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312 lines
10 KiB
Python
312 lines
10 KiB
Python
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from mobject.tex_mobject import TexMobject
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from mobject.vectorized_mobject import VMobject
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from animation.animation import Animation
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from animation.transform import *
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from animation.simple_animations import *
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from topics.geometry import *
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from topics.characters import *
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from topics.functions import *
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from topics.number_line import *
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from topics.numerals import *
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from scene import Scene
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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 mobject.vectorized_mobject import *
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from eola.matrix import *
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from eola.two_d_space import *
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from eola.chapter3 import MatrixVectorMultiplicationAbstract
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class OpeningQuote(Scene):
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def construct(self):
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words = TextMobject([
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"It is my experience that proofs involving",
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"matrices",
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"can be shortened by 50\\% if one",
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"throws the matrices out."
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])
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words.scale_to_fit_width(2*SPACE_WIDTH - 2)
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words.to_edge(UP)
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words.split()[1].highlight(GREEN)
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words.split()[3].highlight(BLUE)
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author = TextMobject("-Emil Artin")
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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(FadeIn(words))
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self.dither(2)
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self.play(Write(author, run_time = 3))
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self.dither()
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class MatrixToBlank(Scene):
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def construct(self):
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matrix = Matrix([[3, 1], [0, 2]])
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arrow = Arrow(LEFT, RIGHT)
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matrix.to_edge(LEFT)
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arrow.next_to(matrix, LEFT)
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matrix.add(arrow)
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self.play(Write(matrix))
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self.dither()
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class RecapTime(TeacherStudentsScene):
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def construct(self):
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self.setup()
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self.teacher_says("Quick recap time!")
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self.random_blink()
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self.dither()
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student = self.get_students()[0]
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everyone = self.get_mobjects()
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everyone.remove(student)
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everyone = VMobject(*everyone)
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self.play(
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ApplyMethod(everyone.fade, 0.7),
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ApplyMethod(student.change_mode, "confused")
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)
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self.play(Blink(student))
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self.dither()
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self.play(ApplyFunction(
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lambda m : m.change_mode("pondering").look(LEFT),
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student
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))
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self.play(Blink(student))
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self.dither()
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class DeterminedByTwoBasisVectors(LinearTransformationScene):
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CONFIG = {
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"show_basis_vectors" : False
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}
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def construct(self):
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self.setup()
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i_hat = self.add_vector([1, 0], color = X_COLOR)
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self.add_transformable_label(
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i_hat, "\\hat{\\imath}", "\\hat{\\imath}",
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color = X_COLOR
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)
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j_hat = self.add_vector([0, 1], color = Y_COLOR)
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self.add_transformable_label(
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j_hat, "\\hat{\\jmath}", "\\hat{\\jmath}",
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color = Y_COLOR
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)
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t_matrix = np.array([[2, 2], [-2, 1]])
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matrix = t_matrix.transpose()
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matrix1 = np.array(matrix)
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matrix1[:,1] = [0, 1]
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matrix2 = np.dot(matrix, np.linalg.inv(matrix1))
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self.dither()
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self.apply_transposed_matrix(matrix1.transpose())
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self.apply_transposed_matrix(matrix2.transpose())
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self.dither()
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class FollowLinearCombination(LinearTransformationScene):
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def construct(self):
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vect_coords = [-1, 2]
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t_matrix = np.array([[2, 2], [-2, 1]])
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#Draw vectors
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self.setup()
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i_label = self.add_transformable_label(
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self.i_hat, "\\hat{\\imath}", animate = False,
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direction = "right", color = X_COLOR
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)
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j_label = self.add_transformable_label(
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self.j_hat, "\\hat{\\jmath}", animate = False,
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direction = "right", color = Y_COLOR
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)
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vect = self.add_vector(vect_coords)
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vect_array = Matrix(["x", "y"], add_background_rectangles = True)
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v_equals = TexMobject(["\\vec{\\textbf{v}}", "="])
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v_equals.split()[0].highlight(YELLOW)
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v_equals.next_to(vect_array, LEFT)
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vect_array.add(v_equals)
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vect_array.to_edge(UP, buff = 0.2)
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background_rect = BackgroundRectangle(vect_array)
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vect_array.get_entries().highlight(YELLOW)
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self.play(ShowCreation(background_rect), Write(vect_array))
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self.add_foreground_mobject(background_rect, vect_array)
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#Show scaled vectors
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x, y = vect_array.get_entries().split()
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scaled_i_label = VMobject(x.copy(), i_label)
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scaled_j_label = VMobject(y.copy(), j_label)
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scaled_i = self.i_hat.copy().scale(vect_coords[0])
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scaled_j = self.j_hat.copy().scale(vect_coords[1])
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for mob in scaled_i, scaled_j:
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mob.fade(0.3)
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scaled_i_label_target = scaled_i_label.copy()
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scaled_i_label_target.arrange_submobjects(buff = 0.1)
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scaled_i_label_target.next_to(scaled_i, DOWN)
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scaled_j_label_target = scaled_j_label.copy()
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scaled_j_label_target.arrange_submobjects(buff = 0.1)
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scaled_j_label_target.next_to(scaled_j, LEFT)
