mirror of
https://github.com/3b1b/manim.git
synced 2025-08-05 22:03:01 +08:00
Merge branch 'master' into eop
This commit is contained in:
Ben Hambrecht
@ -3,16 +3,78 @@ from big_ol_pile_of_manim_imports import *
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class NumberlineTransformationScene(Scene):
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CONFIG = {
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"input_line_center": 2 * UP,
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"output_line_center": 2 * DOWN,
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"number_line_config": {
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"include_numbers": True,
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"x_min": -3.5,
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"x_max": 3.5,
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"unit_size": 2,
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},
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# These would override number_line_config
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"input_line_config": {
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"color": BLUE,
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},
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"output_line_config": {},
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"num_inserted_number_line_anchors": 20,
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}
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def setup(self):
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pass
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self.setup_number_lines()
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self.setup_titles()
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def setup_number_lines(self):
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number_lines = self.number_lines = VGroup()
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added_configs = (self.input_line_config, self.output_line_config)
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centers = (self.input_line_center, self.output_line_center)
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for added_config, center in zip(added_configs, centers):
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full_config = dict(self.number_line_config)
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full_config.update(added_config)
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number_line = NumberLine(**full_config)
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number_line.main_line.insert_n_anchor_points(
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self.num_inserted_number_line_anchors
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)
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number_line.move_to(center)
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number_lines.add(number_line)
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self.input_line, self.output_line = number_lines
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self.add(number_lines)
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def setup_titles(self):
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input_title, output_title = self.titles = VGroup(*[
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TextMobject()
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for word in "Inputs", "Outputs"
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])
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for title, line in zip(self.titles, self.number_lines):
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title.next_to(line, UP)
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title.shift_onto_screen()
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self.add(self.titles)
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def get_line_mapping_animation(self, func, run_time=3, path_arc=30 * DEGREES):
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input_line, output_line = self.number_lines
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input_line_copy = input_line.deepcopy()
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input_line_copy.remove(input_line_copy.numbers)
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input_line_copy.set_stroke(width=2)
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def point_func(point):
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input_number = input_line.point_to_number(point)
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output_number = func(input_number)
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return output_line.number_to_point(output_number)
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return ApplyPointwiseFunction(
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point_func, input_line_copy,
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run_time=run_time,
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path_arc=path_arc,
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)
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class ExampleNumberlineTransformationScene(NumberlineTransformationScene):
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def construct(self):
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pass
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func = lambda x: x**2
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anim = self.get_line_mapping_animation(func)
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self.play(anim)
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self.wait()
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# Scenes
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@ -47,18 +109,14 @@ class WriteOpeningWords(Scene):
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class StartingCalc101(PiCreatureScene):
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CONFIG = {
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# "default_pi_creature_kwargs": {
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# "color": BLUE,
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# "flip_at_start": False,
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# },
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}
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def construct(self):
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randy = self.pi_creature
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deriv_string = "\\frac{df}{dx}(x) = \\lim(\\delta x \\to \\infty)" + \
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"{f(x + \\delta x) - f(x) \\over \\delta x}"
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equations = VGroup(
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TexMobject(*break_up_string_by_terms(deriv_string, "\\delta x"))
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deriv_equation = TexMobject(
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"\\frac{df}{dx}(x) = \\lim_{\\Delta x \\to \\infty}" +
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"{f(x + \\Delta x) - f(x) \\over \\Delta x}",
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tex_to_color_map={"\\Delta x": BLUE}
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)
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title = TextMobject("Calculus 101")
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title.to_edge(UP)
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@ -71,3 +129,273 @@ class StartingCalc101(PiCreatureScene):
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self.wait()
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class StandardDerivativeVisual(GraphScene):
