def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff = 2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(
v_array, TexMobject("+"), w_array, TexMobject("="), sum_array
)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2*UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff = 1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(
Write(syms), Write(arrays),
ShowCreation(arrows, submobject_mode = "one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time = 2
)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.wait()
self.play(
ShowCreation(circle),
ApplyMethod(mathy.change_mode, "plain")
)
self.wait()
def handle_mathy(self, creatures):
self.fade_all_but(creatures, 2)
physy, compy, mathy = creatures
v_color = YELLOW
w_color = BLUE
sum_color = GREEN
v_arrow = Vector([1, 1])
w_arrow = Vector([2, 1])
w_arrow.shift(v_arrow.get_end())
sum_arrow = Vector(w_arrow.get_end())
arrows = VMobject(v_arrow, w_arrow, sum_arrow)
arrows.scale(0.7)
arrows.to_edge(LEFT, buff = 2)
v_array = matrix_to_mobject([3, -5])
w_array = matrix_to_mobject([2, 1])
sum_array = matrix_to_mobject(["3+2", "-5+1"])
arrays = VMobject(
v_array, TexMobject("+"), w_array, TexMobject("="), sum_array
)
arrays.arrange_submobjects(RIGHT)
arrays.scale(0.75)
arrays.to_edge(RIGHT).shift(UP)
v_sym = TexMobject("\\vec{\\textbf{v}}")
w_sym = TexMobject("\\vec{\\textbf{w}}")
syms = VMobject(v_sym, TexMobject("+"), w_sym)
syms.arrange_submobjects(RIGHT)
syms.center().shift(2*UP)
statement = TextMobject("We'll ignore him \\\\ for now")
statement.highlight(PINK)
statement.scale_to_fit_width(arrays.get_width())
statement.next_to(arrays, DOWN, buff = 1.5)
circle = Circle()
circle.shift(syms.get_bottom())
VMobject(v_arrow, v_array, v_sym).highlight(v_color)
VMobject(w_arrow, w_array, w_sym).highlight(w_color)
VMobject(sum_arrow, sum_array).highlight(sum_color)
self.play(
Write(syms), Write(arrays),
ShowCreation(arrows, submobject_mode = "one_at_a_time"),
ApplyMethod(mathy.change_mode, "pondering"),
run_time = 2
)
self.play(Blink(mathy))
self.add_scaling(arrows, syms, arrays)
self.play(Write(statement))
self.play(ApplyMethod(mathy.change_mode, "sad"))
self.dither()
self.play(
ShowCreation(circle),
ApplyMethod(mathy.change_mode, "plain")
)
self.dither()
class NumberPlane(VMobject):
CONFIG = {
"color" : BLUE_D,
"secondary_color" : BLUE_E,
"axes_color" : WHITE,
"secondary_stroke_width" : 1,
"x_radius": None,
"y_radius": None,
"x_unit_size" : 1,
"y_unit_size" : 1,
"center_point" : ORIGIN,
"x_line_frequency" : 1,
"y_line_frequency" : 1,
"secondary_line_ratio" : 1,
"written_coordinate_height" : 0.2,
"propagate_style_to_family" : False,
}
def generate_points(self):
if self.x_radius is None:
center_to_edge = (SPACE_WIDTH + abs(self.center_point[0]))
self.x_radius = center_to_edge / self.x_unit_size
if self.y_radius is None:
center_to_edge = (SPACE_HEIGHT + abs(self.center_point[1]))
self.y_radius = center_to_edge / self.y_unit_size
self.axes = VMobject()
self.main_lines = VMobject()
self.secondary_lines = VMobject()
tuples = [
(
self.x_radius,
self.x_line_frequency,
self.y_radius*DOWN,
self.y_radius*UP,
RIGHT
),
(
self.y_radius,
self.y_line_frequency,
self.x_radius*LEFT,
self.x_radius*RIGHT,
UP,
),
]
for radius, freq, start, end, unit in tuples:
main_range = np.arange(0, radius, freq)
step = freq/float(freq + self.secondary_line_ratio)
for v in np.arange(0, radius, step):
line1 = Line(start+v*unit, end+v*unit)
line2 = Line(start-v*unit, end-v*unit)
if v == 0:
self.axes.add(line1)
