(* :Tests: *)
(* :Examples:

ImplicitPlot3D[x^2 + 2 y^2 + 3 z^2 == 3,
                {x, -3, 3}, {y, -3, 3}, {z, -3, 3}] (* ellipsoid *)
ImplicitPlot3D[x^2 + y^2 + z^2 - 1 ,
                {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]
        (* unit sphere. If the first argument of ImplicitPlot3D
        is not an equation, it is assumed that argument is to be
        set to zero. *)
ImplicitPlot3D[x^2+y^2-z^2==1,
                {x,-2,2}, {y,-2,2}, {z,-2,2},
                PlotPoints->{{2,2,2},{2,2,2},{2,2,2}}]
        (* hyperboloid of one sheet. The ultimate resolution
        is that obtained by making 3 passes of successively
        finer resolution. The first pass divides the
        original range into 8 smaller ranges. Each of those
        subranges that contain the surface are again
        subdivided into 8 subranges. The process is repeated
        for a third pass.*)
ImplicitPlot3D[E^z Cos[x] == Cos[y],
                {x,-6,6}, {y,-6,6}, {z,-6,6},
                PlotPoints->{16,16,12},
                Passes->4]
        (* Scherk's minimal surface. The ultimate resolution
        is equivalent to dividing the range into 16 * 16 *
        12 points. This is realized by making 4 passes of
        successively finer resolution. *)
ImplicitPlot3D[z^2 == 1 - (2 - Sqrt[x^2+y^2])^2,
                {x,-3,3},{y,-3,3},{z,-1,1}, PlotPoints->{15,15,10},
                Passes->Automatic]
        (* A one%holed torus. The option for PlotPoints chooses
        the maximum number of passes possible that can be used in
        rendering the plot with divisions 15 by 15 by 10. *)
ImplicitPlot3D[
        x^2+y^2+z^2 == (1 - 0.2LegendreP[3, z/Sqrt[x^2+y^2+z^2]])^2,
                {x,-1.2,1.2},{y,-1.2,1.2},{z,-1.2,1.2},
                BoxStyle -> Dashing[{0.02, 0.02}],
                Axes -> True]
        (* a spheroid with zonal harmonics. Any options for
        Graphics3D can be used. (The resolution for this plot
        is the default PlotPoints->{{5,5,5},{3,3,3}}). *)
ImplicitPlot3D[x y z == 0,
                {x,-1,1}, {y,-1,1}, {z,-1,1}, PlotPoints->{{3},{3}}]
        (* Surface with points of multiplicity greater
        than 1. PlotPoints->{{3},{3}} is equivalent to
        PlotPoints->{{3,3,3},{3,3,3}} *)
ImplicitPlot3D[x^4 + y^4 == z^4, {x,-1,1}, {y,-1,1}, {z,-1,1},
                PlotPoints->{{3},{3}}]
        (* a quartic Fermat cone, this illustrates a poor choice of
        the option PlotPoints because the vertex of the cone is not
        rendered. To render the vertex either increase the
        resolution or in this case, make sure the vertex of the
        cone lies on one of the vertices of one of the subboxes
        given by PlotPoints. *)
ImplicitPlot3D[x^3 + x^2 y^2 == z^4,
                {x,-1,1}, {y,-1,1}, {z,-1,1},
                PlotPoints->{{3},{-3}}]
        (* error message generated since nonpositive numbers are
        not allowed in the PlotPoints option *)
ImplicitPlot3D[E^(x y^2) + Cos[x^2 + y^2 + z^2] == 0, {x,-3,3},
                {y,-1,1}, {z,-5,5}, PlotPoints->{{{3}},3}]
        (* error message generated because of bad listing of the
        PlotPoints option *)
*)