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