elif v in main_range:
self.main_lines.add(line1, line2)
else:
self.secondary_lines.add(line1, line2)
self.add(self.secondary_lines, self.main_lines, self.axes)
self.stretch(self.x_unit_size, 0)
self.stretch(self.y_unit_size, 1)
self.shift(self.center_point)
#Put x_axis before y_axis
y_axis, x_axis = self.axes.split()
self.axes = VMobject(x_axis, y_axis)
def init_colors(self):
VMobject.init_colors(self)
self.axes.set_stroke(self.axes_color, self.stroke_width)
self.main_lines.set_stroke(self.color, self.stroke_width)
self.secondary_lines.set_stroke(
self.secondary_color, self.secondary_stroke_width
)
return self
def get_center_point(self):
return self.coords_to_point(0, 0)
def coords_to_point(self, x, y):
x, y = np.array([x, y])
result = self.axes.get_center()
result += x*self.get_x_unit_size()*RIGHT
result += y*self.get_y_unit_size()*UP
return result
def point_to_coords(self, point):
new_point = point - self.axes.get_center()
x = new_point[0]/self.get_x_unit_size()
y = new_point[1]/self.get_y_unit_size()
return x, y
def get_x_unit_size(self):
return self.axes.get_width() / (2.0*self.x_radius)
def get_y_unit_size(self):
return self.axes.get_height() / (2.0*self.y_radius)
def get_coordinate_labels(self, x_vals = None, y_vals = None):
coordinate_labels = VGroup()
if x_vals == None:
x_vals = range(-int(self.x_radius), int(self.x_radius)+1)
if y_vals == None:
y_vals = range(-int(self.y_radius), int(self.y_radius)+1)
for index, vals in enumerate([x_vals, y_vals]):
num_pair = [0, 0]
for val in vals:
if val == 0:
continue
num_pair[index] = val
point = self.coords_to_point(*num_pair)
num = TexMobject(str(val))
num.add_background_rectangle()
num.scale_to_fit_height(
self.written_coordinate_height
)
num.next_to(point, DOWN+LEFT, buff = SMALL_BUFF)
coordinate_labels.add(num)
self.coordinate_labels = coordinate_labels
return coordinate_labels
def get_axes(self):
return self.axes
def get_axis_labels(self, x_label = "x", y_label = "y"):
x_axis, y_axis = self.get_axes().split()
quads = [
(x_axis, x_label, UP, RIGHT),
(y_axis, y_label, RIGHT, UP),
]
labels = VGroup()
for axis, tex, vect, edge in quads:
label = TexMobject(tex)
label.add_background_rectangle()
label.next_to(axis, vect)
label.to_edge(edge)
labels.add(label)
self.axis_labels = labels
return labels
def add_coordinates(self, x_vals = None, y_vals = None):
self.add(*self.get_coordinate_labels(x_vals, y_vals))
return self
def get_vector(self, coords, **kwargs):
point = coords[0]*RIGHT + coords[1]*UP
arrow = Arrow(ORIGIN, coords, **kwargs)
return arrow
def prepare_for_nonlinear_transform(self, num_inserted_anchor_points = 50):
for mob in self.family_members_with_points():
num_anchors = mob.get_num_anchor_points()
if num_inserted_anchor_points > num_anchors:
mob.insert_n_anchor_points(num_inserted_anchor_points-num_anchors)
mob.make_smooth()
return self
def apply_function(self, function, maintain_smoothness = True):
VMobject.apply_function(self, function, maintain_smoothness = maintain_smoothness)
class NumberPlane(VMobject):
CONFIG = {
"color" : BLUE_D,
"secondary_color" : BLUE_E,
"axes_color" : WHITE,
"secondary_stroke_width" : 1,
"x_radius": None,
"y_radius": None,
"x_unit_size" : 1,
"y_unit_size" : 1,
"center_point" : ORIGIN,
"x_line_frequency" : 1,
"y_line_frequency" : 1,
"secondary_line_ratio" : 1,
"written_coordinate_height" : 0.2,
"propogate_style_to_family" : False,
}
def generate_points(self):
if self.x_radius is None:
center_to_edge = (SPACE_WIDTH + abs(self.center_point[0]))
self.x_radius = center_to_edge / self.x_unit_size
