new repo due to large gif

3 files changed, 306 insertions, 82 deletions

diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
deleted file mode 100644
index 0a28f22..0000000
--- a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_OrthonormalBasis.py
+++ /dev/null
@@ -1,82 +0,0 @@
-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))
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py
new file mode 100755
index 0000000..81a0888
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file2_sum_of_projections_part1.py
@@ -0,0 +1,133 @@
+from manimlib.imports import *

+class LinearTrans(LinearTransformationScene):

+    CONFIG = {

+    "show_basis_vectors": True,

+    "basis_vector_stroke_width": 1,

+    "leave_ghost_vectors": False,

+    "show_coordinates": True,

+    }

+    

+    def construct(self):

+

+        self.setup()

+

+        matrix = [[0.6,-0.8],[0.8,0.6]]

+        self.apply_matrix(matrix)

+

+        self.wait(2)

+        orthonormal = TextMobject(r"These are 2 orthonormal vectors($v_1$ and $v_2$)")

+        orthonormal.scale(0.7)

+        orthonormal.move_to(DOWN+LEFT*3.5)

+        orthonormal.add_background_rectangle()

+        v1 = TextMobject(r"$v_1$")

+        v1.scale(0.75)

+        v1.set_color(X_COLOR)

+        v1.move_to(0.75*UP+RIGHT)

+        v1.add_background_rectangle()

+        v2 = TextMobject(r"$v_2$")

+        v2.scale(0.75)

+        v2.set_color(Y_COLOR)

+        v2.move_to(0.75*UP+LEFT*1.25)

+        v2.add_background_rectangle()

+        self.play(Write(orthonormal))

+        self.play(Write(v1),Write(v2))

+        self.wait()

+        self.play(FadeOut(orthonormal), FadeOut(v1), FadeOut(v2))

+        

+        arrow = Arrow(start = ORIGIN,end = 3*RIGHT+UP)

+        arrow.scale(1.2)

+        arrow.set_color(BLUE)

+        arrow.apply_matrix(matrix)

+        text3 = TextMobject("v")

+        text3.move_to(3.2*UP+1.2*RIGHT)

+        text3.add_background_rectangle()

+        self.play(ShowCreation(arrow),Write(text3))

+        self.wait()

+        v_cor = TextMobject("(1,3)")

+        v_cor.move_to(3.2*UP+1.3*RIGHT)

+        v_cor.set_color(BLUE)

+        v_cor.scale(0.75)

+        v_cor.add_background_rectangle()

+        self.play(Transform(text3,v_cor))

+

+        line1 = DashedLine(start = 1*UP+3*RIGHT, end = 3*RIGHT)

+        line2 = DashedLine(start = 1*UP+3*RIGHT, end = UP)

+        line1.apply_matrix(matrix)

+        line2.apply_matrix(matrix)

+        self.play(ShowCreation(line1),ShowCreation(line2),run_time = 2)

+        

+        v1 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)

+        v1.scale(1.2)

+        v1.set_color(BLUE)

+        v1.apply_matrix(matrix)

+        arrow1 = Arrow(start = ORIGIN,end = 3*RIGHT)

+        arrow1.scale(1.2)

+        arrow1.set_color("#6B8E23")

+        arrow1.apply_matrix(matrix)

+        self.play(Transform(v1,arrow1))

+        v1_cor = TextMobject(r"$<v,v_1> v_1$")

+        v1_cor.move_to(2.5*UP+3*RIGHT)

+        v1_cor.scale(0.75)

+        v1_cor.add_background_rectangle()

+        self.play(Write(v1_cor))

+        self.wait(0.5)

+        text1 = TextMobject(r"(1.8,2.4)")

+        text1.move_to(2.1*UP+2.5*RIGHT)

+        text1.scale(0.75)

+        text1.set_color("#6B8E23")

+        text1.add_background_rectangle()

+        self.play(Transform(v1_cor,text1))

+

+        v2 = Arrow(start = ORIGIN,end = 3*RIGHT+UP)

+        v2.scale(1.2)

+        v2.set_color("#8b0000")

+        v2.apply_matrix(matrix)

