def transform_extrusion(extrusion: 'Vertex', m: Matrix44) -> Tuple[Vec3, bool]:
"""
Transforms the old `extrusion` vector into a new extrusion vector. Returns the new extrusion vector and a
boolean value: ``True`` if the new OCS established by the new extrusion vector has a uniform scaled xy-plane,
else ``False``.
The new extrusion vector is perpendicular to plane defined by the transformed x- and y-axis.
Args:
extrusion: extrusion vector of the old OCS
m: transformation matrix
Returns:
"""
ocs = OCS(extrusion)
ocs_x_axis_in_wcs = ocs.to_wcs(X_AXIS)
ocs_y_axis_in_wcs = ocs.to_wcs(Y_AXIS)
x_axis, y_axis = m.transform_directions(
(ocs_x_axis_in_wcs, ocs_y_axis_in_wcs))
# Not sure if this is the correct test for a uniform scaled xy-plane
is_uniform = math.isclose(x_axis.magnitude_square,
y_axis.magnitude_square,
abs_tol=1e-9)
new_extrusion = x_axis.cross(y_axis).normalize()
return new_extrusion, is_uniform
def transform(self, m: Matrix44) -> None:
""" Transform ellipse in place by transformation matrix `m`. """
new_center = m.transform(self.center)
# 2021-01-28 removed % math.tau
old_start_param = start_param = self.start_param
old_end_param = end_param = self.end_param
old_minor_axis = minor_axis(self.major_axis, self.extrusion,
self.ratio)
new_major_axis, new_minor_axis = m.transform_directions(
(self.major_axis, old_minor_axis))
# Original ellipse parameters stay untouched until end of transformation
dot_product = new_major_axis.normalize().dot(
new_minor_axis.normalize())
if abs(dot_product) > 1e-6:
new_major_axis, new_minor_axis, new_ratio = rytz_axis_construction(
new_major_axis, new_minor_axis)
new_extrusion = new_major_axis.cross(new_minor_axis).normalize()
adjust_params = True
else:
# New axis are nearly orthogonal:
new_ratio = new_minor_axis.magnitude / new_major_axis.magnitude
# New normal vector:
new_extrusion = new_major_axis.cross(new_minor_axis).normalize()
# Calculate exact minor axis:
new_minor_axis = minor_axis(new_major_axis, new_extrusion,
new_ratio)
adjust_params = False
if adjust_params and not math.isclose(
start_param, end_param, abs_tol=1e-9):
# open ellipse, adjusting start- and end parameter
x_axis = new_major_axis.normalize()
y_axis = new_minor_axis.normalize()
# TODO: use ellipse_param_span()?
# 2021-01-28 this is possibly the source of errors!
old_param_span = (end_param - start_param) % math.tau
def param(vec: 'Vec3') -> float:
dy = y_axis.dot(vec) / new_ratio # adjust to circle
dx = x_axis.dot(vec)
return math.atan2(dy, dx) % math.tau
# transformed start- and end point of old ellipse
start_point = m.transform(
vertex(start_param, self.major_axis, old_minor_axis,
self.center, self.ratio))
end_point = m.transform(
vertex(end_param, self.major_axis, old_minor_axis, self.center,
self.ratio))
start_param = param(start_point - new_center)
end_param = param(end_point - new_center)
# Test if drawing the correct side of the curve
if not math.isclose(old_param_span, math.pi, abs_tol=1e-9):
# Equal param span check works well, except for a span of exact
# pi (180 deg).
# TODO: use ellipse_param_span()?
# 2021-01-28 this is possibly the source of errors!
new_param_span = (end_param - start_param) % math.tau
if not math.isclose(
old_param_span, new_param_span, abs_tol=1e-9):
start_param, end_param = end_param, start_param
else: # param span is exact pi (180 deg)
# expensive but it seem to work:
old_chk_point = m.transform(
vertex(
mid_param(old_start_param, old_end_param),
self.major_axis,
old_minor_axis,
self.center,
self.ratio,
))
new_chk_point = vertex(
mid_param(start_param, end_param),
new_major_axis,
new_minor_axis,
new_center,
new_ratio,
)
if not old_chk_point.isclose(new_chk_point, abs_tol=1e-9):
start_param, end_param = end_param, start_param
if new_ratio > 1:
new_major_axis = minor_axis(new_major_axis, new_extrusion,
new_ratio)
new_ratio = 1.0 / new_ratio
new_minor_axis = minor_axis(new_major_axis, new_extrusion,
new_ratio)
if not (math.isclose(start_param, 0)
and math.isclose(end_param, math.tau)):
start_param -= pi2
end_param -= pi2
# TODO: remove normalize start- and end params?
# 2021-01-28 this is possibly the source of errors!
start_param = start_param % math.tau
end_param = end_param % math.tau
if math.isclose(start_param, end_param):
start_param = 0.0
end_param = math.tau
self.center = new_center
self.major_axis = new_major_axis
self.minor_axis = new_minor_axis
self.extrusion = new_extrusion
self.ratio = new_ratio
self.start_param = start_param
self.end_param = end_param
