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More zooming animations for x^2 example
This commit is contained in:
Grant Sanderson
parent
bf4bac1371
commit
c237780f48
1 changed files with 222 additions and 27 deletions
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@ -36,6 +36,7 @@ class NumberlineTransformationScene(ZoomedScene):
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"run_time": 3,
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# "path_arc": 30 * DEGREES,
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},
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"local_coordinate_num_decimal_places": 2,
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"zoom_factor": 0.1,
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"zoomed_display_height": 2.5,
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"zoomed_display_corner_buff": MED_SMALL_BUFF,
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@ -244,6 +245,9 @@ class NumberlineTransformationScene(ZoomedScene):
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def zoom_in_on_input(self, x,
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local_sample_dots=None,
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local_coordinate_values=None,
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pop_out=True,
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first_added_anims=[],
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second_added_anims=[],
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):
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input_point = self.get_input_point(x)
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@ -292,15 +296,26 @@ class NumberlineTransformationScene(ZoomedScene):
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anims.append(LaggedStart(GrowFromCenter, local_sample_dots))
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zcbr_group.add(local_sample_dots)
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if first_added_anims:
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anims += first_added_anims
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anims.append(Animation(zcbr_group))
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if not pop_out:
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self.activate_zooming(animate=False)
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self.play(*anims)
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if not self.zoom_activated:
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if not self.zoom_activated and pop_out:
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self.activate_zooming(animate=False)
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self.play(self.get_zoomed_display_pop_out_animation())
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added_anims = second_added_anims or []
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self.play(
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self.get_zoomed_display_pop_out_animation(),
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*added_anims
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)
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def get_local_coordinates(self, line, *x_values, **kwargs):
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num_decimal_places = kwargs.get("num_decimal_places", 2)
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num_decimal_places = kwargs.get(
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"num_decimal_places", self.local_coordinate_num_decimal_places
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)
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result = VGroup()
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result.tick_marks = VGroup()
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result.numbers = VGroup()
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@ -872,7 +887,7 @@ class TalkThroughXSquaredExample(IntroduceTransformationView):
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def add_title(self):
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title = self.title = TextMobject("$f(x) = x^2$")
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title.to_edge(UP)
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title.to_edge(UP, buff=MED_SMALL_BUFF)
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self.add(title)
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def show_specific_points_mapping(self):
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@ -923,6 +938,31 @@ class TalkThroughXSquaredExample(IntroduceTransformationView):
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self.sample_dots = sample_dots
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self.sample_dot_ghosts = sample_dot_ghosts
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def get_stretch_words(self, factor, color=RED, less_than_one=False):
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result = TextMobject(
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"Scale \\\\ by", str(factor),
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tex_to_color_map={str(factor): color}
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)
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result.scale(0.7)
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la, ra = TexMobject("\\leftarrow \\rightarrow")
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if less_than_one:
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la, ra = ra, la
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la.next_to(result, LEFT)
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ra.next_to(result, RIGHT)
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result.add(la, ra)
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result.next_to(
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self.zoomed_display.get_top(), DOWN, SMALL_BUFF
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)
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return result
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def get_deriv_equation(self, x, rhs, color=RED):
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deriv_equation = self.deriv_equation = TexMobject(
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"\\frac{df}{dx}(", str(x), ")", "=", str(rhs),
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tex_to_color_map={str(x): color, str(rhs): color}
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)
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deriv_equation.next_to(self.title, DOWN, MED_LARGE_BUFF)
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return deriv_equation
