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https://github.com/3b1b/manim.git
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Added apply_matrix_transformation to LinearTransformationScene
This commit is contained in:
Grant Sanderson
parent
bc229f4f29
commit
96d261840d
1 changed files with 108 additions and 110 deletions
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@ -36,25 +36,27 @@ X_COLOR = GREEN_C
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Y_COLOR = RED_C
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Z_COLOR = BLUE_D
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class VectorScene(Scene):
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CONFIG = {
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"basis_vector_stroke_width" : 6
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"basis_vector_stroke_width": 6
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}
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def add_plane(self, animate = False, **kwargs):
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def add_plane(self, animate=False, **kwargs):
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plane = NumberPlane(**kwargs)
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if animate:
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self.play(ShowCreation(plane, submobject_mode = "lagged_start"))
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self.play(ShowCreation(plane, submobject_mode="lagged_start"))
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self.add(plane)
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return plane
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def add_axes(self, animate = False, color = WHITE, **kwargs):
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axes = Axes(color = color, tick_frequency = 1)
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def add_axes(self, animate=False, color=WHITE, **kwargs):
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axes = Axes(color=color, tick_frequency=1)
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if animate:
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self.play(ShowCreation(axes, submobject_mode = "one_at_a_time"))
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self.play(ShowCreation(axes, submobject_mode="one_at_a_time"))
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self.add(axes)
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return axes
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def lock_in_faded_grid(self, dimness = 0.7, axes_dimness = 0.5):
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def lock_in_faded_grid(self, dimness=0.7, axes_dimness=0.5):
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plane = self.add_plane()
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axes = plane.get_axes()
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plane.fade(dimness)
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@ -63,9 +65,9 @@ class VectorScene(Scene):
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self.add(axes)
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self.freeze_background()
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def add_vector(self, vector, color = YELLOW, animate = True, **kwargs):
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def add_vector(self, vector, color=YELLOW, animate=True, **kwargs):
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if not isinstance(vector, Arrow):
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vector = Vector(vector, color = color, **kwargs)
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vector = Vector(vector, color=color, **kwargs)
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if animate:
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self.play(ShowCreation(vector))
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self.add(vector)
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@ -76,40 +78,41 @@ class VectorScene(Scene):
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self.play(Write(coords))
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return coords
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def get_basis_vectors(self):
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return [
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def get_basis_vectors(self, i_hat_color=X_COLOR, j_hat_color=Y_COLOR):
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return VGroup(*[
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Vector(
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vect, color = color,
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stroke_width = self.basis_vector_stroke_width
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vect,
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color=color,
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stroke_width=self.basis_vector_stroke_width
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)
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for vect, color in [
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([1, 0], X_COLOR),
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([0, 1], Y_COLOR)
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([1, 0], i_hat_color),
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([0, 1], j_hat_color)
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]
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]
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])
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def get_basis_vector_labels(self, **kwargs):
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i_hat, j_hat = self.get_basis_vectors()
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return VGroup(*[
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self.get_vector_label(
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vect, label, color = color,
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label_scale_factor = 1,
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vect, label, color=color,
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label_scale_factor=1,
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**kwargs
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)
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for vect, label , color in [
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for vect, label, color in [
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(i_hat, "\\hat{\\imath}", X_COLOR),
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(j_hat, "\\hat{\\jmath}", Y_COLOR),
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]
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])
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def get_vector_label(self, vector, label,
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direction = "left",
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rotate = False,
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color = None,
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label_scale_factor = VECTOR_LABEL_SCALE_FACTOR):
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def get_vector_label(self, vector, label,
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direction="left",
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rotate=False,
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color=None,
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label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
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if not isinstance(label, TexMobject):
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if len(label) == 1:
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label = "\\vec{\\textbf{%s}}"%label
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label = "\\vec{\\textbf{%s}}" % label
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label = TexMobject(label)
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if color is None:
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color = vector.get_color()
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@ -119,53 +122,53 @@ class VectorScene(Scene):
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angle = vector.get_angle()
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if not rotate:
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label.rotate(-angle, about_point = ORIGIN)
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label.rotate(-angle, about_point=ORIGIN)
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if direction is "left":
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label.shift(-label.get_bottom() + 0.1*UP)
