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https://github.com/3b1b/manim.git
synced 2025-07-30 13:34:19 +08:00
Start of chapter 10
This commit is contained in:
Grant Sanderson
@ -65,9 +65,9 @@ class Write(ShowCreation):
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mobject = TextMobject(mob_or_text)
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else:
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mobject = mob_or_text
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if not hasattr(self, "run_time"):
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if "run_time" not in kwargs:
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self.establish_run_time(mobject)
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if not hasattr(self, "lag_factor"):
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if "lag_factor" not in kwargs:
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self.lag_factor = self.run_time - 1
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ShowCreation.__init__(self, mobject, **kwargs)
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@ -41,12 +41,247 @@ class OpeningQuote(Scene):
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author.highlight(YELLOW)
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author.next_to(words, DOWN, buff = 0.5)
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self.play(Write(words, run_time = 8))
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self.dither(2)
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self.play(Write(author, run_time = 3))
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self.dither(2)
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self.play(Write(words, run_time = 10))
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self.dither()
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self.play(FadeIn(author))
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self.dither(3)
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class NewSceneName(Scene):
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class StudentsFindThisConfusing(TeacherStudentsScene):
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def construct(self):
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title = TextMobject("Eigenvectors and Eigenvalues")
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title.to_edge(UP)
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students = self.get_students()
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self.play(
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Write(title),
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*[
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ApplyMethod(pi.look_at, title)
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for pi in self.get_everyone()
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]
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)
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self.play(
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self.get_teacher().look_at, students[-1].eyes,
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students[0].change_mode, "confused",
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students[1].change_mode, "tired",
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students[2].change_mode, "sassy",
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)
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self.random_blink()
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self.student_says(
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"Why are we doing this?",
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student_index = 0,
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run_time = 2,
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)
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question1 = students[0].bubble.content.copy()
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self.student_says(
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"What does this actually mean?",
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student_index = 2,
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added_anims = [
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question1.scale_in_place, 0.8,
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question1.to_edge, LEFT,
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question1.shift, DOWN,
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]
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)
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question2 = students[2].bubble.content.copy()
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question2.target = question2.copy()
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question2.target.next_to(
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question1, DOWN,
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aligned_edge = LEFT,
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buff = MED_BUFF
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)
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equation = TexMobject(
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"\\det\\left( %s \\right)=0"%matrix_to_tex_string([
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["a-\\lambda", "b"],
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["c", "d-\\lambda"],
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])
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)
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equation.highlight(YELLOW)
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self.teacher_says(
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equation,
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added_anims = [MoveToTarget(question2)]
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)
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self.change_student_modes(*["confused"]*3)
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self.random_blink(3)
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class ShowComments(Scene):
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pass
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class EigenThingsArentAllThatBad(TeacherStudentsScene):
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def construct(self):
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self.teacher_says(
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"Eigen-things aren't \\\\ actually so bad",
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pi_creature_target_mode = "hooray"
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)
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self.random_blink(5)
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class ManyPrerequisites(Scene):
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def construct(self):
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title = TextMobject("Many prerequisites")
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title.to_edge(UP)
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h_line = Line(LEFT, RIGHT).scale(SPACE_WIDTH)
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h_line.next_to(title, DOWN)
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self.add(title)
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self.play(ShowCreation(h_line))
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rect = Rectangle(height = 9, width = 16, color = BLUE)
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rect.scale_to_fit_width(SPACE_WIDTH-2)
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rects = [rect]+[rect.copy() for i in range(3)]
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words = [
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"Linear transformations",
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"Determinants",
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"Linear systems",
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"Change of basis",
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]
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for rect, word in zip(rects, words):
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word_mob = TextMobject(word)
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word_mob.next_to(rect, UP, buff = MED_BUFF)
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rect.add(word_mob)
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Matrix(np.array(rects).reshape((2, 2)))
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rects = VGroup(*rects)
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rects.scale_to_fit_height(2*SPACE_HEIGHT - 1.5)
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rects.next_to(h_line, DOWN, buff = MED_BUFF)
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self.play(Write(rects[0]))
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self.dither()
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self.play(*map(FadeIn, rects[1:]))
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self.dither()
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class ExampleTranformationScene(LinearTransformationScene):
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CONFIG = {
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"t_matrix" : [[3, 0], [1, 2]]
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}
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def setup(self):
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LinearTransformationScene.setup(self)
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self.add_matrix()
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def add_matrix(self):
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matrix = Matrix(self.t_matrix.T)
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matrix.highlight_columns(X_COLOR, Y_COLOR)
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matrix.next_to(ORIGIN, LEFT, buff = MED_BUFF)
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matrix.to_edge(UP)
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matrix.rect = BackgroundRectangle(matrix)
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matrix.add_to_back(matrix.rect)
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self.add_foreground_mobject(matrix)
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self.matrix = matrix
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def remove_matrix(self):
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self.remove(self.matrix)
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self.foreground_mobjects.remove(self.matrix)
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class IntroduceExampleTransformation(ExampleTranformationScene):
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def construct(self):
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self.remove_matrix()
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i_coords = Matrix(self.t_matrix[0])
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j_coords = Matrix(self.t_matrix[1])
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self.apply_transposed_matrix(self.t_matrix)
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for coords, vect in (i_coords, self.i_hat), (j_coords, self.j_hat):
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coords.highlight(vect.get_color())
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coords.scale(0.8)
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coords.rect = BackgroundRectangle(coords)
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coords.add_to_back(coords.rect)
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coords.next_to(vect.get_end(), RIGHT)
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self.play(Write(coords))
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self.dither()
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i_coords_copy = i_coords.copy()
