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Diffstat (limited to 'FSF-2020/calculus/series-and-transformations/Z-Transform/video1_Sampling.py')
| -rw-r--r-- | FSF-2020/calculus/series-and-transformations/Z-Transform/video1_Sampling.py | 81 |
1 files changed, 81 insertions, 0 deletions
diff --git a/FSF-2020/calculus/series-and-transformations/Z-Transform/video1_Sampling.py b/FSF-2020/calculus/series-and-transformations/Z-Transform/video1_Sampling.py new file mode 100644 index 0000000..47615e3 --- /dev/null +++ b/FSF-2020/calculus/series-and-transformations/Z-Transform/video1_Sampling.py @@ -0,0 +1,81 @@ +from manimlib.imports import * +import math + +def func(x): + return math.pow(x,3)-2*math.pow(x,2)-x+3 + +class graphScene(GraphScene): + CONFIG = { + "x_min": -3, + "x_max": 3, + "y_min": -4, + "y_max": 4, + "x_tick_frequency": 0.2, + "graph_origin": ORIGIN, + "function_color": RED, + "axes_color": BLUE, + "x_axis_label": "$t$", + "y_axis_label": "$f(t)$", + "exclude_zero_label": True, + "x_labeled_nums": range(-3, 4, 1), + "y_axis_height": 5, + "x_axis_width": 9, + } + + 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) + + fx=TextMobject("$f(t) = { t }^{ 3 }{ -2t }^{ 2 }-t+3$").set_color(RED).to_corner(UP+RIGHT).scale(0.4) + self.setup_axes(animate=True,scalee=1) + function=self.get_graph(lambda x:math.pow(x,3)-2*math.pow(x,2)-x+3,color=RED,x_min=-1,x_max=2) + functionArea=self.get_riemann_rectangles(function,x_min=-1,x_max=2,dx=0.01,start_color=GREEN,end_color=YELLOW,stroke_color=GREEN,fill_opacity=0.8) + functionDot=Dot(point=self.graph_origin,radius=0.065,color=WHITE) + aboveText1=TextMobject("Continuous","Time Function").shift(4*RIGHT+2*UP).scale(0.4).set_color_by_tex_to_color_map({"Continuous":YELLOW,"Time Function":BLUE}) + aboveText2=TextMobject("Discrete","Time Function").shift(4*RIGHT+2*UP).scale(0.4).set_color_by_tex_to_color_map({"Time Function":BLUE,"Discrete":YELLOW}) + + bottomText1=TextMobject("Instead of considering the","function","over the","entire $t$,").shift(4.5*RIGHT+3*DOWN).scale(0.4).set_color_by_tex_to_color_map({"entire $t$,":RED,"function":YELLOW}) + bottomText2=TextMobject("We consider only at","certain $t$").shift(4.5*RIGHT+3*DOWN).scale(0.4).set_color_by_tex_to_color_map({"certain $t$":RED}) + + self.play(ShowCreation(function),Write(fx),FadeIn(aboveText1)) + self.wait(0.7) + self.play(Write(bottomText1)) + self.play(ShowCreation(functionArea),MoveAlongPath(functionDot,function)) + self.wait(0.7) + self.play(FadeOut(bottomText1)) + self.play(Write(bottomText2),FadeOut(aboveText1)) + + dots=[Dot(radius=0.05) for i in range(10)] + dotShifts=[-1,-0.7,-0.4,0,0.3,0.6,1,1.3,1.6,2] + lines=[] + for x in dotShifts: + lines.append(Line(start=(x*x_each_unit,func(x)*y_each_unit,0),end=(x*x_each_unit,0,0),color=GREEN)) + for i in range(10): + dots[i].shift(ORIGIN+RIGHT*x_each_unit*dotShifts[i]+y_each_unit*UP*func(dotShifts[i])) + updatedGraph=VGroup(dots[0], + dots[1], + dots[2], + dots[3], + dots[4], + dots[5], + dots[6], + dots[7], + dots[8], + dots[9]) + updatedGraph1=VGroup( + lines[0], + lines[1], + lines[2], + lines[3], + lines[4], + lines[5], + lines[6], + lines[7], + lines[8], + lines[9]) + + self.play(FadeOut(functionDot)) + self.play(FadeOut(function),FadeIn(updatedGraph)) + self.play(FadeOut(functionArea),FadeIn(updatedGraph1)) + self.play(FadeOut(bottomText2),FadeIn(aboveText2)) + self.wait(2)
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