def setup(self):
if hasattr(self, "has_setup"):
return
self.has_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):
if hasattr(self, "has_setup"):
return
self.has_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):
self.background_mobjects = []
self.foreground_mobjects = []
self.transformable_mobjects = []
self.moving_vectors = []
self.transformable_labels = []
self.moving_mobjects = []
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 construct(self):
def special_rotate(mob):
mob.rotate(0.9*np.pi/2, RIGHT)
mob.rotate(-np.pi/4, UP)
return mob
plane = NumberPlane()
copies = [
special_rotate(plane.copy().shift(u*n*OUT))
for n in range(1, 3)
for u in -1, 1
]
line = Line(4*IN, 4*OUT)
self.add(plane)
self.play(*[
ApplyFunction(special_rotate, mob, run_time = 3)
for mob in plane, line
])
self.dither()
for copy in copies:
self.play(Transform(plane.copy(), copy))
self.dither()
def construct(self):
axes = XYZAxes()
axes.highlight(WHITE)
plane = NumberPlane()
vects = [
Arrow(point, point+(3./27)*(3*x**2-3*y**2)*OUT, color = MAROON_D)
for x in range(-4, 5, 2)
for y in range(-5, 5, 2)
for point in [x*RIGHT + y*UP]
]
everybody = Mobject(axes, plane, *vects)
self.play(ApplyMethod(
everybody.rotate, 0.9*np.pi/2, RIGHT
))
self.dither()
self.play(ApplyMethod(
everybody.rotate,
np.pi/2,
run_time = 5
))
def add_plane(self):
self.add(NumberPlane().fade())
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": 2 * SPACE_WIDTH,
"y_radius": 2 * SPACE_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_setup"):
return
self.has_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.expression
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())
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" : 2*SPACE_WIDTH,
"y_radius" : 2*SPACE_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_setup"):
return
self.has_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.expression
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())
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)