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from manimlib.imports import *
class OrthonormalBasis(GraphScene):
CONFIG = {
"x_min" : -6,
"x_max" : 6,
"y_min" : -4,
"y_max" : 4,
"graph_origin" : ORIGIN ,
}
def construct(self):
self.setup_axes(animate=True)
XTD = self.x_axis_width/(self.x_max-self.x_min)
YTD = self.y_axis_height/(self.y_max-self.y_min)
arrow1 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*RIGHT)
arrow1.scale(2.25)
arrow1.set_color(DARK_BLUE)
arrow2 = Arrow(start = ORIGIN,end = 0.707*YTD*UP+0.707*XTD*LEFT)
arrow2.scale(2.25)
arrow2.set_color(DARK_BLUE)
square = Polygon(UP*0.4*YTD,0.2*(YTD*UP+XTD*RIGHT),ORIGIN,0.2*(YTD*UP+XTD*LEFT))
square.set_color(DARK_BLUE)
self.play(ShowCreation(arrow2), ShowCreation(arrow1), ShowCreation(square))
ortho = TextMobject("Orthonormal Vectors")
ortho.scale(0.75)
ortho.move_to(DOWN+3*RIGHT)
self.play(Write(ortho))
self.wait()
self.play(FadeOut(ortho))
arrow3 = Arrow(start = ORIGIN,end = YTD*3*UP+XTD*LEFT)
arrow3.scale(1.25)
arrow3.set_color(GOLD_E)
self.play(ShowCreation(arrow3))
arrow4 = Arrow(start = ORIGIN,end = YTD*UP+XTD*RIGHT)
arrow4.scale(1.8)
arrow4.set_color(GOLD_A)
arrow5 = Arrow(start = ORIGIN,end = 2*YTD*UP-2*XTD*RIGHT)
arrow5.scale(1.3)
arrow5.set_color(GOLD_A)
self.play(ShowCreation(arrow5), ShowCreation(arrow4))
self.wait()
self.play(FadeOut(arrow1), FadeOut(arrow2), FadeOut(square))
self.wait()
text1 = TextMobject(r"$<v,v_1> v_1$")
text1.move_to(UP+2*RIGHT)
text1.scale(0.75)
text2 = TextMobject(r"$<v,v_2> v_2$")
text2.move_to(UP+3*LEFT)
text2.scale(0.75)
text3 = TextMobject("v")
text3.move_to(YTD*3.5*UP+XTD*1.5*LEFT)
self.play(Write(text1), Write(text2), Write(text3))
self.wait()
line1 = DashedLine(start = YTD*UP+XTD*RIGHT, end = YTD*3*UP+XTD*1*LEFT)
line2 = DashedLine(start = YTD*2*UP+XTD*2*LEFT, end = YTD*3*UP+XTD*1*LEFT)
self.play(ShowCreation(line1),ShowCreation(line2))
self.wait()
text = TextMobject(r"$v$ is the sum of projections","on the orthonormal vectors")
text[0].move_to(DOWN+3.2*RIGHT)
text[1].move_to(1.5*DOWN+3.2*RIGHT)
self.play(Write(text))
self.wait(2)
self.play(FadeOut(arrow3), FadeOut(arrow4), FadeOut(arrow5), FadeOut(text1), FadeOut(text2), FadeOut(text3), FadeOut(self.axes), FadeOut(line1), FadeOut(line2))
self.play(FadeOut(text))
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