mirror of
https://github.com/3b1b/manim.git
synced 2025-07-31 14:03:59 +08:00
Additive/multiplicative rules
This commit is contained in:
Grant Sanderson
@ -130,19 +130,18 @@ class Homotopy(Animation):
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class PhaseFlow(Animation):
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CONFIG = {
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"virtual_time" : 1
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"virtual_time" : 1,
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"rate_func" : None,
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}
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def __init__(self, function, mobject, **kwargs):
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digest_config(self, kwargs, locals())
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self.get_nudge_func = lambda alpha_diff : \
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lambda point : point + alpha_diff*function(point)
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Animation.__init__(self, mobject, **kwargs)
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def update_mobject(self, alpha):
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if hasattr(self, "last_alpha"):
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nudge = self.virtual_time*(alpha-self.last_alpha)
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dt = self.virtual_time*(alpha-self.last_alpha)
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self.mobject.apply_function(
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self.get_nudge_func(nudge)
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lambda p : p + dt*self.function(p)
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)
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self.last_alpha = alpha
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@ -160,19 +159,25 @@ class MoveAlongPath(Animation):
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class ApplyToCenters(Animation):
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def __init__(self, AnimationClass, mobjects, **kwargs):
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centers = [mob.get_center() for mob in mobjects]
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kwargs["mobject"] = Mobject().add_points(centers)
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self.centers_container = AnimationClass(**kwargs)
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kwargs.pop("mobject")
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Animation.__init__(self, Mobject(*mobjects), **kwargs)
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full_kwargs = AnimationClass.CONFIG
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full_kwargs.update(kwargs)
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full_kwargs["mobject"] = Mobject(*[
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mob.get_point_mobject()
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for mob in mobjects
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])
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self.centers_container = AnimationClass(**full_kwargs)
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full_kwargs.pop("mobject")
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Animation.__init__(self, Mobject(*mobjects), **full_kwargs)
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self.name = str(self) + AnimationClass.__name__
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def update_mobject(self, alpha):
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self.centers_container.update_mobject(alpha)
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points = self.centers_container.mobject.points
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center_mobs = self.centers_container.mobject.split()
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mobjects = self.mobject.split()
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for point, mobject in zip(points, mobjects):
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mobject.center().shift(point)
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for center_mob, mobject in zip(center_mobs, mobjects):
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mobject.shift(
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center_mob.get_center()-mobject.get_center()
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)
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@ -129,6 +129,8 @@ class Camera(object):
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if len(points) == 0:
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continue
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coords = self.points_to_pixel_coords(points)
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if np.all(~self.on_screen_pixels(coords)):
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return result
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start = "M%d %d"%tuple(coords[0])
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#(handle1, handle2, anchor) tripletes
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triplets = zip(*[
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@ -1,7 +1,6 @@
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import numpy as np
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import itertools as it
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from PIL import Image
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import cv2
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from copy import deepcopy
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from mobject import Mobject
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@ -87,9 +87,11 @@ class VMobject(Mobject):
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def get_stroke_color(self):
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try:
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self.stroke_rgb[self.stroke_rgb<0] = 0
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self.stroke_rgb[self.stroke_rgb>1] = 1
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return Color(rgb = self.stroke_rgb)
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except:
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return Color(rgb = 0.99*self.stroke_rgb)
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return Color(WHITE)
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#TODO, get color? Specify if stroke or fill
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#is the predominant color attribute?