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label.shift(-label.get_bottom() + 0.1 * UP)
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else:
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label.shift(-label.get_top() + 0.1*DOWN)
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label.rotate(angle, about_point = ORIGIN)
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label.shift((vector.get_end() - vector.get_start())/2)
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label.shift(-label.get_top() + 0.1 * DOWN)
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label.rotate(angle, about_point=ORIGIN)
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label.shift((vector.get_end() - vector.get_start()) / 2)
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return label
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def label_vector(self, vector, label, animate = True, **kwargs):
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def label_vector(self, vector, label, animate=True, **kwargs):
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label = self.get_vector_label(vector, label, **kwargs)
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if animate:
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self.play(Write(label, run_time = 1))
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self.play(Write(label, run_time=1))
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self.add(label)
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return label
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def position_x_coordinate(self, x_coord, x_line, vector):
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x_coord.next_to(x_line, -np.sign(vector[1])*UP)
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x_coord.next_to(x_line, -np.sign(vector[1]) * UP)
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x_coord.set_color(X_COLOR)
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return x_coord
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def position_y_coordinate(self, y_coord, y_line, vector):
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y_coord.next_to(y_line, np.sign(vector[0])*RIGHT)
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y_coord.next_to(y_line, np.sign(vector[0]) * RIGHT)
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y_coord.set_color(Y_COLOR)
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return y_coord
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def coords_to_vector(self, vector, coords_start = 2*RIGHT+2*UP, clean_up = True):
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def coords_to_vector(self, vector, coords_start=2 * RIGHT + 2 * UP, clean_up=True):
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starting_mobjects = list(self.mobjects)
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array = Matrix(vector)
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array.shift(coords_start)
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arrow = Vector(vector)
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x_line = Line(ORIGIN, vector[0]*RIGHT)
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x_line = Line(ORIGIN, vector[0] * RIGHT)
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y_line = Line(x_line.get_end(), arrow.get_end())
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x_line.set_color(X_COLOR)
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y_line.set_color(Y_COLOR)
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x_coord, y_coord = array.get_mob_matrix().flatten()
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self.play(Write(array, run_time = 1))
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self.play(Write(array, run_time=1))
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self.wait()
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self.play(ApplyFunction(
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lambda x : self.position_x_coordinate(x, x_line, vector),
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lambda x: self.position_x_coordinate(x, x_line, vector),
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x_coord
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))
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self.play(ShowCreation(x_line))
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self.play(
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ApplyFunction(
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lambda y : self.position_y_coordinate(y, y_line, vector),
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lambda y: self.position_y_coordinate(y, y_line, vector),
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y_coord
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),
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FadeOut(array.get_brackets())
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@ -178,7 +181,7 @@ class VectorScene(Scene):
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self.clear()
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self.add(*starting_mobjects)
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def vector_to_coords(self, vector, integer_labels = True, clean_up = True):
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def vector_to_coords(self, vector, integer_labels=True, clean_up=True):
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starting_mobjects = list(self.mobjects)
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show_creation = False
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if isinstance(vector, Arrow):
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@ -187,8 +190,8 @@ class VectorScene(Scene):
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else:
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arrow = Vector(vector)
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show_creation = True
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array = vector_coordinate_label(arrow, integer_labels = integer_labels)
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x_line = Line(ORIGIN, vector[0]*RIGHT)
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array = vector_coordinate_label(arrow, integer_labels=integer_labels)
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x_line = Line(ORIGIN, vector[0] * RIGHT)
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y_line = Line(x_line.get_end(), arrow.get_end())
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x_line.set_color(X_COLOR)
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y_line.set_color(Y_COLOR)
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@ -206,18 +209,18 @@ class VectorScene(Scene):
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self.play(
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ShowCreation(x_line),
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Write(x_coord_start),
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run_time = 1
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run_time=1
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)
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self.play(
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ShowCreation(y_line),
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Write(y_coord_start),
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run_time = 1
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run_time=1
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)
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self.wait()
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self.play(
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Transform(x_coord_start, x_coord, submobject_mode = "all_at_once"),
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Transform(y_coord_start, y_coord, submobject_mode = "all_at_once"),
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Write(brackets, run_time = 1),
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Transform(x_coord_start, x_coord, submobject_mode="all_at_once"),
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Transform(y_coord_start, y_coord, submobject_mode="all_at_once"),
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Write(brackets, run_time=1),
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)
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self.wait()
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@ -236,53 +239,56 @@ class VectorScene(Scene):
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x_max = int(FRAME_X_RADIUS + abs(vector[0]))
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y_max = int(FRAME_Y_RADIUS + abs(vector[1]))