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self.play(*[
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Transform(*pair)
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for pair in [
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(i_coords_copy.rect, self.matrix.rect),
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(i_coords_copy.get_brackets(), self.matrix.get_brackets()),
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(
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i_coords_copy.get_entries(),
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VGroup(*self.matrix.get_mob_matrix()[:,0])
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)
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]
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])
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self.play(Transform(
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j_coords.copy().get_entries(),
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VGroup(*self.matrix.get_mob_matrix()[:,1])
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))
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self.dither()
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class VectorKnockedOffSpan(ExampleTranformationScene):
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def construct(self):
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vector = Vector([2, 1])
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line = Line(vector.get_end()*-4, vector.get_end()*4, color = MAROON_B)
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vector.scale(0.7)
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top_words, off, span_label = all_words = TextMobject(
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"\\centering Vector gets knocked", "\\\\ off", "Span"
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)
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all_words.shift(
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line.point_from_proportion(0.75) - \
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span_label.get_corner(DOWN+RIGHT) + \
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MED_BUFF*LEFT
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)
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for text in all_words:
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text.add_to_back(BackgroundRectangle(text))
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self.add_vector(vector)
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self.dither()
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self.play(
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ShowCreation(line),
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Write(span_label),
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Animation(vector),
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)
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self.add_foreground_mobject(span_label)
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self.dither()
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self.apply_transposed_matrix(self.t_matrix)
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self.play(Animation(span_label.copy()), Write(all_words))
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self.dither()
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class VectorRemainsOnSpan(ExampleTranformationScene):
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def construct(self):
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vector = Vector([1, -1])
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v_end = vector.get_end()
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line = Line(-4*v_end, 4*v_end, color = MAROON_B)
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words = TextMobject("Vector remains on", "\\\\its own span")
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words.next_to(ORIGIN, DOWN+LEFT)
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for part in words:
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part.add_to_back(BackgroundRectangle(part))
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self.add_vector(vector)
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self.play(ShowCreation(line), Animation(vector))
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self.dither()
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self.apply_transposed_matrix(self.t_matrix)
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self.play(Write(words))
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self.dither()
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target_vectors = [
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vector.copy().scale(scalar)
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for scalar in 2, -2, 1
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]
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for target, time in zip(target_vectors, [1, 2, 2]):
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self.play(Transform(vector, target, run_time = time))
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self.dither()
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class IHatAsEigenVector(ExampleTranformationScene):
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def construct(self):
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# self.highlight_first_column()
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def homotopy(x, y, z, t):
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pass
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x_axis = self.plane.axes[0]
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self.play(
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x_axis.highlight, GREEN_E,
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Homotopy(plane_wave_homotopy, x_axis, run_time = 3)
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)
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def highlight_first_column(self):
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faders = VGroup(self.plane, self.i_hat, self.j_hat)
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faders.save_state()
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column1 = VGroup(*self.matrix.get_mob_matrix()[:,0])
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self.play(faders.fade, 0.7, Animation(self.matrix))
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self.play(column1.scale_in_place, 1.3, rate_func = there_and_back)
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self.dither()
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self.play(faders.restore, Animation(self.matrix))
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self.dither()
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class SneakierEigenVector(ExampleTranformationScene):
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def construct(self):
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pass
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class NameEigenvectorsAndEigenvalues(ExampleTranformationScene):
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def construct(self):
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pass
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@ -65,21 +300,6 @@ class NewSceneName(Scene):
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@ -38,6 +38,7 @@ class TexMobject(SVGMobject):
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"initial_scale_factor" : TEX_MOB_SCALE_FACTOR,
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"organize_left_to_right" : False,
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"propogate_style_to_family" : True,
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"alignment" : "",
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}
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def __init__(self, *args, **kwargs):
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digest_config(self, kwargs, locals())
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@ -72,6 +73,8 @@ class TexMobject(SVGMobject):
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result = self.arg_separator.join(self.args)
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if self.enforce_new_line_structure:
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result = result.replace("\n", " \\\\ \n ")
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result = " ".join([self.alignment, result])
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result = result.strip()
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return result
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def get_tex_string(self):
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@ -120,6 +123,7 @@ class TextMobject(TexMobject):
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"template_tex_file" : TEMPLATE_TEXT_FILE,
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"initial_scale_factor" : TEXT_MOB_SCALE_FACTOR,
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"enforce_new_line_structure" : True,
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"alignment" : "\\centering",
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}
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@ -115,6 +115,7 @@ class PiCreature(SVGMobject):
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else:
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point = point_or_mobject
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self.look(point - self.eyes.get_center())
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return self
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def get_looking_direction(self):
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@ -176,33 +177,6 @@ class Blink(ApplyMethod):
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def __init__(self, pi_creature, **kwargs):
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ApplyMethod.__init__(self, pi_creature.blink, **kwargs)
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class DoTheWave(Transform):
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CONFIG = {
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"run_time" : 2
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}
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def __init__(self, pi_creature, **kwargs):
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start_state = pi_creature.copy()
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self.target_states = [
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pi_creature.copy().change_mode("wave_%d"%x)
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for x in 1, 2, 3
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] + [
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pi_creature.copy()
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]
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Transform.__init__(self, pi_creature, self.target_states[0], **kwargs)
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def update_mobject(self, alpha):
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scaled = alpha*len(self.target_states)
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try:
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if scaled-1 > 0:
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self.starting_mobject = self.target_states[int(scaled)-1]
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self.ending_mobject = self.target_states[int(scaled)]
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except IndexError:
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self.ending_mobject = self.target_states[-1]
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Transform.update_mobject(self, scaled%1)
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return self
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class Bubble(SVGMobject):
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