def matrix44(self) -> Matrix44:
"""Returns a transformation matrix of type :class:`Matrix44` to
transform the block entities into :ref:`WCS`.
"""
dxf = self.dxf
sx = dxf.xscale
sy = dxf.yscale
sz = dxf.zscale
ocs = self.ocs()
extrusion = ocs.uz
ux = Vec3(ocs.to_wcs(X_AXIS))
uy = Vec3(ocs.to_wcs(Y_AXIS))
m = Matrix44.ucs(ux=ux * sx, uy=uy * sy, uz=extrusion * sz)
# same as Matrix44.ucs(ux, uy, extrusion) * Matrix44.scale(sx, sy, sz)
angle = math.radians(dxf.rotation)
if angle:
m *= Matrix44.axis_rotate(extrusion, angle)
insert = ocs.to_wcs(dxf.get("insert", NULLVEC))
block_layout = self.block()
if block_layout is not None:
# transform block base point into WCS without translation
insert -= m.transform_direction(
block_layout.block.dxf.base_point) # type: ignore
# set translation
m.set_row(3, insert.xyz) # type: ignore
return m
def matrix44(self) -> Matrix44:
""" Returns a transformation :class:`Matrix44` object to transform block
entities into WCS.
.. versionadded:: 0.13
"""
dxf = self.dxf
sx = dxf.xscale
sy = dxf.yscale
sz = dxf.zscale
ocs = self.ocs()
extrusion = ocs.uz
ux = Vector(ocs.to_wcs(X_AXIS))
uy = Vector(ocs.to_wcs(Y_AXIS))
m = Matrix44.ucs(ux=ux * sx, uy=uy * sy, uz=extrusion * sz)
angle = math.radians(dxf.rotation)
if angle != 0.0:
m = Matrix44.chain(m, Matrix44.axis_rotate(extrusion, angle))
insert = ocs.to_wcs(dxf.get('insert', Vector()))
block_layout = self.block()
if block_layout is not None:
# transform block base point into WCS without translation
insert -= m.transform_direction(block_layout.block.dxf.base_point)
# set translation
m.set_row(3, insert.xyz)
return m
def __init__(
self,
origin: "Vertex" = (0, 0, 0),
ux: "Vertex" = None,
uy: "Vertex" = None,
uz: "Vertex" = None,
):
if ux is None and uy is None:
_ux: Vec3 = X_AXIS
_uy: Vec3 = Y_AXIS
_uz: Vec3 = Z_AXIS
elif ux is None:
_uy = Vec3(uy).normalize()
_uz = Vec3(uz).normalize()
_ux = Vec3(uy).cross(uz).normalize()
elif uy is None:
_ux = Vec3(ux).normalize()
_uz = Vec3(uz).normalize()
_uy = Vec3(uz).cross(ux).normalize()
elif uz is None:
_ux = Vec3(ux).normalize()
_uy = Vec3(uy).normalize()
_uz = Vec3(ux).cross(uy).normalize()
else: # all axis are given
_ux = Vec3(ux).normalize()
_uy = Vec3(uy).normalize()
_uz = Vec3(uz).normalize()
self.matrix: Matrix44 = Matrix44.ucs(_ux, _uy, _uz, Vec3(origin))
def __init__(self,
origin: 'Vertex' = (0, 0, 0),
ux: 'Vertex' = None,
uy: 'Vertex' = None,
uz: 'Vertex' = None):
if ux is None and uy is None:
ux = X_AXIS
uy = Y_AXIS
uz = Z_AXIS
elif ux is None:
uy = Vec3(uy).normalize()
uz = Vec3(uz).normalize()
ux = Vec3(uy).cross(uz).normalize()
elif uy is None:
ux = Vec3(ux).normalize()
uz = Vec3(uz).normalize()
uy = Vec3(uz).cross(ux).normalize()
elif uz is None:
ux = Vec3(ux).normalize()
uy = Vec3(uy).normalize()
uz = Vec3(ux).cross(uy).normalize()
else: # all axis are given
ux = Vec3(ux).normalize()
uy = Vec3(uy).normalize()
uz = Vec3(uz).normalize()
self.matrix: Matrix44 = Matrix44.ucs(ux, uy, uz, origin)
def test_matrix44_to_ocs():
ocs = OCS(EXTRUSION)
matrix = Matrix44.ucs(ocs.ux, ocs.uy, ocs.uz)
assert is_close_points(
matrix.ocs_from_wcs(Vector(-9.56460754, 8.44764172, 9.97894327)),
(9.41378764657076, 13.15481838975576, 0.8689258932616031),
places=6,
)
def test_matrix44_to_wcs():
ocs = OCS(EXTRUSION)
matrix = Matrix44.ucs(ocs.ux, ocs.uy, ocs.uz)
matrix.transpose()
assert is_close_points(
matrix.transform(
(9.41378764657076, 13.15481838975576, 0.8689258932616031)),
(-9.56460754, 8.44764172, 9.97894327),
places=6,
)
def __init__(self, extrusion: "Vertex" = Z_AXIS):
Az = Vec3(extrusion).normalize()
self.transform = not Az.isclose(Z_AXIS)
if self.transform:
if (abs(Az.x) < _1_OVER_64) and (abs(Az.y) < _1_OVER_64):
Ax = Y_AXIS.cross(Az)
else:
Ax = Z_AXIS.cross(Az)
Ax = Ax.normalize()
Ay = Az.cross(Ax).normalize()
self.matrix = Matrix44.ucs(Ax, Ay, Az)
def test_matrix44_rotation():
# normalization is not necessary
ux = Vec3(1, 2, 0)
# only cartesian coord systems work
uy = ux.rotate_deg(90)
ucs = UCS(ux=ux, uy=uy)
m = Matrix44.ucs(ux=ux.normalize(), uy=uy.normalize())
assert m.ux == ux.normalize()
assert m.uy == uy.normalize()
assert m.uz == (0, 0, 1)
assert m.is_cartesian
v = m.transform((1, 2, 3))
assert v == ucs.to_wcs((1, 2, 3))
assert m.ucs_vertex_from_wcs(v).isclose((1, 2, 3))
def test_arbitrary_ucs():
origin = Vec3(3, 3, 3)
ux = Vec3(1, 2, 0)
def_point_in_xy_plane = Vec3(3, 10, 4)
uz = ux.cross(def_point_in_xy_plane - origin)
ucs = UCS(origin=origin, ux=ux, uz=uz)
m = Matrix44.ucs(ucs.ux, ucs.uy, ucs.uz, ucs.origin)
def_point_in_ucs = ucs.from_wcs(def_point_in_xy_plane)
assert ucs.ux == m.ux
assert ucs.uy == m.uy
assert ucs.uz == m.uz
assert ucs.origin == m.origin
assert def_point_in_ucs == m.ucs_vertex_from_wcs(def_point_in_xy_plane)
assert def_point_in_ucs.z == 0
assert ucs.to_wcs(def_point_in_ucs).isclose(def_point_in_xy_plane)
assert ucs.is_cartesian is True
