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Up to graphed integral in eoc chapter1
This commit is contained in:
Grant Sanderson
176
eoc/chapter1.py
176
eoc/chapter1.py
@ -24,6 +24,8 @@ from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from eoc.graph_scene import GraphScene
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class CircleScene(PiCreatureScene):
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CONFIG = {
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"radius" : 1.5,
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@ -1839,9 +1841,177 @@ class IntroduceConcentricRings(CircleScene):
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)
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self.dither(4)
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class AskAboutGeneralCircles(TeacherStudentsScene):
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def construct(self):
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self.student_says("""
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What about integrals
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beyond this circle
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example?
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""")
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self.change_student_modes("confused")
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self.random_blink(2)
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self.teacher_says(
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"All in due time",
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)
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self.change_student_modes(*["happy"]*3)
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self.random_blink(2)
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class GraphIntegral(GraphScene):
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CONFIG = {
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"x_min" : -0.25,
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"x_max" : 4,
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"x_tick_frequency" : 0.25,
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"x_leftmost_tick" : -0.25,
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"x_labeled_nums" : range(1, 5),
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"x_axis_label" : "r",
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"y_min" : -2,
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"y_max" : 25,
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"y_tick_frequency" : 2.5,
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"y_bottom_tick" : 0,
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"y_labeled_nums" : range(5, 30, 5),
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"y_axis_label" : "",
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"dr" : 0.125,
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"R" : 3.5,
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}
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def construct(self):
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integral = TexMobject("\\int_0^R 2\\pi r \\, dr")
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integral.to_edge(UP).shift(LEFT)
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self.play(Write(integral))
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self.dither()
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self.setup_axes()
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self.add_rectangles()
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self.thinner_rectangles()
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self.ask_about_area()
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def add_rectangles(self):
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tick_height = 0.2
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special_tick_index = 12
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ticks = VGroup(*[
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Line(UP, DOWN).move_to(self.coords_to_point(x, 0))
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for x in np.arange(0, self.R+self.dr, self.dr)
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])
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ticks.stretch_to_fit_height(tick_height)
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ticks.highlight(YELLOW)
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R_label = TexMobject("R")
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R_label.next_to(self.coords_to_point(self.R, 0), DOWN)
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values_words = TextMobject("Values of $r$")
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values_words.shift(UP)
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arrows = VGroup(*[
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Arrow(
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values_words.get_bottom(),
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tick.get_center(),
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tip_length = 0.15
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)
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for tick in ticks
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])
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dr_brace = Brace(
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VGroup(*ticks[special_tick_index:special_tick_index+2]),
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buff = SMALL_BUFF
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)
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dr_text = dr_brace.get_text("$dr$", buff = SMALL_BUFF)
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# dr_text.highlight(YELLOW)
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rectangles = self.get_rectangles(self.dr)
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special_rect = rectangles[special_tick_index]
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left_brace = Brace(special_rect, LEFT)
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height_label = left_brace.get_text("$2\\pi r$")
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self.play(
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ShowCreation(ticks, submobject_mode = "lagged_start"),
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Write(R_label)
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)
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self.play(
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Write(values_words),
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ShowCreation(arrows)
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)
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self.dither()
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self.play(
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GrowFromCenter(dr_brace),
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Write(dr_text)
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)
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self.dither()
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rectangles.save_state()
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rectangles.stretch_to_fit_height(0)
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rectangles.move_to(self.graph_origin, DOWN+LEFT)
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self.play(*map(FadeOut, [arrows, values_words]))
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self.play(
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rectangles.restore,
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Animation(ticks),
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run_time = 2
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)
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self.dither()
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self.play(*[
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ApplyMethod(rect.fade, 0.7)
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for rect in rectangles
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if rect is not special_rect
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] + [Animation(ticks)])
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self.play(
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GrowFromCenter(left_brace),
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Write(height_label)
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)
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self.dither()
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graph = self.graph_function(
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lambda r : 2*np.pi*r,
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animate = False
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)
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graph_label = self.label_graph(
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self.graph, "f(r) = 2\\pi r",
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proportion = 0.5,
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direction = LEFT,
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animate = False
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)
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self.play(
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rectangles.restore,
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Animation(ticks),
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FadeOut(left_brace),
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Transform(height_label, graph_label),
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ShowCreation(graph)
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)
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self.dither(3)
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self.play(*map(FadeOut, [ticks, dr_brace, dr_text]))
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self.rectangles = rectangles
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def thinner_rectangles(self):
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for x in range(2, 8):
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new_rects = self.get_rectangles(
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dr = self.dr/x, stroke_width = 1./x
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)
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self.play(Transform(self.rectangles, new_rects))
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self.dither()
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def ask_about_area(self):
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question = TextMobject("What's this \\\\ area")
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question.to_edge(RIGHT).shift(2*UP)
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arrow = Arrow(