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class ZoomInOnXSquaredNearOne(TalkThroughXSquaredExample):
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def setup(self):
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@ -1006,15 +1046,7 @@ class ZoomInOnXSquaredNearOne(TalkThroughXSquaredExample):
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)
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# Transform new zoomed view
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stretch_by_two_words = TextMobject("Stretch by 2")
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stretch_by_two_words.scale(0.5)
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la, ra = TexMobject("\\leftarrow \\rightarrow")
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la.next_to(stretch_by_two_words, LEFT)
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ra.next_to(stretch_by_two_words, RIGHT)
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stretch_by_two_words.add(la, ra)
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stretch_by_two_words.next_to(
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self.zoomed_display.get_top(), DOWN
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)
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stretch_by_two_words = self.get_stretch_words(2)
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self.add_foreground_mobject(stretch_by_two_words)
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sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
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self.apply_function(
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@ -1029,37 +1061,200 @@ class ZoomInOnXSquaredNearOne(TalkThroughXSquaredExample):
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self.wait()
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# Write derivative
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deriv_equation = self.deriv_equation = TexMobject(
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"\\frac{df}{dx}(", "1", ")", "=", "2",
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tex_to_color_map={"1": RED, "2": RED}
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)
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deriv_equation.next_to(self.title, DOWN)
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self.play(
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Write(deriv_equation),
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self.title.shift, MED_SMALL_BUFF * UP
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)
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deriv_equation = self.get_deriv_equation(1, 2, color=RED)
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self.play(Write(deriv_equation))
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self.wait()
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class ZoomInOnXSquaredNearThree(ZoomInOnXSquaredNearOne):
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CONFIG = {
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"zoomed_display_width": 4,
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}
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def construct(self):
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pass
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zoom_words = TextMobject("Zoomed view \\\\ near 3")
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zoom_words.next_to(self.zoomed_display, DOWN)
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x = 3
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local_sample_dots = self.get_local_sample_dots(x)
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local_coordinate_values = self.get_local_coordinate_values(x, dx=0.1)
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target_coordinate_values = self.get_local_coordinate_values(self.func(x), dx=0.1)
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color = self.sample_dots[len(self.sample_dots) / 2].get_color()
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sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
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stretch_words = self.get_stretch_words(2 * x, color)
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deriv_equation = self.get_deriv_equation(x, 2 * x, color)
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self.add(deriv_equation)
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self.zoom_in_on_input(
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x,
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pop_out=False,
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local_sample_dots=local_sample_dots,
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local_coordinate_values=local_coordinate_values
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)
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self.play(Write(zoom_words, run_time=1))
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self.wait()
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self.add_foreground_mobject(stretch_words)
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self.apply_function(
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self.func,
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apply_function_to_number_line=False,
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sample_dots=sample_dot_ghost_copies,
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local_sample_dots=local_sample_dots,
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target_coordinate_values=target_coordinate_values,
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added_anims=[Write(stretch_words)]
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)
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self.wait(2)
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class ZoomInOnXSquaredNearOneFourth(ZoomInOnXSquaredNearOne):
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CONFIG = {
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"zoom_factor": 0.01,
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"local_coordinate_num_decimal_places": 4,
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"zoomed_display_width": 4,
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"default_delta_x": 0.25,
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}
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def construct(self):
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pass
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# Much copy-pasting from previous scenes. Not great, but
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# the fastest way to get the ease-of-tweaking I'd like.
