new animation

4 files changed, 249 insertions, 2 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md
index 871eeaa..17077b6 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/README.md
@@ -10,5 +10,5 @@
 
 
 
-**
-![]()
+**file4_helix**
+![file4_helix](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif)
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py
index eb5f4ab..996ead1 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file2_scalar_line_integral.py
@@ -417,3 +417,5 @@ class LineIntegrationProcess(SpecialThreeDScene):
         
         
   #uploaded by Somnath Pandit.FSF2020_Line_Integrals
+  
+  
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif
new file mode 100644
index 0000000..ceedb1f
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.py
new file mode 100644
index 0000000..50aeb33
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/file4_helix.py
@@ -0,0 +1,245 @@
+from manimlib.imports import *
+
+class ParametricCurve(ThreeDScene):
+
+    CONFIG = {
+        "axes_config": {
+            "x_min": 0,
+            "x_max": 3,
+            "y_min": 0,
+            "y_max": 3,
+            "z_min": 0,
+            "z_max": 4,
+            "a":0 ,"b": 2, "c":0 , "d":2,
+            "axes_shift":2*IN+1.4*RIGHT+1.4*DOWN,
+            "x_axis_config": {
+                "tick_frequency": 1,
+                "include_tip": False,
+            },
+            "y_axis_config": {
+                "tick_frequency": 1,
+                "include_tip": False,
+            },
+            "z_axis_config": {
+                "tick_frequency": 1,
+             #   "include_tip": False,
+            },
+        },
+        
+    }
+
+
+    def construct(self):
+
+        self.setup_axes()
+        
+        self.set_camera_orientation(
+            distance=25,
+            phi=60 * DEGREES,
+            theta=40 * DEGREES,
+        )
+        
+        label=TextMobject("Helix",color=PURPLE).scale(1.6)
+        label.to_corner(UR,buff=2)
+        self.add_fixed_in_frame_mobjects(label) 
+   
+        helix=self.get_helix(
+            radius=1.5,
+            t_min= 0,
+            t_max= 4*PI, 
+            color=PURPLE 
+        )
+        parameter_label=TextMobject(
+            "Parametric equation: ",
+            color=TEAL
+            ).next_to(label,DOWN,buff=.3
+        )
+        parametric_eqn=TextMobject(
+            "$x=\cos$ (","t",
+            r")\\$y=\sin $(","t",
+            r")\\$z$=","t"
+        ).next_to(parameter_label,DOWN,buff=.1)  
+        parametric_eqn.set_color_by_tex("t",RED)
+        self.parametric_eqn=parametric_eqn
+        
+        parametriztion=VGroup(
+            parameter_label,
+            parametric_eqn
+            )
+        
+        
+        self.play(ShowCreation(helix),run_time=2)
+        self.begin_ambient_camera_rotation(.1)
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(parametriztion) 
+        self.play(Write(parametriztion))
+        self.wait(1)
+        self.stop_ambient_camera_rotation()
+        self.move_camera(
+            distance=20,
+            phi=85 * DEGREES,
+     #       theta=-90 * DEGREES,
+            run_time=3
+        )
+        scale_axes=VGroup(self.axes,helix).scale(1.2)
+        self.show_the_parameter()
+        self.wait(2)
+    
+    
+    
+    def get_helix(self,radius=1, **kwargs):
+        config = {
+            "t_min": 0,
+            "t_max": 2*PI,    
+        }
+        config.update(kwargs)
+        helix= ParametricFunction(
+            lambda  t : self.axes.c2p(
+                radius*np.cos(t),
+                radius*np.sin(t),
+                t/4
+            ),
+            **config
+        )
+        
+        self.helix=helix
+        return helix
+ 
+    def show_the_parameter(self):              
