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This commit is contained in:
Sridhar Ramesh
2018-02-15 11:57:45 -08:00
parent ced8275f6e
commit e4ba832aac
2 changed files with 194 additions and 58 deletions
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239
active_projects/WindingNumber.py
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@ -33,15 +33,60 @@ from topics.graph_scene import *
# (and it will be done, but first I'll figure out what I'm doing with all this...)
# -SR
positive_color = GREEN
negative_color = RED
neutral_color = YELLOW
def rev_to_rgba(alpha):
alpha = (0.5 - alpha) % 1 # For convenience, to go CW from red on left instead of CCW from right
# 0 is red, 1/6 is yellow, 1/3 is green, 2/3 is blue
hue_list = [0, 0.5/6.0, 1/6.0, 1.1/6.0, 2/6.0, 3/6.0, 4/6.0, 5/6.0]
num_hues = len(hue_list)
start_index = int(np.floor(num_hues * alpha)) % num_hues
end_index = (start_index + 1) % num_hues
beta = (alpha % (1.0/num_hues)) * num_hues
start_hue = hue_list[start_index]
end_hue = hue_list[end_index]
if end_hue < start_hue:
end_hue = end_hue + 1
hue = interpolate(start_hue, end_hue, beta)
return color_to_rgba(Color(hue = hue, saturation = 1, luminance = 0.5))
# alpha = alpha % 1
# colors = colorslist
# num_colors = len(colors)
# beta = (alpha % (1.0/num_colors)) * num_colors
# start_index = int(np.floor(num_colors * alpha)) % num_colors
# end_index = (start_index + 1) % num_colors
# return interpolate(colors[start_index], colors[end_index], beta)
def rev_to_color(alpha):
return rgba_to_color(rev_to_rgba(alpha))
def point_to_rev((x, y), allow_origin = False):
# Warning: np.arctan2 would happily discontinuously returns the value 0 for (0, 0), due to
# design choices in the underlying atan2 library call, but for our purposes, this is
# illegitimate, and all winding number calculations must be set up to avoid this
if not(allow_origin) and (x, y) == (0, 0):
print "Error! Angle of (0, 0) computed!"
return
return fdiv(np.arctan2(y, x), TAU)
def point_to_rgba(point):
rev = point_to_rev(point, allow_origin = True)
rgba = rev_to_rgba(rev)
base_size = np.sqrt(point[0]**2 + point[1]**2)
rescaled_size = np.sqrt(base_size/(base_size + 1))
return rgba * rescaled_size
positive_color = rev_to_color(0)
negative_color = rev_to_color(0.5)
neutral_color = rev_to_color(0.25)
class EquationSolver1d(GraphScene, ZoomedScene):
CONFIG = {
"camera_config" :
{
#"use_z_coordinate_for_display_order": True,
"use_z_coordinate_for_display_order": True,
},
"func" : lambda x : x,
"targetX" : 0,
@ -140,9 +185,9 @@ class EquationSolver1d(GraphScene, ZoomedScene):
lowerDotPoint = self.input_to_graph_point(lowerX, self.graph)
lowerDotXPoint = self.coords_to_point(lowerX, 0)
lowerDotYPoint = self.coords_to_point(0, self.func(lowerX))
lowerDot = Dot(lowerDotPoint, color = negative_color)
lowerDot = Dot(lowerDotPoint + OUT, color = negative_color)
upperDotPoint = self.input_to_graph_point(upperX, self.graph)
upperDot = Dot(upperDotPoint, color = positive_color)
upperDot = Dot(upperDotPoint + OUT, color = positive_color)
upperDotXPoint = self.coords_to_point(upperX, 0)
upperDotYPoint = self.coords_to_point(0, self.func(upperX))
@ -154,15 +199,22 @@ class EquationSolver1d(GraphScene, ZoomedScene):