+        arrow2 = Arrow(start = ORIGIN,end = UP)

+        arrow2.scale(2.1)

+        arrow2.set_color("#8b0000")

+        arrow2.apply_matrix(matrix)

+        self.wait(0.5)

+        self.play(Transform(v2,arrow2))

+        self.wait(0.5)

+        v2_cor = TextMobject(r"$<v,v_2> v_2$")

+        v2_cor.move_to(0.75*UP+2.5*LEFT)

+        v2_cor.scale(0.75)

+        v2_cor.add_background_rectangle()

+        self.play(Write(v2_cor))

+        self.wait(0.5)

+        text2 = TextMobject(r"(-0.8,0.6)")

+        text2.move_to(0.75*UP+1.75*LEFT)

+        text2.scale(0.75)

+        text2.set_color("#8b0000")

+        text2.add_background_rectangle()

+        self.play(Transform(v2_cor,text2))

+

+        self.wait()

+

+        self.play(ApplyMethod(v2.move_to,1.4*RIGHT+2.7*UP),FadeOut(v1_cor),FadeOut(v2_cor),FadeOut(v_cor))

+

+        self.wait()

+

+        ending = TextMobject(r"$v = <v,v_1> v_1 + <v,v_2> v_2$")

+        ending.scale(0.7)

+        ending.move_to(DOWN)

+        ending.add_background_rectangle()

+        self.play(Write(ending))

+        self.wait()

+        self.play(FadeOut(ending))

+        

+        ending = TextMobject(r"$\left[ \begin{array} {c} 1\\ 3 \end{array}\right] = \left[ \begin{array} {c}1.8 \\ 2.4 \end{array}\right] + \left[ \begin{array} {c} -0.8\\ 0.6 \end{array}\right]$")

+        ending.scale(0.7)

+        ending.move_to(DOWN)

+        ending.add_background_rectangle()

+        self.play(Write(ending))

+        self.wait()

+        self.play(FadeOut(ending))

+

+        ending = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")

+        ending.scale(0.7)

+        ending.move_to(DOWN)

+        ending.add_background_rectangle()

+        self.play(Write(ending))

+        self.wait()

