from manimlib.imports import * class IntegrationProcess(SpecialThreeDScene): CONFIG = { "axes_config": { "x_min": 0, "x_max": 5, "y_min": 0, "y_max": 7, "z_min": 0, "z_max": 3, "a":0 ,"b":4 , "c":0 , "d":6, "axes_shift":1.5*IN+2*LEFT+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, }, "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*(1+(x+y)/10) } def construct(self): self.setup_axes() axes=self.axes self.set_camera_orientation(#distance=35, phi=60 * DEGREES, theta=10 * DEGREES, ) fn_text=TextMobject("$z=(1+x+y)$").set_color(PINK) self.add_fixed_in_frame_mobjects(fn_text) fn_text.to_edge(TOP,buff=.1) self.fn_text=fn_text R=TextMobject("R").set_color(BLACK).scale(3).rotate(PI/2) 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=0.75, fill_color=PINK, stroke_width=0.8, stroke_color=WHITE, ) slice_curve=(self.get_y_slice_graph( axes,self.Func,5,color=YELLOW)) self.begin_ambient_camera_rotation(rate=0.04) # self.play(Write(surface)) self.add(surface) self.get_lines() self.show_process(axes) self.wait() 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=0, fill_color=BLUE_E, fill_opacity=.65, )) 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() first_x_text=TextMobject("First the $x$ integration..",color=YELLOW) first_x_text.to_corner(UR,buff=1.1) x_func=TextMobject("$\\frac 3 2 + y$",color=BLUE) '''x_func.next_to(self.fn_text,DOWN) x_func.align_to(self.fn_text,LEFT)''' x_func.to_edge(LEFT,buff=1) then_y_text=TextMobject("Then the $y$ integration..",color=YELLOW) then_y_text.to_corner(UR,buff=1.1) self.add_fixed_in_frame_mobjects(first_x_text) self.play(Write(first_x_text)) self.add_fixed_in_frame_mobjects(x_func) self.play( Write(VGroup(graph,plane,x_func)), run_time=3 ) self.wait() self.remove(first_x_text) self.add_fixed_in_frame_mobjects(then_y_text) self.play(Write(then_y_text)) self.add(plane.copy(),plane_side1,plane_side2) graph.resume_updating() plane.resume_updating() plane_side1.resume_updating() plane_side2.resume_updating() self.play( ApplyMethod( y_tracker.set_value, axes.d, rate_func=linear, run_time=6, ) ) graph.suspend_updating() 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, LEFT, 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=0.3, fill_color=TEAL, stroke_width=.2, 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 = [ ("1", axes.b), ] tex_vals_y=[ ("2", 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_Double_Integral