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Added apply_matrix_transformation to LinearTransformationScene

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This commit is contained in:
Grant Sanderson 2018-04-06 13:07:02 -07:00
parent bc229f4f29
commit 96d261840d
1 changed files with 108 additions and 110 deletions
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218
scene/vector_space_scene.py
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@ -36,25 +36,27 @@ X_COLOR = GREEN_C
Y_COLOR = RED_C Y_COLOR = RED_C
Z_COLOR = BLUE_D Z_COLOR = BLUE_D
class VectorScene(Scene): class VectorScene(Scene):
CONFIG = { CONFIG = {
"basis_vector_stroke_width" : 6 "basis_vector_stroke_width": 6
} }
def add_plane(self, animate = False, **kwargs):
def add_plane(self, animate=False, **kwargs):
plane = NumberPlane(**kwargs) plane = NumberPlane(**kwargs)
if animate: if animate:
self.play(ShowCreation(plane, submobject_mode = "lagged_start")) self.play(ShowCreation(plane, submobject_mode="lagged_start"))
self.add(plane) self.add(plane)
return plane return plane
def add_axes(self, animate = False, color = WHITE, **kwargs): def add_axes(self, animate=False, color=WHITE, **kwargs):
axes = Axes(color = color, tick_frequency = 1) axes = Axes(color=color, tick_frequency=1)
if animate: if animate:
self.play(ShowCreation(axes, submobject_mode = "one_at_a_time")) self.play(ShowCreation(axes, submobject_mode="one_at_a_time"))
self.add(axes) self.add(axes)
return axes return axes
def lock_in_faded_grid(self, dimness = 0.7, axes_dimness = 0.5): def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5):
plane = self.add_plane() plane = self.add_plane()
axes = plane.get_axes() axes = plane.get_axes()
plane.fade(dimness) plane.fade(dimness)
@ -63,9 +65,9 @@ class VectorScene(Scene):
self.add(axes) self.add(axes)
self.freeze_background() self.freeze_background()
def add_vector(self, vector, color = YELLOW, animate = True, **kwargs): def add_vector(self, vector, color=YELLOW, animate=True, **kwargs):
if not isinstance(vector, Arrow): if not isinstance(vector, Arrow):
vector = Vector(vector, color = color, **kwargs) vector = Vector(vector, color=color, **kwargs)
if animate: if animate:
self.play(ShowCreation(vector)) self.play(ShowCreation(vector))
self.add(vector) self.add(vector)
@ -76,40 +78,41 @@ class VectorScene(Scene):
self.play(Write(coords)) self.play(Write(coords))
return coords return coords
def get_basis_vectors(self): def get_basis_vectors(self, i_hat_color=X_COLOR, j_hat_color=Y_COLOR):
return [ return VGroup(*[
Vector( Vector(
vect, color = color, vect,
stroke_width = self.basis_vector_stroke_width color=color,
stroke_width=self.basis_vector_stroke_width
) )
for vect, color in [ for vect, color in [
([1, 0], X_COLOR), ([1, 0], i_hat_color),
([0, 1], Y_COLOR) ([0, 1], j_hat_color)
] ]
] ])
def get_basis_vector_labels(self, **kwargs): def get_basis_vector_labels(self, **kwargs):
i_hat, j_hat = self.get_basis_vectors() i_hat, j_hat = self.get_basis_vectors()
return VGroup(*[ return VGroup(*[
self.get_vector_label( self.get_vector_label(
vect, label, color = color, vect, label, color=color,
label_scale_factor = 1, label_scale_factor=1,
**kwargs **kwargs
) )
for vect, label , color in [ for vect, label, color in [
(i_hat, "\\hat{\\imath}", X_COLOR), (i_hat, "\\hat{\\imath}", X_COLOR),
(j_hat, "\\hat{\\jmath}", Y_COLOR), (j_hat, "\\hat{\\jmath}", Y_COLOR),
] ]
]) ])
def get_vector_label(self, vector, label, def get_vector_label(self, vector, label,
direction = "left", direction="left",
rotate = False, rotate=False,
color = None, color=None,
label_scale_factor = VECTOR_LABEL_SCALE_FACTOR): label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject): if not isinstance(label, TexMobject):
if len(label) == 1: if len(label) == 1:
