy.linalg.norm(_normals[i])

        self.normals[:] = _normals
        return self

    #####################################################################
    # Analyze functions
    # 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def transform(x_vec, z_vec):
    '''
    Construct a transformation matrix to transform r_vec to the new coordinate system defined by x_vec and z_vec
    '''

    x_vec = x_vec/np.linalg.norm(np.asarray(x_vec))
    z_vec = z_vec/np.linalg.norm(np.asarray(z_vec))
    assert x_vec.dot(z_vec) == 0
    y_vec = np.cross(x_vec,z_vec)
    new = np.asarray([x_vec, y_vec, z_vec])
    original = np.asarray([[1,0,0],[0,1,0],[0,0,1]])

    tran_matrix = np.empty([3,3])
    for row in range(3):
        for col in range(3):
            tran_matrix[row,col] = np.cos(angle(original[row],new[col]))

    return tran_matrix.T 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def __init__(self, **kw):
    """  
      Constructor of affine, equidistant 3d mesh class
      ucell : unit cell vectors (in coordinate space)
      Ecut  : Energy cutoff to parametrize the discretization 
    """
    from scipy.fftpack import next_fast_len
    
    self.ucell = kw['ucell'] if 'ucell' in kw else 30.0*np.eye(3) # Not even unit cells vectors are required by default
    self.Ecut = Ecut = kw['Ecut'] if 'Ecut' in kw else 50.0 # 50.0 Hartree by default
    luc = np.sqrt(np.einsum('ix,ix->i', self.ucell, self.ucell))
    self.shape = nn = np.array([next_fast_len( int(np.rint(l * np.sqrt(Ecut)/2))) for l in luc], dtype=int)
    self.size  = np.prod(self.shape)
    gc = self.ucell/(nn) # This is probable the best for finite systems, for PBC use nn, not (nn-1)
    self.dv = np.abs(np.dot(gc[0], np.cross(gc[1], gc[2] )))
    rr = [np.array([gc[i]*j for j in range(nn[i])]) for i in range(3)]
    self.rr = rr
    self.origin = kw['origin'] if 'origin' in kw else np.zeros(3) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def slice_normal(self):
        #The std_slice_normal comes from the cross product of the directions 
        #in the ImageOrientationPatient
        std_slice_normal = super(SiemensWrapper, self).slice_normal
        csa_slice_normal = csar.get_slice_normal(self.csa_header)
        if std_slice_normal is None and csa_slice_normal is None:
            return None
        elif std_slice_normal is None:
            return np.array(csa_slice_normal)
        elif csa_slice_normal is None:
            return std_slice_normal
        else:
            #Make sure the two normals are very close to parallel unit vectors
            dot_prod = np.dot(csa_slice_normal, std_slice_normal)
            assert np.allclose(np.fabs(dot_prod), 1.0, atol=1e-5)
            #Use the slice normal computed with the cross product as it will 
            #always be the most orthogonal, but take the sign from the CSA
            #slice normal
            if dot_prod < 0:
                return -std_slice_normal
            else:
                return std_slice_normal 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def _calculate_dadt_ccd(msh, ccd_file, coil_matrix, didt, geo_fn):
    """ auxiliary function to calculate the dA/dt field from a ccd file """
    # read ccd file
    d_position, d_moment = read_ccd(ccd_file)
    # transfrom positions to mm
    d_position *= 1e3
    # add a column to the position in order to apply the transformation matrix
    d_position = np.hstack([d_position, np.ones((d_position.shape[0], 1))])
    d_position = coil_matrix.dot(d_position.T).T[:, :3]
    # rotate the moment
    d_moment = coil_matrix[:3, :3].dot(d_moment.T).T
    A = np.zeros((msh.nodes.nr, 3), dtype=float)
    for p, m in zip(d_position, d_moment):
        # get distance of point to dipole, transform back to meters
        r = (msh.nodes.node_coord - p) * 1e-3
        A += 1e-7 * didt * np.cross(m, r) / (np.linalg.norm(r, axis=1)[:, None] ** 3)
    node_data = mesh_io.NodeData(A)