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zoom_words = TextMobject("Zoomed view \\\\ near $1/4$")
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zoom_words.next_to(self.zoomed_display, DOWN)
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x = 0.25
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local_sample_dots = self.get_local_sample_dots(
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x, sample_radius=2.5 * self.zoomed_camera.frame.get_width(),
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)
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local_coordinate_values = self.get_local_coordinate_values(
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x, dx=0.01,
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)
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target_coordinate_values = self.get_local_coordinate_values(
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self.func(x), dx=0.01,
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)
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color = RED
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sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
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stretch_words = self.get_stretch_words("1/2", color, less_than_one=True)
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deriv_equation = self.get_deriv_equation("1/4", "1/2", color)
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one_fourth_point = self.get_input_point(x)
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one_fourth_arrow = Vector(0.5 * UP, color=WHITE)
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one_fourth_arrow.stem.stretch(0.75, 0)
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one_fourth_arrow.tip.scale(0.75, about_edge=DOWN)
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one_fourth_arrow.next_to(one_fourth_point, DOWN, SMALL_BUFF)
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one_fourth_label = TexMobject("0.25")
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one_fourth_label.match_height(self.input_line.numbers)
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one_fourth_label.next_to(one_fourth_arrow, DOWN, SMALL_BUFF)
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self.add(deriv_equation)
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self.zoom_in_on_input(
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x,
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local_sample_dots=local_sample_dots,
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local_coordinate_values=local_coordinate_values,
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pop_out=False,
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first_added_anims=[
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FadeIn(one_fourth_label),
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GrowArrow(one_fourth_arrow),
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]
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)
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self.play(Write(zoom_words, run_time=1))
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self.wait()
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self.add_foreground_mobject(stretch_words)
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self.apply_function(
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self.func,
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apply_function_to_number_line=False,
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sample_dots=sample_dot_ghost_copies,
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local_sample_dots=local_sample_dots,
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target_coordinate_values=target_coordinate_values,
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added_anims=[Write(stretch_words)]
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)
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self.wait(2)
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class ZoomInOnXSquaredNearZero(ZoomInOnXSquaredNearOne):
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CONFIG = {
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"zoom_factor": 0.1,
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"zoomed_display_width": 4,
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"scale_by_term": "???",
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}
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def construct(self):
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pass
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zoom_words = TextMobject(
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"Zoomed %sx \\\\ near 0" % "{:,}".format(int(1.0 / self.zoom_factor))
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)
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zoom_words.next_to(self.zoomed_display, DOWN)
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x = 0
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local_sample_dots = self.get_local_sample_dots(
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x, sample_radius=2 * self.zoomed_camera.frame.get_width()
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)
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local_coordinate_values = self.get_local_coordinate_values(
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x, dx=self.zoom_factor
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)
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# target_coordinate_values = self.get_local_coordinate_values(
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# self.func(x), dx=self.zoom_factor
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# )
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color = self.sample_dots[len(self.sample_dots) / 2].get_color()
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sample_dot_ghost_copies = self.sample_dot_ghosts.copy()
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stretch_words = self.get_stretch_words(
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self.scale_by_term, color, less_than_one=True
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)
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deriv_equation = self.get_deriv_equation(x, 2 * x, color)
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self.add(deriv_equation)
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self.zoom_in_on_input(
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x,
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pop_out=False,
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local_sample_dots=local_sample_dots,
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local_coordinate_values=local_coordinate_values
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)
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self.play(Write(zoom_words, run_time=1))
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self.wait()
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self.add_foreground_mobject(stretch_words)
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self.apply_function(
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self.func,
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apply_function_to_number_line=False,
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sample_dots=sample_dot_ghost_copies,
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local_sample_dots=local_sample_dots,
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# target_coordinate_values=target_coordinate_values,
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added_anims=[
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Write(stretch_words),
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MaintainPositionRelativeTo(
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self.local_coordinates,
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self.zoomed_camera.frame
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)
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]
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)
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self.wait(2)
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class ZoomInOnXSquared100xZero(ZoomInOnXSquaredNearZero):
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CONFIG = {
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"zoom_factor": 0.01
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}
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class ZoomInOnXSquared1000xZero(ZoomInOnXSquaredNearZero):
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CONFIG = {
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"zoom_factor": 0.001,
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"local_coordinate_num_decimal_places": 3,
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}
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class ZoomInOnXSquared10000xZero(ZoomInOnXSquaredNearZero):
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CONFIG = {
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"zoom_factor": 0.0001,
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"local_coordinate_num_decimal_places": 4,
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"scale_by_term": "0",
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}
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class XSquaredForNegativeInput(TalkThroughXSquaredExample):
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CONFIG = {
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"input_line_config": {},
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"input_line_config": {
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"x_min": -3,
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"x_max": 3,
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},
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"output_line_config": {},
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}
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