diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves')
9 files changed, 140 insertions, 19 deletions
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md index f5313c9..a2f71d7 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md @@ -1,11 +1,8 @@ -**file1_simple_visualization.py** +**file1_simple_visualization.py** <br>  **file2_circle_curvature.py** <br>  -**file3_curvature_intuition.gif** <br> - - -**file4_different_curvature_single_curve.py** +**file4_different_curvature_single_curve.py** <br>  diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md index d6b89ef..29d2f6a 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/equations-of-planes-and-lines/README.md @@ -1,14 +1,14 @@ **file1_line_eqn.py**<br>  -**file2_point_normal_form_plane.py** +**file2_point_normal_form_plane.py**<br>  -**file3_intercept_form_plane.py** +**file3_intercept_form_plane.py**<br>  -**file4_3d_plane.py** +**file4_3d_plane.py**<br>  -**file5_vector_form_line.py** +**file5_vector_form_line.py**<br>  diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md index be358ac..8a47a0e 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/README.md @@ -1,11 +1,11 @@ -**file1_parametric_circle..py** +**file1_parametric_circle..py** <br>  -**file2_cycloid_manim.py** +**file2_cycloid_manim.py** <br>  -**file3_brachistochrone.py** +**file3_brachistochrone.py** <br>  -**file4_helix_visualization.py** +**file4_helix_visualization.py** <br>  diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md index 18516b7..42f5df1 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/space-curves/README.md @@ -1,7 +1,7 @@ -**file1_parametric_ellipse.py** +**file1_parametric_ellipse.py** <br>  -**file2_parametric_helix.py** +**file2_parametric_helix.py** <br>  **file3_circletosphere.py** <br> 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 new file mode 100644 index 0000000..34885b2 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md @@ -0,0 +1,2 @@ +**file2_tnb_frame_manim.py** <br> + 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 differindex 097652f..097652f 100644 --- 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 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 differnew file mode 100644 index 0000000..784b6a6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_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/file2_tnb_frame_manim.py new file mode 100644 index 0000000..ee5e717 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py @@ -0,0 +1,125 @@ +from manimlib.imports import * + +class tnb(ThreeDScene): + def construct(self): + self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES) + + 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) + + text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP) + + 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 + ) + + helix3 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -1.33*np.pi/3, t_max = -np.pi/3, color = WHITE + ) + + helix4 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -np.pi/3, t_max = -1.3*np.pi/6, color = WHITE + ) + + helix5 = ParametricFunction( + lambda t: np.array([ + np.cos(TAU*t), + np.sin(TAU*t), + 0.4*t + ]), t_min = -1.3*np.pi/6, t_max = 0, color = WHITE + ) + + helix_dot = Dot(radius = 0.16, color = RED) + + dot0 = Dot(np.array([np.cos(-2*np.pi/3), np.sin(-2*np.pi/3), -0.8*np.pi/3]), radius = 0.16, color=RED).shift(np.array([4.65,0,-0.8])) + tgt0 = Arrow((0,0,0), (1,2,0), color = YELLOW).shift(dot0.get_center() - np.array([0.04,0.2,0])) + nm0 = Arrow((0,0,0), (-2,1,0), color = BLUE).shift(dot0.get_center() + np.array([0.3,0,0])) + bnm0 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(6.1*LEFT + 3*DOWN) + plane0 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot0.get_center() + np.array([-0.35, 0.85, 0])).scale(1.2).rotate(65*DEGREES) + point0 = VGroup(*[dot0, tgt0, nm0, bnm0, plane0]).scale(0.8).shift(np.array([1,0,0])) + + 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(3.68*RIGHT+2.48*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([1,6.25,0])) + + dot2 = Dot(np.array([np.cos(-np.pi/6), np.sin(-np.pi/6), -0.2*np.pi/3]) - np.array([1.9,0,0]), radius=0.16,color=RED) + tgt2 = Arrow((0,0,0), (1,-2,0), color = YELLOW).shift(dot2.get_center() + np.array([-0.2,0.2,0])) + nm2 = Arrow((0,0,0), (2,1,0), color = BLUE).shift(dot2.get_center() + np.array([-0.2,-0.06,0])) + bnm2 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(0.4*RIGHT + 0.16*DOWN) + plane2 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot2.get_center() + np.array([0.92, -0.5, 0])).rotate(23*DEGREES).scale(1.2) + point2 = VGroup(*[dot2, tgt2, nm2, bnm2, plane2]) + + helix = VGroup(*[helix1, helix2, helix3, helix4, helix5]) + self.add_fixed_in_frame_mobjects(text) + 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.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.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)) + + 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])) + nm3 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(helix_dot.get_center() + np.array([0.25,0,0])) + bnm3 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.87*LEFT + 1.24*DOWN) + plane3 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(helix_dot.get_center() + np.array([-0.5, 0.62, 0])) + point3 = VGroup(*[dot3, tgt3, nm3, bnm3, plane3]).shift(np.array([0,0,0])) + + dot4 = Dot(np.array([np.cos(-np.pi/12), np.sin(-np.pi/12), -0.1*np.pi/3]) + np.array([-3.4,3.4,0]), radius = 0.16, color=RED) + tgt4 = Arrow((0,0,0), (-2,-0.85,0), color = YELLOW).shift(dot4.get_center() - np.array([-0.05,0,0])) + nm4 = Arrow((0,0,0), (0.8,-2,0), color = BLUE).shift(dot4.get_center() + np.array([-0.1,0.25,0])) + bnm4 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(4.03*RIGHT + 0.5*DOWN) + plane4 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot4.get_center() + np.array([-0.4,-1,0])).rotate(22*DEGREES).scale(1.2) + point4 = VGroup(*[dot4, tgt4, nm4, bnm4, plane4]) + + dot5 = Dot((1,0,0) + np.array([2.3,-1,1])) + tgt5 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(dot5.get_center() - np.array([-0.05,0.2,0])) + nm5 = Arrow((0,0,0), (-2,0,0), color = BLUE).shift(dot5.get_center() + np.array([0.25,0,0])) + bnm5 = Arrow((0,0,0), (0,2,0), color = GREEN_E).shift(3.34*LEFT+0.3*UP) + plane5 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot5.get_center() + np.array([-0.5,0.5,0])) + 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.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.add_fixed_in_frame_mobjects(bnm5) + self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5)) + self.wait(2) + + self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot]))) diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md index 8092cf7..bc571c6 100644 --- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md +++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/velocity-and-differentiability/README.md @@ -1,5 +1,2 @@ -**file1_smooth_curves.gif** - - -**file2_tangent_space_curve.py** +**file2_tangent_space_curve.py** <br>  |