label = "\\vec{\\textbf{%s}}"%label label = "\\vec{\\textbf{%s}}" % label
label = TexMobject(label) label = TexMobject(label)
if color is None: if color is None:
color = vector.get_color() color = vector.get_color()
@ -119,53 +122,53 @@ class VectorScene(Scene):
angle = vector.get_angle() angle = vector.get_angle()
if not rotate: if not rotate:
label.rotate(-angle, about_point = ORIGIN) label.rotate(-angle, about_point=ORIGIN)
if direction is "left": if direction is "left":
label.shift(-label.get_bottom() + 0.1*UP) label.shift(-label.get_bottom() + 0.1 * UP)
else: else:
label.shift(-label.get_top() + 0.1*DOWN) label.shift(-label.get_top() + 0.1 * DOWN)
label.rotate(angle, about_point = ORIGIN) label.rotate(angle, about_point=ORIGIN)
label.shift((vector.get_end() - vector.get_start())/2) label.shift((vector.get_end() - vector.get_start()) / 2)
return label return label
def label_vector(self, vector, label, animate = True, **kwargs): def label_vector(self, vector, label, animate=True, **kwargs):
label = self.get_vector_label(vector, label, **kwargs) label = self.get_vector_label(vector, label, **kwargs)
if animate: if animate:
self.play(Write(label, run_time = 1)) self.play(Write(label, run_time=1))
self.add(label) self.add(label)
return label return label
def position_x_coordinate(self, x_coord, x_line, vector): def position_x_coordinate(self, x_coord, x_line, vector):
x_coord.next_to(x_line, -np.sign(vector[1])*UP) x_coord.next_to(x_line, -np.sign(vector[1]) * UP)
x_coord.set_color(X_COLOR) x_coord.set_color(X_COLOR)
return x_coord return x_coord
def position_y_coordinate(self, y_coord, y_line, vector): def position_y_coordinate(self, y_coord, y_line, vector):
y_coord.next_to(y_line, np.sign(vector[0])*RIGHT) y_coord.next_to(y_line, np.sign(vector[0]) * RIGHT)
y_coord.set_color(Y_COLOR) y_coord.set_color(Y_COLOR)
return y_coord return y_coord
def coords_to_vector(self, vector, coords_start = 2*RIGHT+2*UP, clean_up = True): def coords_to_vector(self, vector, coords_start=2 * RIGHT + 2 * UP, clean_up=True):
starting_mobjects = list(self.mobjects) starting_mobjects = list(self.mobjects)
array = Matrix(vector) array = Matrix(vector)
array.shift(coords_start) array.shift(coords_start)
arrow = Vector(vector) arrow = Vector(vector)
x_line = Line(ORIGIN, vector[0]*RIGHT) x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end()) y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR) x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR) y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten() x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time = 1)) self.play(Write(array, run_time=1))
self.wait() self.wait()
self.play(ApplyFunction( self.play(ApplyFunction(
lambda x : self.position_x_coordinate(x, x_line, vector), lambda x: self.position_x_coordinate(x, x_line, vector),
x_coord x_coord
)) ))
self.play(ShowCreation(x_line)) self.play(ShowCreation(x_line))
self.play( self.play(
ApplyFunction( ApplyFunction(
lambda y : self.position_y_coordinate(y, y_line, vector), lambda y: self.position_y_coordinate(y, y_line, vector),
y_coord y_coord
), ),
FadeOut(array.get_brackets()) FadeOut(array.get_brackets())
@ -178,7 +181,7 @@ class VectorScene(Scene):
self.clear() self.clear()
self.add(*starting_mobjects) self.add(*starting_mobjects)
def vector_to_coords(self, vector, integer_labels = True, clean_up = True): def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
starting_mobjects = list(self.mobjects) starting_mobjects = list(self.mobjects)
show_creation = False show_creation = False
if isinstance(vector, Arrow): if isinstance(vector, Arrow):
@ -187,8 +190,8 @@ class VectorScene(Scene):
else: else:
arrow = Vector(vector) arrow = Vector(vector)
show_creation = True show_creation = True