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self.show_scaled_vectors(vect_array, vect_coords, i_label, j_label)
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self.apply_transposed_matrix(t_matrix)
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self.show_scaled_vectors(vect_array, vect_coords, i_label, j_label)
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self.record_basis_coordinates(vect_array, vect)
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def show_scaled_vectors(self, vect_array, vect_coords, i_label, j_label):
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x, y = vect_array.get_entries().split()
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scaled_i_label = VMobject(x.copy(), i_label.copy())
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scaled_j_label = VMobject(y.copy(), j_label.copy())
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scaled_i = self.i_hat.copy().scale(vect_coords[0])
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scaled_j = self.j_hat.copy().scale(vect_coords[1])
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for mob in scaled_i, scaled_j:
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mob.fade(0.3)
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scaled_i_label_target = scaled_i_label.copy()
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scaled_i_label_target.arrange_submobjects(buff = 0.1)
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scaled_i_label_target.next_to(scaled_i.get_center(), DOWN)
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scaled_j_label_target = scaled_j_label.copy()
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scaled_j_label_target.arrange_submobjects(buff = 0.1)
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scaled_j_label_target.next_to(scaled_j.get_center(), LEFT)
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self.play(
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Transform(self.i_hat.copy(), scaled_i),
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Transform(scaled_i_label, scaled_i_label_target)
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)
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scaled_i = self.get_mobjects_from_last_animation()[0]
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self.play(
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Transform(self.j_hat.copy(), scaled_j),
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Transform(scaled_j_label, scaled_j_label_target)
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)
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scaled_j = self.get_mobjects_from_last_animation()[0]
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self.play(*[
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ApplyMethod(mob.shift, scaled_i.get_end())
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for mob in scaled_j, scaled_j_label
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])
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self.dither()
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self.play(*map(FadeOut, [
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scaled_i, scaled_j, scaled_i_label, scaled_j_label,
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]))
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def record_basis_coordinates(self, vect_array, vect):
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i_label = vector_coordinate_label(self.i_hat)
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i_label.highlight(X_COLOR)
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j_label = vector_coordinate_label(self.j_hat)
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j_label.highlight(Y_COLOR)
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for mob in i_label, j_label:
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mob.scale_in_place(0.8)
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background = BackgroundRectangle(mob)
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self.play(ShowCreation(background), Write(mob))
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self.dither()
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x, y = vect_array.get_entries().split()
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pre_formula = VMobject(
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x, i_label, TexMobject("+"),
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y, j_label
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)
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post_formula = pre_formula.copy()
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pre_formula.split()[2].fade(1)
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post_formula.arrange_submobjects(buff = 0.1)
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post_formula.next_to(vect, DOWN)
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background = BackgroundRectangle(post_formula)
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everything = self.get_mobjects()
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everything.remove(vect)
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self.play(*[
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ApplyMethod(m.fade) for m in everything
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] + [
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ShowCreation(background, run_time = 2, rate_func = squish_rate_func(smooth, 0.5, 1)),
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Transform(pre_formula.copy(), post_formula, run_time = 2),
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ApplyMethod(vect.set_stroke, width = 7)
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])
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self.dither()
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class MatrixVectorMultiplicationCopy(MatrixVectorMultiplicationAbstract):
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pass ## Here just for stage_animations.py purposes
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class RecapOver(TeacherStudentsScene):
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def construct(self):
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self.setup()
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self.teacher_says("Recap over!")
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class TwoSuccessiveTransformations(LinearTransformationScene):
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def construct(self):
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self.setup()
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self.apply_transposed_matrix([[2, 1],[1, 2]])
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self.apply_transposed_matrix([[-1, -0.5],[0, -0.5]])
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self.dither()
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class RotationThenShear(LinearTransformationScene):
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CONFIG = {
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"foreground_plane_kwargs" : {
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"x_radius" : SPACE_WIDTH,
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"y_radius" : 2*SPACE_WIDTH,
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"secondary_line_ratio" : 0
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},
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}
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def construct(self):
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self.setup()
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rot_words = TextMobject("$90^\\circ$ rotation counterclockwise")
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shear_words = TextMobject("followed by a shear")
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rot_words.highlight(YELLOW)
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shear_words.highlight(PINK)
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VMobject(rot_words, shear_words).arrange_submobjects(DOWN).to_edge(UP)
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for words in rot_words, shear_words:
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words.add_background_rectangle()
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self.play(Write(rot_words, run_time = 1))
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self.add_foreground_mobject(rot_words)
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self.apply_transposed_matrix([[0, 1], [-1, 0]])
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self.play(Write(shear_words, run_time = 1))
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self.add_foreground_mobject(shear_words)
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self.apply_transposed_matrix([[1, 0], [1, 1]])
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self.dither()
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class IntroduceIdeaOfComposition(RotationThenShear):
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def construct(self):
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self.setup()
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self.show_composition()
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self.track_basis_vectors()
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def show_composition(self):
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words = TextMobject([
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"``Composition''",
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"of a",
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"rotation",
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"and a",
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"shear"
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])
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words.split()[0].submobject_gradient_highlight(YELLOW, PINK, use_color_range_to = False)
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words.split()[2].highlight(YELLOW)
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words.split()[4].highlight(PINK)
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words.add_background_rectangle()
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words.to_edge(UP)
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self.apply_transposed_matrix([[0, 1], [-1, 0]], run_time = 2)
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self.apply_transposed_matrix([[1, 0], [1, 1]], run_time = 2)
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self.play(Write(words))
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self.dither()
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def track_basis_vectors(self):
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pass
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