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@ -192,6 +194,16 @@ class VMobject(Mobject):
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self.submobjects
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)
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def arrange_submobjects(self,
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direction = RIGHT,
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buff = DEFAULT_MOBJECT_TO_MOBJECT_BUFFER,
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center = True):
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for m1, m2 in zip(self.submobjects, self.submobjects[1:]):
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m2.next_to(m1, direction, buff = buff)
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if center:
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self.center()
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return self
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## Information about line
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def component_curves(self):
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@ -56,10 +56,10 @@ class PiCreature(SVGMobject):
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self.set_stroke(color = BLACK, width = self.stroke_width)
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if not self.parts_named:
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self.name_parts()
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self.mouth.set_fill(BLACK)
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self.body.set_fill(self.color)
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self.pupils.set_fill(BLACK)
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self.eyes.set_fill(WHITE)
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self.mouth.set_fill(BLACK, opacity = 1)
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self.body.set_fill(self.color, opacity = 1)
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self.pupils.set_fill(BLACK, opacity = 1)
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self.eyes.set_fill(WHITE, opacity = 1)
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return self
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@ -98,6 +98,9 @@ class UnitInterval(NumberLine):
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class Axes(VMobject):
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CONFIG = {
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"propogate_style_to_family" : True
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}
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def generate_points(self, **kwargs):
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self.x_axis = NumberLine(**kwargs)
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self.y_axis = NumberLine(**kwargs).rotate(np.pi/2)
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@ -116,9 +119,10 @@ class NumberPlane(VMobject):
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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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"written_coordinate_height" : 0.5,
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"written_coordinate_height" : 0.2,
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"written_coordinate_nudge" : 0.1*(DOWN+RIGHT),
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"num_pair_at_center" : (0, 0),
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"propogate_style_to_family" : False,
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}
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def generate_points(self):
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@ -160,7 +164,7 @@ class NumberPlane(VMobject):
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def init_colors(self):
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VMobject.init_colors(self)
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self.axes.set_stroke(self.axes_color)
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# self.main_lines.set_stroke(self.color)
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self.main_lines.set_stroke(self.color)
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self.secondary_lines.set_stroke(self.secondary_color, 1)
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return self
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@ -82,7 +82,7 @@ def get_top_inverse(i, j):
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class TOP(VMobject):
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CONFIG = {
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"triangle_height_to_number_height" : 3,
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"offset_multiple" : 1.2,
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"offset_multiple" : 1.5,
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"radius" : 1.5,
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"propogate_style_to_family" : False,
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}
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@ -121,7 +121,7 @@ class TOP(VMobject):
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value = TexMobject(value)
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if isinstance(value, TOP):
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return self.put_top_on_vertix(index, value)
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value.scale_to_fit_height(self.get_value_height())
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self.rescale_corner_mobject(value)
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value.center()
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if index == 0:
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offset = -value.get_corner(UP+RIGHT)
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@ -134,6 +134,26 @@ class TOP(VMobject):
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value.shift(anchors[index])
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return value
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def put_top_on_vertix(self, index, top):
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top.scale_to_fit_height(2*self.get_value_height())
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vertices = top.get_vertices()
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vertices[index] = 0
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start = reduce(op.add, vertices)/2
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end = self.triangle.get_anchors_and_handles()[0][index]
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top.shift(end-start)
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return top
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def put_in_vertex(self, index, mobject):
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self.rescale_corner_mobject(mobject)
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mobject.center()
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mobject.shift(interpolate(
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self.get_center(),
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self.get_vertices()[index],
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0.7
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))
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return mobject
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def get_surrounding_circle(self, color = YELLOW):
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return Circle(
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radius = 1.7*self.radius,
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@ -143,20 +163,20 @@ class TOP(VMobject):
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(self.triangle.get_height()/6)*DOWN
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)
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def put_top_on_vertix(self, index, top):
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top.scale_to_fit_height(2*self.get_value_height())
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top_anchors = list(
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top.triangle.get_anchors_and_handles()[0][:3]
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)
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top_anchors[index] = 0
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start = reduce(op.add, top_anchors)/2
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end = self.triangle.get_anchors_and_handles()[0][index]
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top.shift(end-start)
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return top
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def rescale_corner_mobject(self, mobject):
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if mobject.get_height() > self.get_value_height():