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dots = VMobject(*[
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Dot(x*RIGHT + y*UP)
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Dot(x * RIGHT + y * UP)
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for x in range(-x_max, x_max)
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for y in range(-y_max, y_max)
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])
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dots.set_fill(BLACK, opacity = 0)
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dots_halfway = dots.copy().shift(vector/2).set_fill(WHITE, 1)
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dots.set_fill(BLACK, opacity=0)
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dots_halfway = dots.copy().shift(vector / 2).set_fill(WHITE, 1)
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dots_end = dots.copy().shift(vector)
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self.play(Transform(
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dots, dots_halfway, rate_func = rush_into
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dots, dots_halfway, rate_func=rush_into
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))
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self.play(Transform(
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dots, dots_end, rate_func = rush_from
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dots, dots_end, rate_func=rush_from
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))
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self.remove(dots)
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class LinearTransformationScene(VectorScene):
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CONFIG = {
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"include_background_plane" : True,
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"include_foreground_plane" : True,
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"foreground_plane_kwargs" : {
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"x_radius" : FRAME_WIDTH,
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"y_radius" : FRAME_HEIGHT,
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"secondary_line_ratio" : 0
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"include_background_plane": True,
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"include_foreground_plane": True,
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"foreground_plane_kwargs": {
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"x_radius": FRAME_WIDTH,
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"y_radius": FRAME_HEIGHT,
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"secondary_line_ratio": 0
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},
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"background_plane_kwargs" : {
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"color" : GREY,
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"secondary_color" : DARK_GREY,
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"axes_color" : GREY,
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"stroke_width" : 2,
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"background_plane_kwargs": {
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"color": GREY,
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"secondary_color": DARK_GREY,
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"axes_color": GREY,
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"stroke_width": 2,
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},
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"show_coordinates" : False,
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"show_basis_vectors" : True,
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"i_hat_color" : X_COLOR,
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"j_hat_color" : Y_COLOR,
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"leave_ghost_vectors" : False,
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"t_matrix" : [[3, 0], [1, 2]],
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"show_coordinates": False,
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"show_basis_vectors": True,
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"basis_vector_stroke_width": 6,
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"i_hat_color": X_COLOR,
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"j_hat_color": Y_COLOR,
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"leave_ghost_vectors": False,
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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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if hasattr(self, "has_already_setup"):
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return
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self.has_already_setup = True
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##^This is to not break all the old Scenes
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# ^This is to not break all the old Scenes
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self.background_mobjects = []
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self.foreground_mobjects = []
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self.foreground_mobjects = []
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self.transformable_mobjects = []
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self.moving_vectors = []
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self.moving_vectors = []
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self.transformable_labels = []
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self.moving_mobjects = []
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@ -293,21 +299,18 @@ class LinearTransformationScene(VectorScene):
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if self.show_coordinates:
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self.background_plane.add_coordinates()
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if self.include_background_plane:
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if self.include_background_plane:
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self.add_background_mobject(self.background_plane)
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if self.include_foreground_plane:
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self.plane = NumberPlane(**self.foreground_plane_kwargs)
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self.add_transformable_mobject(self.plane)
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if self.show_basis_vectors:
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self.i_hat, self.j_hat = [
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self.add_vector(
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coords, color, animate = False, stroke_width = 6
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)
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for coords, color in [
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((1, 0), self.i_hat_color),
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((0, 1), self.j_hat_color),
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]
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]
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self.basis_vectors = self.get_basis_vectors(
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i_hat_color=self.i_hat_color,
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j_hat_color=self.j_hat_color,
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)
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self.moving_vectors += list(self.basis_vectors)
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self.i_hat, self.j_hat = self.basis_vectors
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def add_special_mobjects(self, mob_list, *mobs_to_add):
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for mobject in mobs_to_add:
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@ -324,13 +327,13 @@ class LinearTransformationScene(VectorScene):
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def add_transformable_mobject(self, *mobjects):
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self.add_special_mobjects(self.transformable_mobjects, *mobjects)
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def add_moving_mobject(self, mobject, target_mobject = None):
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def add_moving_mobject(self, mobject, target_mobject=None):
