unfinished work

1 files changed, 479 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py
new file mode 100644
index 0000000..9cdb976
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/line-integrals/unfinished_vector_line_integral.py
@@ -0,0 +1,479 @@
+from manimlib.imports import *
+
+class LineIntegrationProcess(SpecialThreeDScene):
+
+    CONFIG = {
+        "axes_config": {
+            "x_min": 0,
+            "x_max": 4,
+            "y_min": 0,
+            "y_max": 4,
+            "z_min": 0,
+            "z_max": 3,
+            "a":-3 ,"b": 3, "c":0 , "d":3,
+            "axes_shift":IN+2*DL,
+            "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,
+            },
+            "num_axis_pieces": 20,
+        },
+        "default_vector_field_config": {
+            "delta_x": .5,
+            "delta_y": .5,
+            "x_min": -3,
+            "x_max": 2,
+            "y_min": -3,
+            "y_max": 2,
+            "min_magnitude": 0,
+            "max_magnitude": 4,
+            "colors": [GREEN,YELLOW,RED],
+            "length_func": lambda norm : .4*sigmoid(norm),
+            "opacity": 1.0,
+            "vector_config": {
+                "stroke_width":2
+            },
+        },
+        "default_graph_style": {
+            "stroke_width": 2,
+            "stroke_color": WHITE,
+        },
+
+    "Func": lambda x,y: 1+x**2*y/15
+    }
+
+
+    def construct(self):
+
+        self.setup_axes()
+        axes=self.axes
+        
+        self.set_camera_orientation(distance=10,
+            phi=0 * DEGREES,
+            theta=-90 * DEGREES,
+        )
+        
+        fn_text=TexMobject(
+            r"\vec F = x^2\hat i-xy\hat j"
+        ).set_color_by_gradient(
+            *self.default_vector_field_config["colors"]
+        )
+        fn_text.to_corner(UR,buff=.8).shift(DOWN)
+        
+        origin=axes.c2p(0,0,0)
+        v_field=self.get_vector_field(
+            lambda v: np.array([
+            (v[0]-origin[0])**2,
+            -(v[0]-origin[0])*(v[1]-origin[1]),  
+            0,
+            ]),
+        )
+        
+     #   self.play(Write(surface)) 
+        self.add_fixed_in_frame_mobjects(fn_text)   
+     #   self.play(Write(v_field),Write(fn_text))
+        self.add(v_field, fn_text)
+        self.get_line_of_int()
+      #  self.begin_ambient_camera_rotation(rate=0.04)
+        self.get_dot_product_values()
+        '''self.get_field_values_on_line()
+        self.wait(1.5)
+        self.area=self.get_area()
+        area_text=TextMobject("Line"," Integral in the",r" scalar field\\"," means this" ,"area")
+        area_text.set_color_by_tex_to_color_map({
+            "Line": PINK, "scalar":BLUE, "area":TEAL_A
+        })
+        area_text.to_edge(TOP,buff=MED_SMALL_BUFF)
+        
+        self.remove(self.values_on_line_text)
+        self.add_fixed_in_frame_mobjects(area_text) 
+        self.play(Write(area_text))
+        self.play(Write(self.area),run_time=2)
+        self.play(FadeOut(VGroup(surface,fn_text)))
+        self.wait()
+        
+        self.stop_ambient_camera_rotation()
+    #    self.get_lines()
+   
+        self.remove(axes,surface)
+        self.trasform_to_graphs()'''
+        self.wait(2)
+            
+            
+    def get_vector_field(self,func,**kwargs):
+        config = dict()
+        config.update(self.default_vector_field_config)
+        config.update(kwargs)
+        vector_field= VectorField(func,**config)
+        self.vector_field=vector_field
+        
+        return vector_field
+        
+    def get_line_of_int(self): 
+        line_of_int_text=TextMobject(r"Line of integration is\\","$\\vec r(t)=\cos(t)\hat i+\sin(t)\hat j$")
+        line_of_int_text[1].set_color(PINK)
+        line_of_int_text.to_edge(TOP,buff=SMALL_BUFF)
+        
+        
+        line_of_int=(self.get_curve(
+            self.Func,on_surface=False
+        ))
+        line_of_int.set_style(
+            stroke_width=5,
+            stroke_color=PINK,
+        )
+        
+        self.add_fixed_in_frame_mobjects(line_of_int_text) 