array = vector_coordinate_label(arrow, integer_labels = integer_labels) array = vector_coordinate_label(arrow, integer_labels=integer_labels)
x_line = Line(ORIGIN, vector[0]*RIGHT) x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end()) y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR) x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR) y_line.set_color(Y_COLOR)
@ -206,18 +209,18 @@ class VectorScene(Scene):
self.play( self.play(
ShowCreation(x_line), ShowCreation(x_line),
Write(x_coord_start), Write(x_coord_start),
run_time = 1 run_time=1
) )
self.play( self.play(
ShowCreation(y_line), ShowCreation(y_line),
Write(y_coord_start), Write(y_coord_start),
run_time = 1 run_time=1
) )
self.wait() self.wait()
self.play( self.play(
Transform(x_coord_start, x_coord, submobject_mode = "all_at_once"), Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
Transform(y_coord_start, y_coord, submobject_mode = "all_at_once"), Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
Write(brackets, run_time = 1), Write(brackets, run_time=1),
) )
self.wait() self.wait()
@ -236,53 +239,56 @@ class VectorScene(Scene):
x_max = int(FRAME_X_RADIUS + abs(vector[0])) x_max = int(FRAME_X_RADIUS + abs(vector[0]))
y_max = int(FRAME_Y_RADIUS + abs(vector[1])) y_max = int(FRAME_Y_RADIUS + abs(vector[1]))
dots = VMobject(*[ dots = VMobject(*[
Dot(x*RIGHT + y*UP) Dot(x * RIGHT + y * UP)
for x in range(-x_max, x_max) for x in range(-x_max, x_max)
for y in range(-y_max, y_max) for y in range(-y_max, y_max)
]) ])
dots.set_fill(BLACK, opacity = 0) dots.set_fill(BLACK, opacity=0)
dots_halfway = dots.copy().shift(vector/2).set_fill(WHITE, 1) dots_halfway = dots.copy().shift(vector / 2).set_fill(WHITE, 1)
dots_end = dots.copy().shift(vector) dots_end = dots.copy().shift(vector)
self.play(Transform( self.play(Transform(
dots, dots_halfway, rate_func = rush_into dots, dots_halfway, rate_func=rush_into
)) ))
self.play(Transform( self.play(Transform(
dots, dots_end, rate_func = rush_from dots, dots_end, rate_func=rush_from
)) ))
self.remove(dots) self.remove(dots)
class LinearTransformationScene(VectorScene): class LinearTransformationScene(VectorScene):
CONFIG = { CONFIG = {
"include_background_plane" : True, "include_background_plane": True,
"include_foreground_plane" : True, "include_foreground_plane": True,
"foreground_plane_kwargs" : { "foreground_plane_kwargs": {
"x_radius" : FRAME_WIDTH, "x_radius": FRAME_WIDTH,
"y_radius" : FRAME_HEIGHT, "y_radius": FRAME_HEIGHT,
"secondary_line_ratio" : 0 "secondary_line_ratio": 0
}, },
"background_plane_kwargs" : { "background_plane_kwargs": {
"color" : GREY, "color": GREY,
"secondary_color" : DARK_GREY, "secondary_color": DARK_GREY,
"axes_color" : GREY, "axes_color": GREY,
"stroke_width" : 2, "stroke_width": 2,
}, },
"show_coordinates" : False, "show_coordinates": False,
"show_basis_vectors" : True, "show_basis_vectors": True,
"i_hat_color" : X_COLOR, "basis_vector_stroke_width": 6,
"j_hat_color" : Y_COLOR, "i_hat_color": X_COLOR,
"leave_ghost_vectors" : False, "j_hat_color": Y_COLOR,
"t_matrix" : [[3, 0], [1, 2]], "leave_ghost_vectors": False,
"t_matrix": [[3, 0], [1, 2]],
} }
def setup(self): def setup(self):
if hasattr(self, "has_already_setup"): if hasattr(self, "has_already_setup"):
return return
self.has_already_setup = True self.has_already_setup = True
##^This is to not break all the old Scenes # ^This is to not break all the old Scenes
self.background_mobjects = [] self.background_mobjects = []
self.foreground_mobjects = [] self.foreground_mobjects = []
self.transformable_mobjects = [] self.transformable_mobjects = []
self.moving_vectors = [] self.moving_vectors = []
self.transformable_labels = [] self.transformable_labels = []
self.moving_mobjects = [] self.moving_mobjects = []
@ -293,21 +299,18 @@ class LinearTransformationScene(VectorScene):
if self.show_coordinates: if self.show_coordinates:
self.background_plane.add_coordinates() self.background_plane.add_coordinates()
if self.include_background_plane: if self.include_background_plane:
self.add_background_mobject(self.background_plane) self.add_background_mobject(self.background_plane)
if self.include_foreground_plane: if self.include_foreground_plane:
self.plane = NumberPlane(**self.foreground_plane_kwargs) self.plane = NumberPlane(**self.foreground_plane_kwargs)
self.add_transformable_mobject(self.plane) self.add_transformable_mobject(self.plane)
if self.show_basis_vectors: if self.show_basis_vectors:
self.i_hat, self.j_hat = [ self.basis_vectors = self.get_basis_vectors(
self.add_vector( i_hat_color=self.i_hat_color,
coords, color, animate = False, stroke_width = 6 j_hat_color=self.j_hat_color,
) )
for coords, color in [ self.moving_vectors += list(self.basis_vectors)
((1, 0), self.i_hat_color), self.i_hat, self.j_hat = self.basis_vectors
((0, 1), self.j_hat_color),
]
]
def add_special_mobjects(self, mob_list, *mobs_to_add): def add_special_mobjects(self, mob_list, *mobs_to_add):
for mobject in mobs_to_add: for mobject in mobs_to_add:
@ -324,13 +327,13 @@ class LinearTransformationScene(VectorScene):
def add_transformable_mobject(self, *mobjects): def add_transformable_mobject(self, *mobjects):
self.add_special_mobjects(self.transformable_mobjects, *mobjects) self.add_special_mobjects(self.transformable_mobjects, *mobjects)
def add_moving_mobject(self, mobject, target_mobject = None): def add_moving_mobject(self, mobject, target_mobject=None):
mobject.target = target_mobject mobject.target = target_mobject
self.add_special_mobjects(self.moving_mobjects, mobject) self.add_special_mobjects(self.moving_mobjects, mobject)
def add_unit_square(self, color = YELLOW, opacity = 0.3, animate = False): def add_unit_square(self, color=YELLOW, opacity=0.3, animate=False):
square = Square(color = color, side_length = 1) square = Square(color=color, side_length=1)
square.shift(-square.get_corner(DOWN+LEFT)) square.shift(-square.get_corner(DOWN + LEFT))
if animate: if animate:
added_anims = map(Animation, self.moving_vectors) added_anims = map(Animation, self.moving_vectors)
self.play(ShowCreation(square), *added_anims) self.play(ShowCreation(square), *added_anims)
@ -338,13 +341,13 @@ class LinearTransformationScene(VectorScene):
else: else:
square.set_fill(color, opacity) square.set_fill(color, opacity)
self.add_transformable_mobject(square) self.add_transformable_mobject(square)
self.bring_to_front(*self.moving_vectors) self.bring_to_front(*self.moving_vectors)
self.square = square self.square = square
return self return self
def add_vector(self, vector, color = YELLOW, **kwargs): def add_vector(self, vector, color=YELLOW, **kwargs):
vector = VectorScene.add_vector( vector = VectorScene.add_vector(
self, vector, color = color, **kwargs self, vector, color=color, **kwargs
) )
self.moving_vectors.append(vector) self.moving_vectors.append(vector)
return vector return vector
@ -354,12 +357,12 @@ class LinearTransformationScene(VectorScene):
self.add_foreground_mobject(coords) self.add_foreground_mobject(coords)
return coords return coords
def add_transformable_label(self, vector, label, new_label = None, **kwargs): def add_transformable_label(self, vector, label, new_label=None, **kwargs):
label_mob = self.label_vector(vector, label, **kwargs) label_mob = self.label_vector(vector, label, **kwargs)
if new_label: if new_label:
label_mob.target_text = new_label label_mob.target_text = new_label
else: else:
label_mob.target_text = "L(%s)"%label_mob.get_tex_string() label_mob.target_text = "L(%s)" % label_mob.get_tex_string()
label_mob.vector = vector label_mob.vector = vector
label_mob.kwargs = kwargs label_mob.kwargs = kwargs
if "animate" in label_mob.kwargs: if "animate" in label_mob.kwargs:
