diff options
Diffstat (limited to 'FSF-2020/calculus/series-and-transformations/Z-Transform/video2_ZTransformOfDelta.py')
| -rw-r--r-- | FSF-2020/calculus/series-and-transformations/Z-Transform/video2_ZTransformOfDelta.py | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/FSF-2020/calculus/series-and-transformations/Z-Transform/video2_ZTransformOfDelta.py b/FSF-2020/calculus/series-and-transformations/Z-Transform/video2_ZTransformOfDelta.py new file mode 100644 index 0000000..3063aa6 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Z-Transform/video2_ZTransformOfDelta.py @@ -0,0 +1,121 @@ +from manimlib.imports import * +import numpy as np +import math + +class deltaTransformation(GraphScene): + CONFIG = { + "x_min": -3, + "x_max": 3, + "y_min": -5, + "y_max": 5, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": BLUE, + "x_axis_label": "$t$", + "y_axis_label": "$f(t)$", + "x_labeled_nums": range(-3, 4, 1), + # "y_axis_height": 4, + # "x_axis_width": 6, + } + def construct(self): + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + self.setup_axes(animate=True,scalee=0.8) + function=TextMobject("$f(t) = 2{ \delta }_{ 0 }(t)+3{ \delta }_{ 1 }(t)+4{ \delta }_{ 2 }(t)$").scale(0.4).shift(5*RIGHT+3*UP).set_color(RED) + self.play(FadeIn(function)) + twoDGraph=[ + Line(start=(0,0,0),end=(0,2*y_each_unit,0),color=GREEN), + Line(start=(1*x_each_unit,0,0),end=(x_each_unit,3*y_each_unit,0),color=GREEN), + Line(start=(2*x_each_unit,0,0),end=(2*x_each_unit,4*y_each_unit,0),color=GREEN) + ] + groupGraph=VGroup(twoDGraph[1],twoDGraph[2],self.axes,twoDGraph[0]) + self.play(Write(twoDGraph[0]),ShowCreation(twoDGraph[1]),ShowCreation(twoDGraph[2])) + self.wait(1.2) + self.play(ApplyMethod(groupGraph.scale,0.7)) + self.play(ApplyMethod(groupGraph.shift,5*LEFT),ApplyMethod(function.move_to,5*LEFT+3*UP)) + self.graph_origin=2*RIGHT+2.5*DOWN + self.x_axis_width=6 + self.x_axis_label="$|z|$" + self.y_axis_label="$|F(t)|$" + self.x_min=-3 + self.x_max=6 + self.y_min=-1 + self.y_max=7 + self.x_labeled_nums=range(-3,7,1) + self.setup_axes(animate=True,scalee=0.6) + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + rightSideGraphs=[ + self.get_graph(lambda x:2,x_min=0,x_max=6,color=GREEN), + self.get_graph(lambda x:2+3/x,x_min=0.6,x_max=6,color=GREEN), + self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=6,color=GREEN) + ] + graphCoeff=[ + TextMobject("$2$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*2+UP*y_each_unit*2+DOWN*y_each_unit*0.5).set_color(RED), + TextMobject("$2+\\frac { 3 }{ |z| }$").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3+UP*y_each_unit*2).set_color(RED), + TextMobject("$2+\\frac { 3 }{ |z| } +\\frac { 4 }{ { |z| }^{ 2 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3.5+UP*y_each_unit*2).set_color(RED) + ] + self.play(ReplacementTransform(twoDGraph[0],rightSideGraphs[0]),FadeIn(graphCoeff[0])) + self.wait(0.5) + self.play(FadeOut(rightSideGraphs[0]),ReplacementTransform(twoDGraph[1],rightSideGraphs[1]),ReplacementTransform(graphCoeff[0],graphCoeff[1])) + self.wait(0.5) + self.play(FadeOut(rightSideGraphs[1]),ReplacementTransform(twoDGraph[2],rightSideGraphs[2]),ReplacementTransform(graphCoeff[1],graphCoeff[2])) + + self.wait(2) + + +class graphCont(GraphScene,MovingCameraScene): + CONFIG = { + "x_min": -3, + "x_max": 6, + "y_min": -1, + "y_max": 7, + "graph_origin": 2*RIGHT+2.5*DOWN, + "function_color": RED, + "axes_color": BLUE, + "x_axis_label": "$|z|$", + "y_axis_label": "$|F(t)|$", + "exclude_zero_label": True, + "x_labeled_nums": range(-3, 7, 1), + "x_axis_width": 6, + } + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + + def construct(self): + x_each_unit = self.x_axis_width / (self.x_max - self.x_min) + y_each_unit = self.y_axis_height / (self.y_max - self.y_min) + + coeff=TextMobject("$2+\\frac { 3 }{ |z| } +\\frac { 4 }{ { |z| }^{ 2 } } $").scale(0.4).shift(self.graph_origin+x_each_unit*RIGHT*3.5+UP*y_each_unit*2).set_color(RED) + self.setup_axes(scalee=0.6) + graph=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=6,color=GREEN) + xAxis=self.get_graph(lambda x:0,x_min=1.24,x_max=6).shift(3*LEFT) + self.add(graph) + self.add(coeff) + self.play(ApplyMethod((self.axes).shift,3*LEFT),ApplyMethod(coeff.shift,3*LEFT),ApplyMethod(graph.shift,3*LEFT)) + topText=TextMobject("Here we get","output","for","any value of $|z|$").scale(0.4).shift(3*UP+3*RIGHT).set_color_by_tex_to_color_map({"output":YELLOW,"any value of $|z|$":BLUE}) + topText1=TextMobject("Except for $|z|=0$").scale(0.7).shift(2.5*UP+3*RIGHT).set_color(RED) + dot1=Dot(color=WHITE,radius=0.06) + dot2=Dot(color=WHITE,radius=0.06) + self.play(Write(topText)) + self.play(MoveAlongPath(dot1,graph),MoveAlongPath(dot2,xAxis),run_time=2) + self.play(Write(topText1)) + self.play(FadeOut(dot1),FadeOut(dot2)) + self.wait(0.5) + path=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=1.24,x_max=0.8) + path1=self.get_graph(lambda x:0,x_min=1.24,x_max=0.8) + graphUpdated=self.get_graph(lambda x:2+(3/x)+(4/x**2),x_min=0.8,x_max=6,color=GREEN) + self.camera_frame.save_state() + self.play(FadeOut(graph),Write(graphUpdated)) + self.play(self.camera_frame.set_width, 30, + MoveAlongPath(dot1,path),MoveAlongPath(dot2,path1),run_time=2) + self.wait(1) + + self.play(FadeOut(dot1),FadeOut(dot2),FadeOut(graphUpdated),FadeIn(graph),self.camera_frame.set_width,15) + self.wait(1) + + + + + |