def my_arc(self, gc, fill, j, X, r, n, A, d):
if self.images.shapes is not None:
rx = (self.images.shapes[j, 0]).round().astype(int)
ry = (self.images.shapes[j, 1]).round().astype(int)
rz = (self.images.shapes[j, 2]).round().astype(int)
circle = rx == ry and ry == rz
if not circle:
Q = Quaternion(self.images.Q[self.frame][j])
X2d = np.array([X[j][0], X[j][1]])
Ellipsoid = np.array([[1. / (rx * rx), 0, 0],
[0, 1. / (ry * ry), 0],
[0, 0, 1. / (rz * rz)]])
# Ellipsoid rotated by quaternion as Matrix X' = R X R_transpose
El_r = np.dot(
Q.rotation_matrix(),
np.dot(Ellipsoid, np.transpose(Q.rotation_matrix())))
# Ellipsoid rotated by quaternion and axes as
# Matrix X' = R_axes X' R_axes
El_v = np.dot(np.transpose(self.axes), np.dot(El_r, self.axes))
# Projection of rotated ellipsoid on xy plane
El_p = Ell = np.array(
[[
El_v[0][0] - El_v[0][2] * El_v[0][2] / El_v[2][2],
El_v[0][1] - El_v[0][2] * El_v[1][2] / El_v[2][2]
],
[
El_v[0][1] - El_v[0][2] * El_v[1][2] / El_v[2][2],
El_v[1][1] - El_v[1][2] * El_v[1][2] / El_v[2][2]
]])
# diagonal matrix der Ellipse gibt halbachsen
El_p_diag = np.linalg.eig(El_p)
# Winkel mit dem Ellipse in xy gedreht ist aus
# eigenvektor der diagonal matrix
phi = atan(El_p_diag[1][0][1] / El_p_diag[1][0][0])
tupl = []
alpha = np.array(range(16)) * 2 * np.pi / 16
El_xy = np.array([
sqrt(1. /
(El_p_diag[0][0])) * np.cos(alpha) * np.cos(phi) -
sqrt(1. / (El_p_diag[0][1])) * np.sin(alpha) * np.sin(phi),
sqrt(1. /
(El_p_diag[0][0])) * np.cos(alpha) * np.sin(phi) +
sqrt(1. / (El_p_diag[0][1])) * np.sin(alpha) * np.cos(phi)
])
tupl = (El_xy.transpose() * self.scale +
X[j][:2]).round().astype(int)
# XXX there must be a better way
tupl = [tuple(i) for i in tupl]
return self.pixmap.draw_polygon(gc, fill, tupl)
else:
return self.pixmap.draw_arc(gc, fill, A[j, 0], A[j, 1], d[j],
d[j], 0, 23040)
else:
return self.pixmap.draw_arc(gc, fill, A[j, 0], A[j, 1], d[j], d[j],
0, 23040)
def my_arc(self, gc, fill, j, X, r, n, A, d):
if self.images.shapes is not None:
rx = (self.images.shapes[j, 0]).round().astype(int)
ry = (self.images.shapes[j, 1]).round().astype(int)
rz = (self.images.shapes[j, 2]).round().astype(int)
circle = rx == ry and ry == rz
if not circle:
Q = Quaternion(self.images.Q[self.frame][j])
X2d = np.array([X[j][0], X[j][1]])
Ellipsoid = np.array([[1. / (rx*rx), 0, 0],
[0, 1. / (ry*ry), 0],
[0, 0, 1. / (rz*rz)]
])
# Ellipsoid rotated by quaternion as Matrix X' = R X R_transpose
El_r = np.dot(Q.rotation_matrix(),
np.dot(Ellipsoid,
np.transpose(Q.rotation_matrix())))
# Ellipsoid rotated by quaternion and axes as
# Matrix X' = R_axes X' R_axes
El_v = np.dot(np.transpose(self.axes), np.dot(El_r, self.axes))
# Projection of rotated ellipsoid on xy plane
El_p = Ell = np.array([
[El_v[0][0] - El_v[0][2] * El_v[0][2] / El_v[2][2],
El_v[0][1] - El_v[0][2] * El_v[1][2] / El_v[2][2]],
[El_v[0][1] - El_v[0][2] * El_v[1][2] / El_v[2][2],
El_v[1][1] - El_v[1][2] * El_v[1][2] / El_v[2][2]]
])
# diagonal matrix der Ellipse gibt halbachsen
El_p_diag = np.linalg.eig(El_p)
# Winkel mit dem Ellipse in xy gedreht ist aus
# eigenvektor der diagonal matrix
phi = atan(El_p_diag[1][0][1] / El_p_diag[1][0][0])
tupl = []
alpha = np.array(range(16)) * 2 * np.pi / 16
El_xy = np.array([sqrt(1. / (El_p_diag[0][0])) *
np.cos(alpha)*np.cos(phi)
- sqrt(1./(El_p_diag[0][1])) *
np.sin(alpha) * np.sin(phi),
sqrt(1./(El_p_diag[0][0])) *
np.cos(alpha)*np.sin(phi)
+ sqrt(1./(El_p_diag[0][1])) *
np.sin(alpha) * np.cos(phi)])
tupl = (El_xy.transpose() * self.scale +
X[j][:2]).round().astype(int)
# XXX there must be a better way
tupl = [tuple(i) for i in tupl]
return self.pixmap.draw_polygon( gc, fill, tupl)
else:
return self.pixmap.draw_arc(gc, fill, A[j, 0], A[j, 1], d[j],
d[j], 0, 23040)
else:
return self.pixmap.draw_arc(gc, fill, A[j, 0], A[j, 1], d[j], d[j],
0, 23040)
def rotation(axis, angle):
"""
Generate the rotation matrix
given the rotation axis and angle
"""
norm = n.linalg.norm(axis)
tol = 2 * n.finfo(n.float).eps
q = [n.cos(angle / 2)]
for a in axis:
q.append(n.sin(angle / 2.0) * a / norm)
q = Quaternion(q)
matrix = q.rotation_matrix()
matrix[abs(matrix) < tol] = 0.0
return matrix