+        self.play(Write(line_of_int_text))
+        self.wait(.5)
+        self.play(ShowCreation(line_of_int),run_time=1.5)
+      #  self.add(line_of_int)
+        
+        self.line_of_int=line_of_int
+        self.line_of_int_text=line_of_int_text
+    
+    def get_dot_product_values(self):    
+        self.get_vector_and_tangent()
+        
+        
+        
+    def get_vector_and_tangent(self):
+        dot=self.dots[self.index]
+        self.show_specific_vectors(dot)
+        self.play(Write(self.func_val))
+        self.wait(1)
+        self.show_tangent(dot)
+        self.play(FadeIn(VGroup(*[
+            dot.set_color(ORANGE).scale(1.4)
+                for dot in self.dots ]
+        )))
+        
+        
+    def show_specific_vectors(self,dots):
+        for dot in dots:
+            vector=self.vector_field.get_vector(dot.get_center()) 
+            vector.set_color(ORANGE)
+
+            self.play(Write(vector),run_time=.2)
+
+        
+    def show_tangent(self,dot):
+        tangent_sym=TextMobject("$\\vec T(x_i,y_i)$",color="#DC75CD").scale(.8)
+        x=dot.get_center()
+        angle=self.angle_of_tangent( 
+             self.point_to_coords(x)[0],
+             self.curve, 
+             dx=0.01
+        )
+        vect = Vector().rotate(angle,about_point=x)
+        vect.set_color("#DC75CD")
+        tangent=vect.next_to(x,DR,buff=0)
+        tangent_sym.next_to(tangent,DOWN,buff=.1)
+        self.play(Write(VGroup(tangent,tangent_sym)))
+        
+        self.tangent_sym=tangent_sym
+         
+    def dot_product(self):
+        
+        dot_sym=Dot().next_to(self.func_val,RIGHT)
+        
+        self.play(FadeOut(VGroup(
+            self.at_any_points_text,
+            self.evaluate_text
+        )))
+        self.play(Write(self.dot_prod_text))
+        self.play(
+            FadeIn(dot_sym),
+            ApplyMethod(
+            self.tangent_sym.next_to,
+            dot_sym, RIGHT
+        ))
+
+        self.dot_sym=dot_sym
+    def get_field_values_on_line(self):
+        self.remove(self.line_of_int_text)
+          
+        values_on_line_text=TextMobject("Values"," of"," function","on the ","line")
+        values_on_line_text.set_color_by_tex_to_color_map({
+            "Values":YELLOW, "function":BLUE,"line":PINK
+        })
+        values_on_line_text.to_edge(TOP,buff=SMALL_BUFF)
+        
+        values_on_surface=(self.get_curve(
+            self.Func,on_surface=True
+        ))
+        values_on_surface.set_style(
+            stroke_width=5,
+            stroke_color=YELLOW,
+        ) 
+        
+        self.add_fixed_in_frame_mobjects(values_on_line_text) 
+        self.play(Write(values_on_line_text))
+    #    self.wait()
+        self.play(ShowCreation(values_on_surface),run_time=3)
+     #   self.add(values_on_surface)
+        
+        self.values_on_surface=values_on_surface
+        self.values_on_line_text=values_on_line_text
+       
+     
+    def trasform_to_graphs(self):        
+        on_surface_graph=(self.get_graph(
+            self.Func,on_surface=True
+        ))
+        on_surface_graph.set_style(
+            stroke_width=5,
+            stroke_color=YELLOW,
+        ) 
+        
+        line_graph=(self.get_graph(
+            self.Func,on_surface=False
+        ))
+        line_graph.set_style(
+            stroke_width=5,
+            stroke_color=PINK,
+        )
+        
+        self.on_surface_graph=on_surface_graph
+        self.line_graph=line_graph
+        graph_area=self.get_area(graph=True) 
+        
+        into_graph=[
+            ReplacementTransform(
+            self.values_on_surface,
+            on_surface_graph
+            ),
+            ReplacementTransform(
+            self.line_of_int,
+            line_graph
+            ),
+            ReplacementTransform(
+            self.area,
+            graph_area
+            ),
+        ]
+        
+        self.move_camera(
+          #  distance=20,
+            phi=90 * DEGREES,
+            theta=-90 * DEGREES,