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question.get_bottom(),
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self.rectangles,
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buff = SMALL_BUFF
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)
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self.play(
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Write(question),
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ShowCreation(arrow)
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)
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self.dither()
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def get_rectangles(self, dr, stroke_width = 1):
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rectangles = VGroup()
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for r in np.arange(0, self.R, dr):
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points = VGroup(
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VectorizedPoint(self.coords_to_point(r, 0)),
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VectorizedPoint(self.coords_to_point(r+dr, 2*np.pi*r)),
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)
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rect = Rectangle()
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rect.replace(points, stretch = True)
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rect.set_fill(opacity = 1)
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rectangles.add(rect)
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rectangles.gradient_highlight(BLUE, GREEN)
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rectangles.set_stroke(BLACK, width = stroke_width)
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return rectangles
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136
eoc/graph_scene.py
Normal file
136
eoc/graph_scene.py
Normal file
@ -0,0 +1,136 @@
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from helpers import *
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from scene import Scene
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# from topics.geometry import
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from mobject.tex_mobject import TexMobject
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from mobject.vectorized_mobject import VGroup
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from animation.simple_animations import Write, ShowCreation
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from topics.number_line import NumberLine
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from topics.functions import ParametricFunction
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class GraphScene(Scene):
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CONFIG = {
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"x_min" : -1,
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"x_max" : 10,
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"x_axis_width" : 9,
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"x_tick_frequency" : 1,
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"x_leftmost_tick" : -1,
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"x_labeled_nums" : range(1, 10),
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"x_axis_label" : "x",
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"y_min" : -1,
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"y_max" : 10,
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"y_axis_height" : 6,
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"y_tick_frequency" : 1,
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"y_bottom_tick" : -1,
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"y_labeled_nums" : range(1, 10),
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"y_axis_label" : "y",
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"axes_color" : GREY,
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"graph_origin" : 2.5*DOWN + 4*LEFT,
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"y_axis_numbers_nudge" : 0.4*UP+0.5*LEFT,
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}
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def setup_axes(self, animate = True):
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x_num_range = float(self.x_max - self.x_min)
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x_axis = NumberLine(
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x_min = self.x_min,
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x_max = self.x_max,
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space_unit_to_num = self.x_axis_width/x_num_range,
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tick_frequency = self.x_tick_frequency,
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leftmost_tick = self.x_leftmost_tick,
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numbers_with_elongated_ticks = self.x_labeled_nums,
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color = self.axes_color
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)
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x_axis.shift(self.graph_origin - x_axis.number_to_point(0))
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x_axis.add_numbers(*self.x_labeled_nums)
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x_label = TexMobject(self.x_axis_label)
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x_label.next_to(x_axis, RIGHT+UP, buff = SMALL_BUFF)
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y_num_range = float(self.y_max - self.y_min)
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y_axis = NumberLine(
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x_min = self.y_min,
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x_max = self.y_max,
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space_unit_to_num = self.y_axis_height/y_num_range,
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tick_frequency = self.y_tick_frequency,
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leftmost_tick = self.y_bottom_tick,
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numbers_with_elongated_ticks = self.y_labeled_nums,
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color = self.axes_color
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)
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y_axis.shift(self.graph_origin-y_axis.number_to_point(0))
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y_axis.rotate(np.pi/2, about_point = y_axis.number_to_point(0))
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y_axis.add_numbers(*self.y_labeled_nums)
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y_axis.numbers.shift(self.y_axis_numbers_nudge)
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y_label = TexMobject(self.y_axis_label)
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y_label.next_to(y_axis.get_top(), RIGHT, buff = 2*MED_BUFF)
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if animate:
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self.play(Write(VGroup(x_axis, y_axis)))
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else:
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selfe.add(x_axis, y_axis_label)
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self.x_axis, self.y_axis = x_axis, y_axis
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def coords_to_point(self, x, y):
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assert(hasattr(self, "x_axis") and hasattr(self, "y_axis"))
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result = self.x_axis.number_to_point(x)[0]*RIGHT
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result += self.y_axis.number_to_point(y)[1]*UP
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return result
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def graph_function(self, func,
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color = BLUE,
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animate = True,
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is_main_graph = True,
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):
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def parameterized_graph(alpha):
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x = interpolate(self.x_min, self.x_max, alpha)
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return self.coords_to_point(x, func(x))
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graph = ParametricFunction(parameterized_graph, color = color)
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if is_main_graph:
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self.graph = graph
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if animate:
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self.play(ShowCreation(graph))
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self.add(graph)
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return graph
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def input_to_graph_point(self, x):
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assert(hasattr(self, "graph"))
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alpha = (x - self.x_min)/(self.x_max - self.x_min)
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return self.graph.point_from_proportion(alpha)
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def angle_of_tangent(self, x, dx = 0.01):
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assert(hasattr(self, "graph"))
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vect = self.graph_point(x + dx) - self.graph_point(x)
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return angle_of_vector(vect)
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def label_graph(self, graph, label = "f(x)",
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proportion = 0.7,
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direction = LEFT,
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buff = 2*MED_BUFF,
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animate = True
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):
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label = TexMobject(label)
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label.highlight(graph.get_color())
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label.next_to(
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graph.point_from_proportion(proportion),
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direction,
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buff = buff
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)
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if animate:
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self.play(Write(label))
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self.add(label)
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return label
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