+        t_tracker = ValueTracker(0)
+        t=t_tracker.get_value
+ 
+        t_label = TexMobject(
+            "t = ",color=RED
+            ).next_to(self.parametric_eqn,DL,buff=.85)
+        
+        t_text = always_redraw(
+            lambda: DecimalNumber(
+                t(),
+                color=GOLD,
+            ).next_to(t_label, RIGHT, MED_SMALL_BUFF)
+        )
+        t_text.suspend_updating()
+        
+        dot = Sphere(
+                radius= 1.5*DEFAULT_DOT_RADIUS,
+                stroke_width= 1,
+                fill_opacity= 1.0,
+               )
+        dot.set_color(GOLD)
+        dot.add_updater(lambda v: v.move_to(
+            self.helix.get_point_from_function(PI*t())
+        ))
+        
+        pi = TexMobject(
+            "\\pi ",
+            color=GOLD,
+        ).next_to(t_text,RIGHT,buff=-.3)
+            
+        group = VGroup(t_text,t_label,pi).scale(1.5)
+
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(group)
+        t_text.resume_updating()
+        self.play(FadeIn(group))
+        self.add(dot)
+        self.play(
+            t_tracker.set_value,2,
+            rate_func=linear,
+            run_time=5
+            )
+ 
+ 
+#--------------------------------------------------------  
+        
+    #customize 3D axes        
+    def get_three_d_axes(self, include_labels=True, include_numbers=False, **kwargs):
+        config = dict(self.axes_config)
+        config.update(kwargs)
+        axes = ThreeDAxes(**config)
+        axes.set_stroke(width=1.5)
+
+        if include_numbers:
+            self.add_axes_numbers(axes)
+
+        if include_labels:
+            self.add_axes_labels(axes)
+
+        # Adjust axis orientation
+        axes.x_axis.rotate(
+            90 * DEGREES, LEFT,
+            about_point=axes.c2p(0, 0, 0),
+        )
+        axes.y_axis.rotate(
+            90 * DEGREES, UP,
+            about_point=axes.c2p(0, 0, 0),
+        )
+ 
+        
+        return axes
+        
+        
+    def setup_axes(self):
+        axes = self.get_three_d_axes(include_labels=True)
+        axes.scale(1)
+     #   axes.center()
+        axes.shift(axes.axes_shift)
+        self.add(axes)
+        self.axes = axes
+        
+    def add_axes_numbers(self, axes):
+        x_axis = axes.x_axis
+        y_axis = axes.y_axis
+        tex_vals_x = [
+            ("1", axes.b),
+        ]
+        tex_vals_y=[
+            ("1", axes.d)
+        ]
+        x_labels = VGroup()
+        y_labels = VGroup()
+        for tex, val in tex_vals_x:
+            label = TexMobject(tex)
+            label.scale(1)
+            label.next_to(x_axis.n2p(val), DOWN)
+            label.rotate(180 * DEGREES)
+            x_labels.add(label)
+        x_axis.add(x_labels)
+        x_axis.numbers = x_labels
+
+        for tex, val in tex_vals_y:
+            label = TexMobject(tex)
+            label.scale(1)
+            label.next_to(y_axis.n2p(val), LEFT)
+            label.rotate(90 * DEGREES)
+            y_labels.add(label)
+            
+        y_axis.add(y_labels)
+        y_axis.numbers = y_labels
+        
+        return axes
+    
+    def add_axes_labels(self, axes):
+        x_label = TexMobject("x")
+        x_label.next_to(axes.x_axis.get_end(), RIGHT)
+        axes.x_axis.label = x_label
+
+        y_label = TextMobject("y")
+        y_label.rotate(90 * DEGREES, OUT)
+        y_label.next_to(axes.y_axis.get_end(), UP)
+        axes.y_axis.label = y_label
+
+        z_label = TextMobject("z")
+        z_label.rotate(90 * DEGREES, LEFT)
+        z_label.next_to(axes.z_axis.get_zenith(), LEFT)
+        axes.z_axis.label = z_label
+        for axis in axes:
+            axis.add(axis.label)
+        return axes  
+        
+  #uploaded by Somnath Pandit.FSF2020_Line_integrals
+  
+  
+          
+        
+