    if geo_fn is not None:
        mesh_io.write_geo_spheres(d_position, geo_fn,
                               np.linalg.norm(d_moment, axis=1),
                               'coil_dipoles')

    return node_data 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def tms_sphere(sphere3_msh):
    m = sphere3_msh.crop_mesh(elm_type=4)
    dipole_pos = np.array([0., 0., 300])
    dipole_moment = np.array([1., 0., 0.])
    didt = 1e6
    r = (m.nodes.node_coord - dipole_pos) * 1e-3
    dAdt = 1e-7 * didt * np.cross(dipole_moment, r) / (np.linalg.norm(r, axis=1)[:, None] ** 3)
    dAdt = mesh_io.NodeData(dAdt, mesh=m)
    dAdt.field_name = 'dAdt'
    dAdt.mesh = m
    pos = m.elements_baricenters().value
    E_analytical = analytical_solutions.tms_E_field(dipole_pos * 1e-3,
                                                    dipole_moment, didt,
                                                    pos * 1e-3)
    cond = mesh_io.ElementData(np.ones(m.elm.nr))
    cond.mesh = m
    return m, cond, dAdt, E_analytical 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def camera_info(param):
    theta = np.deg2rad(param[0])
    phi = np.deg2rad(param[1])

    camY = param[3] * np.sin(phi)
    temp = param[3] * np.cos(phi)
    camX = temp * np.cos(theta)    
    camZ = temp * np.sin(theta)        
    cam_pos = np.array([camX, camY, camZ])        

    axisZ = cam_pos.copy()
    axisY = np.array([0, 1, 0], dtype=np.float32)
    axisX = np.cross(axisY, axisZ)
    axisY = np.cross(axisZ, axisX)
    
    # cam_mat = np.array([axisX, axisY, axisZ])
    cam_mat = np.array([unit(axisX), unit(axisY), unit(axisZ)])
    
    return cam_mat, cam_pos


##################################################### 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def shear_matrix(angle, direction, point, normal):
    """Return matrix to shear by angle along direction vector on shear plane.
    The shear plane is defined by a point and normal vector. The direction
    vector must be orthogonal to the plane's normal vector.
    A point P is transformed by the shear matrix into P" such that
    the vector P-P" is parallel to the direction vector and its extent is
    given by the angle of P-P'-P", where P' is the orthogonal projection
    of P onto the shear plane.
    >>> angle = (random.random() - 0.5) * 4*math.pi
    >>> direct = numpy.random.random(3) - 0.5
    >>> point = numpy.random.random(3) - 0.5
    >>> normal = numpy.cross(direct, numpy.random.random(3))
    >>> S = shear_matrix(angle, direct, point, normal)
    >>> numpy.allclose(1.0, numpy.linalg.det(S))
    True
    """
    normal = unit_vector(normal[:3])
    direction = unit_vector(direction[:3])
    if abs(numpy.dot(normal, direction)) > 1e-6:
        raise ValueError("direction and normal vectors are not orthogonal")
    angle = math.tan(angle)
    M = numpy.identity(4)
    M[:3, :3] += angle * numpy.outer(direction, normal)
    M[:3, 3] = -angle * numpy.dot(point[:3], normal) * direction
    return M 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import cross [as 別名]
def mesh_adjust_winding_order(verts, faces, normals):
  n0 = normals[faces[:,0]]
  n1 = normals[faces[:,1]]
  n2 = normals[faces[:,2]]
  fnormals = (n0 + n1 + n2) / 3

  v0 = verts[faces[:,0]]
  v1 = verts[faces[:,1]]
  v2 = verts[faces[:,2]]

  e0 = v1 - v0
  e1 = v2 - v0
  fn = np.cross(e0, e1)

  dot = np.sum(fnormals * fn, axis=1)
  ma = dot < 0

  nfaces = faces.copy()
  nfaces[ma,1], nfaces[ma,2] = nfaces[ma,2], nfaces[ma,1]

  return nfaces