def test_multiply_is_associative(self):
R = rotate(45)
S = scale(3, 2)
T = translate(5, -1)
# T*(S*R)
M1 = matrix_multiply(T, matrix_multiply(S, R))
# (T*S)*R
M2 = matrix_multiply(matrix_multiply(T, S), R)
assert M1 == M2
assert M1 == matrix_multiply(T, S, R)
def _get_transform(bounding_box, rotation, _scale):
"""Get the transformation required to go from the user's desired
coordinate space to PDF user space, taking into account rotation,
scaling, translation (for things like weird media boxes).
"""
# Unrotated width and height, in pts
W = bounding_box[2] - bounding_box[0]
H = bounding_box[3] - bounding_box[1]
scale_matrix = scale(*_scale)
x_translate = 0 + min(bounding_box[0], bounding_box[2])
y_translate = 0 + min(bounding_box[1], bounding_box[3])
mb_translate = translate(x_translate, y_translate)
# Because of how rotation works the point isn't rotated around an axis,
# but the axis itself shifts. So we have to represent the rotation as
# rotation + translation.
rotation_matrix = rotate(rotation)
translate_matrix = identity()
if rotation == 90:
translate_matrix = translate(W, 0)
elif rotation == 180:
translate_matrix = translate(W, H)
elif rotation == 270:
translate_matrix = translate(0, H)
# Order matters here - the transformation matrices are applied in
# reverse order. So first we scale to get the points in PDF user space,
# since all other operations are in that space. Then we rotate and
# scale to capture page rotation, then finally we translate to account
# for offset media boxes.
transform = matrix_multiply(
mb_translate,
translate_matrix,
rotation_matrix,
scale_matrix,
)
return transform
def test_invert_rotation(self):
assert rotate(-45) == matrix_inverse(rotate(45))
assert rotate(90) == matrix_inverse(rotate(-90))
assert identity() == matrix_multiply(rotate(45), rotate(-45))
assert identity() == matrix_multiply(rotate(-45), rotate(45))
assert identity() == matrix_multiply(rotate(90), rotate(-90))
assert identity() == matrix_multiply(rotate(-90), rotate(90))
def test_rotations_add(self):
R1 = rotate(90)
R2 = rotate(45)
assert rotate(135) == matrix_multiply(R1, R2)
assert rotate(135) == matrix_multiply(R2, R1)