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mobject.target = target_mobject
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self.add_special_mobjects(self.moving_mobjects, mobject)
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def add_unit_square(self, color = YELLOW, opacity = 0.3, animate = False):
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square = Square(color = color, side_length = 1)
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square.shift(-square.get_corner(DOWN+LEFT))
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def add_unit_square(self, color=YELLOW, opacity=0.3, animate=False):
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square = Square(color=color, side_length=1)
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square.shift(-square.get_corner(DOWN + LEFT))
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if animate:
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added_anims = map(Animation, self.moving_vectors)
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self.play(ShowCreation(square), *added_anims)
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@ -338,13 +341,13 @@ class LinearTransformationScene(VectorScene):
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else:
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square.set_fill(color, opacity)
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self.add_transformable_mobject(square)
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self.bring_to_front(*self.moving_vectors)
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self.bring_to_front(*self.moving_vectors)
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self.square = square
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return self
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def add_vector(self, vector, color = YELLOW, **kwargs):
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def add_vector(self, vector, color=YELLOW, **kwargs):
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vector = VectorScene.add_vector(
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self, vector, color = color, **kwargs
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self, vector, color=color, **kwargs
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)
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self.moving_vectors.append(vector)
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return vector
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@ -354,12 +357,12 @@ class LinearTransformationScene(VectorScene):
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self.add_foreground_mobject(coords)
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return coords
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def add_transformable_label(self, vector, label, new_label = None, **kwargs):
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def add_transformable_label(self, vector, label, new_label=None, **kwargs):
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label_mob = self.label_vector(vector, label, **kwargs)
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if new_label:
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label_mob.target_text = new_label
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else:
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label_mob.target_text = "L(%s)"%label_mob.get_tex_string()
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label_mob.target_text = "L(%s)" % label_mob.get_tex_string()
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label_mob.vector = vector
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label_mob.kwargs = kwargs
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if "animate" in label_mob.kwargs:
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@ -367,7 +370,7 @@ class LinearTransformationScene(VectorScene):
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self.transformable_labels.append(label_mob)
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return label_mob
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def add_title(self, title, scale_factor = 1.5, animate = False):
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def add_title(self, title, scale_factor=1.5, animate=False):
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if not isinstance(title, Mobject):
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title = TextMobject(title).scale(scale_factor)
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title.to_edge(UP)
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@ -378,7 +381,10 @@ class LinearTransformationScene(VectorScene):
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self.title = title
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return self
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def get_matrix_transformation(self, transposed_matrix):
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def get_matrix_transformation(self, matrix):
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return self.get_transposed_matrix_transformation(np.array(matrix).T)
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def get_transposed_matrix_transformation(self, transposed_matrix):
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transposed_matrix = np.array(transposed_matrix)
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if transposed_matrix.shape == (2, 2):
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new_matrix = np.identity(3)
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@ -389,11 +395,11 @@ class LinearTransformationScene(VectorScene):
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return lambda point: np.dot(point, transposed_matrix)
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def get_piece_movement(self, pieces):
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start = VMobject(*pieces)
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start = VMobject(*pieces)
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target = VMobject(*[mob.target for mob in pieces])
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if self.leave_ghost_vectors:
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self.add(start.copy().fade(0.7))
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return Transform(start, target, submobject_mode = "all_at_once")
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return Transform(start, target, submobject_mode="all_at_once")
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def get_moving_mobject_movement(self, func):
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for m in self.moving_mobjects:
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@ -405,7 +411,7 @@ class LinearTransformationScene(VectorScene):
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def get_vector_movement(self, func):
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for v in self.moving_vectors:
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v.target = Vector(func(v.get_end()), color = v.get_color())
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||||
v.target = Vector(func(v.get_end()), color=v.get_color())
|
||||
norm = np.linalg.norm(v.target.get_end())
|
||||
if norm < 0.1:
|
||||
v.target.get_tip().scale_in_place(norm)
|
||||
|
|
@ -418,12 +424,15 @@ class LinearTransformationScene(VectorScene):
|
|||
)
|
||||
return self.get_piece_movement(self.transformable_labels)
|
||||
|
||||
def apply_matrix(self, matrix, **kwargs):
|
||||
self.apply_transposed_matrix(np.array(matrix).T, **kwargs)
|
||||
|
||||
def apply_transposed_matrix(self, transposed_matrix, **kwargs):
|
||||
func = self.get_matrix_transformation(transposed_matrix)
|
||||
func = self.get_transposed_matrix_transformation(transposed_matrix)
|
||||
if "path_arc" not in kwargs:
|
||||
net_rotation = np.mean([
|
||||
angle_of_vector(func(RIGHT)),
|
||||
angle_of_vector(func(UP))-np.pi/2
|
||||
angle_of_vector(func(UP)) - np.pi / 2
|
||||
])
|
||||
kwargs["path_arc"] = net_rotation
|
||||
self.apply_function(func, **kwargs)
|
||||
|
|
@ -436,7 +445,7 @@ class LinearTransformationScene(VectorScene):
|
|||
self.plane.prepare_for_nonlinear_transform()
|
||||
self.apply_function(function, **kwargs)
|
||||
|
||||
def apply_function(self, function, added_anims = [], **kwargs):
|
||||
def apply_function(self, function, added_anims=[], **kwargs):
|
||||
if "run_time" not in kwargs:
|
||||
kwargs["run_time"] = 3
|
||||
anims = [
|
||||
|
|
@ -451,14 +460,3 @@ class LinearTransformationScene(VectorScene):
|
|||
for f_mob in self.foreground_mobjects
|
||||
] + added_anims
|
||||
self.play(*anims, **kwargs)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue