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https://github.com/3b1b/manim.git
synced 2025-07-31 22:13:30 +08:00
Work in progress on building up WindingNumber animations
This commit is contained in:
Sridhar Ramesh
@ -29,64 +29,40 @@ 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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class EquationSolver1d(GraphScene, ZoomedScene, ReconfigurableScene):
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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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"graph_func" : lambda x : x,
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"targetX" : 0,
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"targetY" : 0,
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"initial_lower_x" : 0,
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"initial_upper_x" : 10,
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"num_iterations" : 10,
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"iteration_at_which_to_start_zoom" : None,
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"graph_label" : None,
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"show_target_line" : True
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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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def drawGraph(self):
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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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self.graph = self.get_graph(self.graph_func)
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self.add(self.graph)
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inverseZoomFactor = 1/float(self.zoom_factor)
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if self.graph_label != None:
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self.add(self.get_graph_label(self.graph, self.graph_label,
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x_val = 4, direction = RIGHT))
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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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if self.show_target_line:
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target_line_object = DashedLine(
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self.coords_to_point(self.x_min, self.targetY),
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self.coords_to_point(self.x_max, self.targetY),
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dashed_segment_length = 0.1)
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self.add(targetYLine)
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self.add(target_line_object)
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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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target_line_label = TexMobject("y = " + str(self.targetY))
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target_line_label.next_to(target_line_object.get_left(), UP + RIGHT)
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self.add(target_line_label)
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def solveEquation(self):
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leftBrace, rightBrace = xBraces = TexMobject("||")
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xBraces.stretch(2, 0)
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@ -94,10 +70,10 @@ class GraphTest(GraphScene, ZoomedScene):
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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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lowerX = self.initial_lower_x
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lowerY = self.graph_func(lowerX)
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upperX = self.initial_upper_x
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upperY = self.graph_func(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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@ -131,14 +107,14 @@ class GraphTest(GraphScene, ZoomedScene):
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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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lowerDotPoint = self.input_to_graph_point(lowerX, self.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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lowerDotYPoint = self.coords_to_point(0, self.graph_func(lowerX))
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lowerDot = Dot(lowerDotPoint)
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upperDotPoint = self.input_to_graph_point(upperX, graph)
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upperDotPoint = self.input_to_graph_point(upperX, self.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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upperDotYPoint = self.coords_to_point(0, self.graph_func(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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@ -146,16 +122,14 @@ class GraphTest(GraphScene, ZoomedScene):
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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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for i in range(self.num_iterations):
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if i == self.iteration_at_which_to_start_zoom:
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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.coords_to_point(self.targetX, self.targetY))
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inverseZoomFactor = 1/float(self.zoom_factor)
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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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@ -165,9 +139,9 @@ class GraphTest(GraphScene, ZoomedScene):
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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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newY = self.graph_func(newX)
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graphPoint = self.input_to_graph_point(newX,
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graph)
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self.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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@ -179,7 +153,7 @@ class GraphTest(GraphScene, ZoomedScene):
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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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midY = self.graph_func(midX)
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midCoords = self.coords_to_point(midX, midY)
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midColor = RED
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@ -190,13 +164,14 @@ class GraphTest(GraphScene, ZoomedScene):
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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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if(self.iteration_at_which_to_start_zoom != None and
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i >= self.iteration_at_which_to_start_zoom):
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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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if midY < self.targetY:
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movingGroup = Group(lowerDot,
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leftBrace, downBrace,
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lowerXLine, lowerYLine)
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@ -216,3 +191,134 @@ class GraphTest(GraphScene, ZoomedScene):
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self.remove(midXLine, midDot, midYLine)
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self.dither()
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def construct(self):
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self.drawGraph()
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self.solveEquation()
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class FirstSqrtScene(EquationSolver1d):
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CONFIG = {
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"x_min" : 0,
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"x_max" : 2,
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"y_min" : 0,
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"y_max" : 4,
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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" : 2.25 * UP + 1.75 * LEFT,
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"graph_func" : lambda x : x**2,
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"targetX" : np.sqrt(2),
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"targetY" : 2,
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"initial_lower_x" : 1,
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"initial_upper_x" : 2,
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"num_iterations" : 2,
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"iteration_at_which_to_start_zoom" : 1,
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"graph_label" : "y = x^2",
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"show_target_line" : True,
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}
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class SecondSqrtScene(FirstSqrtScene, ReconfigurableScene):
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def setup(self):
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FirstSqrtScene.setup(self)
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ReconfigurableScene.setup(self)
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def construct(self):
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shiftVal = self.targetY
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self.drawGraph()
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newOrigin = self.coords_to_point(0, shiftVal)
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self.transition_to_alt_config(
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graph_func = lambda x : x**2 - shiftVal,
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targetY = 0,
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graph_label = "y = x^2 - " + str(shiftVal),
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y_min = self.y_min - shiftVal,
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y_max = self.y_max - shiftVal,
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show_target_line = False,
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graph_origin = newOrigin)
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self.solveEquation()
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class LoopSplitScene(Scene):
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def construct(self):
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# Original loop
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tl = UP + LEFT
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tm = UP
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tr = UP + RIGHT
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mr = RIGHT
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br = DOWN + RIGHT
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bm = DOWN
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bl = DOWN + LEFT
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lm = LEFT
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loop_color = BLUE
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top_line = Line(tl, tr, color = loop_color)
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right_line = Line(tr, br, color = loop_color)
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bottom_line = Line(br, bl, color = loop_color)
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left_line = Line(bl, tl, color = loop_color)
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loop = Group(top_line, right_line, bottom_line, left_line)
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self.add(loop)
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# TODO: Make the following a continual animation, and on all split loops do the same
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bullet = TexMobject("*", fill_color = RED)
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bullet.move_to(tl)
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self.add(bullet)
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list_of_args = reduce(op.add,
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[
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[ApplyMethod, bullet.move_to, point, {"rate_func" : None}] for
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point in [tr, br, bl, tl]
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]
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)
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succ_anim = Succession(*list_of_args)
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self.add(CycleAnimation(succ_anim))
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# Splits in middle
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split_line = DashedLine(interpolate(tl, tr, 0.5), interpolate(bl, br, 0.5))
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self.play(ShowCreation(split_line))
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self.remove(split_line)
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mid_line_left = Line(tm, bm, color = loop_color)
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mid_line_right = Line(tm, bm, color = loop_color)
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self.add(mid_line_left, mid_line_right)
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top_line_left_half = Line(tl, tm, color = loop_color)
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top_line_right_half = Line(tm, tr, color = loop_color)
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bottom_line_left_half = Line(bl, bm, color = loop_color)
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bottom_line_right_half = Line(bm, br, color = loop_color)
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self.remove(top_line)
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self.add(top_line_left_half)
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self.add(top_line_right_half)
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self.remove(bottom_line)
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self.add(bottom_line_left_half)
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self.add(bottom_line_right_half)
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left_open_loop = VGroup(top_line_left_half, left_line, bottom_line_left_half)
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left_closed_loop = VGroup(left_open_loop, mid_line_left)
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right_open_loop = VGroup(top_line_right_half, right_line, bottom_line_right_half)
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right_closed_loop = VGroup(right_open_loop, mid_line_right)
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self.play(
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ApplyMethod(left_closed_loop.shift, LEFT),
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ApplyMethod(right_closed_loop.shift, RIGHT)
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)
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self.dither()
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self.play(
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ApplyMethod(left_open_loop.shift, LEFT),
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ApplyMethod(right_open_loop.shift, RIGHT)
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)
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self.dither()
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mid_lines = VGroup(mid_line_left, mid_line_right)
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circle = Circle()
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circle.surround(mid_lines)
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self.play(ShowCreation(circle))
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class EquationSolver2d(ZoomedScene):
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#TODO
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CONFIG = {}
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