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from manimlib.imports import*
class TangenttoSurface(ThreeDScene):
def construct(self):
axes = ThreeDAxes()
#----graph of first function f(x,y) = -x**2-y**2
f = ParametricSurface(
lambda u, v: np.array([
u,
v,
-u**2-v**2
]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [YELLOW_D, YELLOW_E],
resolution = (20, 20)).scale(1)
f_text = TextMobject("Tangent plane at relative maxima").to_corner(UL).scale(0.5)
#----graph of second function f(x,y) = -x**2+y**2
f2 = ParametricSurface(
lambda u, v: np.array([
u,
v,
-u**2+v**2
]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [RED_D, RED_E],
resolution = (20, 20)).scale(1)
f2_text = TextMobject("Tangent plane at saddle point").to_corner(UL).scale(0.5)
#----graph of third function f(x,y) = x**2+y**2
f3 = ParametricSurface(
lambda u, v: np.array([
u,
v,
u**2+v**2
]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [GREEN_D, GREEN_E],
resolution = (20, 20)).scale(1)
f3_text = TextMobject("Tangent plane at relative minima").to_corner(UL).scale(0.5)
self.set_camera_orientation(phi = 75 * DEGREES, theta = -45 * DEGREES )
d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point
r = Rectangle(height = 2,breadth = 1,color = PURPLE).scale(0.5)
self.begin_ambient_camera_rotation(rate = 0.3)
self.add(axes)
self.play(Write(f),Write(d))
self.wait(1)
self.add_fixed_in_frame_mobjects(f_text)
self.play(ShowCreation(r))
self.wait(1)
self.play(FadeOut(r),FadeOut(f),FadeOut(d),FadeOut(f_text))
self.wait(1)
self.play(Write(f2),Write(d))
self.wait(1)
self.add_fixed_in_frame_mobjects(f2_text)
self.play(ShowCreation(r))
self.wait(1)
self.play(FadeOut(r),FadeOut(f2),FadeOut(d),FadeOut(f2_text))
self.wait(1)
self.play(Write(f3),Write(d))
self.wait(1)
self.add_fixed_in_frame_mobjects(f3_text)
self.play(ShowCreation(r))
self.wait(1)
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