Points In Three-Dimensional Space

Initialization

Needs["Graphics`Colors`"];

Getting Started

You have seen and used a 2-dimensional coordinate axes to graph points and lines.  We will now extend the axes to 3-dimensions so we can visualize points, planes, and lines in space.  Let's look at the 3-D axis.

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->{{-h,h},{-h,h},{-h,h}},
			AspectRatio->Automatic,
			Axes->True,
			AxesLabel->{"x","y","z"}];

Points in 3-D

When the z axis is added, the ordered pairs (x,y) become ordered triples (x,y,z).  These graphs show points in various locations in 3-D space.  Study the position of the point according to the coordinates shown to the right.

Clear[w,t,h]
Table[Show[GraphicsArray[{Show[threedims,
ParametricPlot3D[{2.5 Sin[w],2.5 Cos[w],w},{w,-Pi-.01,t},
			AspectRatio->Automatic,
			Axes->True,
			AxesLabel->{"x","y","z"},
			ViewPoint->{2.951, 1.338, 0.975},
			DisplayFunction->Identity],
           Graphics3D[
             {RGBColor[Abs[Sin[t]],Abs[Cos[t]],Abs[N[t/Pi]]],
		      PointSize[.02],
		      Point[{2.5 Sin[t],2.5 Cos[t],t}]}],
		    PlotRange->All,
			AspectRatio->Automatic,
			Axes->True,
			AxesLabel->{"x","y","z"},
			ViewPoint->{2.951, 1.338, 0.975},
			DisplayFunction->Identity], 
	Graphics[{Text["X-Coordinate ", {3,3}, {1,0}],
               Text[N[Sin[t]],{3,3},{-1,0}],
	           Text["Y-Coordinate ", {3,4}, {1,0}],
	           Text[N[Cos[t]],{3,4},{-1,0}],
	           Text["Z-Coordinate ", {3,5}, {1,0}],
	           Text[N[t],{3,5},{-1,0}]}]}],
	           DisplayFunction->$DisplayFunction],
{t,-Pi,Pi,Pi/6}];