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.highlight(X_COLOR)
y_line.highlight(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time=1))
self.dither()
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.dither()
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.highlight(X_COLOR)
y_line.highlight(Y_COLOR)
x_coord, y_coord = array.get_mob_matrix().flatten()
self.play(Write(array, run_time = 1))
self.dither()
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.dither()
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.highlight(X_COLOR)
y_line.highlight(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.dither()
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.dither()
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
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.highlight(X_COLOR)
y_line.highlight(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.dither()
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.dither()
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" : BLUE,
"x_min" : -SPACE_WIDTH,
"x_max" : SPACE_WIDTH,
"unit_size" : 1,
"tick_size" : 0.1,
"tick_frequency" : 1,
"leftmost_tick" : None, #Defaults to ceil(x_min)
"numbers_with_elongated_ticks" : [0],
"numbers_to_show" : None,
"longer_tick_multiple" : 2,
"number_at_center" : 0,
"number_scale_val" : 0.75,
"line_to_number_vect" : 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:
self.leftmost_tick = np.ceil(self.x_min)
VMobject.__init__(self, **kwargs)
if self.include_tip:
self.add_tip()
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)
for x in self.get_tick_numbers():
if x in self.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 = 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.line_to_number_vect,
self.line_to_number_buff,
)
result.add(mob)
return result
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.highlight(self.color)
self.tip = tip
self.add(tip)
class NumberLine(VMobject):
CONFIG = {
"color": BLUE,
"x_min": -SPACE_WIDTH,
"x_max": SPACE_WIDTH,
"space_unit_to_num": 1,
"tick_size": 0.1,
"tick_frequency": 1,
"leftmost_tick": None, #Defaults to ceil(x_min)
"numbers_with_elongated_ticks": [0],
"numbers_to_show": None,
"longer_tick_multiple": 2,
"number_at_center": 0,
"propogate_style_to_family": True
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
self.leftmost_tick = np.ceil(self.x_min)
VMobject.__init__(self, **kwargs)
def generate_points(self):
self.main_line = Line(self.x_min * RIGHT, self.x_max * RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple * self.tick_size)
self.stretch(self.space_unit_to_num, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size):
self.tick_marks.add(
Line(
x * RIGHT + size * DOWN,
x * RIGHT + size * UP,
))
return self
def get_tick_marks(self):
return self.tick_marks
def get_tick_numbers(self):
return np.arange(self.leftmost_tick, self.x_max + self.tick_frequency,
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(self.leftmost_tick, self.x_max, 1)
def get_vertical_number_offset(self, direction=DOWN):
return 4 * direction * self.tick_size
def get_number_mobjects(self, *numbers, **kwargs):
#TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = VGroup()
for number in numbers:
mob = TexMobject(str(int(number)))
mob.scale_to_fit_height(3 * self.tick_size)
mob.shift(self.number_to_point(number),
self.get_vertical_number_offset(**kwargs))
result.add(mob)
return result
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(*numbers, **kwargs)
self.add(*self.numbers)
return self
class NumberLine(VMobject):
CONFIG = {
"color" : BLUE,
"x_min" : -SPACE_WIDTH,
"x_max" : SPACE_WIDTH,
"unit_size" : 1,
"tick_size" : 0.1,
"tick_frequency" : 1,
"leftmost_tick" : None, #Defaults to ceil(x_min)
"numbers_with_elongated_ticks" : [0],
"numbers_to_show" : None,
"longer_tick_multiple" : 2,
"number_at_center" : 0,
"propogate_style_to_family" : True
}
def __init__(self, **kwargs):
digest_config(self, kwargs)
if self.leftmost_tick is None:
self.leftmost_tick = np.ceil(self.x_min)
VMobject.__init__(self, **kwargs)
def generate_points(self):
self.main_line = Line(self.x_min*RIGHT, self.x_max*RIGHT)
self.tick_marks = VMobject()
self.add(self.main_line, self.tick_marks)
for x in self.get_tick_numbers():
self.add_tick(x, self.tick_size)
for x in self.numbers_with_elongated_ticks:
self.add_tick(x, self.longer_tick_multiple*self.tick_size)
self.stretch(self.unit_size, 0)
self.shift(-self.number_to_point(self.number_at_center))
def add_tick(self, x, size):
self.tick_marks.add(Line(
x*RIGHT+size*DOWN,
x*RIGHT+size*UP,
))
return self
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(self.leftmost_tick, self.x_max, 1)
def get_vertical_number_offset(self, direction = DOWN):
return 4*direction*self.tick_size
def get_number_mobjects(self, *numbers, **kwargs):
#TODO, handle decimals
if len(numbers) == 0:
numbers = self.default_numbers_to_display()
result = VGroup()
for number in numbers:
mob = TexMobject(str(int(number)))
mob.scale_to_fit_height(3*self.tick_size)
mob.shift(
self.number_to_point(number),
self.get_vertical_number_offset(**kwargs)
)
result.add(mob)
return result
def add_numbers(self, *numbers, **kwargs):
self.numbers = self.get_number_mobjects(
*numbers, **kwargs
)
self.add(*self.numbers)
return self
