manim vectors & matrices

Scene1

产生向量，并显示坐标

class myjob(VectorScene):  # 注意继承的是VectorScene
    def construct(self):
        plane = self.add_plane(animate=True).add_coordinates()
        vector = self.add_vector([-3,-2], color=YELLOW)

        basis = self.get_basis_vectors()
        self.add(basis)
        self.vector_to_coords(vector=vector)

        vector2 = self.add_vector([2,2])
        self.write_vector_coordinates(vector=vector2)

 

Scene2

坐标系线性变换

class myjob(LinearTransformationScene):
    # 在运行时报错，尚未找到错误：
TypeError: __init__() got an unexpected keyword argument 'renderer'
    def __init__(self):
        LinearTransformationScene.__init__(
            self,
            show_coordinates=True,
            leave_ghost_vectors=True,
            show_basis_vectors=True
        )
    def construct(self):
        matrix = [[1,2], [2,1]]
        matrix_tex = MathTex("A = \\begin{bmatrix} 1 & 2 \\\ 2 & 1 \\end{bmatrix}").to_edge(UL).add_background_rectangle()

        unit_square = self.get_unit_square()
        text = always_redraw(lambda : text("Det(A)").set(width=0.7).move_to(unit_square.get_center()))

        vect = self.get_vector([1,-2], color = PURPLE_B)

        rect1 = Rectangle(height = 2, width = 1, stroke_color = BLUE_A, fill_color = BLUE_D, fill_opacity = 0.6).shift(UP*2+LEFT*2)

        circ1 = Circle(radius = 1, stroke_color = BLUE_A, fill_color = BLUE_D, fill_opacity = 0.6).shift(DOWN*2+RIGHT*1)

        self.add_transformable_mobject(vect, unit_square, rect1, circ1)
        self.add_background_mobject(matrix_tex, text)
        self.apply_matrix(matrix)
        self.wait()

 

Scene3

产生三个向量，并一同放缩

class myjob(Scene):
    def construct(self):
        plane = NumberPlane(x_range=[-5,5,1], y_range=[-4,4,1], x_length=10, y_length=7)
        plane.add_coordinates()
        plane.shift(RIGHT*2)

        vect1 = Line(start=plane.coords_to_point(0,0), end=plane.coords_to_point(3,2), stroke_color=YELLOW).add_tip()  # 即定位到plane的坐标点，add_tip()为添加箭头
        vect1_name = MathTex("\\vec{v}").next_to(vect1, RIGHT, buff=0).set_color(YELLOW)

        vect2 = Line(start=plane.coords_to_point(0,0), end=plane.coords_to_point(-2,1), stroke_color=RED).add_tip()
        vect2_name = MathTex("\\vec{w}").next_to(vect2, LEFT, buff=0).set_color(RED)

        vect3 = Line(start=plane.coords_to_point(3,2), end=plane.coords_to_point(1,3), stroke_color=RED).add_tip()

        vect4 = Line(start=plane.coords_to_point(0,0), end=plane.coords_to_point(1,3), stroke_color=GREEN).add_tip()
        vect4_name = MathTex("\\vec{v} + \\vec{w}").next_to(vect4, LEFT, buff=0.1).set_color(GREEN)

        stuff = VGroup(plane, vect1, vect1_name, vect2, vect2_name, vect3, vect4, vect4_name)

        box = RoundedRectangle(height = 1.5, width = 1.5, corner_radius = 0.1, stroke_color = PINK).to_edge(DL)

        self.play(DrawBorderThenFill(plane), run_time = 2)
        self.wait()
        self.play(GrowFromPoint(vect1, point=vect1.get_start()), Write(vect1_name), run_time = 2)
        self.wait()
        self.play(GrowFromPoint(vect2, point=vect2.get_start()), Write(vect2_name), run_time = 2)
        self.wait()
        self.play(Transform(vect2, vect3), vect2_name.animate.next_to(vect3, UP, buff=0.1), run_time = 2)
        self.wait()
        self.play(LaggedStart(GrowFromPoint(vect4, point=vect4.get_start())), Write(vect4_name), run_time=3, lag_radio=1)
        self.wait()
        self.add(box)
        self.wait()
        self.play(stuff.animate.move_to(box.get_center()).set(width=1.2), run_time=3)
        self.wait()