Planes in 3-Dimensional Space

Initialization

Needs["Graphics`Colors`"];

Planes

A plane is defined by 3 non-collinear points, or 2 parallel lines, or 2 intersecting lines, or a line and a point not on the line.  The graph shows a plane moving through 3-D space.

h=5;
spacer=h/10;
threedims=
	Graphics3D[{
			{Blue,Line[{{-h,0,0},{h,0,0}}]},
				Text["x",{h + spacer,0,0}],
			{Purple,Line[{{0,-h,0},{0,h,0}}]},
				Text["y",{0, h+spacer,0}],
			{Red,Line[{{0,0,-h},{0,0,h}}]},
				Text["z",{0,0,h + spacer}]}];

Show[threedims, PlotRange->All,Boxed->False,
				ViewPoint->{2.549, 1.547, 1.600}];

plane1=Graphics3D[Polygon[{{0,2,2},{0,2,-2},{0,-2,-2},
						  {0,-2,2}}]];
plane2=Graphics3D[Polygon[{{2,0,2},{2,0,-2},{-2,0,-2},
						  {-2,0,2}}]];

plane3=Graphics3D[Polygon[{{2,2,0},{2,-2,0},{-2,-2,0},
						  {-2,2,0}}]];

Do[Show[Graphics3D[Polygon[{{x,2,2},{x,2,-2},{x,-2,-2},{x,-2,2}}]],
	     threedims,PlotRange->All,Boxed->False],
   {x,-2,2}]

Notice that the plane is parallel to the z-axis and perpendicular to the x- and y-axes.

Visualizing Planes in 3-D space

Now let's look at 3 different planes from various viewpoints.

Do[vp=-0.5v;
   Show[plane1,plane2,plane3,threedims,
        PlotRange->All,
        AspectRatio->1,
        Boxed->False, 
        ViewPoint->{2+vp,-vp+1,2+vp}],
   {v,-2,2,0.5}]

viewlist2=Table[Show[plane1,plane2,plane3,threedims,
                      PlotRange->All,
                      AspectRatio->1,
                       Boxed->False, 
        ViewPoint->{2,vp+1,2-vp}],
   {vp,-2,2,0.5}];

Summary--Lights...Camera...Action!!!!!!!!!!!!

By combining this as one movie you can see how different portions of the picture disappear and then reappear depending on our point of view.

Do[Show[GraphicsArray[{
Show[plane1,plane2,plane3,threedims,
                      PlotRange->All,
                      AspectRatio->1,
                      Boxed->False, 
                      ViewPoint->{2,vp+1,2-vp},
                      SphericalRegion->True,
                      DisplayFunction->Identity],
Show[plane1,plane2,plane3,threedims,
                     PlotRange->All,
                     AspectRatio->1,
                     Boxed->False, 
                     SphericalRegion->True,
                     ViewPoint->{2+vp,-vp+1,2+vp},
                     DisplayFunction->Identity]}],
DisplayFunction->$DisplayFunction],{vp,-2,2,0.5}];