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CONFIG = {
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"y_max": 8,
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"y_axis_height": 5,
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}
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def construct(self):
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self.add_title()
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self.show_function_graph()
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self.show_slope_of_graph()
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self.encourage_not_to_think_of_slope_as_definition()
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self.show_sensitivity()
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def add_title(self):
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title = self.title = TextMobject("Standard derivative visual")
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT)
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h_line.scale_to_fit_width(FRAME_WIDTH - 2 * LARGE_BUFF)
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h_line.next_to(title, DOWN)
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self.add(title, h_line)
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def show_function_graph(self):
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self.setup_axes()
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def func(x):
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x -= 5
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return 0.1 * (x + 3) * (x - 3) * x + 3
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graph = self.get_graph(func)
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graph_label = self.get_graph_label(graph, x_val=9.5)
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input_tracker = ValueTracker(4)
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def get_x_value():
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return input_tracker.get_value()
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def get_y_value():
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return graph.underlying_function(get_x_value())
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def get_x_point():
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return self.coords_to_point(get_x_value(), 0)
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def get_y_point():
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return self.coords_to_point(0, get_y_value())
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def get_graph_point():
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return self.coords_to_point(get_x_value(), get_y_value())
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def get_v_line():
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return DashedLine(get_x_point(), get_graph_point(), stroke_width=2)
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def get_h_line():
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return DashedLine(get_graph_point(), get_y_point(), stroke_width=2)
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input_triangle = RegularPolygon(n=3, start_angle=TAU / 4)
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output_triangle = RegularPolygon(n=3, start_angle=0)
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for triangle in input_triangle, output_triangle:
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triangle.set_fill(WHITE, 1)
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triangle.set_stroke(width=0)
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triangle.scale(0.1)
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input_triangle_update = ContinualUpdateFromFunc(
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input_triangle, lambda m: m.move_to(get_x_point(), UP)
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)
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output_triangle_update = ContinualUpdateFromFunc(
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output_triangle, lambda m: m.move_to(get_y_point(), RIGHT)
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)
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x_label = TexMobject("x")
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x_label_update = ContinualUpdateFromFunc(
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x_label, lambda m: m.next_to(input_triangle, DOWN, SMALL_BUFF)
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)
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output_label = TexMobject("f(x)")
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output_label_update = ContinualUpdateFromFunc(
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output_label, lambda m: m.next_to(
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output_triangle, LEFT, SMALL_BUFF)
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)
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v_line = get_v_line()
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v_line_update = ContinualUpdateFromFunc(
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v_line, lambda vl: Transform(vl, get_v_line()).update(1)
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)
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h_line = get_h_line()
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h_line_update = ContinualUpdateFromFunc(
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h_line, lambda hl: Transform(hl, get_h_line()).update(1)
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)
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graph_dot = Dot(color=YELLOW)
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graph_dot_update = ContinualUpdateFromFunc(
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graph_dot, lambda m: m.move_to(get_graph_point())
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)
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self.play(
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ShowCreation(graph),
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Write(graph_label),
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)
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self.play(
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DrawBorderThenFill(input_triangle, run_time=1),
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Write(x_label),
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ShowCreation(v_line),
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GrowFromCenter(graph_dot),
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)
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self.add_foreground_mobject(graph_dot)
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self.play(
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ShowCreation(h_line),
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Write(output_label),
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DrawBorderThenFill(output_triangle, run_time=1)
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)
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self.add(
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input_triangle_update,
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x_label_update,
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graph_dot_update,
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v_line_update,
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h_line_update,
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output_triangle_update,
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output_label_update,
