def get_ctm(x1, y1, x2, y2):
"""Get the scaled and translated CTM for an image to be placed in the
bounding box defined by [x1, y1, x2, y2].
"""
return matrix_multiply(
translate(x1, y1),
scale(x2 - x1, y2 - y1),
)
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_scale(self):
assert scale(2, 4) == matrix_inverse(scale(0.5, 0.25))
assert scale(0.1, 8) == matrix_inverse(scale(10, 0.125))
assert identity() == matrix_multiply(scale(2, 4), scale(0.5, 0.25))
assert identity() == matrix_multiply(scale(0.1, 8), scale(10, 0.125))
def test_scales_multiply(self):
S1 = scale(2, 3)
S2 = scale(5, 2)
assert scale(10, 6) == matrix_multiply(S1, S2)
assert scale(10, 6) == matrix_multiply(S2, S1)