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from manimlib.imports import *
class ClariantRule(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
function = ParametricSurface(
lambda u, v: np.array([
3.5*np.sin(u)*np.cos(v),
3.5*np.sin(u)*np.sin(v),
3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) )
]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
resolution=(15, 32)).scale(1)
function_x = ParametricSurface(
lambda u, v: np.array([
3.5*np.sin(u)*np.cos(v),
3.5*np.sin(u)*np.sin(v),
-4*3.5*3.5*3.5*np.sin(u)*np.sin(u)*np.sin(u)*(2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u))
]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,
resolution=(15, 32)).scale(1)
func_x =ParametricFunction(
lambda u : np.array([
u,
-1,
(u*u )*np.exp(1-u*u)
]),color=RED_E,t_min=-3.5,t_max=3.5,
)
func_y =ParametricFunction(
lambda u : np.array([
0,
u,
(3*u*u)*np.exp(1-u*u)
]),color=PINK,t_min=-3.5,t_max=3.5,
)
plane_x = Polygon(np.array([-3.5,-1,-3]),np.array([3.5,-1,-3]),np.array([3.5,-1,3]),np.array([-3.5,-1,3]),np.array([-3.5,-1,-3]), color = YELLOW_E, fill_color = YELLOW_B, fill_opacity = 0.1)
plane_text_x = TextMobject(r"$y = -1$", color = YELLOW_C).move_to(np.array([5,0,2.7])).scale(0.7)
plane_y = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = GREEN_E, fill_color = GREEN_B, fill_opacity = 0.1)
plane_text_y = TextMobject(r"$x = 0$", color = GREEN_C).move_to(np.array([0,4,2.7])).scale(0.7)
surface_eqn = TextMobject("Surface", r"$z = f(x,y) = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([4.1*LEFT+3.8*UP]))
surface_eqn[0].set_color(BLUE_C)
number_plane = NumberPlane()
line = Line(np.array([0,-1,3]), np.array([0,-1,-3]), color = PURPLE)
self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)
self.add(axes)
axis = TextMobject(r"X",r"Y",r"Z")
axis[0].move_to(6*RIGHT)
axis[1].move_to(6*UP)
axis[2].move_to(np.array([0,0,3.7]))
self.add_fixed_orientation_mobjects(axis[2])
self.add_fixed_orientation_mobjects(axis[0])
self.add_fixed_orientation_mobjects(axis[1])
self.play(ShowCreation(function))
self.wait()
self.play(ShowCreation(number_plane))
self.add_fixed_in_frame_mobjects(surface_eqn)
self.play(ShowCreation(plane_x), ShowCreation(plane_y), ShowCreation(line))
self.add_fixed_orientation_mobjects(plane_text_x, plane_text_y)
self.move_camera(phi=0* DEGREES,theta=45*DEGREES)
self.wait(3)
self.move_camera(phi=60* DEGREES,theta=45*DEGREES)
#self.play(ShowCreation(func_x), ShowCreation(func_y))
dot_x = Dot().rotate(PI/2).set_color(YELLOW_C)
alpha_x = ValueTracker(0)
vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)
dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))
self.play(
ShowCreation(func_x),
GrowFromCenter(dot_x),
GrowArrow(vector_x)
)
vector_x.add_updater(
lambda m: m.become(
self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)
)
)
dot_y = Dot().rotate(PI/2).set_color(GREEN_E)
alpha_y = ValueTracker(0)
vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)
dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))
self.play(
ShowCreation(func_y),
GrowFromCenter(dot_y),
GrowArrow(vector_y)
)
vector_y.add_updater(
lambda m: m.become(
self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)
)
)
self.add(vector_x,dot_x)
self.play(alpha_x.increment_value, 1, run_time=5, rate_func=linear)
self.add(vector_y,dot_y)
self.play(alpha_y.increment_value, 1, run_time=5, rate_func=linear)
self.wait(2)
def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
coord_i = curve.point_from_proportion(proportion)
coord_f = curve.point_from_proportion(proportion + dx)
reference_line = Line(coord_i,coord_f)
unit_vector = reference_line.get_unit_vector() * scale
vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = ORANGE, buff=0)
return vector
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