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)
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self.play(
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input_tracker.set_value, 8,
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run_time=6,
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rate_func=there_and_back
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)
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self.input_tracker = input_tracker
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self.graph = graph
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def show_slope_of_graph(self):
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input_tracker = self.input_tracker
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deriv_input_tracker = ValueTracker(input_tracker.get_value())
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# Slope line
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def get_slope_line():
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return self.get_secant_slope_group(
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x=deriv_input_tracker.get_value(),
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graph=self.graph,
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dx=0.01,
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secant_line_length=4
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).secant_line
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slope_line = get_slope_line()
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slope_line_update = ContinualUpdateFromFunc(
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slope_line, lambda sg: Transform(sg, get_slope_line()).update(1)
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)
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def position_deriv_label(deriv_label):
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deriv_label.next_to(slope_line, UP)
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return deriv_label
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deriv_label = TexMobject(
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"\\frac{df}{dx}(x) =", "\\text{Slope}", "="
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)
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deriv_label.get_part_by_tex("Slope").match_color(slope_line)
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deriv_label_update = ContinualUpdateFromFunc(
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deriv_label, position_deriv_label
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)
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slope_decimal = DecimalNumber(slope_line.get_slope())
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slope_decimal.match_color(slope_line)
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slope_decimal_update = ContinualChangingDecimal(
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slope_decimal, lambda dt: slope_line.get_slope(),
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position_update_func=lambda m: m.next_to(
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deriv_label, RIGHT, SMALL_BUFF
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).shift(0.2 * SMALL_BUFF * DOWN)
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)
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self.play(
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ShowCreation(slope_line),
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Write(deriv_label),
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Write(slope_decimal),
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run_time=1
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)
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self.wait()
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self.add(
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slope_line_update,
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# deriv_label_update,
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slope_decimal_update,
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)
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for x in 9, 2, 4:
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self.play(
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input_tracker.set_value, x,
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deriv_input_tracker.set_value, x,
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run_time=3
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)
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self.wait()
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self.deriv_input_tracker = deriv_input_tracker
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def encourage_not_to_think_of_slope_as_definition(self):
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morty = Mortimer(height=2)
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morty.to_corner(DR)
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self.play(FadeIn(morty))
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self.play(PiCreatureSays(
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||||
morty, "Don't think of \\\\ this as the definition",
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||||
bubble_kwargs={"height": 2, "width": 4}
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||||
))
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||||
self.play(Blink(morty))
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||||
self.wait()
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||||
self.play(
|
||||
RemovePiCreatureBubble(morty),
|
||||
UpdateFromAlphaFunc(
|
||||
morty, lambda m, a: m.set_fill(opacity=1 - a),
|
||||
remover=True
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||||
)
|
||||
)
|
||||
|
||||
def show_sensitivity(self):
|
||||
input_tracker = self.input_tracker
|
||||
deriv_input_tracker = self.deriv_input_tracker
|
||||
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||||
self.wiggle_input()
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||||
for x in 9, 7, 2:
|
||||
self.play(
|
||||
input_tracker.set_value, x,
|
||||
deriv_input_tracker.set_value, x,
|
||||
run_time=3
|
||||
)
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||||
self.wiggle_input()
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||||
|
||||
###
|
||||
def wiggle_input(self, dx=0.5, run_time=3):
|
||||
input_tracker = self.input_tracker
|
||||
|
||||
x = input_tracker.get_value()
|
||||
x_min = x - dx
|
||||
x_max = x + dx
|
||||
y, y_min, y_max = map(
|
||||
self.graph.underlying_function,
|
||||
[x, x_min, x_max]
|
||||
)
|
||||
x_line = Line(
|
||||
self.coords_to_point(x_min, 0),
|
||||
self.coords_to_point(x_max, 0),
|
||||
)
|
||||
y_line = Line(
|
||||
self.coords_to_point(0, y_min),
|
||||
self.coords_to_point(0, y_max),
|
||||
)
|
||||
|
||||
x_rect, y_rect = rects = VGroup(Rectangle(), Rectangle())
|
||||
rects.set_stroke(width=0)
|
||||
rects.set_fill(YELLOW, 0.5)
|
||||
x_rect.match_width(x_line)
|
||||
x_rect.stretch_to_fit_height(0.25)
|
||||
x_rect.move_to(x_line)
|
||||
y_rect.match_height(y_line)
|
||||
y_rect.stretch_to_fit_width(0.25)
|
||||
y_rect.move_to(y_line)
|
||||
|
||||
self.play(
|
||||
ApplyMethod(
|
||||
input_tracker.set_value, input_tracker.get_value() + dx,
|
||||
rate_func=lambda t: wiggle(t, 6)
|
||||
),
|
||||
FadeIn(
|
||||
rects,
|
||||
rate_func=squish_rate_func(smooth, 0, 0.33),
|
||||
remover=True,
|
||||
),
|
||||
run_time=run_time,
|
||||
)
|
||||
self.play(FadeOut(rects))
|
||||
|
||||
|
||||
class EoCWrapper(Scene):
|
||||
def construct(self):
|
||||
title = Title("Essence of calculus")
|
||||
self.play(Write(title))
|
||||
self.wait()
