def setup(self):
if hasattr(self, "has_already_setup"):
return
self.has_already_setup = True
##^This is to not break all the old Scenes
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 = NumberPlane(**self.background_plane_kwargs)
if self.show_coordinates:
self.background_plane.add_coordinates()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs)
self.add_transformable_mobject(self.plane)
if self.show_basis_vectors:
self.i_hat, self.j_hat = [
self.add_vector(coords, color, animate=False, stroke_width=6)
for coords, color in [
((1, 0), self.i_hat_color),
((0, 1), self.j_hat_color),
]
]
def setup(self):
# The has_already_setup attr is to not break all the old Scenes
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 = NumberPlane(
**self.background_plane_kwargs
)
if self.show_coordinates:
self.background_plane.add_coordinates()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs)
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,
)
self.moving_vectors += list(self.basis_vectors)
self.i_hat, self.j_hat = self.basis_vectors
self.add(self.basis_vectors)
def add_plane(self, animate=False, **kwargs):
plane = NumberPlane(**kwargs)
if animate:
self.play(ShowCreation(plane, submobject_mode="lagged_start"))
self.add(plane)
return plane
class LinearTransformationScene(VectorScene):
CONFIG = {
"include_background_plane": True,
"include_foreground_plane": True,
"foreground_plane_kwargs": {
"x_radius": FRAME_WIDTH,
"y_radius": FRAME_HEIGHT,
"secondary_line_ratio": 0
},
"background_plane_kwargs": {
"color": GREY,
"secondary_color": DARK_GREY,
"axes_color": GREY,
"stroke_width": 2,
},
"show_coordinates": False,
"show_basis_vectors": True,
"i_hat_color": X_COLOR,
"j_hat_color": Y_COLOR,
"leave_ghost_vectors": False,
"t_matrix": [[3, 0], [1, 2]],
}
def setup(self):
if hasattr(self, "has_already_setup"):
return
self.has_already_setup = True
##^This is to not break all the old Scenes
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 = NumberPlane(**self.background_plane_kwargs)
if self.show_coordinates:
self.background_plane.add_coordinates()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs)
self.add_transformable_mobject(self.plane)
if self.show_basis_vectors:
self.i_hat, self.j_hat = [
self.add_vector(coords, color, animate=False, stroke_width=6)
for coords, color in [
((1, 0), self.i_hat_color),
((0, 1), self.j_hat_color),
]
]
def add_special_mobjects(self, mob_list, *mobs_to_add):
for mobject in mobs_to_add:
if mobject not in mob_list:
mob_list.append(mobject)
self.add(mobject)
def add_background_mobject(self, *mobjects):
self.add_special_mobjects(self.background_mobjects, *mobjects)
def add_foreground_mobject(self, *mobjects):
self.add_special_mobjects(self.foreground_mobjects, *mobjects)
def add_transformable_mobject(self, *mobjects):
self.add_special_mobjects(self.transformable_mobjects, *mobjects)
def add_moving_mobject(self, mobject, target_mobject=None):
mobject.target = target_mobject
self.add_special_mobjects(self.moving_mobjects, mobject)
def add_unit_square(self, color=YELLOW, opacity=0.3, animate=False):
square = Square(color=color, side_length=1)
square.shift(-square.get_corner(DOWN + LEFT))
if animate:
added_anims = map(Animation, self.moving_vectors)
self.play(ShowCreation(square), *added_anims)
self.play(square.set_fill, color, opacity, *added_anims)
else:
square.set_fill(color, opacity)
self.add_transformable_mobject(square)
self.bring_to_front(*self.moving_vectors)
self.square = square
return self
def add_vector(self, vector, color=YELLOW, **kwargs):
vector = VectorScene.add_vector(self, vector, color=color, **kwargs)
self.moving_vectors.append(vector)
return vector
def write_vector_coordinates(self, vector, **kwargs):
coords = VectorScene.write_vector_coordinates(self, vector, **kwargs)
self.add_foreground_mobject(coords)
return coords
def add_transformable_label(self, vector, label, new_label=None, **kwargs):
label_mob = self.label_vector(vector, label, **kwargs)
if new_label:
label_mob.target_text = new_label
else:
label_mob.target_text = "L(%s)" % label_mob.get_tex_string()
label_mob.vector = vector
label_mob.kwargs = kwargs
if "animate" in label_mob.kwargs:
label_mob.kwargs.pop("animate")
self.transformable_labels.append(label_mob)
return label_mob
def add_title(self, title, scale_factor=1.5, animate=False):
if not isinstance(title, Mobject):
title = TextMobject(title).scale(scale_factor)
