diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py | 355 |
1 files changed, 355 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py new file mode 100644 index 0000000..5a8cec0 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py @@ -0,0 +1,355 @@ +from manimlib.imports import * + +class IntegrationProcess(SpecialThreeDScene): + + CONFIG = { + "axes_config": { + "x_min": 0, + "x_max": 7, + "y_min": 0, + "y_max": 7, + "z_min": 0, + "z_max": 4, + "a":1 ,"b": 6, "c":2 , "d":6, + "axes_shift":-3*OUT, + "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": 1, + }, + "default_graph_style": { + "stroke_width": 2, + "stroke_color": WHITE, + }, + "default_surface_config": { + "fill_opacity": 0.5, + "checkerboard_colors": [LIGHT_GREY], + "stroke_width": 0.5, + "stroke_color": WHITE, + "stroke_opacity": 0.5, + }, + "Func": lambda x,y: 2+y/4+np.cos(x/1.4) + } + + + def construct(self): + + self.setup_axes() + axes=self.axes + + self.camera.frame_center.shift(axes.c2p(3,4,1.7)) + self.set_camera_orientation(distance=35, + phi= 80 * DEGREES, + theta= -80 * DEGREES, + gamma = 0 * DEGREES + ) + + fn_text=TextMobject("$z=f(x,y)$").set_color(PINK) + self.add_fixed_in_frame_mobjects(fn_text) + + + R=TextMobject("R").set_color(BLACK).scale(3) + R.move_to(axes.input_plane,IN) + self.add(R) + + # get the surface + surface= self.get_surface( + axes, lambda x , y: + self.Func(x,y) + ) + surface.set_style( + fill_opacity=.65, + fill_color=PINK, + stroke_width=0.8, + stroke_color=WHITE, + ) + fn_text.next_to(surface,UP,buff=MED_LARGE_BUFF) + slice_curve=(self.get_y_slice_graph( + axes,self.Func,5,color=YELLOW)) + + + self.begin_ambient_camera_rotation(rate=0.08) + # self.play(Write(surface)) + self.add(surface) + + self.get_lines() + + self.show_process(axes) + + self.wait(3) + + + + def show_process(self,axes): + y_tracker = ValueTracker(axes.c) + self.y_tracker=y_tracker + y=y_tracker.get_value + + graph = always_redraw( + lambda: self.get_y_slice_graph( + axes, self.Func, y(), + stroke_color=YELLOW, + stroke_width=4, + ) + ) + graph.suspend_updating() + + + plane = always_redraw(lambda: Polygon( + *[ + axes.c2p(x,y(),self.Func(x,y())) + for x in np.arange(axes.a,axes.b,0.01) + ], + *[ + axes.c2p(x, y(), 0) + for x in [ axes.b, axes.a,] + ], + stroke_width=2, + fill_color=BLUE_D, + fill_opacity=.4, + )) + + plane_side1 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.a,y,self.Func(axes.a,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.a, y, 0) + for y in [ y(),axes.c, ] + ], + stroke_width=2.5, + fill_color=BLUE_C, + fill_opacity=.2, + )) + plane_side2 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.b,y,self.Func(axes.b,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.b, y, 0) + for y in [y(),axes.c,] + ], + stroke_width=2.5, + fill_color=BLUE_E, + fill_opacity=.45, + )) + plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() + + self.play(Write(VGroup(graph,plane)),run_time=2) + self.add(plane.copy(),plane_side1,plane_side2) + + + plane_side1.resume_updating() + plane_side2.resume_updating() + + self.move_camera( + distance=30, + phi= 85 * DEGREES, + theta= -10 * DEGREES, + run_time=1.5 + ) + self.play( + ApplyMethod( + y_tracker.set_value, axes.d, + rate_func=linear, + run_time=6, + ) + ) + plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() + + + + def get_y_slice_graph(self, axes, func, y, **kwargs): + config = dict() + config.update(self.default_graph_style) + config.update({ + "t_min": axes.a, + "t_max": axes.b, + }) + config.update(kwargs) + slice_curve=ParametricFunction( + lambda x: axes.c2p( + x, y, func(x, y) + ), + **config, + ) + return slice_curve + + + def get_surface(self,axes, func, **kwargs): + config = { + "u_min": axes.a, + "u_max": axes.b, + "v_min": axes.c, + "v_max": axes.d, + "resolution": ( + (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_lines(self): + axes = self.axes + + 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,"RED")) + + labels=[ + (axes.a,0,0), + (axes.b,0,0), + (0,axes.d,0), + (0,axes.c,0) + ] + self.region_corners[-1]=self.region_corners[0] + for start , end in zip(labels, + self.region_corners): + lines.add(self.draw_lines(start,end,"WHITE")) + 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) + + 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, RIGHT, + about_point=axes.c2p(0, 0, 0), + ) + axes.y_axis.rotate( + 90 * DEGREES, UP, + about_point=axes.c2p(0, 0, 0), + ) + + # Add xy-plane + input_plane = self.get_surface( + axes, lambda x, t: 0 + ) + input_plane.set_style( + fill_opacity=0.5, + fill_color=TEAL, + stroke_width=0, + stroke_color=WHITE, + ) + + axes.input_plane = input_plane + + self.region_corners=[ + input_plane.get_corner(pos) for pos in (DL,DR,UL,UR)] + + return axes + + + def setup_axes(self): + axes = self.get_three_d_axes(include_labels=True) + axes.add(axes.input_plane) + 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 = [ + ("a", axes.a), + ("b", axes.b), + ] + tex_vals_y=[ + ("c", axes.c), + ("d", 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) + 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(1.5) + 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, RIGHT) + z_label.next_to(axes.z_axis.get_zenith(), RIGHT) + axes.z_axis.label = z_label + for axis in axes: + axis.add(axis.label) + return axes + + + + #uploaded by Somnath Pandit.FSF2020_Double_Integral |