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from manimlib.imports import *
class Scaling(GraphScene):
CONFIG = {
"x_min" : -5,
"x_max" : 5,
"y_min" : -5,
"y_max" : 5,
"graph_origin" : ORIGIN+3.5*LEFT,
"x_axis_width" : 7,
"y_axis_height" : 7
#"x_labeled_nums" : list(range(-5,6)),
#"y_labeled_nums" : list(range(-5,6)),
}
def construct(self):
XTD = self.x_axis_width/(self.x_max-self.x_min)
YTD = self.y_axis_height/(self.y_max-self.y_min)
introText = TextMobject("Scaling")
self.play(Write(introText))
self.wait(1)
self.play(FadeOut(introText))
introText = TextMobject("Uniform Scaling")
self.play(Write(introText))
self.wait(1)
self.play(FadeOut(introText))
Text1 = TextMobject("Let $\overrightarrow{v}$ be $3\hat{i}+3\hat{j}$")
Text2 = TextMobject("$\overrightarrow{v} = 3\hat{i}+3\hat{j}$")
Text1.move_to(4*RIGHT+2*UP)
Text2.move_to(4*RIGHT+1*UP)
self.play(Write(Text1))
self.wait()
self.play(Transform(Text1,Text2))
self.setup_axes(animate=True)
arrow_v = Arrow(stroke_width = 4, start = self.graph_origin + 0.15*LEFT + 0.15*DOWN, end = self.graph_origin+3*XTD*RIGHT+3*YTD*UP+ 0.15*RIGHT + 0.15*UP)
vector_v = TextMobject(r"$\vec{v}$")
vector_v.move_to(self.graph_origin + 1*XTD*RIGHT + 2*YTD*UP )
self.play(ShowCreation(arrow_v),Write(vector_v))
scaling_factor = TextMobject(r"Scaling Factor = $\frac{4}{3}$")
scaling_factor.scale(0.75)
scaled_vector = TextMobject(r"$T(\vec{v}) = \frac{4}{3} \left[ \begin{array} {c} 3 \\ 3 \end{array} \right] = \left[ \begin{array} {c} 4 \\ 4 \end{array} \right]$")
scaled_vector.set_color(DARK_BLUE)
scaled_vector.scale(0.75)
scaling_factor.move_to(4*RIGHT)
scaled_vector.move_to(4*RIGHT+DOWN)
self.play(Write(scaling_factor))
self.wait()
self.play(Write(scaled_vector))
transformed_arrow_v = Arrow(stroke_width = 2, start = self.graph_origin + 0.15*LEFT + 0.15*DOWN, end = self.graph_origin+4*XTD*RIGHT+4*YTD*UP+ 0.15*RIGHT + 0.15*UP)
transformed_arrow_v.set_color(DARK_BLUE)
transformed_vector_v = TextMobject(r"$T(\vec{v})$")
transformed_vector_v.move_to(self.graph_origin + 4.5*XTD*RIGHT + 4.5*YTD*UP )
transformed_vector_v.set_color(DARK_BLUE)
self.play(ShowCreation(transformed_arrow_v), Write(transformed_vector_v))
self.wait()
represent_text1 = TextMobject("Representation of scaling")
represent_text2 = TextMobject("of vectors in point form")
represent_text1.move_to(4*RIGHT+3*UP)
represent_text2.move_to(4*RIGHT+2*UP)
self.play(Write(represent_text1), Write(represent_text2))
dot_init = Dot(self.graph_origin+3*XTD*RIGHT+3*YTD*UP)
dot_trans = Dot(self.graph_origin+4*XTD*RIGHT+4*YTD*UP)
self.play(ApplyMethod(vector_v.move_to,self.graph_origin+2.5*XTD*RIGHT+2.5*YTD*UP),
ApplyMethod(transformed_vector_v.move_to,self.graph_origin+4.5*XTD*RIGHT+4.5*YTD*UP),
ShowCreation(dot_init),
Transform(arrow_v,dot_init),
Transform(transformed_arrow_v,dot_trans))
self.wait(2)
self.play(FadeOut(dot_init),
FadeOut(arrow_v),
FadeOut(transformed_arrow_v),
FadeOut(represent_text1),
FadeOut(represent_text2),
FadeOut(self.axes),
FadeOut(scaling_factor),
FadeOut(scaled_vector),
FadeOut(transformed_vector_v),
FadeOut(vector_v),
FadeOut(Text1))
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