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mobject.scale_to_fit_height(self.get_value_height())
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return self
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def get_value_height(self):
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return self.triangle.get_height()/self.triangle_height_to_number_height
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def get_center(self):
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return center_of_mass(self.get_vertices())
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def get_vertices(self):
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return self.triangle.get_anchors_and_handles()[0][:3]
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def reset_submobjects(self):
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self.submobjects = [self.triangle] + self.values
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return self
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@ -501,6 +521,251 @@ class AdditiveProperty(Scene):
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self.remove(copies)
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class DrawInsideTriangle(Scene):
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def construct(self):
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top = TOP()
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top.scale(2)
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dot = top.put_in_vertex(0, Dot())
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plus = top.put_in_vertex(1, TexMobject("+"))
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times = top.put_in_vertex(2, TexMobject("\\times"))
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plus.highlight(GREEN)
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times.highlight(YELLOW)
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self.add(top)
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self.dither()
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for mob in dot, plus, times:
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self.play(Write(mob, run_time = 1))
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self.dither()
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class ConstantOnTop(Scene):
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def construct(self):
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top = TOP()
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dot = top.put_in_vertex(1, Dot())
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times1 = top.put_in_vertex(0, TexMobject("\\times"))
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times2 = top.put_in_vertex(2, TexMobject("\\times"))
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times1.highlight(YELLOW)
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times2.highlight(YELLOW)
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three = top.put_on_vertex(1, "3")
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lower_left_x = top.put_on_vertex(0, "x")
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lower_right_x = top.put_on_vertex(2, "x")
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x_cubed = TexMobject("x^3").to_edge(UP)
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x_cubed.submobjects.reverse() #To align better
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cube_root_x = TexMobject("\\sqrt[3]{x}").to_edge(UP)
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self.add(top)
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self.play(ShowCreation(three))
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self.play(
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FadeIn(lower_left_x),
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Write(x_cubed),
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run_time = 1
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)
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self.dither()
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self.play(*[
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Transform(*pair, path_arc = np.pi)
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for pair in [
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(lower_left_x, lower_right_x),
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(x_cubed, cube_root_x),
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]
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])
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self.dither(2)
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for mob in dot, times1, times2:
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self.play(ShowCreation(mob))
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self.dither()
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def get_const_top_TOP(*args):
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top = TOP(*args)
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dot = top.put_in_vertex(1, Dot())
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times1 = top.put_in_vertex(0, TexMobject("\\times"))
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times2 = top.put_in_vertex(2, TexMobject("\\times"))
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times1.highlight(YELLOW)
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times2.highlight(YELLOW)
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top.add(dot, times1, times2)
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return top
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class MultiplyWithConstantTop(Scene):
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def construct(self):
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top1 = get_const_top_TOP("x", "3")
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top2 = get_const_top_TOP("y", "3")
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top3 = get_const_top_TOP("xy", "3")
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times = TexMobject("\\times")
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equals = TexMobject("=")
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top_exp_equation = VMobject(
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top1, times, top2, equals, top3
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)
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top_exp_equation.arrange_submobjects()
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old_style_exp = TexMobject("(x^3)(y^3) = (xy)^3")
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old_style_exp.to_edge(UP)
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old_style_exp.highlight(GREEN)
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old_style_rad = TexMobject("\\sqrt[3]{x} \\sqrt[3]{y} = \\sqrt[3]{xy}")
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old_style_rad.to_edge(UP)
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old_style_rad.highlight(RED)
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self.add(top_exp_equation, old_style_exp)
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self.dither(3)
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old_tops = [top1, top2, top3]
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new_tops = []
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for top in old_tops:
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new_top = top.copy()
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new_top.put_on_vertex(2, new_top.values[0])
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new_top.shift(0.5*LEFT)
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new_tops.append(new_top)
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self.play(
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Transform(old_style_exp, old_style_rad),
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Transform(
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VMobject(*old_tops),
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VMobject(*new_tops),
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path_arc = np.pi/2
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)
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)
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self.dither(3)
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class RightStaysConstantQ(Scene):
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def construct(self):
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top1, top2, top3 = old_tops = [
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TOP(None, s, "8")
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for s in "x", "y", TexMobject("x?y")
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]
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q_mark = TexMobject("?").scale(2)
