def setup(self):
if hasattr(self, "has_already_setup"):
return
self.has_already_setup = True
self.background_mobjects = []
self.foreground_mobjects = []
self.transformable_mobjects = []
self.moving_vectors = []
self.transformable_labels = []
self.moving_mobjects = []
self.t_matrix = np.array(self.t_matrix)
self.background_plane = ThreeDAxes()
if self.show_coordinates:
self.background_plane.add_3d_pieces()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = ThreeDAxes()
self.add_transformable_mobject(self.plane)
if self.show_basis_vectors:
self.basis_vectors = self.get_basis_vectors(
i_hat_color=self.i_hat_color,
j_hat_color=self.j_hat_color,
k_hat_color=self.k_hat_color,
)
self.moving_vectors += list(self.basis_vectors)
self.i_hat, self.j_hat, self.k_hat = self.basis_vectors
self.add(self.basis_vectors)
self.set_camera_orientation(
**self.default_angled_camera_orientation_kwargs)
def get_axes(self):
"""
Returns a set of 3D Axes.
Returns
-------
ThreeDAxes object
"""
axes = ThreeDAxes(**self.three_d_axes_config)
for axis in axes:
if self.cut_axes_at_radius:
p0 = axis.get_start()
p1 = axis.number_to_point(-1)
p2 = axis.number_to_point(1)
p3 = axis.get_end()
new_pieces = VGroup(
Line(p0, p1),
Line(p1, p2),
Line(p2, p3),
)
for piece in new_pieces:
piece.shade_in_3d = True
new_pieces.match_style(axis.pieces)
axis.pieces.submobjects = new_pieces.submobjects
for tick in axis.tick_marks:
tick.add(VectorizedPoint(1.5 * tick.get_center(), ))
return axes
def construct(self):
axes = ThreeDAxes()
circle = Circle()
self.set_camera_orientation(phi=0 * DEGREES)
self.play(ShowCreation(circle), ShowCreation(axes))
self.wait()
class LinearTransformationScene3D(ThreeDScene, LinearTransformationScene):
"""
This a 3D scene, and it contains special methods that make
it especially suitable for showing Linear Transformations.
"""
CONFIG = {
"camera_class": ThreeDCamera,
"ambient_camera_rotation": None,
"default_angled_camera_orientation_kwargs": {
"phi": 70 * DEGREES,
"theta": -135 * DEGREES,
},
"include_background_plane": True,
"include_foreground_plane": True,
"foreground_plane_kwargs": {
"x_max": FRAME_WIDTH / 2,
"x_min": -FRAME_WIDTH / 2,
"y_max": FRAME_WIDTH / 2,
"y_min": -FRAME_WIDTH / 2,
"faded_line_ratio": 0
},
"background_plane_kwargs": {
"color": GREY,
"axis_config": {
"stroke_color": LIGHT_GREY,
},
"axis_config": {
"color": GREY,
},
"background_line_style": {
"stroke_color": GREY,
"stroke_width": 1,
},
},
"show_coordinates": False,
"show_basis_vectors": False,
"basis_vector_stroke_width": 6,
"i_hat_color": X_COLOR,
"j_hat_color": Y_COLOR,
"k_hat_color": Z_COLOR,
"leave_ghost_vectors": False,
"t_matrix": [[1, 0, 0], [0, 1, 0], [0, 0, 1]],
}
def setup(self):
if hasattr(self, "has_already_setup"):
return
self.has_already_setup = True
self.background_mobjects = []
self.foreground_mobjects = []
self.transformable_mobjects = []
self.moving_vectors = []
self.transformable_labels = []
self.moving_mobjects = []
self.t_matrix = np.array(self.t_matrix)
self.background_plane = ThreeDAxes()
if self.show_coordinates:
self.background_plane.add_3d_pieces()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = ThreeDAxes()
self.add_transformable_mobject(self.plane)
if self.show_basis_vectors:
self.basis_vectors = self.get_basis_vectors(
i_hat_color=self.i_hat_color,
j_hat_color=self.j_hat_color,
k_hat_color=self.k_hat_color,
)
self.moving_vectors += list(self.basis_vectors)
self.i_hat, self.j_hat, self.k_hat = self.basis_vectors
self.add(self.basis_vectors)
self.set_camera_orientation(
**self.default_angled_camera_orientation_kwargs)
def get_basis_vectors(self,
i_hat_color=X_COLOR,
j_hat_color=Y_COLOR,
k_hat_color=Z_COLOR):
"""
Returns a VGroup of the Basis Vectors (1,0,0)、(0,1,0) and (0,0,1)
Parameters
----------
i_hat_color (str)
The hex colour to use for the basis vector in the x direction
j_hat_color (str)
The hex colour to use for the basis vector in the z direction
k_hat_color (str)
The hex colour to use for the basis vector in the y direction
Returns
-------
VGroup
VGroup of the Vector Mobjects representing the basis vectors.
"""
return VGroup(*[
Vector(
vect, color=color, stroke_width=self.basis_vector_stroke_width)
for vect, color in [
([1, 0, 0], i_hat_color),
([0, 1, 0], j_hat_color),
([0, 0, 1], k_hat_color),
]
])
def get_transposed_matrix_transformation(self, transposed_matrix):
"""
Returns a function corresponding to the linear
transformation represented by the transposed
matrix passed.
Parameters
----------
matrix (np.ndarray, list, tuple)
The matrix.
"""
transposed_matrix = np.array(transposed_matrix)
return lambda point: np.dot(point, transposed_matrix)
