load("draw");

draw2d(nticks=5000,parametric(fresnel_s(t),fresnel_c(t),t,0,50));

F(x,y) := x**3+y**3-3*x*y;
draw3d(contour_levels=15,contour=both,
  explicit(F(x,y),x,1,1.5,y,1.4,1.7),
  color=red,line_width=3,
  parametric(3*cos(t)*sin(t)/(cos(t)**3+sin(t)**3)*cos(t),3*cos(t)*sin(t)/(cos(t)**3+sin(t)**3)*sin(t),0, t,0.7,1),
  xrange=[1,1.5],yrange=[1.4,1.7],
  xlabel="x", ylabel="y", zlabel="z"
);


F(x,y) := x**2-y**3;
draw3d(contour_levels=15,contour=both,
  explicit(F(x,y),x,-5,5,y,-5,5),
  color=red,line_width=3,
  parametric(x,(x**2)**(1/3),0,x,-5,5),
  xrange=[-5,5],yrange=[-5,5],zrange=[-30,30],
  xlabel="x", ylabel="y", zlabel="z"
);

F(x,y) := x**4-x**2-y**2+2*y-1;
draw3d(contour_levels=15,contour=both,
  explicit(F(x,y),x,-1,1,y,0,2),
  color=red,point_type=7,point_size=2,
  points([[0,1,0]]),
  xrange=[-1,1],yrange=[0,2],
  xlabel="x", ylabel="y", zlabel="z"
);

F(x,y) := (x**2+y**2)**2 - 2*(x**2-y**2);
draw3d(contour_levels=15,contour=both,
  explicit(F(x,y),x,-1,1,y,-1,1),
  color=red,line_width=3,nticks=50,
  parametric(sqrt(2*cos(2*t))*cos(t), sqrt(2*cos(2*t))*sin(t),0,t,-%pi/4,%pi/4),
  parametric(sqrt(2*cos(2*t))*cos(t), sqrt(2*cos(2*t))*sin(t),0,t,3*%pi/4,5*%pi/4),
  xrange=[-1,1],yrange=[-1,1],zrange=[-1,1],
  xlabel="x", ylabel="y", zlabel="z"
);

F(x,y) := max(1, sqrt(x**2+y**2))-1;
draw3d(contour_levels=15,contour=both,
  explicit(F(x,y),x,-3,3,y,-3,3),
  color=red,line_width=5,nticks=50,
  parametric_surface(r*cos(t),r*sin(t),0,r,0,1,t,0,2*%pi),
  xrange=[-3,3],yrange=[-3,3],zrange=[0,2],
  xlabel="x", ylabel="y", zlabel="z"
);