summaryrefslogtreecommitdiff
path: root/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py
diff options
context:
space:
mode:
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py')
-rw-r--r--FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py286
1 files changed, 0 insertions, 286 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py
deleted file mode 100644
index c998f3b..0000000
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py
+++ /dev/null
@@ -1,286 +0,0 @@
-from manimlib.imports import *
-
-class SurfacesAnimation(ThreeDScene):
-
- CONFIG = {
- "axes_config": {
- "x_min": 0,
- "x_max": 4,
- "y_min": 0,
- "y_max": 4,
- "z_min": -2,
- "z_max": 4,
- "a":0 ,"b": 4, "c":0 , "d":4,
- "axes_shift":IN+2*LEFT+2*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: x*y/4
- }
-
-
- def construct(self):
-
- self.setup_axes()
- self.set_camera_orientation(
- distance=30,
- phi=75 * DEGREES,
- theta=20 * DEGREES,
- )
-
- fn_text=TextMobject("$z=xy$").set_color(BLUE).scale(1.5)
- fn_text.to_corner(UR,buff=2)
- self.add_fixed_in_frame_mobjects(fn_text)
-
-
- #get the surface
- surface= self.get_surface(
- self.axes, lambda x , y:
- self.Func(x,y)
- )
- surface.set_style(
- fill_opacity=.5,
- fill_color=BLUE_E,
- stroke_width=0.2,
- stroke_color=WHITE,
- )
- #get boundary curves
- c1=self.get_curve(
- self.axes, lambda x: x**2/4
- )
- c1_label=TextMobject("$y=x^2$").next_to(c1,IN+OUT).shift(DOWN+RIGHT)
- c1_label.rotate(PI)
- c1_group=VGroup(c1,c1_label).set_color(ORANGE)
-
- c2=self.get_curve(
- self.axes, lambda x: x
- ).set_color(PINK)
- c2_label=TextMobject("$y=x$").next_to(c2,IN+OUT)
- c2_label.rotate(PI/2,about_point=(c2_label.get_corner(UL)))
- c2_group=VGroup(c2,c2_label).set_color(YELLOW_E)
-
-
-
- self.add(c1,c2,c1_label,c2_label)
-
- self.begin_ambient_camera_rotation(rate=0.4)
- self.get_region(self.axes,c1,c2)
- self.play(Write(surface))
- self.get_lines()
- self.wait(1)
- self.stop_ambient_camera_rotation()
- self.move_camera(
- distance=20,
- phi=10 * DEGREES,
- theta=80 * DEGREES,
- run_time=2.5
- )
- self.wait(2)
-
-
-
- def get_curve(self,axes, func, **kwargs):
- config = {
- "t_min": axes.x_min,
- "t_max": axes.x_max,
- }
- config.update(kwargs)
- return ParametricFunction(
- lambda x : axes.c2p(
- x, func(x),0
- ),
- **config
- )
-
- def get_region(self,axes,curve1,curve2,**kwargs):
- x_vals=np.arange(axes.x_min,axes.x_max,.1)
- c1_points=[curve1.get_point_from_function(x) for x in x_vals]
- c2_points=[curve2.get_point_from_function(x) for x in x_vals]
- c2_points.reverse()
- points=c1_points+c2_points
- region=Polygon(*points,
- stroke_width=0,
- fill_color=PINK,
- fill_opacity=.5
- )
- R=TextMobject("R").set_color(PINK).scale(2).rotate(180*DEGREES , OUT)
- R.move_to(region,IN+RIGHT)
-
- self.play(Write(region))
- self.add(R)
-
- def get_surface(self,axes, func, **kwargs):
- config = {
- "u_min": axes.x_max,
- "u_max": axes.x_min,
- "v_min": axes.y_max,
- "v_max": axes.y_min,
- "resolution": (10,10),
- }
-
- 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
- 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,"YELLOW"))
-
- 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))
-
-
- 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=PINK,
- stroke_width=.2,
- stroke_color=WHITE,
- )
-
- axes.input_plane = input_plane
-
- self.region_corners=[
- input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)]
-
- 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=[
- ("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_Fubini's_Theorem
-
-
generated by cgit (git 2.34.1) at 2025-01-10 20:06:16 +0000