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https://github.com/3b1b/manim.git
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Moved complex transformation out of zeta
This commit is contained in:
Grant Sanderson
@ -1,11 +1,174 @@
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from helpers import *
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from mobject import VGroup
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from mobject.tex_mobject import TexMobject, TextMobject
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from number_line import NumberPlane
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from animation import Animation
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from animation.transform import ApplyPointwiseFunction
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from animation.simple_animations import Homotopy
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from scene import Scene
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class ComplexTransformationScene(Scene):
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CONFIG = {
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"plane_config" : {
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"x_line_frequency" : 1,
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"y_line_frequency" : 1,
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"secondary_line_ratio" : 1,
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},
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"background_fade_factor" : 0.5,
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"x_min" : -int(SPACE_WIDTH),
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"x_max" : int(SPACE_WIDTH),
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"y_min" : -SPACE_HEIGHT,
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"y_max" : SPACE_HEIGHT,
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"use_multicolored_plane" : False,
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"vert_start_color" : MAROON_B,
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"vert_end_color" : RED,
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"horiz_start_color" : GREEN_B,
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"horiz_end_color" : YELLOW,
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"num_anchors_to_add_per_line" : 50,
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"post_transformation_stroke_width" : None,
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"default_apply_complex_function_kwargs" : {
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"run_time" : 5,
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},
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"background_label_scale_val" : 0.5,
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}
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def setup(self):
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self.foreground_mobjects = []
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self.transformable_mobjects = []
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self.add_background_plane()
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def add_foreground_mobject(self, mobject):
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self.add_foreground_mobjects(mobject)
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def add_transformable_mobjects(self, *mobjects):
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self.transformable_mobjects += list(mobjects)
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self.add(*mobjects)
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def add_foreground_mobjects(self, *mobjects):
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self.foreground_mobjects += list(mobjects)
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Scene.add(self, *mobjects)
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def add(self, *mobjects):
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Scene.add(self, *list(mobjects)+self.foreground_mobjects)
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def play(self, *animations, **kwargs):
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Scene.play(
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self,
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*list(animations)+map(Animation, self.foreground_mobjects),
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**kwargs
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)
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def add_background_plane(self):
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background = NumberPlane(**self.plane_config).fade(
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self.background_fade_factor
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)
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real_labels = VGroup(*[
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TexMobject(str(x)).shift(
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background.num_pair_to_point((x, 0))
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)
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for x in range(-int(self.x_max), int(self.x_max))
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])
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imag_labels = VGroup(*[
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TexMobject("%di"%y).shift(
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background.num_pair_to_point((0, y))
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)
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for y in range(-int(self.y_max), int(self.y_max))
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if y != 0
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])
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for labels in real_labels, imag_labels:
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for label in labels:
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label.scale_in_place(self.background_label_scale_val)
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label.next_to(label.get_center(), DOWN+LEFT, buff = SMALL_BUFF)
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label.add_background_rectangle()
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background.add(labels)
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self.real_labels = real_labels
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self.imag_labels = imag_labels
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self.add(background)
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self.background = background
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def add_transformable_plane(self, animate = False):
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self.plane_config.update({
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"x_radius" : (self.x_max - self.x_min)/2.,
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"y_radius" : (self.y_max - self.y_min)/2.,
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})
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plane = NumberPlane(**self.plane_config)
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plane.shift(
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(self.x_max+self.x_min)*RIGHT/2.,
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(self.y_max+self.y_min)*UP/2.,
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)
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self.paint_plane(plane)
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if animate:
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self.play(ShowCreation(plane, run_time = 2))
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else:
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self.add(plane)
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self.plane = plane
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def prepare_for_transformation(self, mob):
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if hasattr(mob, "prepare_for_nonlinear_transform"):
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mob.prepare_for_nonlinear_transform(
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self.num_anchors_to_add_per_line
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)
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#TODO...