|
||||
|
||||
@ -1,15 +1,17 @@
|
||||
from utils.config_ops import digest_config
|
||||
|
||||
# Currently, this is only used by both Scene and MOBject.
|
||||
# Currently, this is only used by both Scene and Mobject.
|
||||
# Still, we abstract its functionality here, albeit purely nominally.
|
||||
# All actual implementation has to be handled by derived classes for now.
|
||||
#
|
||||
# Note that although the prototypical instances add and remove MObjects,
|
||||
# Note that although the prototypical instances add and remove Mobjects,
|
||||
# there is also the possibility to add ContinualAnimations to Scenes. Thus,
|
||||
# in the Container class in general, we do not make any presumptions about
|
||||
# what types of objects may be added; this is again dependent on the specific
|
||||
# derived instance.
|
||||
|
||||
# TODO: Move the "remove" functionality of Scene to this class
|
||||
|
||||
|
||||
class Container(object):
|
||||
def __init__(self, *submobjects, **kwargs):
|
||||
|
||||
@ -616,23 +616,19 @@ class Mobject(Container):
|
||||
##
|
||||
|
||||
def reduce_across_dimension(self, points_func, reduce_func, dim):
|
||||
try:
|
||||
points = self.get_points_defining_boundary()
|
||||
values = [points_func(points[:, dim])]
|
||||
except:
|
||||
values = []
|
||||
values += [
|
||||
mob.reduce_across_dimension(points_func, reduce_func, dim)
|
||||
for mob in self.nonempty_submobjects()
|
||||
]
|
||||
try:
|
||||
return reduce_func(values)
|
||||
except:
|
||||
points = self.get_all_points()
|
||||
if points is None or len(points) == 0:
|
||||
# Note, this default means things like empty VGroups
|
||||
# will appear to have a center at [0, 0, 0]
|
||||
return 0
|
||||
values = points_func(points[:, dim])
|
||||
return reduce_func(values)
|
||||
|
||||
def nonempty_submobjects(self):
|
||||
return [submob for submob in self.submobjects
|
||||
if len(submob.submobjects) != 0 or len(submob.points) != 0]
|
||||
return [
|
||||
submob for submob in self.submobjects
|
||||
if len(submob.submobjects) != 0 or len(submob.points) != 0
|
||||
]
|
||||
|
||||
def get_merged_array(self, array_attr):
|
||||
result = None
|
||||
|
||||
@ -13,7 +13,7 @@ from utils.config_ops import digest_config
|
||||
|
||||
class NumberLine(VMobject):
|
||||
CONFIG = {
|
||||
"color": BLUE,
|
||||
"color": LIGHT_GREY,
|
||||
"x_min": -FRAME_X_RADIUS,
|
||||
"x_max": FRAME_X_RADIUS,
|
||||
"unit_size": 1,
|
||||
@ -21,6 +21,7 @@ class NumberLine(VMobject):
|
||||
"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,
|
||||
@ -39,6 +40,8 @@ class NumberLine(VMobject):
|
||||
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)
|
||||
@ -133,7 +136,7 @@ class NumberLine(VMobject):
|
||||
self.numbers = self.get_number_mobjects(
|
||||
*numbers, **kwargs
|
||||
)
|
||||
self.add(*self.numbers)
|
||||
self.add(self.numbers)
|
||||
return self
|
||||
|
||||
def add_tip(self):
|
||||
|
||||
@ -175,7 +175,7 @@ class CompleteGraph(Graph):
|
||||
return Graph.__str__(self) + str(self.num_vertices)
|
||||
|
||||
|
||||
class GraphScene(Scene):
|
||||
class DiscreteGraphScene(Scene):
|
||||
args_list = [
|
||||
(CubeGraph(),),
|
||||
(SampleGraph(),),
|
||||
|
||||
@ -50,8 +50,8 @@ class GraphScene(Scene):
|
||||
"default_input_color": YELLOW,
|
||||
"default_riemann_start_color": BLUE,
|
||||
"default_riemann_end_color": GREEN,