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equation = VMobject(
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top1, q_mark, top2, TexMobject("="), top3
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)
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equation.arrange_submobjects(buff = 0.7)
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symbols_at_top = VMobject(*[
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top.values[1]
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for top in top1, top2, top3
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])
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symbols_at_lower_right = VMobject(*[
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top.put_on_vertex(0, top.values[1].copy())
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for top in top1, top2, top3
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])
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old_style_eq1 = TexMobject("\\sqrt[x]{8} ? \\sqrt[y]{8} = \\sqrt[x?y]{8}")
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old_style_eq1.highlight(BLUE)
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old_style_eq2 = TexMobject("\\log_x(8) ? \\log_y(8) = \\log_{x?y}(8)")
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old_style_eq2.highlight(YELLOW)
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for eq in old_style_eq1, old_style_eq2:
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eq.to_edge(UP)
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randy = Randolph()
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randy.to_corner()
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bubble = ThoughtBubble().pin_to(randy)
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bubble.add_content(TOP(None, None, "8"))
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self.add(randy, bubble)
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self.play(ApplyMethod(randy.change_mode, "pondering"))
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self.dither(3)
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triangle = bubble.content.triangle
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eight = bubble.content.values[2]
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bubble.clear()
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self.play(
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Transform(triangle, equation),
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FadeOut(eight),
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ApplyPointwiseFunction(
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lambda p : (p+2*DOWN)*15/np.linalg.norm(p+2*DOWN),
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bubble
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),
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FadeIn(old_style_eq1),
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ApplyMethod(randy.shift, 3*DOWN + 3*LEFT),
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run_time = 2
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)
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self.remove(triangle)
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self.add(equation)
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self.dither(4)
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self.play(
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Transform(
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symbols_at_top, symbols_at_lower_right,
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path_arc = np.pi/2
|
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),
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Transform(old_style_eq1, old_style_eq2)
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)
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self.dither(2)
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class AOplusB(Scene):
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def construct(self):
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self.add(TexMobject(
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"a \\oplus b = \\dfrac{1}{\\frac{1}{a} + \\frac{1}{b}}"
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).scale(2))
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self.dither()
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class ConstantLowerRight(Scene):
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def construct(self):
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top = TOP()
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times = top.put_in_vertex(0, TexMobject("\\times"))
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times.highlight(YELLOW)
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oplus = top.put_in_vertex(1, TexMobject("\\oplus"))
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oplus.highlight(BLUE)
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dot = top.put_in_vertex(2, Dot())
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eight = top.put_on_vertex(2, TexMobject("8"))
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self.add(top)
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self.play(ShowCreation(eight))
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for mob in dot, oplus, times:
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self.play(ShowCreation(mob))
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self.dither()
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top.add(eight)
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top.add(times, oplus, dot)
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top1, top2, top3 = tops = [
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top.copy() for i in range(3)
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]
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big_oplus = TexMobject("\\oplus").scale(2).highlight(BLUE)
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equals = TexMobject("=")
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equation = VMobject(
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top1, big_oplus, top2, equals, top3
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)
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equation.arrange_submobjects()
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top3.shift(0.5*RIGHT)
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x, y, xy = [
|
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t.put_on_vertex(0, s)
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for t, s in zip(tops, ["x", "y", "xy"])
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]
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old_style_eq = TexMobject(
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"\\dfrac{1}{\\frac{1}{\\log_x(8)} + \\frac{1}{\\log_y(8)}} = \\log_{xy}(8)"
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||||
)
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old_style_eq.to_edge(UP).highlight(RED)
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triple_top_copy = VMobject(*[
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top.copy() for i in range(3)
|
||||
])
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self.clear()
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||||
self.play(
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Transform(triple_top_copy, VMobject(*tops)),
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FadeIn(VMobject(x, y, xy, big_oplus, equals))
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)
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self.remove(triple_top_copy)
|
||||
self.add(*tops)
|
||||
self.play(Write(old_style_eq))
|
||||
self.dither(3)
|
||||
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||||
syms = VMobject(x, y, xy)
|
||||
new_syms = VMobject(*[
|
||||
t.put_on_vertex(1, s)
|
||||
for t, s in zip(tops, ["x", "y", "x \\oplus y"])
|
||||
])
|
||||
new_old_style_eq = TexMobject(
|
||||
"\\sqrt[x]{8} \\sqrt[y]{8} = \\sqrt[X]{8}"
|
||||
)
|
||||
X = new_old_style_eq.split()[-4]
|
||||
frac = TexMobject("\\frac{1}{\\frac{1}{x} + \\frac{1}{y}}")
|
||||
frac.replace(X)
|
||||
frac_lower_right = frac.get_corner(DOWN+RIGHT)
|
||||
frac.scale(2)
|
||||
frac.shift(frac_lower_right - frac.get_corner(DOWN+RIGHT))
|
||||
new_old_style_eq.submobjects[-4] = frac
|
||||
new_old_style_eq.to_edge(UP)
|
||||
new_old_style_eq.highlight(RED)
|
||||
big_times = TexMobject("\\times").highlight(YELLOW)
|
||||
big_times.shift(big_oplus.get_center())
|
||||
self.play(
|
||||
Transform(old_style_eq, new_old_style_eq),
|
||||
Transform(syms, new_syms, path_arc = np.pi/2),
|
||||
Transform(big_oplus, big_times)
|
||||
)
|
||||
self.dither(4)
|
||||
|
||||
|
||||
|
||||
class Test(Scene):
|
||||
|
||||
Reference in New Issue
Block a user