+            added_anims=into_graph,
+            run_time=2
+        )
+    
+    def get_area(self,graph=False):
+        axes=self.axes
+        if graph:
+            on_surface=self.on_surface_graph
+            on_base=self.line_graph
+        else:
+            on_surface=self.values_on_surface
+            on_base=self.line_of_int
+        area =Polygon(
+            *[
+            on_surface.get_point_from_function(t)
+                for t in np.arange(0,PI,0.01)
+            ],
+            *[
+             on_base.get_point_from_function(t)
+                for t in np.arange(PI,0,-0.01)
+            ],
+            stroke_width=0,
+            fill_color=TEAL_A,
+            fill_opacity=.6,
+        )
+
+        return area
+
+    def get_curve(self,func,on_surface=False ,**kwargs):
+        config = dict()
+        config.update(self.default_graph_style)
+        config.update({
+            "t_min": 0,
+            "t_max": PI/2,
+        })
+        config.update(kwargs)
+        r=abs(self.axes.a)
+        curve=ParametricFunction(
+            lambda t: self.axes.c2p(
+                r*np.cos(t), 
+                r*np.sin(t), 
+                func(r*np.cos(t), r*np.sin(t))*bool(on_surface)
+            ),
+            **config,
+        )
+        return curve
+        
+        
+    def get_surface(self, func, **kwargs):
+        axes=self.axes
+        config = {
+            "u_min": axes.a-.2,
+            "u_max": axes.b+.2,
+            "v_min": axes.c-.1,
+            "v_max": axes.d,
+            "resolution": (
+                2*(axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
+                (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
+            ),
+        }
+        
+        config.update(self.default_surface_config)
+        config.update(kwargs)
+        return ParametricSurface(
+            lambda  x,y : axes.c2p(
+                x, y, func(x, y)
+            ),
+            **config
+        )
+    
+    def get_graph(self,func,on_surface=False ,**kwargs):
+        config = dict()
+        config.update(self.default_graph_style)
+        config.update({
+            "t_min": 0,
+            "t_max": PI,
+        })
+        config.update(kwargs)
+        slice_curve=ParametricFunction(
+            lambda t: self.axes.c2p(
+                4*np.cos(t), 
+                0, 
+                2+func(3*np.cos(t), 3*np.sin(t))*bool(on_surface)
+            ),
+            **config,
+        )
+        return slice_curve
+        
+    def get_lines(self):
+        pass
+        axes = self.axes
+        labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c),       
+            axes.y_axis.n2p(axes.d)]
+        
+        
+        surface_corners=[]
+        for x,y,z in self.region_corners:
+            surface_corners.append([x,y,self.Func(x,y)])
+            
+        lines=VGroup()
+        for start , end in zip(surface_corners,
+        self.region_corners):
+            lines.add(self.draw_lines(start,end,"PINK"))
+            
+        for start , end in zip(labels,
+        self.region_corners):
+         #   lines.add(self.draw_lines(start,end,"BLUE"))
+         #   print (start,end)
+            pass
+       # self.play(ShowCreation(lines))
+        self.add(lines)
+        
+              
+    def draw_lines(self,start,end,color):
+        start=self.axes.c2p(*start)
+        end=self.axes.c2p(*end)
+        line=DashedLine(start,end,color=color)
+        
+        return line
+        
+#-------------------------------------------------------            
+    #customize 3D axes        
+    def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs):
+        config = dict(self.axes_config)
+        config.update(kwargs)
+        axes = ThreeDAxes(**config)
+        axes.set_stroke(width=2)
+        self.axes=axes
+        
+        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 = TexMobject("")
+        z_label.rotate(90 * DEGREES, RIGHT)
+        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