title.to_edge(UP)
title.add_background_rectangle()
if animate:
self.play(Write(title))
self.add_foreground_mobject(title)
self.title = title
return self
def get_matrix_transformation(self, transposed_matrix):
transposed_matrix = np.array(transposed_matrix)
if transposed_matrix.shape == (2, 2):
new_matrix = np.identity(3)
new_matrix[:2, :2] = transposed_matrix
transposed_matrix = new_matrix
elif transposed_matrix.shape != (3, 3):
raise "Matrix has bad dimensions"
return lambda point: np.dot(point, transposed_matrix)
def get_piece_movement(self, pieces):
start = VMobject(*pieces)
target = VMobject(*[mob.target for mob in pieces])
if self.leave_ghost_vectors:
self.add(start.copy().fade(0.7))
return Transform(start, target, submobject_mode="all_at_once")
def get_moving_mobject_movement(self, func):
for m in self.moving_mobjects:
if m.target is None:
m.target = m.copy()
target_point = func(m.get_center())
m.target.move_to(target_point)
return self.get_piece_movement(self.moving_mobjects)
def get_vector_movement(self, func):
for v in self.moving_vectors:
v.target = Vector(func(v.get_end()), color=v.get_color())
norm = np.linalg.norm(v.target.get_end())
if norm < 0.1:
v.target.get_tip().scale_in_place(norm)
return self.get_piece_movement(self.moving_vectors)
def get_transformable_label_movement(self):
for l in self.transformable_labels:
l.target = self.get_vector_label(l.vector.target, l.target_text,
**l.kwargs)
return self.get_piece_movement(self.transformable_labels)
def apply_transposed_matrix(self, transposed_matrix, **kwargs):
func = self.get_matrix_transformation(transposed_matrix)
if "path_arc" not in kwargs:
net_rotation = np.mean([
angle_of_vector(func(RIGHT)),
angle_of_vector(func(UP)) - np.pi / 2
])
kwargs["path_arc"] = net_rotation
self.apply_function(func, **kwargs)
def apply_inverse_transpose(self, t_matrix, **kwargs):
t_inv = np.linalg.inv(np.array(t_matrix).T).T
self.apply_transposed_matrix(t_inv, **kwargs)
def apply_nonlinear_transformation(self, function, **kwargs):
self.plane.prepare_for_nonlinear_transform()
self.apply_function(function, **kwargs)
def apply_function(self, function, added_anims=[], **kwargs):
if "run_time" not in kwargs:
kwargs["run_time"] = 3
anims = [
ApplyPointwiseFunction(function, t_mob)
for t_mob in self.transformable_mobjects
] + [
self.get_vector_movement(function),
self.get_transformable_label_movement(),
self.get_moving_mobject_movement(function),
] + [Animation(f_mob)
for f_mob in self.foreground_mobjects] + added_anims
self.play(*anims, **kwargs)
class LinearTransformationScene(VectorScene):
CONFIG = {
"include_background_plane": True,
"include_foreground_plane": True,
"foreground_plane_kwargs": {
"x_radius": FRAME_WIDTH,
"y_radius": FRAME_HEIGHT,
"secondary_line_ratio": 0
},
"background_plane_kwargs": {
"color": GREY,
"secondary_color": DARK_GREY,
"axes_color": GREY,
"stroke_width": 2,
},
"show_coordinates": False,
"show_basis_vectors": True,
"basis_vector_stroke_width": 6,
"i_hat_color": X_COLOR,
"j_hat_color": Y_COLOR,
"leave_ghost_vectors": False,
"t_matrix": [[3, 0], [1, 2]],
}
def setup(self):
# The has_already_setup attr is to not break all the old Scenes
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 = NumberPlane(
**self.background_plane_kwargs
)
if self.show_coordinates:
self.background_plane.add_coordinates()
if self.include_background_plane:
self.add_background_mobject(self.background_plane)
if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs)
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,
)
self.moving_vectors += list(self.basis_vectors)
self.i_hat, self.j_hat = self.basis_vectors
self.add(self.basis_vectors)
def add_special_mobjects(self, mob_list, *mobs_to_add):
for mobject in mobs_to_add:
if mobject not in mob_list:
mob_list.append(mobject)
self.add(mobject)
def add_background_mobject(self, *mobjects):
self.add_special_mobjects(self.background_mobjects, *mobjects)
# TODO, this conflicts with Scene.add_fore
def add_foreground_mobject(self, *mobjects):
self.add_special_mobjects(self.foreground_mobjects, *mobjects)
def add_transformable_mobject(self, *mobjects):
self.add_special_mobjects(self.transformable_mobjects, *mobjects)
def add_moving_mobject(self, mobject, target_mobject=None):
mobject.target = target_mobject
self.add_special_mobjects(self.moving_mobjects, mobject)
def get_unit_square(self, color=YELLOW, opacity=0.3, stroke_width=3):
