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| author | Purusharth Saxena | 2020-07-01 15:56:29 +0530 |
|---|---|---|
| committer | GitHub | 2020-07-01 15:56:29 +0530 |
| commit | 434acc8c07ab8132aa4e6f226a9d631ef78889ac (patch) | |
| tree | b42d6e1a806d68d8e341bdbcf8e292e67991d2db /FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae | |
| parent | 2e5aea0731545ac17c158d21e99adb581280db90 (diff) | |
| parent | 2fee7bc2a219755e6018d3c1a5fb995d8eccf287 (diff) | |
| download | FSF-mathematics-python-code-archive-434acc8c07ab8132aa4e6f226a9d631ef78889ac.tar.gz FSF-mathematics-python-code-archive-434acc8c07ab8132aa4e6f226a9d631ef78889ac.tar.bz2 FSF-mathematics-python-code-archive-434acc8c07ab8132aa4e6f226a9d631ef78889ac.zip | |
Merge pull request #46 from saarthdeshpande/master
Tnb, curvature updated
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae')
14 files changed, 180 insertions, 13 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md index 34885b2..7874f43 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md @@ -1,2 +1,15 @@ -**file2_tnb_frame_manim.py** <br> - +**file1_tnb_creation.py**<br> + + + +**file2_tnb_basic.py** <br> + + +**file3_tnb_frame_manim.py** <br> + + +**file4_fs1.py** <br> + + +**file5_fs2.py** <br> + diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif Binary files differdeleted file mode 100644 index c8668e3..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif Binary files differnew file mode 100644 index 0000000..eae8686 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py new file mode 100644 index 0000000..80372ee --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py @@ -0,0 +1,66 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + helix1 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE + ) + + helix2 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE + ) + + pointText = TextMobject(r'Consider an arbitrary point \\ on the given curve.').scale(0.8).shift(1.5*UP) + tgtText = TextMobject(r'Unit', ' tangent ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + tgtText.set_color_by_tex_to_color_map({ + "tangent": YELLOW + }) + normalText = TextMobject(r'Unit', ' normal ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP) + normalText.set_color_by_tex_to_color_map({ + "normal": BLUE + }) + planeText = TextMobject(r'$\overrightarrow{T}$ and $\overrightarrow{N}$ \\ prescribe a plane.').scale(0.8).shift(1.5*UP) + bnmText = TextMobject(r'The vector normal to this plane \\ is called the', ' binormal ', 'vector.').scale(0.8).shift(1.5*UP) + bnmText.set_color_by_tex_to_color_map({ + "binormal": GREEN_E + }) + + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + + + + helix = VGroup(*[helix1, helix2]) + self.play(FadeIn(helix)) + self.play(ApplyMethod(helix.scale, 4)) + self.add_fixed_in_frame_mobjects(pointText) + self.play(FadeIn(dot1), FadeIn(pointText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(tgtText) + self.play(Write(tgt1), ReplacementTransform(pointText, tgtText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(normalText) + self.play(Write(nm1), ReplacementTransform(tgtText, normalText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(planeText) + self.play(FadeIn(plane1), ReplacementTransform(normalText, planeText)) + self.wait(2) + self.add_fixed_in_frame_mobjects(bnmText) + self.add_fixed_in_frame_mobjects(bnm1) + self.play(ReplacementTransform(planeText, bnmText), Write(bnm1)) + self.wait(2) + self.play(FadeOut(VGroup(*[helix, bnm1, bnmText, dot1, tgt1, nm1, plane1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif Binary files differnew file mode 100644 index 0000000..67aaea2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py new file mode 100644 index 0000000..c870210 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py @@ -0,0 +1,36 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + t = TextMobject(r'T', color = YELLOW) + n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0) + b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0) + frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2) + f1 = TextMobject(r'$\overrightarrow{B}$ ', color = GREEN_E) + f2 = TextMobject(r' = $\overrightarrow{T}$', color = YELLOW).next_to(f1, RIGHT, buff=0.2) + f3 = TextMobject(r'$\times\overrightarrow{N}$', color = BLUE).next_to(f2, RIGHT, buff=0.1) + formula = VGroup(*[f1, f2, f3]).move_to(ORIGIN).shift(3*UP) + + # text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) + curve = ParametricFunction( + lambda t: np.array([ + np.sin(TAU*t), + np.cos(TAU*t), + 0 + ]) + ).scale(2.5) + dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT) + tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT) + normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN) + binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN) + square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2) + group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0])) + + self.add_fixed_in_frame_mobjects(formula) + self.add(curve, group) + self.wait(1) + self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2) + self.add_fixed_in_frame_mobjects(formula) + self.begin_ambient_camera_rotation(rate = 0.5) + self.wait(5) + self.play(FadeOut(VGroup(*[formula, curve, dot, tgt, normal, square, binormal]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif Binary files differdeleted file mode 100644 index 097652f..