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Began a project for the winding number video
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Sridhar Ramesh
218
active_projects/WindingNumber.py
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218
active_projects/WindingNumber.py
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from helpers import *
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from mobject.tex_mobject import TexMobject
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from mobject import Mobject
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from mobject.image_mobject import ImageMobject
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from mobject.vectorized_mobject import *
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from animation.animation import Animation
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from animation.transform import *
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from animation.simple_animations import *
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from animation.playground import *
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from animation.continual_animation import *
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from topics.geometry import *
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from topics.characters import *
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from topics.functions import *
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from topics.fractals import *
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from topics.number_line import *
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from topics.combinatorics import *
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from topics.numerals import *
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from topics.three_dimensions import *
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from topics.objects import *
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from topics.probability import *
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from topics.complex_numbers import *
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from scene import Scene
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from scene.reconfigurable_scene import ReconfigurableScene
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from scene.zoomed_scene import *
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from camera import Camera
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from mobject.svg_mobject import *
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from mobject.tex_mobject import *
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from topics.graph_scene import *
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class Test(Scene):
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def construct(self):
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firstname = TextMobject("Sridhar")
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lastname = TextMobject("Ramesh")
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texObject1 = TexMobject(r"\sum_{x = 0}^{n} \frac{1}{x^2}")
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texObject2 = TexMobject(r"\int_{x = 0}^{n} \frac{1}{x^2}")
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squareObject = Square(side_length = 2)
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squareGroup = Group(*[Square(side_length = x) for x in range(3)])
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squareGroup.arrange_submobjects(RIGHT)
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#self.play(ReplacementTransform(texObject1, texObject2), run_time = 5)
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#self.play(texObject2.shift, 2*RIGHT)
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#self.play(Write(firstname))
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#self.play(Write(squareGroup))
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polygonObject = Polygon(ORIGIN, UP + RIGHT, UP + LEFT)
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polygonObject.set_stroke(color = YELLOW, width = 3)
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polygonObject.set_fill(color = WHITE, opacity = 0.5)
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self.play(DrawBorderThenFill(polygonObject), run_time = 5)
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class GraphTest(GraphScene, ZoomedScene):
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CONFIG = {
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"x_min" : 0,
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"x_max" : 6,
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"y_min" : -1,
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"y_max" : 20,
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"graph_origin" : 2*DOWN + 5 * LEFT,
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"x_axis_width" : 12,
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"zoom_factor" : 3,
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"zoomed_canvas_center" : 2 * UP + 1.5 * LEFT
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}
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def construct(self):
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# Convenient for skipping animations:
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# self.force_skipping()
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# self.revert_to_original_skipping_status()
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self.setup_axes()
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graphFunc = lambda x : x**2
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graph = self.get_graph(graphFunc)
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self.add(graph)
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inverseZoomFactor = 1/float(self.zoom_factor)
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graphLabel = self.get_graph_label(graph, "y = x^2",
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x_val = 4, direction = RIGHT)
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self.add(graphLabel)
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targetY = 6
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targetYLine = DashedLine(
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self.coords_to_point(self.x_min, targetY),
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self.coords_to_point(self.x_max, targetY),
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dashed_segment_length = 0.1)
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self.add(targetYLine)
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targetYLineLabel = TexMobject("y = " + str(targetY))
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targetYLineLabel.next_to(targetYLine.get_left(), UP + RIGHT)
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self.add(targetYLineLabel)
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leftBrace, rightBrace = xBraces = TexMobject("||")
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xBraces.stretch(2, 0)
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downBrace, upBrace = yBraces = TexMobject("||")
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yBraces.stretch(2, 0)
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yBraces.rotate(np.pi/2)
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lowerX = 1
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lowerY = graphFunc(lowerX)
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upperX = 5
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upperY = graphFunc(upperX)
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leftBrace.move_to(self.coords_to_point(lowerX, 0))
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leftBraceLabel = DecimalNumber(lowerX)
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leftBraceLabel.next_to(leftBrace, DOWN + LEFT, buff = SMALL_BUFF)
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leftBraceLabelAnimation = ContinualChangingDecimal(leftBraceLabel,
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lambda alpha : self.point_to_coords(leftBrace.get_center())[0],
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tracked_mobject = leftBrace)
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self.add(leftBraceLabelAnimation)
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rightBrace.move_to(self.coords_to_point(upperX, 0))
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rightBraceLabel = DecimalNumber(upperX)