square = Rectangle(
color=color,
width=self.plane.get_x_unit_size(),
height=self.plane.get_y_unit_size(),
stroke_color=color,
stroke_width=stroke_width,
fill_color=color,
fill_opacity=opacity
)
square.move_to(self.plane.coords_to_point(0, 0), DL)
return square
def add_unit_square(self, animate=False, **kwargs):
square = self.get_unit_square(**kwargs)
if animate:
self.play(
DrawBorderThenFill(square),
Animation(Group(*self.moving_vectors))
)
self.add_transformable_mobject(square)
self.bring_to_front(*self.moving_vectors)
self.square = square
return self
def add_vector(self, vector, color=YELLOW, **kwargs):
vector = VectorScene.add_vector(
self, vector, color=color, **kwargs
)
self.moving_vectors.append(vector)
return vector
def write_vector_coordinates(self, vector, **kwargs):
coords = VectorScene.write_vector_coordinates(self, vector, **kwargs)
self.add_foreground_mobject(coords)
return coords
def add_transformable_label(
self, vector, label,
transformation_name="L",
new_label=None,
**kwargs):
label_mob = self.label_vector(vector, label, **kwargs)
if new_label:
label_mob.target_text = new_label
else:
label_mob.target_text = "%s(%s)" % (
transformation_name,
label_mob.get_tex_string()
)
label_mob.vector = vector
label_mob.kwargs = kwargs
if "animate" in label_mob.kwargs:
label_mob.kwargs.pop("animate")
self.transformable_labels.append(label_mob)
return label_mob
def add_title(self, title, scale_factor=1.5, animate=False):
if not isinstance(title, Mobject):
title = TextMobject(title).scale(scale_factor)
title.to_edge(UP)
title.add_background_rectangle()
if animate:
self.play(Write(title))
self.add_foreground_mobject(title)
self.title = title
return self
def get_matrix_transformation(self, matrix):
return self.get_transposed_matrix_transformation(np.array(matrix).T)
def get_transposed_matrix_transformation(self, transposed_matrix):
transposed_matrix = np.array(transposed_matrix)
if transposed_matrix.shape == (2, 2):
new_matrix = np.identity(3)
new_matrix[:2, :2] = transposed_matrix
transposed_matrix = new_matrix
elif transposed_matrix.shape != (3, 3):
raise "Matrix has bad dimensions"
return lambda point: np.dot(point, transposed_matrix)
def get_piece_movement(self, pieces):
start = VMobject(*pieces)
target = VMobject(*[mob.target for mob in pieces])
if self.leave_ghost_vectors:
self.add(start.copy().fade(0.7))
return Transform(start, target, submobject_mode="all_at_once")
def get_moving_mobject_movement(self, func):
for m in self.moving_mobjects:
if m.target is None:
m.target = m.copy()
target_point = func(m.get_center())
m.target.move_to(target_point)
return self.get_piece_movement(self.moving_mobjects)
def get_vector_movement(self, func):
for v in self.moving_vectors:
v.target = Vector(func(v.get_end()), color=v.get_color())
norm = np.linalg.norm(v.target.get_end())
if norm < 0.1:
v.target.get_tip().scale_in_place(norm)
return self.get_piece_movement(self.moving_vectors)
def get_transformable_label_movement(self):
for l in self.transformable_labels:
l.target = self.get_vector_label(
l.vector.target, l.target_text, **l.kwargs
)
return self.get_piece_movement(self.transformable_labels)
def apply_matrix(self, matrix, **kwargs):
self.apply_transposed_matrix(np.array(matrix).T, **kwargs)
def apply_inverse(self, matrix, **kwargs):
self.apply_matrix(np.linalg.inv(matrix), **kwargs)
def apply_transposed_matrix(self, transposed_matrix, **kwargs):
func = self.get_transposed_matrix_transformation(transposed_matrix)
if "path_arc" not in kwargs:
net_rotation = np.mean([
angle_of_vector(func(RIGHT)),
angle_of_vector(func(UP)) - np.pi / 2
])
kwargs["path_arc"] = net_rotation
self.apply_function(func, **kwargs)
def apply_inverse_transpose(self, t_matrix, **kwargs):
t_inv = np.linalg.inv(np.array(t_matrix).T).T
self.apply_transposed_matrix(t_inv, **kwargs)
def apply_nonlinear_transformation(self, function, **kwargs):
self.plane.prepare_for_nonlinear_transform()
self.apply_function(function, **kwargs)
def apply_function(self, function, added_anims=[], **kwargs):
if "run_time" not in kwargs:
kwargs["run_time"] = 3
anims = [
ApplyPointwiseFunction(function, t_mob)
for t_mob in self.transformable_mobjects
] + [
self.get_vector_movement(function),
self.get_transformable_label_movement(),
self.get_moving_mobject_movement(function),
] + [
Animation(f_mob)
for f_mob in self.foreground_mobjects
] + added_anims
self.play(*anims, **kwargs)