@ -367,7 +370,7 @@ class LinearTransformationScene(VectorScene):
self.transformable_labels.append(label_mob) self.transformable_labels.append(label_mob)
return label_mob return label_mob
def add_title(self, title, scale_factor = 1.5, animate = False): def add_title(self, title, scale_factor=1.5, animate=False):
if not isinstance(title, Mobject): if not isinstance(title, Mobject):
title = TextMobject(title).scale(scale_factor) title = TextMobject(title).scale(scale_factor)
title.to_edge(UP) title.to_edge(UP)
@ -378,7 +381,10 @@ class LinearTransformationScene(VectorScene):
self.title = title self.title = title
return self return self
def get_matrix_transformation(self, transposed_matrix): 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) transposed_matrix = np.array(transposed_matrix)
if transposed_matrix.shape == (2, 2): if transposed_matrix.shape == (2, 2):
new_matrix = np.identity(3) new_matrix = np.identity(3)
@ -389,11 +395,11 @@ class LinearTransformationScene(VectorScene):
return lambda point: np.dot(point, transposed_matrix) return lambda point: np.dot(point, transposed_matrix)
def get_piece_movement(self, pieces): def get_piece_movement(self, pieces):
start = VMobject(*pieces) start = VMobject(*pieces)
target = VMobject(*[mob.target for mob in pieces]) target = VMobject(*[mob.target for mob in pieces])
if self.leave_ghost_vectors: if self.leave_ghost_vectors:
self.add(start.copy().fade(0.7)) self.add(start.copy().fade(0.7))
return Transform(start, target, submobject_mode = "all_at_once") return Transform(start, target, submobject_mode="all_at_once")
def get_moving_mobject_movement(self, func): def get_moving_mobject_movement(self, func):
for m in self.moving_mobjects: for m in self.moving_mobjects:
@ -405,7 +411,7 @@ class LinearTransformationScene(VectorScene):
def get_vector_movement(self, func): def get_vector_movement(self, func):
for v in self.moving_vectors: for v in self.moving_vectors:
v.target = Vector(func(v.get_end()), color = v.get_color()) v.target = Vector(func(v.get_end()), color=v.get_color())
norm = np.linalg.norm(v.target.get_end()) norm = np.linalg.norm(v.target.get_end())
if norm < 0.1: if norm < 0.1:
v.target.get_tip().scale_in_place(norm) v.target.get_tip().scale_in_place(norm)
@ -418,12 +424,15 @@ class LinearTransformationScene(VectorScene):
) )
return self.get_piece_movement(self.transformable_labels) 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_transposed_matrix(self, transposed_matrix, **kwargs): def apply_transposed_matrix(self, transposed_matrix, **kwargs):
func = self.get_matrix_transformation(transposed_matrix) func = self.get_transposed_matrix_transformation(transposed_matrix)
if "path_arc" not in kwargs: if "path_arc" not in kwargs:
net_rotation = np.mean([ net_rotation = np.mean([
angle_of_vector(func(RIGHT)), angle_of_vector(func(RIGHT)),
angle_of_vector(func(UP))-np.pi/2 angle_of_vector(func(UP)) - np.pi / 2
]) ])
kwargs["path_arc"] = net_rotation kwargs["path_arc"] = net_rotation
self.apply_function(func, **kwargs) self.apply_function(func, **kwargs)
@ -436,7 +445,7 @@ class LinearTransformationScene(VectorScene):
self.plane.prepare_for_nonlinear_transform() self.plane.prepare_for_nonlinear_transform()
self.apply_function(function, **kwargs) self.apply_function(function, **kwargs)
def apply_function(self, function, added_anims = [], **kwargs): def apply_function(self, function, added_anims=[], **kwargs):
if "run_time" not in kwargs: if "run_time" not in kwargs:
kwargs["run_time"] = 3 kwargs["run_time"] = 3
anims = [ anims = [
@ -451,14 +460,3 @@ class LinearTransformationScene(VectorScene):
for f_mob in self.foreground_mobjects for f_mob in self.foreground_mobjects
] + added_anims ] + added_anims
self.play(*anims, **kwargs) self.play(*anims, **kwargs)