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rightBraceLabel.next_to(rightBrace, DOWN + RIGHT, buff = SMALL_BUFF)
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rightBraceLabelAnimation = ContinualChangingDecimal(rightBraceLabel,
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lambda alpha : self.point_to_coords(rightBrace.get_center())[0],
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tracked_mobject = rightBrace)
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self.add(rightBraceLabelAnimation)
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downBrace.move_to(self.coords_to_point(0, lowerY))
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downBraceLabel = DecimalNumber(lowerY)
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downBraceLabel.next_to(downBrace, LEFT + DOWN, buff = SMALL_BUFF)
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downBraceLabelAnimation = ContinualChangingDecimal(downBraceLabel,
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lambda alpha : self.point_to_coords(downBrace.get_center())[1],
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tracked_mobject = downBrace)
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self.add(downBraceLabelAnimation)
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upBrace.move_to(self.coords_to_point(0, upperY))
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upBraceLabel = DecimalNumber(upperY)
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upBraceLabel.next_to(upBrace, LEFT + UP, buff = SMALL_BUFF)
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upBraceLabelAnimation = ContinualChangingDecimal(upBraceLabel,
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lambda alpha : self.point_to_coords(upBrace.get_center())[1],
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tracked_mobject = upBrace)
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self.add(upBraceLabelAnimation)
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lowerDotPoint = self.input_to_graph_point(lowerX, graph)
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lowerDotXPoint = self.coords_to_point(lowerX, 0)
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lowerDotYPoint = self.coords_to_point(0, graphFunc(lowerX))
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lowerDot = Dot(lowerDotPoint)
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upperDotPoint = self.input_to_graph_point(upperX, graph)
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upperDot = Dot(upperDotPoint)
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upperDotXPoint = self.coords_to_point(upperX, 0)
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upperDotYPoint = self.coords_to_point(0, graphFunc(upperX))
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lowerXLine = Line(lowerDotXPoint, lowerDotPoint, stroke_width = 1, color = YELLOW)
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upperXLine = Line(upperDotXPoint, upperDotPoint, stroke_width = 1, color = YELLOW)
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lowerYLine = Line(lowerDotYPoint, lowerDotPoint, stroke_width = 1, color = YELLOW)
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upperYLine = Line(upperDotYPoint, upperDotPoint, stroke_width = 1, color = YELLOW)
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self.add(lowerXLine, upperXLine, lowerYLine, upperYLine)
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# TODO: Display lines at start, not just on update
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self.add(xBraces, yBraces, lowerDot, upperDot)
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zoomStage = 5
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for i in range(10):
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if i == zoomStage:
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self.activate_zooming()
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self.little_rectangle.move_to(
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self.coords_to_point(np.sqrt(targetY), targetY))
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self.play(
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lowerDot.scale_in_place, inverseZoomFactor,
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upperDot.scale_in_place, inverseZoomFactor)
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def makeUpdater(xAtStart):
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def updater(group, alpha):
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dot, xBrace, yBrace, xLine, yLine = group
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newX = interpolate(xAtStart, midX, alpha)
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newY = graphFunc(newX)
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graphPoint = self.input_to_graph_point(newX,
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graph)
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dot.move_to(graphPoint)
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xAxisPoint = self.coords_to_point(newX, 0)
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xBrace.move_to(xAxisPoint)
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yAxisPoint = self.coords_to_point(0, newY)
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yBrace.move_to(yAxisPoint)
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xLine.put_start_and_end_on(xAxisPoint, graphPoint)
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yLine.put_start_and_end_on(yAxisPoint, graphPoint)
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return group
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return updater
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midX = (lowerX + upperX)/float(2)
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midY = graphFunc(midX)
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midCoords = self.coords_to_point(midX, midY)
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midColor = RED
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midXPoint = Dot(self.coords_to_point(midX, 0), color = midColor)
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self.play(
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ReplacementTransform(leftBrace.copy(), midXPoint),
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ReplacementTransform(rightBrace.copy(), midXPoint))
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midXLine = Line(self.coords_to_point(midX, 0), midCoords, color = midColor)
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self.play(ShowCreation(midXLine))
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midDot = Dot(midCoords, color = midColor)
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if(i >= zoomStage):
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midDot.scale_in_place(inverseZoomFactor)
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self.add(midDot)
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midYLine = Line(midCoords, self.coords_to_point(0, midY), color = midColor)
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self.play(ShowCreation(midYLine))
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if midY < targetY:
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movingGroup = Group(lowerDot,
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leftBrace, downBrace,
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lowerXLine, lowerYLine)
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self.play(
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UpdateFromAlphaFunc(movingGroup, makeUpdater(lowerX)))
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lowerX = midX
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lowerY = midY
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else:
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movingGroup = Group(upperDot,
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rightBrace, upBrace,
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upperXLine, upperYLine)
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self.play(
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UpdateFromAlphaFunc(movingGroup, makeUpdater(upperX)))
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upperX = midX
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upperY = midY
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self.remove(midXLine, midDot, midYLine)
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self.dither()
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