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Introducing inverse mapping as weaving
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Grant Sanderson
parent
4f57551344
commit
0acc694c54
1 changed files with 145 additions and 17 deletions
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@ -27,7 +27,8 @@ from region import region_from_polygon_vertices
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import displayer as disp
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from hilbert.curves import \
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TransformOverIncreasingOrders, FlowSnake
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TransformOverIncreasingOrders, FlowSnake, HilbertCurve, \
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SnakeCurve
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from helpers import *
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@ -126,7 +127,6 @@ class AboutSpaceFillingCurves(TransformOverIncreasingOrders):
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class PostponePhilosophizing(Scene):
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def construct(self):
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abstract, arrow, concrete = TextMobject([
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@ -144,6 +144,12 @@ class PostponePhilosophizing(Scene):
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])
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self.dither()
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class SectionOne(Scene):
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def construct(self):
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self.add(TextMobject("Section 1: Seeing with your ears"))
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self.dither()
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class WriteSomeSoftware(Scene):
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pass #Done viea screen capture, written here for organization
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@ -266,13 +272,11 @@ class GridOfPixels(Scene):
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def construct(self):
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low_res = ImageMobject("low_resolution_lion", invert = False)
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high_res = ImageMobject("Lion", invert = False)
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grid = get_grid()
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grid = get_grid().scale(0.8)
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for mob in low_res, high_res:
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mob.replace(grid, stretch = True)
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for mob in low_res, high_res, grid:
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mob.sort_points(np.linalg.norm)
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side_brace = Brace(grid, LEFT)
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top_brace = Brace(grid, UP)
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side_brace = Brace(low_res, LEFT)
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top_brace = Brace(low_res, UP)
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top_words = TextMobject("256 Px", size = "\\normal")
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side_words = top_words.copy().rotate(np.pi/2)
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top_words.next_to(top_brace, UP)
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@ -282,9 +286,6 @@ class GridOfPixels(Scene):
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self.dither()
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self.play(DelayByOrder(Transform(high_res, low_res)))
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self.dither()
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self.play(DelayByOrder(Transform(high_res, grid)))
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self.clear()
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self.add(grid)
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self.play(
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GrowFromCenter(top_brace),
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GrowFromCenter(side_brace),
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@ -292,6 +293,10 @@ class GridOfPixels(Scene):
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ShimmerIn(side_words)
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)
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self.dither()
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for mob in grid, high_res:
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mob.sort_points(np.linalg.norm)
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self.play(DelayByOrder(Transform(high_res, grid)))
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self.dither()
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class ShowFrequencySpace(Scene):
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@ -373,7 +378,7 @@ class AssociatePixelWithFrequency(Scene):
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self.play(loud_vibration)
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self.play(
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TransformAnimations(loud_vibration, quiet_vibration),
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ApplyMethod(dot.fade, 0.1)
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ApplyMethod(dot.fade, 0.9)
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)
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self.clear()
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self.add(freq_line, dot, arrow)
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@ -503,12 +508,135 @@ class LeverageExistingIntuitions(Scene):
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class ThinkInTermsOfReverseMapping(Scene):
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def construct(self):
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grid = get_grid()
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grid.scale_to_fit_width(6)
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grid.to_edge(LEFT)
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freq_line = get_freq_line()
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freq_line.scale_to_fit_width(6)
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freq_line.center().to_edge(RIGHT)
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arrow = Arrow(grid, freq_line)
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color1, color2 = YELLOW_C, RED
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square_length = 0.01
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dot1 = Dot(color = color1)
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dot1.shift(3*RIGHT)
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dot2 = Dot(color = color2)
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dot2.shift(3.1*RIGHT)
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arrow1 = Arrow(2*RIGHT+UP, dot1, color = color1, buffer = 0.1)
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arrow2 = Arrow(4*RIGHT+UP, dot2, color = color2, buffer = 0.1)
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dot3, arrow3 = [
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mob.copy().shift(5*LEFT+UP)
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for mob in dot1, arrow1
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]
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dot4, arrow4 = [
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mob.copy().shift(5*LEFT+0.9*UP)
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for mob in dot2, arrow2
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]
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self.add(grid, freq_line, arrow)
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self.dither()
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self.play(ApplyMethod(
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arrow.rotate, np.pi,
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interpolation_function = clockwise_path()
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))
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self.dither()
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self.play(ShowCreation(arrow1))
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self.add(dot1)
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self.play(ShowCreation(arrow2))
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self.add(dot2)
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self.dither()
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self.remove(arrow1, arrow2)
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self.play(
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Transform(dot1, dot3),
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Transform(dot2, dot4)
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)
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self.play(
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ApplyMethod(grid.fade, 0.8),
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Animation(Mobject(dot3, dot4))
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)
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self.play(ShowCreation(arrow3))
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self.play(ShowCreation(arrow4))
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self.dither()
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class WeaveLineThroughPixels(Scene):
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def construct(self):
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start_color, end_color = RED, GREEN
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curve = HilbertCurve(order = 2)
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line = Line(5*LEFT, 5*RIGHT)
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for mob in curve, line:
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mob.gradient_highlight(start_color, end_color)
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freq_line = get_freq_line()
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freq_line.replace(line, stretch = True)
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unit = 6./4 #sidelength of pixel
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up = unit*UP
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right = unit*RIGHT
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lower_left = 3*(LEFT+DOWN)
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squares = Mobject(*[
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Square(
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side_length = unit,
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color = WHITE
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).shift(x*right+y*up)
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for x, y in it.product(range(4), range(4))
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])
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squares.center()
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targets = Mobject()
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for square in squares.sub_mobjects:
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center = square.get_center()
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distances = np.apply_along_axis(
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lambda p : np.linalg.norm(p-center),
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1,
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curve.points
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)
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index_along_curve = np.argmin(distances)
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fraction_along_curve = index_along_curve/float(curve.get_num_points())
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target = square.copy().center().scale(0.2)
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line_index = int(fraction_along_curve*line.get_num_points())
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target.shift(line.points[line_index])
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targets.add(target)
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self.add(squares)
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self.play(ShowCreation(
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curve,
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run_time = 5,
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alpha_func = None
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))
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self.dither()
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self.play(
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Transform(curve, line),
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Transform(squares, targets),
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run_time = 3
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)
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self.dither()
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self.play(ShowCreation(freq_line))
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self.dither()
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class WellPlayedGameOfSnake(Scene):
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def construct(self):
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grid = Grid(16, 16).fade()
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snake_curve = SnakeCurve(order = 4)
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words = TextMobject("``Snake Curve''")
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words.next_to(grid, UP)
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self.add(grid)
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self.play(ShowCreation(
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snake_curve,
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run_time = 7,
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alpha_func = None
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))
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self.dither()
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self.play(ShimmerIn(words))
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self.dither()
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class TellMathematicianFriend(Scene):
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def construct(self):
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pass
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