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif Binary files differdeleted file mode 100644 index 784b6a6..0000000 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif Binary files differnew file mode 100644 index 0000000..78e3aa3 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py index ee5e717..176cac5 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py @@ -79,15 +79,16 @@ class tnb(ThreeDScene): self.play(FadeIn(helix), FadeIn(text)) self.play(ApplyMethod(helix.scale, 4)) self.add_fixed_in_frame_mobjects(bnm0) - self.play(FadeIn(point0), MoveAlongPath(helix_dot, helix1, run_time=5)) + self.play(FadeIn(point0)) + self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5)) self.add_fixed_in_frame_mobjects(bnm1) - self.play(ApplyMethod(point0.set_color, GRAY), FadeIn(point1)) - self.play(MoveAlongPath(helix_dot, helix2, run_time = 5)) + self.play(FadeIn(point1)) + self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5)) self.add_fixed_in_frame_mobjects(bnm2) - self.play(ApplyMethod(point1.set_color, GRAY), ApplyMethod(bnm1.set_color, GRAY), FadeIn(point2)) - self.play(MoveAlongPath(helix_dot, helix3, run_time=5)) + self.play(FadeIn(point2)) + self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5)) dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED) tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0])) @@ -111,15 +112,15 @@ class tnb(ThreeDScene): point5 = VGroup(*[tgt5, nm5, bnm5, plane5]) self.add_fixed_in_frame_mobjects(bnm3) - self.play(ApplyMethod(point2.set_color, GRAY), FadeIn(point3)) - self.play(MoveAlongPath(helix_dot, helix4, run_time=5)) + self.play(FadeIn(point3)) + self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5)) self.add_fixed_in_frame_mobjects(bnm4) - self.play(ApplyMethod(point3.set_color, GRAY), FadeIn(point4)) - self.play(MoveAlongPath(helix_dot, helix5, run_time=5)) + self.play(FadeIn(point4)) + self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5)) self.add_fixed_in_frame_mobjects(bnm5) - self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5)) + self.play(FadeIn(point5)) self.wait(2) - self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) + self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif Binary files differnew file mode 100644 index 0000000..6b4b438 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py new file mode 100644 index 0000000..c719a1d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py @@ -0,0 +1,23 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(bnm1), FadeIn(text)) + self.wait() + self.play(TransformFromCopy(tgt1, nm1, run_time = 2)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnm1, text, point1, nm1]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif Binary files differnew file mode 100644 index 0000000..ce367b6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py new file mode 100644 index 0000000..0261fed --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py @@ -0,0 +1,28 @@ +from manimlib.imports import * + +class fs1(ThreeDScene): + def construct(self): + + + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED) + tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0])) + nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8) + bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN) + + bnms = Line((0,0,0), (0,0,1.6), color = GREEN_E).shift(np.array([3.1,5.2,0])).scale(0.6) + bnmsa = ArrowTip(color = GREEN_E).next_to(bnms, np.array([0,0,1]), buff = 0).rotate(45*DEGREES) + bns = VGroup(*[bnms, bnmsa]) + + plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2) + point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES) + t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN) + n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT) + b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1) + text = VGroup(*[t, n, b]) + self.add_fixed_in_frame_mobjects(bnm1, text) + self.play(FadeIn(point1), FadeIn(text), FadeIn(bnm1)) + self.wait() + self.play(TransformFromCopy(bnms, nm1, run_time = 3)) + self.wait(2) + self.play(FadeOut(VGroup(*[bnms, text, point1, nm1, bnm1]))) |