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def paint_plane(self, plane):
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if self.use_multicolored_plane:
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for lines in plane.main_lines, plane.secondary_lines:
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lines.gradient_highlight(
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self.vert_start_color,
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self.vert_end_color,
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self.horiz_start_color,
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self.horiz_end_color,
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)
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plane.axes.gradient_highlight(
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self.horiz_start_color,
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self.vert_start_color
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)
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def z_to_point(self, z):
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return self.background.num_pair_to_point((z.real, z.imag))
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def get_transformer(self, **kwargs):
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transform_kwargs = dict(self.default_apply_complex_function_kwargs)
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transform_kwargs.update(kwargs)
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plane = self.plane
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self.prepare_for_transformation(plane)
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transformer = VGroup(
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plane, *self.transformable_mobjects
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)
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return transformer, transform_kwargs
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def apply_complex_function(self, func, added_anims = [], **kwargs):
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transformer, transform_kwargs = self.get_transformer(**kwargs)
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transformer.generate_target()
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transformer.target.apply_complex_function(func)
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for mob in transformer.target[0].family_members_with_points():
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mob.make_smooth()
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if self.post_transformation_stroke_width is not None:
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transformer.target.set_stroke(width = self.post_transformation_stroke_width)
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self.play(
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MoveToTarget(transformer, **transform_kwargs),
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*added_anims
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)
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def apply_complex_homotopy(self, complex_homotopy, added_anims = [], **kwargs):
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transformer, transform_kwargs = self.get_transformer(**kwargs)
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def homotopy(x, y, z, t):
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output = complex_homotopy(complex(x, y), t)
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return (output.real, output.imag, z)
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self.play(
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SmoothedVectorizedHomotopy(
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homotopy, transformer,
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**transform_kwargs
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),
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*added_anims
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)
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##### Unsure about what comes under here...
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def complex_string(complex_num):
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return filter(lambda c : c not in "()", str(complex_num))
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@ -99,107 +262,22 @@ class ComplexHomotopy(Homotopy):
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Homotopy.__init__(self, homotopy, mobject, *args, **kwargs)
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class ComplexMultiplication(Scene):
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@staticmethod
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def args_to_string(multiplier, mark_one = False):
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num_str = complex_string(multiplier)
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arrow_str = "MarkOne" if mark_one else ""
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return num_str + arrow_str
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@staticmethod
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def string_to_args(arg_string):
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parts = arg_string.split()
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multiplier = complex(parts[0])
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mark_one = len(parts) > 1 and parts[1] == "MarkOne"
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return (multiplier, mark_one)
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def construct(self, multiplier, mark_one = False, **plane_config):
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norm = np.linalg.norm(multiplier)
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arg = np.log(multiplier).imag
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plane_config["faded_line_frequency"] = 0
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plane_config.update(DEFAULT_PLANE_CONFIG)
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if norm > 1 and "density" not in plane_config:
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plane_config["density"] = norm*DEFAULT_POINT_DENSITY_1D
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if "radius" not in plane_config:
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radius = SPACE_WIDTH
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if norm > 0 and norm < 1:
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radius /= norm
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else:
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radius = plane_config["radius"]
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plane_config["x_radius"] = plane_config["y_radius"] = radius
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plane = ComplexPlane(**plane_config)
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self.plane = plane
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self.add(plane)
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# plane.add_spider_web()
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self.anim_config = {
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"run_time" : 2.0,
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"path_func" : path_along_arc(arg)
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}
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plane_config["faded_line_frequency"] = 0.5
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background = ComplexPlane(color = "grey", **plane_config)
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# background.add_spider_web()
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labels = background.get_coordinate_labels()
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self.paint_into_background(background, *labels)
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self.mobjects_to_move_without_molding = []
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if mark_one:
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self.draw_dot("1", 1, True)
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self.draw_dot("z", multiplier)
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self.mobjects_to_multiply = [plane]
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self.additional_animations = []
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self.multiplier = multiplier
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if self.__class__ == ComplexMultiplication:
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self.apply_multiplication()
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def draw_dot(self, tex_string, value, move_dot = False):
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dot = Dot(
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self.plane.number_to_point(value),
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radius = 0.1*self.plane.unit_to_spatial_width,
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color = BLUE if value == 1 else YELLOW
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)
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label = TexMobject(tex_string)
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label.shift(dot.get_center()+1.5*UP+RIGHT)
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arrow = Arrow(label, dot)
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self.add(label)
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self.play(ShowCreation(arrow))
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self.play(ShowCreation(dot))
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self.dither()
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self.remove(label, arrow)
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if move_dot:
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self.mobjects_to_move_without_molding.append(dot)
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return dot
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def apply_multiplication(self):
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def func((x, y, z)):
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complex_num = self.multiplier*complex(x, y)
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return (complex_num.real, complex_num.imag, z)
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mobjects = self.mobjects_to_multiply
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mobjects += self.mobjects_to_move_without_molding
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mobjects += [anim.mobject for anim in self.additional_animations]
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self.add(*mobjects)
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full_multiplications = [
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ApplyMethod(mobject.apply_function, func, **self.anim_config)
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for mobject in self.mobjects_to_multiply
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]
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movements_with_plane = [
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ApplyMethod(
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mobject.shift,
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func(mobject.get_center())-mobject.get_center(),
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**self.anim_config
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)
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for mobject in self.mobjects_to_move_without_molding
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]
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self.dither()
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self.play(*reduce(op.add, [
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full_multiplications,
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movements_with_plane,
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self.additional_animations
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]))
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self.dither()
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