def setup(self): self.input_color = YELLOW_C self.output_color = RED def spiril(t): theta = 2*np.pi*t return t*np.cos(theta)*RIGHT+t*np.sin(theta)*UP self.spiril1 = ParametricFunction( lambda t : 1.5*RIGHT + DOWN + 2*spiril(t), density = 5*DEFAULT_POINT_DENSITY_1D, ) self.spiril2 = ParametricFunction( lambda t : 5.5*RIGHT + UP - 2*spiril(1-t), density = 5*DEFAULT_POINT_DENSITY_1D, ) Mobject.align_data(self.spiril1, self.spiril2) self.output = Mobject(self.spiril1, self.spiril2) self.output.ingest_submobjects() self.output.highlight(GREEN_A) self.interval = UnitInterval() self.interval.scale_to_fit_width(SPACE_WIDTH-1) self.interval.to_edge(LEFT) self.input_dot = Dot(color = self.input_color) self.output_dot = self.input_dot.copy().highlight(self.output_color) left, right = self.interval.get_left(), self.interval.get_right() self.input_homotopy = lambda (x, y, z, t) : (x, y, t) + interpolate(left, right, t) output_size = self.output.get_num_points()-1 output_points = self.output.points self.output_homotopy = lambda (x, y, z, t) : (x, y, z) + output_points[int(t*output_size)]
def construct(self): words = TextMobject([ "One does not simply define the limit \\\\ \ of a sequence of", "curves", "\\dots" ]) top_words = TextMobject(["curves", "are functions"]).to_edge(UP) curves1 = words.split()[1] curves2 = top_words.split()[0] words.ingest_submobjects() number = TexMobject("0.27") pair = TexMobject("(0.53, 0.02)") pair.next_to(number, buff=2) arrow = Arrow(number, pair) Mobject(number, arrow, pair).center().shift(UP) number_line = UnitInterval() number_line.stretch_to_fit_width(5) number_line.to_edge(LEFT).shift(DOWN) grid = Grid(4, 4).scale(0.4) grid.next_to(number_line, buff=2) low_arrow = Arrow(number_line, grid) self.play(ShimmerIn(words)) self.dither() self.play(FadeOut(words), ApplyMethod(curves1.replace, curves2), ShimmerIn(top_words.split()[1])) self.dither() self.play(FadeIn(number)) self.play(ShowCreation(arrow)) self.play(FadeIn(pair)) self.dither() self.play(ShowCreation(number_line)) self.play(ShowCreation(low_arrow)) self.play(ShowCreation(grid)) self.dither()
def construct(self): val = 0.3 text = TextMobject([ "PHC", "$_n", "(", "%3.1f"%val, ")$", " has a ", "limit point ", "as $n \\to \\infty$" ]) func_parts = text.copy().split()[:5] Mobject(*func_parts).center().to_edge(UP) num_str, val_str = func_parts[1], func_parts[3] curve = UnitInterval() curve.sort_points(lambda p : p[0]) dot = Dot().shift(curve.number_to_point(val)) arrow = Arrow(val_str, dot, buff = 0.1) curve.add_numbers(0, 1) self.play(ShowCreation(curve)) self.play( ShimmerIn(val_str), ShowCreation(arrow), ShowCreation(dot) ) self.wait() self.play( FadeOut(arrow), *[ FadeIn(func_parts[i]) for i in 0, 1, 2, 4 ] ) for num in range(2,9): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())]) new_num_str = TexMobject(str(num)).replace(num_str) self.play( Transform(curve, new_curve), Transform(dot, new_dot), Transform(num_str, new_num_str) ) self.wait() text.to_edge(UP) text_parts = text.split() for index in 1, -1: text_parts[index].highlight() starters = Mobject(*func_parts + [ Point(mob.get_center(), stroke_width=1) for mob in text_parts[5:] ]) self.play(Transform(starters, text)) arrow = Arrow(text_parts[-2].get_bottom(), dot, buff = 0.1) self.play(ShowCreation(arrow)) self.wait()
def construct(self): val = 0.7 text = TexMobject([ "\\text{HC}(", "x", ")", "=\\lim_{n \\to \\infty}\\text{PHC}_n(", "x", ")" ]) text.to_edge(UP) x1 = text.split()[1] x2 = text.split()[-2] x2.highlight(BLUE) explanation = TextMobject("Actual Hilbert curve function") exp_arrow = Arrow(explanation, text.split()[0]) curve = UnitInterval() dot = Dot(curve.number_to_point(val)) x_arrow = Arrow(x1.get_bottom(), dot, buff = 0) curve.sort_points(lambda p : p[0]) curve.add_numbers(0, 1) self.add(*text.split()[:3]) self.play( ShimmerIn(explanation), ShowCreation(exp_arrow) ) self.wait() self.remove(explanation, exp_arrow) self.play(ShowCreation(curve)) self.play( ApplyMethod(x1.highlight, BLUE), ShowCreation(x_arrow), ShowCreation(dot) ) self.wait() self.remove(x_arrow) limit = Mobject(*text.split()[3:]).ingest_submobjects() limit.stroke_width = 1 self.play(ShimmerIn(limit)) for num in range(1, 9): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dot = Dot(new_curve.points[int(val*new_curve.get_num_points())]) self.play( Transform(curve, new_curve), Transform(dot, new_dot), )
def construct(self): text = TextMobject([ "PHC", "_n", "(", "x", ")$", " has a limit point ", "as $n \\to \\infty$", "\\\\ for all $x$" ]) parts = text.split() parts[-1].next_to(Mobject(*parts[:-1]), DOWN) parts[-1].highlight(BLUE) parts[3].highlight(BLUE) parts[1].highlight() parts[-2].highlight() text.to_edge(UP) curve = UnitInterval() curve.sort_points(lambda p : p[0]) vals = np.arange(0.1, 1, 0.1) dots = Mobject(*[ Dot(curve.number_to_point(val)) for val in vals ]) curve.add_numbers(0, 1) starter_dots = dots.copy().ingest_submobjects() starter_dots.shift(2*UP) self.add(curve, text) self.wait() self.play(DelayByOrder(ApplyMethod(starter_dots.shift, 2*DOWN))) self.wait() self.remove(starter_dots) self.add(dots) for num in range(1, 10): new_curve = HilbertCurve(order = num) new_curve.scale(0.8) new_dots = Mobject(*[ Dot(new_curve.points[int(val*new_curve.get_num_points())]) for val in vals ]) self.play( Transform(curve, new_curve), Transform(dots, new_dots), )
def get_freq_line(): return UnitInterval().shift(2*DOWN) ##Change?