from manimlib.imports import*

class ExampleAnimation(ThreeDScene):
    def construct(self):
        axes = ThreeDAxes()

        f_text = TextMobject("$f(x,y) = (y-x)(1-2x-3y)$").to_corner(UL)        
        d = Dot(np.array([0,0,0]), color = '#800000')  #---- Critical Point
        d_text = TextMobject("$(0.2,0.2)$",color = '#DC143C').scale(0.5).shift(0.2*UP)  #----x = 0.2, y = 0.2
        r_text=TextMobject("Critical Point",color = '#00FFFF').shift(0.3*DOWN).scale(0.6)

        #----f(x,y) = (y-x)(1-2x-3y)
        f = ParametricSurface(
            lambda u, v: np.array([
                u,
                v,
                (v-u)*(1-2*u-3*v)
            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_D, PURPLE_E],
            resolution=(20, 20)).scale(1)       
        
        self.set_camera_orientation(phi = 75 * DEGREES)
        self.begin_ambient_camera_rotation(rate=0.5)

        self.add_fixed_in_frame_mobjects(f_text)
        self.wait(1) 
        self.add(axes)
        self.play(Write(f),Write(d))
        self.wait(1)
        self.add_fixed_in_frame_mobjects(d_text)
        self.wait(1)
        self.add_fixed_in_frame_mobjects(r_text)
        self.wait(3)