def from_axis_angle(axis, angle, is_normalized=False):
# adapted from
# https://github.com/matthew-brett/transforms3d/blob/master/transforms3d/quaternions.py
axis = Vector(axis) if not isinstance(axis, Vector) else axis
if not is_normalized:
axis.normalize()
x, y, z = axis
c = math.cos(angle)
s = math.sin(angle)
C = 1 - c
xs = x * s
ys = y * s
zs = z * s
xC = x * C
yC = y * C
zC = z * C
xyC = x * yC
yzC = y * zC
zxC = z * xC
return Orientation(np.array([
[x * xC + c, xyC - zs, zxC + ys],
[xyC + zs, y * yC + c, yzC - xs],
[zxC - ys, yzC + xs, z * zC + c],
]))
def from_yz(y_vec, z_vec):
"""
Generate a new Orientation from two vectors using y as reference
"""
if not isinstance(y_vec, Vector):
y_vec = Vector(y_vec)
if not isinstance(z_vec, Vector):
z_vec = Vector(z_vec)
y_vec.normalize()
z_vec.normalize()
orient = Orientation()
orient.data[:, 1] = y_vec.data
orient.data[:, 0] = y_vec.cross(z_vec).normalized().data
orient.data[:, 2] = Vector(np.cross(orient.data[:, 0], y_vec.data)).normalized().data
return orient
def from_xy(x_vec, y_vec):
"""
Generate a new Orientation from two vectors using x as reference
"""
if not isinstance(x_vec, Vector):
x_vec = Vector(x_vec)
if not isinstance(y_vec, Vector):
y_vec = Vector(y_vec)
x_vec.normalize()
y_vec.normalize()
orient = Orientation()
orient.data[:, 0] = x_vec.data
orient.data[:, 2] = x_vec.cross(y_vec).normalized().data
orient.data[:, 1] = Vector(np.cross(orient.data[:, 2], x_vec.data)).normalized().data
return orient
def from_xz(x_vec, z_vec):
"""
Generate a new Orientation from two vectors using x as reference
"""
if not isinstance(x_vec, Vector):
x_vec = Vector(x_vec)
if not isinstance(z_vec, Vector):
z_vec = Vector(z_vec)
x_vec.normalize()
z_vec.normalize()
orient = Orientation()
orient._data[:, 0] = x_vec.data
orient._data[:, 1] = z_vec.cross(x_vec).data
orient._data[:, 2] = np.cross(x_vec.data, orient._data[:, 1])
return orient
def from_xz(x_vec, z_vec, ref='x'):
"""
Generate a new Orientation from two vectors using x as reference
"""
if not isinstance(x_vec, Vector):
x_vec = Vector(x_vec)
if not isinstance(z_vec, Vector):
z_vec = Vector(z_vec)
x_vec.normalize()
z_vec.normalize()
orient = Orientation()
orient.data[:, 1] = z_vec.cross(x_vec).normalized().data
if ref == 'x':
orient.data[:, 0] = x_vec.data
orient.data[:, 2] = Vector(np.cross(x_vec.data, orient.data[:, 1])).normalized().data
elif ref == 'z':
orient.data[:, 2] = z_vec.data
orient.data[:, 0] = Vector(np.cross(orient.data[:, 1], z_vec.data)).normalized().data
else:
raise ValueError('Value of ref can only be x or z')
return orient