if self.y_radius is None:
center_to_edge = (SPACE_HEIGHT + abs(self.center_point[1]))
self.y_radius = center_to_edge / self.y_unit_size
self.axes = VMobject()
self.main_lines = VMobject()
self.secondary_lines = VMobject()
tuples = [
(
self.x_radius,
self.x_line_frequency,
self.y_radius*DOWN,
self.y_radius*UP,
RIGHT
),
(
self.y_radius,
self.y_line_frequency,
self.x_radius*LEFT,
self.x_radius*RIGHT,
UP,
),
]
for radius, freq, start, end, unit in tuples:
main_range = np.arange(0, radius, freq)
step = freq/float(freq + self.secondary_line_ratio)
for v in np.arange(0, radius, step):
line1 = Line(start+v*unit, end+v*unit)
line2 = Line(start-v*unit, end-v*unit)
if v == 0:
self.axes.add(line1)
elif v in main_range:
self.main_lines.add(line1, line2)
else:
self.secondary_lines.add(line1, line2)
self.add(self.secondary_lines, self.main_lines, self.axes)
self.stretch(self.x_unit_size, 0)
self.stretch(self.y_unit_size, 1)
self.shift(self.center_point)
#Put x_axis before y_axis
y_axis, x_axis = self.axes.split()
self.axes = VMobject(x_axis, y_axis)
def init_colors(self):
VMobject.init_colors(self)
self.axes.set_stroke(self.axes_color, self.stroke_width)
self.main_lines.set_stroke(self.color, self.stroke_width)
self.secondary_lines.set_stroke(
self.secondary_color, self.secondary_stroke_width
)
return self
def get_center_point(self):
return self.coords_to_point(0, 0)
def coords_to_point(self, x, y):
x, y = np.array([x, y])
result = self.axes.get_center()
result += x*self.get_x_unit_size()*RIGHT
result += y*self.get_y_unit_size()*UP
return result
def point_to_coords(self, point):
new_point = point - self.axes.get_center()
x = new_point[0]/self.get_x_unit_size()
y = new_point[1]/self.get_y_unit_size()
return x, y
def get_x_unit_size(self):
return self.axes.get_width() / (2.0*self.x_radius)
def get_y_unit_size(self):
return self.axes.get_height() / (2.0*self.y_radius)
def get_coordinate_labels(self, x_vals = None, y_vals = None):
result = []
if x_vals == None and y_vals == None:
x_vals = range(-int(self.x_radius), int(self.x_radius))
y_vals = range(-int(self.y_radius), int(self.y_radius))
for index, vals in enumerate([x_vals, y_vals]):
num_pair = [0, 0]
for val in vals:
if val == 0:
continue
num_pair[index] = val
point = self.coords_to_point(*num_pair)
num = TexMobject(str(val))
num.add_background_rectangle()
num.scale_to_fit_height(
self.written_coordinate_height
)
vect = DOWN if index == 0 else LEFT
num.next_to(point, vect, buff = SMALL_BUFF)
result.append(num)
return result
def get_axes(self):
return self.axes
def get_axis_labels(self, x_label = "x", y_label = "y"):
x_axis, y_axis = self.get_axes().split()
quads = [
(x_axis, x_label, UP, RIGHT),
(y_axis, y_label, RIGHT, UP),
]
labels = VGroup()
for axis, tex, vect, edge in quads:
label = TexMobject(tex)
label.add_background_rectangle()
label.next_to(axis, vect)
label.to_edge(edge)
labels.add(label)
self.axis_labels = labels
return labels
def add_coordinates(self, x_vals = None, y_vals = None):
self.add(*self.get_coordinate_labels(x_vals, y_vals))
return self
def get_vector(self, coords, **kwargs):
point = coords[0]*RIGHT + coords[1]*UP
arrow = Arrow(ORIGIN, coords, **kwargs)
return arrow
def prepare_for_nonlinear_transform(self, num_inserted_anchor_points = 50):
for mob in self.family_members_with_points():
num_anchors = mob.get_num_anchor_points()
if num_inserted_anchor_points > num_anchors:
mob.insert_n_anchor_points(num_inserted_anchor_points-num_anchors)
mob.make_smooth()
return self