|
||||
"area_opacity" : 0.8,
|
||||
"num_rects" : 50,
|
||||
"area_opacity": 0.8,
|
||||
"num_rects": 50,
|
||||
}
|
||||
|
||||
def setup(self):
|
||||
@ -294,17 +294,16 @@ class GraphScene(Scene):
|
||||
for n in range(n_iterations)
|
||||
]
|
||||
|
||||
|
||||
def get_area(self, graph, t_min, t_max):
|
||||
numerator = max(t_max - t_min, 0.0001)
|
||||
dx = float(numerator) / self.num_rects
|
||||
return self.get_riemann_rectangles(
|
||||
graph,
|
||||
x_min = t_min,
|
||||
x_max = t_max,
|
||||
dx = dx,
|
||||
stroke_width = 0,
|
||||
).set_fill(opacity = self.area_opacity)
|
||||
x_min=t_min,
|
||||
x_max=t_max,
|
||||
dx=dx,
|
||||
stroke_width=0,
|
||||
).set_fill(opacity=self.area_opacity)
|
||||
|
||||
def transform_between_riemann_rects(self, curr_rects, new_rects, **kwargs):
|
||||
transform_kwargs = {
|
||||
@ -443,29 +442,28 @@ class GraphScene(Scene):
|
||||
|
||||
return group
|
||||
|
||||
|
||||
def add_T_label(self, x_val, side = RIGHT, label = None, color = WHITE, animated = False, **kwargs):
|
||||
triangle = RegularPolygon(n=3, start_angle = np.pi/2)
|
||||
def add_T_label(self, x_val, side=RIGHT, label=None, color=WHITE, animated=False, **kwargs):
|
||||
triangle = RegularPolygon(n=3, start_angle=np.pi / 2)
|
||||
triangle.scale_to_fit_height(MED_SMALL_BUFF)
|
||||
triangle.move_to(self.coords_to_point(x_val, 0), UP)
|
||||
triangle.set_fill(color, 1)
|
||||
triangle.set_stroke(width = 0)
|
||||
triangle.set_stroke(width=0)
|
||||
if label == None:
|
||||
T_label = TexMobject(self.variable_point_label, fill_color = color)
|
||||
T_label = TexMobject(self.variable_point_label, fill_color=color)
|
||||
else:
|
||||
T_label = TexMobject(label, fill_color = color)
|
||||
|
||||
T_label = TexMobject(label, fill_color=color)
|
||||
|
||||
T_label.next_to(triangle, DOWN)
|
||||
v_line = self.get_vertical_line_to_graph(
|
||||
x_val, self.v_graph,
|
||||
color = YELLOW
|
||||
color=YELLOW
|
||||
)
|
||||
|
||||
if animated:
|
||||
self.play(
|
||||
DrawBorderThenFill(triangle),
|
||||
ShowCreation(v_line),
|
||||
Write(T_label, run_time = 1),
|
||||
Write(T_label, run_time=1),
|
||||
**kwargs
|
||||
)
|
||||
|
||||
@ -478,16 +476,13 @@ class GraphScene(Scene):
|
||||
self.right_v_line = v_line
|
||||
self.add(self.right_T_label_group, self.right_v_line)
|
||||
|
||||
|
||||
|
||||
|
||||
def get_animation_integral_bounds_change(
|
||||
self,
|
||||
graph,
|
||||
new_t_min,
|
||||
new_t_max,
|
||||
fade_close_to_origin = True,
|
||||
run_time = 1.0
|
||||
fade_close_to_origin=True,
|
||||
run_time=1.0
|
||||
):
|
||||
curr_t_min = self.x_axis.point_to_number(self.area.get_left())
|
||||
curr_t_max = self.x_axis.point_to_number(self.area.get_right())
|
||||
@ -506,8 +501,8 @@ class GraphScene(Scene):
|
||||
area, left_v_line, left_T_label, right_v_line, right_T_label = group
|
||||
t_min = interpolate(curr_t_min, new_t_min, alpha)
|
||||
t_max = interpolate(curr_t_max, new_t_max, alpha)
|
||||
new_area = self.get_area(graph,t_min, t_max)
|
||||
|
||||
new_area = self.get_area(graph, t_min, t_max)
|
||||
|
||||
new_left_v_line = self.get_vertical_line_to_graph(
|
||||
t_min, graph
|
||||
)
|
||||
@ -523,19 +518,16 @@ class GraphScene(Scene):
|
||||
# Fade close to 0
|
||||
if fade_close_to_origin:
|
||||
if len(left_T_label) > 0:
|
||||
left_T_label[0].set_fill(opacity = min(1, np.abs(t_min)))