self.add(xBraces, yBraces, lowerDot, upperDot)
x_guess_line = Line(lowerDotXPoint, upperDotXPoint, color = neutral_color)
self.add(x_guess_line)
lowerGroup = Group(
lowerDot,
leftBrace, downBrace,
lowerXLine, lowerYLine)
lowerXLine, lowerYLine,
x_guess_line
)
upperGroup = Group(
upperDot,
rightBrace, upBrace,
upperXLine, upperYLine)
upperXLine, upperYLine,
x_guess_line
)
initialLowerXDot = Dot(lowerDotXPoint, color = negative_color)
initialUpperXDot = Dot(upperDotXPoint, color = positive_color)
@ -181,9 +233,9 @@ class EquationSolver1d(GraphScene, ZoomedScene):
upperDot.scale_in_place, inverseZoomFactor)
def makeUpdater(xAtStart):
def makeUpdater(xAtStart, fixed_guess_x):
def updater(group, alpha):
dot, xBrace, yBrace, xLine, yLine = group
dot, xBrace, yBrace, xLine, yLine, guess_line = group
newX = interpolate(xAtStart, midX, alpha)
newY = self.func(newX)
graphPoint = self.input_to_graph_point(newX,
@ -195,15 +247,20 @@ class EquationSolver1d(GraphScene, ZoomedScene):
yBrace.move_to(yAxisPoint)
xLine.put_start_and_end_on(xAxisPoint, graphPoint)
yLine.put_start_and_end_on(yAxisPoint, graphPoint)
fixed_guess_point = self.coords_to_point(fixed_guess_x, 0)
guess_line.put_start_and_end_on(xAxisPoint, fixed_guess_point)
return group
return updater
midX = (lowerX + upperX)/float(2)
midY = self.func(midX)
in_negative_branch = midY < self.targetY
sign_color = negative_color if in_negative_branch else positive_color
midCoords = self.coords_to_point(midX, midY)
midColor = neutral_color
midXPoint = Dot(self.coords_to_point(midX, 0), color = midColor)
# Hm... even the z buffer isn't helping keep this above x_guess_line
midXPoint = Dot(self.coords_to_point(midX, 0) + OUT, color = midColor)
x_guess_label_caption = TextMobject("New guess: x = ", fill_color = midColor)
x_guess_label_num = DecimalNumber(midX, fill_color = midColor)
@ -211,7 +268,7 @@ class EquationSolver1d(GraphScene, ZoomedScene):
x_guess_label_caption.next_to(x_guess_label_num, LEFT)
x_guess_label = Group(x_guess_label_caption, x_guess_label_num)
y_guess_label_caption = TextMobject(", y = ", fill_color = midColor)
y_guess_label_num = DecimalNumber(midY, fill_color = midColor)
y_guess_label_num = DecimalNumber(midY, fill_color = sign_color)
y_guess_label_caption.next_to(x_guess_label_num, RIGHT)
y_guess_label_num.next_to(y_guess_label_caption, RIGHT)
y_guess_label = Group(y_guess_label_caption, y_guess_label_num)
@ -222,35 +279,43 @@ class EquationSolver1d(GraphScene, ZoomedScene):
ReplacementTransform(rightBrace.copy(), midXPoint),
FadeIn(x_guess_label))
midXLine = Line(self.coords_to_point(midX, 0), midCoords, color = midColor)
midXLine = DashedLine(self.coords_to_point(midX, 0), midCoords, color = midColor)
self.play(ShowCreation(midXLine))
midDot = Dot(midCoords, color = midColor)
midDot = Dot(midCoords, color = sign_color)
if(self.iteration_at_which_to_start_zoom != None and
i >= self.iteration_at_which_to_start_zoom):
midDot.scale_in_place(inverseZoomFactor)
self.add(midDot)
midYLine = Line(midCoords, self.coords_to_point(0, midY), color = midColor)
midYLine = DashedLine(midCoords, self.coords_to_point(0, midY), color = sign_color)
self.play(
ShowCreation(midYLine),
FadeIn(y_guess_label))
midYPoint = Dot(self.coords_to_point(0, midY), color = midColor)
FadeIn(y_guess_label),
ApplyMethod(midXPoint.set_color, sign_color),
ApplyMethod(midXLine.set_color, sign_color))
midYPoint = Dot(self.coords_to_point(0, midY), color = sign_color)
self.add(midYPoint)
if midY < self.targetY:
if in_negative_branch:
self.play(
UpdateFromAlphaFunc(lowerGroup, makeUpdater(lowerX)),
UpdateFromAlphaFunc(lowerGroup,
makeUpdater(lowerX,
fixed_guess_x = upperX
)
),
FadeOut(guess_labels),
ApplyMethod(midXPoint.set_color, negative_color),
ApplyMethod(midYPoint.set_color, negative_color))
)
lowerX = midX
lowerY = midY
else:
self.play(
UpdateFromAlphaFunc(upperGroup, makeUpdater(upperX)),
UpdateFromAlphaFunc(upperGroup,
makeUpdater(upperX,
fixed_guess_x = lowerX
)
),
FadeOut(guess_labels),
ApplyMethod(midXPoint.set_color, positive_color),
ApplyMethod(midYPoint.set_color, positive_color))
)
upperX = midX
upperY = midY
#mid_group = Group(midXLine, midDot, midYLine) Removing groups doesn't flatten as expected?
@ -262,37 +327,6 @@ class EquationSolver1d(GraphScene, ZoomedScene):
self.drawGraph()
self.solveEquation()
colorslist = map(color_to_rgba, ["#FF0000", "#FFFF00", "#00FF00", "#0000FF"])
def rev_to_rgba(alpha):
alpha = alpha % 1
colors = colorslist
num_colors = len(colors)
beta = (alpha % (1.0/num_colors)) * num_colors
start_index = int(np.floor(num_colors * alpha)) % num_colors
end_index = (start_index + 1) % num_colors
return interpolate(colors[start_index], colors[end_index], beta)
def rev_to_color(alpha):
return rgba_to_color(rev_to_rgba(alpha))
def point_to_rev((x, y), allow_origin = False):
# Warning: np.arctan2 would happily discontinuously returns the value 0 for (0, 0), due to
# design choices in the underlying atan2 library call, but for our purposes, this is
# illegitimate, and all winding number calculations must be set up to avoid this
if not(allow_origin) and (x, y) == (0, 0):
print "Error! Angle of (0, 0) computed!"
return
return fdiv(np.arctan2(y, x), TAU)
def point_to_rgba(point):
rev = point_to_rev(point, allow_origin = True)
rgba = rev_to_rgba(rev)
base_size = np.sqrt(point[0]**2 + point[1]**2)
rescaled_size = np.sqrt(base_size/(base_size + 1))
return rgba * rescaled_size
# Returns the value with the same fractional component as x, closest to m
def resit_near(x, m):
frac_diff = (x - m) % 1
@ -520,6 +554,11 @@ class ColorMappedByFuncScene(Scene):
)
)
class PureColorMap(ColorMappedByFuncScene):
CONFIG = {
"show_num_plane" : False
}
class ColorMappedByFuncStill(ColorMappedByFuncScene):
def construct(self):
ColorMappedByFuncScene.construct(self)
@ -896,6 +935,37 @@ class SecondSqrtScene(FirstSqrtScene):
# TODO: Pi creatures intrigued
class RewriteEquation(Scene):
def construct(self):
# Can maybe fitz around with smoothening the transform, so just = goes to - and new stuff
# is added at the right end, while things re-center
f_old = TexMobject("f(x)")
f_new = f_old.copy()
equals_old = TexMobject("=")
equals_old_2 = equals_old.copy()
equals_new = equals_old.copy()
g_old = TexMobject("g(x)")
g_new = g_old.copy()
minus_new = TexMobject("-")
zero_new = TexMobject("0")
f_old.next_to(equals_old, LEFT)
g_old.next_to(equals_old, RIGHT)
minus_new.next_to(g_new, LEFT)
f_new.next_to(minus_new, LEFT)
equals_new.next_to(g_new, RIGHT)
zero_new.next_to(equals_new, RIGHT)
self.add(f_old, equals_old, equals_old_2, g_old)
self.wait()
self.play(
ReplacementTransform(f_old, f_new),
ReplacementTransform(equals_old, equals_new),
ReplacementTransform(g_old, g_new),
ReplacementTransform(equals_old_2, minus_new),
ShowCreation(zero_new),
)
self.wait()
class SignsExplanation(Scene):
def construct(self):
num_line = NumberLine(stroke_width = 1)
@ -911,12 +981,12 @@ class SignsExplanation(Scene):
num_line.number_to_point(0),
num_line.number_to_point(pos_num),
buff = 0,
color = YELLOW)
color = positive_color)
neg_arrow = Arrow(
num_line.number_to_point(0),
num_line.number_to_point(neg_num),
buff = 0,
color = RED)
color = negative_color)
#num_line.add_numbers(pos_num)
self.play(ShowCreation(pos_arrow))
@ -1300,6 +1370,55 @@ class DiffOdometer(OdometerScene):
"biased_display_start" : 0
}
class CombineInterval(Scene):
def construct(self):
plus_sign = TexMobject("+", fill_color = positive_color)
minus_sign = TexMobject("-", fill_color = negative_color)
left_point = Dot(LEFT, color = positive_color)
right_point = Dot(RIGHT, color = negative_color)
line1 = Line(LEFT, RIGHT)
interval1 = Group(line1, left_point, right_point)
plus_sign.next_to(left_point, UP)
minus_sign.next_to(right_point, UP)
self.add(interval1, plus_sign, minus_sign)
self.wait()
mid_point = Dot(ORIGIN, color = GREY)
question_mark = TexMobject("?", fill_color = GREY)
plus_sign_copy = plus_sign.copy()
minus_sign_copy = minus_sign.copy()
new_signs = Group(question_mark, plus_sign_copy, minus_sign_copy)
for sign in new_signs: sign.next_to(mid_point, UP)
self.play(ShowCreation(mid_point), ShowCreation(question_mark))
self.wait()
self.play(
ApplyMethod(mid_point.set_color, positive_color),
ReplacementTransform(question_mark, plus_sign_copy),
)
self.play(
HighlightCircle(plus_sign_copy),
HighlightCircle(minus_sign),
)
self.wait()
self.play(
ApplyMethod(mid_point.set_color, negative_color),
ReplacementTransform(plus_sign_copy, minus_sign_copy),
)
self.play(
HighlightCircle(minus_sign_copy),
HighlightCircle(plus_sign),
)
self.wait()
# TODO: Brouwer's fixed point theorem visuals
# class BFTScene(Scene):
@ -1351,4 +1470,10 @@ class ShowBack(PiWalkerRect):
"func" : plane_poly_with_roots((1, 2), (-1, 1.5), (-1, 1.5))
}
class Diagnostic(Scene):
def construct(self):
testList = map( (lambda n : (n, rev_to_rgba(n))), [0, 0.25, 0.5, 0.9])
print "rev_to_rgbas", testList
self.wait()
# FIN

13
animation/transform.py
View File

@ -8,7 +8,7 @@ from helpers import *
from animation import Animation
from mobject import Mobject, Point, VMobject, Group
from topics.geometry import Dot
from topics.geometry import Dot, Circle
class Transform(Animation):
CONFIG = {
@ -214,6 +214,17 @@ class Indicate(Transform):
target.highlight(self.color)
Transform.__init__(self, mobject, target, **kwargs)
class HighlightCircle(Indicate):
CONFIG = {
"rate_func" : squish_rate_func(there_and_back, 0, 0.8),
"remover" : True
}
def __init__(self, mobject, **kwargs):
digest_config(self, kwargs)
circle = Circle(color = self.color, **kwargs)
circle.surround(mobject)
Indicate.__init__(self, circle, **kwargs)
class Rotate(ApplyMethod):
CONFIG = {
"in_place" : False,