def construct(self): formula = TexMobject(*([ "{%d \\over %d} \\cdot" % (wallis_numer(n), wallis_denom(n)) for n in range(1, self.n_terms + 1) ] + ["\\cdots"])) result = TexMobject("=", "{\\pi \\over 2}") result.scale(2) pi = result[-1][0] pi.set_color(YELLOW) circle = Circle(color=YELLOW) circle.surround(pi) question = TexMobject("?", color=YELLOW) question.scale(2).next_to(circle, RIGHT, buff=0.4) result_group = VGroup(result, circle, question) result_group.next_to(formula, DOWN) group = VGroup(formula, result_group) group.center().set_width(10) bg_rect = BackgroundRectangle(group, fill_opacity=0.5, buff=0.2) random_walks = VGroup(*[ RandomWalk1DArrow(random_walk_string(30), step_size=0.5) for k in range(self.n_walks) ]) for k, walk in enumerate(random_walks): walk.shift(random.randrange(-5, 5) * 2 * walk.step_size * UP) random_walks.center() text = TextMobject(self.part).scale(3).set_color(YELLOW) text.to_corner(RIGHT + DOWN) self.add(random_walks) self.add(FullScreenFadeRectangle()) self.add(bg_rect, group, text)
def scroll_through_patrons(self): logo_box = Square(side_length=2.5) logo_box.to_corner(DOWN + LEFT, buff=MED_LARGE_BUFF) total_width = FRAME_X_RADIUS - logo_box.get_right()[0] black_rect = Rectangle( fill_color=BLACK, fill_opacity=1, stroke_width=0, width=FRAME_WIDTH, height=0.6 * FRAME_HEIGHT, ) black_rect.to_edge(UP, buff=0) line = DashedLine(FRAME_X_RADIUS * LEFT, FRAME_X_RADIUS * RIGHT) line.move_to(ORIGIN) self.add(line) thanks = TextMobject("Funded by the community, with special thanks to:") thanks.scale(0.9) thanks.next_to(black_rect.get_bottom(), UP, SMALL_BUFF) thanks.set_color(YELLOW) underline = Line(LEFT, RIGHT) underline.scale_to_fit_width(thanks.get_width() + MED_SMALL_BUFF) underline.next_to(thanks, DOWN, SMALL_BUFF) thanks.add(underline) self.add(thanks) patrons = VGroup(*map(TextMobject, self.specific_patrons)) patrons.scale(self.patron_scale_val) for patron in patrons: if patron.get_width() > self.max_patron_width: patron.scale_to_fit_width(self.max_patron_width) columns = VGroup(*[ VGroup(*patrons[i::self.n_patron_columns]) for i in range(self.n_patron_columns) ]) for column in columns: for n, name in enumerate(column): name.shift(n * self.name_y_spacing * DOWN) columns.arrange_submobjects( RIGHT, buff=LARGE_BUFF, aligned_edge=UP, ) columns.scale_to_fit_width(total_width - 1) columns.next_to(black_rect, DOWN, 3 * LARGE_BUFF) columns.to_edge(RIGHT) thanks.align_to(columns, alignment_vect=RIGHT) self.play( columns.move_to, 2 * DOWN, DOWN, columns.to_edge, RIGHT, Animation(black_rect), Animation(line), Animation(thanks), rate_func=None, run_time=self.run_time, )
def generate_points(self): body = Cube(side_length=1) for dim, scale_factor in enumerate(self.body_dimensions): body.stretch(scale_factor, dim=dim) body.scale_to_fit_width(self.width) body.set_fill(self.shaded_body_color, opacity=1) body.sort_submobjects(lambda p: p[2]) body[-1].set_fill(self.body_color) screen_plate = body.copy() keyboard = VGroup(*[ VGroup(*[ Square(**self.key_color_kwargs) for x in range(12 - y % 2) ]).arrange_submobjects(RIGHT, buff=SMALL_BUFF) for y in range(4) ]).arrange_submobjects(DOWN, buff=MED_SMALL_BUFF) keyboard.stretch_to_fit_width( self.keyboard_width_to_body_width * body.get_width(), ) keyboard.stretch_to_fit_height( self.keyboard_height_to_body_height * body.get_height(), ) keyboard.next_to(body, OUT, buff=0.1 * SMALL_BUFF) keyboard.shift(MED_SMALL_BUFF * UP) body.add(keyboard) screen_plate.stretch(self.screen_thickness / self.body_dimensions[2], dim=2) screen = Rectangle( stroke_width=0, fill_color=BLACK, fill_opacity=1, ) screen.replace(screen_plate, stretch=True) screen.scale_in_place(self.screen_width_to_screen_plate_width) screen.next_to(screen_plate, OUT, buff=0.1 * SMALL_BUFF) screen_plate.add(screen) screen_plate.next_to(body, UP, buff=0) screen_plate.rotate( self.open_angle, RIGHT, about_point=screen_plate.get_bottom() ) self.screen_plate = screen_plate self.screen = screen axis = Line( body.get_corner(UP + LEFT + OUT), body.get_corner(UP + RIGHT + OUT), color=BLACK, stroke_width=2 ) self.axis = axis self.add(body, screen_plate, axis) self.rotate(5 * np.pi / 12, LEFT, about_point=ORIGIN) self.rotate(np.pi / 6, DOWN, about_point=ORIGIN)
def generate_points(self): body = Cube(side_length=1) for dim, scale_factor in enumerate(self.body_dimensions): body.stretch(scale_factor, dim=dim) body.scale_to_fit_width(self.width) body.set_fill(self.shaded_body_color, opacity=1) body.sort_submobjects(lambda p: p[2]) body[-1].set_fill(self.body_color) keyboard = VGroup(*[ VGroup(*[ Square(**self.key_color_kwargs) for x in range(12 - y % 2) ]).arrange_submobjects(RIGHT, buff=SMALL_BUFF) for y in range(4) ]).arrange_submobjects(DOWN, buff=MED_SMALL_BUFF) keyboard.stretch_to_fit_width( self.keyboard_width_to_body_width * body.get_width(), ) keyboard.stretch_to_fit_height( self.keyboard_height_to_body_height * body.get_height(), ) keyboard.next_to(body, OUT, buff=0.1 * SMALL_BUFF) keyboard.shift(MED_SMALL_BUFF * UP) body.add(keyboard) screen_plate = body.copy() screen_plate.stretch(self.screen_thickness / self.body_dimensions[2], dim=2) screen = Rectangle( stroke_width=0, fill_color=BLACK, fill_opacity=1, ) screen.replace(screen_plate, stretch=True) screen.scale_in_place(self.screen_width_to_screen_plate_width) screen.next_to(screen_plate, OUT, buff=0.1 * SMALL_BUFF) screen_plate.add(screen) screen_plate.next_to(body, UP, buff=0) screen_plate.rotate( self.open_angle, RIGHT, about_point=screen_plate.get_bottom() ) self.screen_plate = screen_plate self.screen = screen axis = Line( body.get_corner(UP + LEFT + OUT), body.get_corner(UP + RIGHT + OUT), color=BLACK, stroke_width=2 ) self.axis = axis self.add(body, screen_plate, axis) self.rotate(5 * np.pi / 12, LEFT, about_point=ORIGIN) self.rotate(np.pi / 6, DOWN, about_point=ORIGIN)
def add_words(self): # Wallis product product = TexMobject(*(["\\text{Wallis公式:}"] + [ "{%d \\over %d} \\," % (wallis_numer(n), wallis_denom(n)) for n in range(1, 8) ] + ["\\cdots = {\\pi \\over 2}"])).set_color(YELLOW) rect = SurroundingRectangle(product, color=YELLOW, buff=0.25) wallis_product = VGroup(product, rect) wallis_product.set_width(6) # All those steps nums = [TextMobject("%d. " % k) for k in [1, 2, 3, 4]] words = [ TextMobject(word) for word in [ "构造合适的矩形边长", "同种颜色的矩形的面积之和恒为1", "整个图形又像一个${1 \\over 4}$圆,半径是", "比较${1 \\over 4}$圆与矩形的面积", ] ] formulae = [ TextMobject(formula) for formula in [ "$a_0 = 1,\\, a_n = {1 \\over 2} \cdot {3 \\over 4} \cdots {2n-1 \\over 2n} (n \geq 1)$", "$a_0 a_n + a_1 a_{n-1} + \\cdots + a_n a_0 = 1$", "$\\begin{aligned} \ r_n & = a_0 + a_1 + \\cdots + a_{n-1} \\\\ \ & = \\textstyle{3 \\over 2} \cdot {5 \\over 4} \cdots {2n-1 \\over 2n-2} \ \\quad (n \geq 2) \ \\end{aligned}$", "${1 \\over 4} \\pi {r_n}^2 \\approx n \\quad \\Rightarrow \\quad \\text{Wallis公式}$" ] ] steps = VGroup() for num, word, formula in zip(nums, words, formulae): num.next_to(word, LEFT) formula.next_to(word, DOWN, aligned_edge=LEFT) steps.add(VGroup(num, word, formula)) steps.arrange_submobjects(DOWN, buff=0.6, aligned_edge=LEFT) steps.set_width(6) steps.next_to(wallis_product, DOWN) VGroup(wallis_product, steps).center().to_edge(RIGHT, buff=0.15) # Sep line and QED sep_line = DashedLine(2 * TOP, 2 * BOTTOM, color=GREY, buff=0.5) sep_line.next_to(steps, LEFT) qed = QEDSymbol(height=0.570 / 2) qed.next_to(steps[-1][-1][-1], RIGHT, aligned_edge=DOWN) # Add everything self.add(wallis_product, steps, sep_line, qed)
def scroll_through_patrons(self): logo_box = Square(side_length=2.5) logo_box.to_corner(DOWN + LEFT, buff=MED_LARGE_BUFF) total_width = FRAME_X_RADIUS - logo_box.get_right()[0] black_rect = Rectangle(fill_color=BLACK, fill_opacity=1, stroke_width=0, width=FRAME_WIDTH, height=1.1 * FRAME_Y_RADIUS) black_rect.to_edge(UP, buff=0) line = DashedLine(FRAME_X_RADIUS * LEFT, FRAME_X_RADIUS * RIGHT) line.move_to(black_rect, DOWN) line.shift(SMALL_BUFF * SMALL_BUFF * DOWN) self.add(line) patrons = VGroup(*map(TextMobject, self.specific_patrons)) patrons.scale(self.patron_scale_val) for patron in patrons: if patron.get_width() > self.max_patron_width: patron.scale_to_fit_width(self.max_patron_width) columns = VGroup(*[ VGroup(*patrons[i::self.n_patron_columns]) for i in range(self.n_patron_columns) ]) for column in columns: for n, name in enumerate(column): name.shift(n * self.name_y_spacing * DOWN) columns.arrange_submobjects( RIGHT, buff=LARGE_BUFF, aligned_edge=UP, ) columns.scale_to_fit_width(total_width - 1) columns.next_to(black_rect, DOWN, 3 * LARGE_BUFF) columns.to_edge(RIGHT) self.play( columns.move_to, 2 * DOWN, DOWN, columns.to_edge, RIGHT, Animation(black_rect), rate_func=None, run_time=self.run_time, )