Points represented by spheres:

It's highly recommended to define our own variables for all points and vectors we want to use by "#declare". This makes it much easier to use these values in the graphical presentation. Notice: The center O =<0,0,0> is predefined in POV-Ray by "o"!
Sample:
Definition of the points:

#declare P  = < 3, 2, 1.5>;
#declare Q  = < 0, 1, 2>;
#declare R  = < 1.5, 0,-4>;

The representation
(drawing) of the points P, Q and R
will take place by this:

sphere{ P, Rp  pigment{color Red}}
sphere{ Q, Rp  pigment{color Red}}
sphere{ R, Rp  pigment{color Red}}

Points: represented by "sphere{ P, Rp tpigment{color ...}}".
Problem: The concret position in the space is not unequivocal!

Unequivocal Marking of Positions:

Method 1:
Cylinder to the Ground Plane

Here we use a macro of my include file for the analytical geometry analytical_g.inc, which put a cylinder vertical beneath the according point:

sphere{ P, Rp  pigment{color Red}}
object{ Show_Y( P, Rl/2)
        pigment{color Yellow}}

Unequivocal representation of points: Method 1: Marking the positions by connecting point with cylinders to the ground plane.

Unequivocal Marking of Positions:

Method 2:
Wireframe Box

The following sample shows how this works:

sphere{ P, Rp  pigment{color Red}}
object{ Wire_Box( o, P, Rl/2,0)
        pigment{color Yellow }}

The Wire_box macro can also be used if one or more components are zero, it works also with "degenerated" boxes!!!

Unequivocal representation of points Method 2: Marking the positions with wireframe boxes.

Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file