+        self.play(FadeOut(ending))
\ No newline at end of file
diff --git a/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py
new file mode 100644
index 0000000..9d25192
--- /dev/null
+++ b/FSF-2020/linear-algebra/linear-transformations/Orthonormal Basis/file3_sum_of_projections_part2.py
@@ -0,0 +1,173 @@
+from manimlib.imports import *
+class ThreeDExplanation(ThreeDScene):
+    
+    def construct(self):
+
+        text = TextMobject("Let us consider the example discussed above again. These are the things we know:-")
+        text.scale(0.75)
+        self.add_fixed_in_frame_mobjects(text)
+        text.move_to(3*UP)
+        self.play(Write(text))
+        self.wait(2)
+        basis = TextMobject(r"Set of Orthonormal Basis - $\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}\frac{-1}{\sqrt{2}}\\\frac{1}{\sqrt{2}}\\0\end{array}\right),\left(\begin{array}{c}0\\0\\1\end{array}\right)$")
+        basis.scale(0.75)
+        basis.move_to(UP*1.5)
+        self.play(Write(basis))
+        v = TextMobject(r"$v_1$",r"$v_2$",r"$v_3$")
+        v[0].move_to(UP*0.5+RIGHT*0.75)
+        v[1].move_to(UP*0.5+RIGHT*2.5)
+        v[2].move_to(UP*0.5+RIGHT*4)
+        eq = TextMobject(r"$v = \left(\begin{array}{c}3\\4\\5\end{array}\right)$")
+        eq1 = TextMobject(r"$<v,v_1> = \frac{3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 = \frac{7}{\sqrt{2}}$")
+        eq2 = TextMobject(r"$<v,v_2> = \frac{-3}{\sqrt{2}} + \frac{4}{\sqrt{2}} + 0 =\frac{1}{\sqrt{2}}$")
+        eq3 = TextMobject(r"$<v,v_3> =  0 + 0 + 5 =5$")
+        eq.move_to(4*LEFT+DOWN)
+        eq1.move_to(0.5*DOWN+2*RIGHT)
+        eq2.move_to(1.5*DOWN+2*RIGHT)
+        eq3.move_to(2.5*DOWN+2*RIGHT)
+        self.play(Write(v))
+        self.play(Write(eq))
+        self.play(Write(eq1))
+        self.play(Write(eq2))
+        self.play(Write(eq3))
+        self.wait()
+        self.play(FadeOut(text), FadeOut(basis), FadeOut(eq), FadeOut(v), FadeOut(eq1), FadeOut(eq2), FadeOut(eq3))
+        self.wait()
+        
+        text = TextMobject("These are the 3 mutually orthonormal basis of the set(", r"$v_1$, ", r"$v_2$, ", r"$v_3$",")")
+        text[1].set_color(DARK_BLUE)
+        text[2].set_color(RED)
+        text[3].set_color(YELLOW)
+        text.scale(0.75)
+        self.add_fixed_in_frame_mobjects(text)
+        text.move_to(3*DOWN)
+        self.play(Write(text))
+        self.wait()
+
+        axes = ThreeDAxes(x_min = -9,x_max=9,y_min=-9,y_max=9,z_min=-9,z_max=9)
+        self.play(ShowCreation(axes))
+        self.move_camera(distance = 100, phi=30*DEGREES,theta=45*DEGREES,run_time=3)
+        self.begin_ambient_camera_rotation(rate=0.3)
+
+        dashedline1 = DashedLine(start = -12*(UP+RIGHT), end = 12*(UP+RIGHT))
+        dashedline2 = DashedLine(start = -12*(UP+LEFT), end = 12*(UP+LEFT))
+        dashedline3 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 3.5*UP+3.5*RIGHT)
+        dashedline4 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = 0.5*UP+0.5*LEFT)
+        dashedline5 = DashedLine(start = 4*UP+3*RIGHT+[0,0,5], end = [0,0,5])
+
+        self.play(ShowCreation(dashedline1), ShowCreation(dashedline2))
+
+        line1 = Line(start = ORIGIN,end = 0.707*RIGHT + 0.707*UP)
+        line1.set_color(DARK_BLUE)
+        tip1 = Polygon(0.707*RIGHT + 0.707*UP, 0.707*RIGHT + 0.607*UP, 0.607*RIGHT + 0.707*UP)
+        tip1.set_opacity(1)
+        tip1.set_fill(DARK_BLUE)
+        tip1.set_color(DARK_BLUE)
+        self.play(ShowCreation(line1), ShowCreation(tip1))
+
+        line2 = Line(start = ORIGIN,end = 0.707*LEFT + 0.707*UP)
+        line2.set_color(RED)
+        tip2 = Polygon(0.707*LEFT + 0.707*UP, 0.707*LEFT + 0.607*UP, 0.607*LEFT + 0.707*UP)
+        tip2.set_opacity(1)
+        tip2.set_fill(RED)
+        tip2.set_color(RED)
+
+        self.play(ShowCreation(line2), ShowCreation(tip2))
+
+        line3 = Line(start = ORIGIN,end = [0,0,1])