|
||||
left_T_label[0].set_fill(opacity=min(1, np.abs(t_min)))
|
||||
if len(right_T_label) > 0:
|
||||
right_T_label[0].set_fill(opacity = min(1, np.abs(t_max)))
|
||||
right_T_label[0].set_fill(opacity=min(1, np.abs(t_max)))
|
||||
|
||||
Transform(area, new_area).update(1)
|
||||
Transform(left_v_line, new_left_v_line).update(1)
|
||||
Transform(right_v_line, new_right_v_line).update(1)
|
||||
return group
|
||||
|
||||
return UpdateFromAlphaFunc(group, update_group, run_time = run_time)
|
||||
|
||||
|
||||
|
||||
return UpdateFromAlphaFunc(group, update_group, run_time=run_time)
|
||||
|
||||
def animate_secant_slope_group_change(
|
||||
self, secant_slope_group,
|
||||
@ -578,23 +570,3 @@ class GraphScene(Scene):
|
||||
)
|
||||
secant_slope_group.kwargs["x"] = target_x
|
||||
secant_slope_group.kwargs["dx"] = target_dx
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
81
utils/tex_file_writing.py
Normal file
81
utils/tex_file_writing.py
Normal file
@ -0,0 +1,81 @@
|
||||
import os
|
||||
from constants import TEX_DIR
|
||||
from constants import TEX_TEXT_TO_REPLACE
|
||||
|
||||
|
||||
def tex_hash(expression, template_tex_file):
|
||||
return str(hash(expression + template_tex_file))
|
||||
|
||||
|
||||
def tex_to_svg_file(expression, template_tex_file):
|
||||
tex_file = generate_tex_file(expression, template_tex_file)
|
||||
dvi_file = tex_to_dvi(tex_file)
|
||||
return dvi_to_svg(dvi_file)
|
||||
|
||||
|
||||
def generate_tex_file(expression, template_tex_file):
|
||||
result = os.path.join(
|
||||
TEX_DIR,
|
||||
tex_hash(expression, template_tex_file)
|
||||
) + ".tex"
|
||||
if not os.path.exists(result):
|
||||
print("Writing \"%s\" to %s" % (
|
||||
"".join(expression), result
|
||||
))
|
||||
with open(template_tex_file, "r") as infile:
|
||||
body = infile.read()
|
||||
body = body.replace(TEX_TEXT_TO_REPLACE, expression)
|
||||
with open(result, "w") as outfile:
|
||||
outfile.write(body)
|
||||
return result
|
||||
|
||||
|
||||
def get_null():
|
||||
if os.name == "nt":
|
||||
return "NUL"
|
||||
return "/dev/null"
|
||||
|
||||
|
||||
def tex_to_dvi(tex_file):
|
||||
result = tex_file.replace(".tex", ".dvi")
|
||||
if not os.path.exists(result):
|
||||
commands = [
|
||||
"latex",
|
||||
"-interaction=batchmode",
|
||||
"-halt-on-error",
|
||||
"-output-directory=" + TEX_DIR,
|
||||
tex_file,
|
||||
">",
|
||||
get_null()
|
||||
]
|
||||
exit_code = os.system(" ".join(commands))
|
||||
if exit_code != 0:
|
||||
log_file = tex_file.replace(".tex", ".log")
|
||||
raise Exception(
|
||||
"Latex error converting to dvi. "
|
||||
"See log output above or the log file: %s" % log_file)
|
||||
return result
|
||||
|
||||
|
||||
def dvi_to_svg(dvi_file, regen_if_exists=False):
|
||||
"""
|
||||
Converts a dvi, which potentially has multiple slides, into a
|
||||
directory full of enumerated pngs corresponding with these slides.
|
||||
Returns a list of PIL Image objects for these images sorted as they
|
||||
where in the dvi
|
||||
"""
|
||||
result = dvi_file.replace(".dvi", ".svg")
|
||||
if not os.path.exists(result):
|
||||
commands = [
|
||||
"dvisvgm",
|
||||
dvi_file,
|
||||
"-n",
|
||||
"-v",
|
||||
"0",
|
||||
"-o",
|
||||
result,
|
||||
">",
|
||||
get_null()
|
||||
]
|
||||
os.system(" ".join(commands))
|
||||
return result
|
||||
Reference in New Issue
Block a user