def make_hcs_2d_scaled(a, b):
"""build a 2D homogeneus coordiate system from two vectors, but scale with distance between input point"""
u = b - a
if tol_eq(norm(u), 0.0): # 2006/6/30
return None
#else:
# u = u / norm(u)
v = vector([-u[1], u[0]])
hcs = matrix_factory([[u[0], v[0], a[0]], [u[1], v[1], a[1]],
[0.0, 0.0, 1.0]])
return hcs
def make_hcs_2d(a, b):
"""build a 2D homogeneus coordiate system from two vectors"""
u = b - a
if tol_eq(norm(u), 0.0): # 2006/6/30
return None
else:
u = u / norm(u)
v = vector([-u[1], u[0]])
hcs = matrix_factory([[u[0], v[0], a[0]], [u[1], v[1], a[1]],
[0.0, 0.0, 1.0]])
return hcs
def make_hcs_3d(a, b, c):
"""build a 3D homogeneus coordiate system from three vectors"""
u = b - a
u = u / norm(u)
v = c - a
v = v / norm(v)
w = cross(u, v)
v = cross(w, u)
hcs = matrix_factory([[u[0], v[0], w[0], a[0]], [u[1], v[1], w[1], a[1]],
[u[2], v[2], w[2], a[2]], [0.0, 0.0, 0.0, 1.0]])
return hcs
def make_hcs_3d_scaled(a, b, c):
"""build a 3D homogeneus coordiate system from three vectors"""
# create orthnormal basis
u = b - a
u = u / norm(u)
v = c - a
v = v / norm(v)
w = cross(u, v)
v = cross(w, u)
# scale
u = u / norm(u) / norm(b - a)
v = v / norm(v) / norm(c - a)
hcs = matrix_factory([[u[0], v[0], w[0], a[0]], [u[1], v[1], w[1], a[1]],
[u[2], v[2], w[2], a[2]], [0.0, 0.0, 0.0, 1.0]])
return hcs
def uniform_scale_3D(scale):
mat = matrix_factory([[scale, 0.0, 0.0, 0.0], [0.0, scale, 0.0, 0.0],
[0.0, 0.0, scale, 0.0], [0.0, 0.0, 0.0, 1.0]])
return mat
def scale_3D(sx, sy, sz):
mat = matrix_factory([[sx, 0.0, 0.0, 0.0], [0.0, sy, 0.0, 0.0],
[0.0, 0.0, sz, 0.0], [0.0, 0.0, 0.0, 1.0]])
return mat
def translate_3D(dx, dy, dz):
mat = matrix_factory([[1.0, 0.0, 0.0, dx], [0.0, 1.0, 0.0, dy],
[0.0, 0.0, 1.0, dz], [0.0, 0.0, 0.0, 1.0]])
return mat
def rotate_2D(angle):
mat = matrix_factory([[math.sin[angle], math.cos[angle], 0.0],
[math.cos[angle], -math.sin[angle], 0.0],
[0.0, 0.0, 1.0]])
return mat