+        line3.set_color(YELLOW)
+        tip3 = Polygon([0,0,1],[0,0,0.8]-0.2*RIGHT,[0,0,0.8]-0.2*LEFT)
+        tip3.set_opacity(1)
+        tip3.set_fill(YELLOW)
+        tip3.set_color(YELLOW)
+        self.play(ShowCreation(line3), ShowCreation(tip3))
+        self.wait()
+
+        self.play(FadeOut(text))
+
+        text = TextMobject("Take the projection of ", r"$v$", " on the mutually orthonormal vectors")
+        text[1].set_color(GOLD_E)
+        text.scale(0.75)
+        self.add_fixed_in_frame_mobjects(text)
+        text.move_to(3*DOWN)
+        self.play(Write(text))
+        self.wait(2)
+        
+        a_line = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+        a_line.set_color(GOLD_E)
+        a_tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+        a_tip.set_opacity(1)
+        a_tip.set_fill(GOLD_E)
+        a_tip.set_color(GOLD_E)
+
+        self.play(ShowCreation(a_line), ShowCreation(a_tip))
+        self.wait(9)
+        self.play(ShowCreation(dashedline3),ShowCreation(dashedline4),ShowCreation(dashedline5))
+        self.wait(6)
+
+        pv1 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+        pv1.set_color(GOLD_E)
+        pv1tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+        pv1tip.set_opacity(1)
+        pv1tip.set_fill(GOLD_E)
+        pv1tip.set_color(GOLD_E)
+
+        v1_p = Line(start = ORIGIN,end = 3.5*RIGHT + 3.5*UP)
+        v1_p.set_color(BLUE_E)
+        v1_p_tip = Polygon(3.5*RIGHT + 3.5*UP, 3.5*RIGHT + 3.4*UP, 3.4*RIGHT + 3.5*UP)
+        v1_p_tip.set_opacity(1)
+        v1_p_tip.set_fill(BLUE_E)
+        v1_p_tip.set_color(BLUE_E)
+
+        pv2 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+        pv2.set_color(GOLD_E)
+        pv2tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+        pv2tip.set_opacity(1)
+        pv2tip.set_fill(GOLD_E)
+        pv2tip.set_color(GOLD_E)
+
+        v2_p = Line(start = ORIGIN,end = 0.5*LEFT + 0.5*UP)
+        v2_p.set_color(RED_E)
+        v2_p_tip = Polygon(0.5*LEFT + 0.5*UP, 0.5*LEFT + 0.4*UP, 0.4*LEFT + 0.5*UP)
+        v2_p_tip.set_opacity(1)
+        v2_p_tip.set_fill(RED_E)
+        v2_p_tip.set_color(RED_E)
+
+        pv3 = Line(start = ORIGIN,end = 4*UP+3*RIGHT+[0,0,5])
+        pv3.set_color(GOLD_E)
+        pv3tip = Polygon(4*UP+3*RIGHT+[0,0,5],3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*UP+0.1*LEFT,3.6*UP+2.7*RIGHT+[0,0,4.5]+0.1*DOWN+0.1*RIGHT)
+        pv3tip.set_opacity(1)
+        pv3tip.set_fill(GOLD_E)
+        pv3tip.set_color(GOLD_E)
+
+        v3_p = Line(start = ORIGIN,end = [0,0,5])
+        v3_p.set_color(YELLOW_E)
+        v3_p_tip = Polygon([0,0,5],[0,0,4.8]+0.2*RIGHT,[0,0,4.8]+0.2*LEFT)
+        v3_p_tip.set_opacity(1)
+        v3_p_tip.set_fill(YELLOW_E)
+        v3_p_tip.set_color(YELLOW_E)
+
+        self.stop_ambient_camera_rotation()
+        self.play(Transform(pv1,v1_p), Transform(pv1tip,v1_p_tip), Transform(pv2,v2_p), Transform(pv2tip,v2_p_tip), Transform(pv3,v3_p), Transform(pv3tip,v3_p_tip))
+        self.play(FadeOut(dashedline1),
+        FadeOut(dashedline2),
+        FadeOut(dashedline3),
+        FadeOut(dashedline4),
+        FadeOut(dashedline5),
+        FadeOut(line1),
+        FadeOut(tip1),
+        FadeOut(line2),
+        FadeOut(tip2),
+        FadeOut(line3),
+        FadeOut(tip3),
+        FadeOut(text))
+
+        text = TextMobject(r"$v$ is the sum of projections on the orthonormal vectors")
+        text.set_color(GOLD_E)
+        text.scale(0.75)
+        self.add_fixed_in_frame_mobjects(text)
+        text.move_to(3*DOWN)
+        self.play(Write(text), ApplyMethod(pv2.move_to,(3.5*RIGHT + 3.5*UP+3*RIGHT+4*UP)/2), ApplyMethod(pv2tip.move_to,(3.1*RIGHT + 3.9*UP)))
+        self.play(ApplyMethod(pv3.move_to,3*RIGHT + 4*UP + [0,0,2.5]), ApplyMethod(pv3tip.move_to,(3*RIGHT + 4*UP + [0,0,4.8])))
+
+        self.wait(3)
\ No newline at end of file