def coords_to_vector(self,
vector,
coords_start=2 * RIGHT + 2 * UP,
clean_up=True):
starting_mobjects = list(self.mobjects)
array = Matrix(vector)
array.shift(coords_start)
arrow = Vector(vector)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.wait()
self.play(
ApplyFunction(
lambda x: self.position_x_coordinate(x, x_line, vector),
x_coord))
self.play(ShowCreation(x_line))
self.play(
ApplyFunction(
lambda y: self.position_y_coordinate(y, y_line, vector),
y_coord), FadeOut(array.get_brackets()))
y_coord, brackets = self.get_mobjects_from_last_animation()
self.play(ShowCreation(y_line))
self.play(ShowCreation(arrow))
self.wait()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def coords_to_vector(self, vector, coords_start=2 * RIGHT + 2 * UP, clean_up=True):
starting_mobjects = list(self.mobjects)
array = Matrix(vector)
array.shift(coords_start)
arrow = Vector(vector)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.wait()
self.play(ApplyFunction(
lambda x: self.position_x_coordinate(x, x_line, vector),
x_coord
))
self.play(ShowCreation(x_line))
self.play(
ApplyFunction(
lambda y: self.position_y_coordinate(y, y_line, vector),
y_coord
),
FadeOut(array.get_brackets())
)
y_coord, brackets = self.get_mobjects_from_last_animation()
self.play(ShowCreation(y_line))
self.play(ShowCreation(arrow))
self.wait()
if clean_up:
self.clear()
self.add(*starting_mobjects)
def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
starting_mobjects = list(self.mobjects)
show_creation = False
if isinstance(vector, Arrow):
arrow = vector
vector = arrow.get_end()[:2]
else:
arrow = Vector(vector)
show_creation = True
array = vector_coordinate_label(arrow, integer_labels=integer_labels)
x_line = Line(ORIGIN, vector[0] * RIGHT)
y_line = Line(x_line.get_end(), arrow.get_end())
x_line.set_color(X_COLOR)
y_line.set_color(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
x_coord_start = self.position_x_coordinate(
x_coord.copy(), x_line, vector
)
y_coord_start = self.position_y_coordinate(
y_coord.copy(), y_line, vector
)
brackets = array.get_brackets()
if show_creation:
self.play(ShowCreation(arrow))
self.play(
ShowCreation(x_line),
Write(x_coord_start),
run_time=1
)
self.play(
ShowCreation(y_line),
Write(y_coord_start),
run_time=1
)
self.wait()
self.play(
Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
Write(brackets, run_time=1),
)
self.wait()
self.remove(x_coord_start, y_coord_start, brackets)
self.add(array)
if clean_up:
self.clear()
self.add(*starting_mobjects)
return array, x_line, y_line
class NumberLine(VMobject):
CONFIG = {
"color": LIGHT_GREY,
"x_min": -FRAME_X_RADIUS,
"x_max": FRAME_X_RADIUS,
"unit_size": 1,
"tick_size": 0.1,
"tick_frequency": 1,
"leftmost_tick": None, # Defaults to value near x_min s.t. 0 is a tick
"numbers_with_elongated_ticks": [0],
"include_numbers": False,
"numbers_to_show": None,
"longer_tick_multiple": 2,
"number_at_center": 0,
"number_scale_val": 0.75,
"label_direction": DOWN,
"line_to_number_buff": MED_SMALL_BUFF,
"include_tip": False,
"propagate_style_to_family": True,
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
tf = self.tick_frequency
self.leftmost_tick = tf * np.ceil(self.x_min / tf)
VMobject.__init__(self, **kwargs)
if self.include_tip:
self.add_tip()
if self.include_numbers:
self.add_numbers()
def generate_points(self):
self.main_line = Line(self.x_min * RIGHT, self.x_max * RIGHT)
self.tick_marks = VGroup()
self.add(self.main_line, self.tick_marks)
rounding_value = int(-np.log10(0.1 * self.tick_frequency))
rounded_numbers_with_elongated_ticks = np.round(
self.numbers_with_elongated_ticks, rounding_value)
for x in self.get_tick_numbers():
rounded_x = np.round(x, rounding_value)
if rounded_x in rounded_numbers_with_elongated_ticks:
tick_size_used = self.longer_tick_multiple * self.tick_size
else:
tick_size_used = self.tick_size
self.add_tick(x, tick_size_used)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size=None):
self.tick_marks.add(self.get_tick(x, size))
return self
def get_tick(self, x, size=None):
if size is None:
size = self.tick_size
result = Line(size * DOWN, size * UP)
result.rotate(self.main_line.get_angle())
result.move_to(self.number_to_point(x))
return result
def get_tick_marks(self):
return self.tick_marks
def get_tick_numbers(self):
epsilon = 0.001
return np.arange(self.leftmost_tick, self.x_max + epsilon,
self.tick_frequency)
def number_to_point(self, number):
alpha = float(number - self.x_min) / (self.x_max - self.x_min)
return interpolate(self.main_line.get_start(),
self.main_line.get_end(), alpha)
def point_to_number(self, point):
left_point, right_point = self.main_line.get_start_and_end()
full_vect = right_point - left_point
def distance_from_left(p):
return np.dot(p - left_point,
full_vect) / np.linalg.norm(full_vect)
return interpolate(
self.x_min, self.x_max,
distance_from_left(point) / distance_from_left(right_point))
def default_numbers_to_display(self):
if self.numbers_to_show is not None:
return self.numbers_to_show
return np.arange(int(self.leftmost_tick), int(self.x_max) + 1)
def get_number_mobjects(self, *numbers, **kwargs):
# TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
if "force_integers" in kwargs and kwargs["force_integers"]:
numbers = list(map(int, numbers))
result = VGroup()
for number in numbers:
mob = TexMobject(str(number))
mob.scale(self.number_scale_val)
mob.next_to(
self.number_to_point(number),
self.label_direction,
self.line_to_number_buff,
)
result.add(mob)
return result
def get_labels(self):
return self.get_number_mobjects()
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(*numbers, **kwargs)
self.add(self.numbers)
return self
def add_tip(self):
start, end = self.main_line.get_start_and_end()
vect = (end - start) / np.linalg.norm(end - start)
arrow = Arrow(start, end + MED_SMALL_BUFF * vect, buff=0)
tip = arrow.tip
tip.set_color(self.color)
self.tip = tip
self.add(tip)