Column_N
A column with N edges

Pyramid_N
A pyramid with N edges

Regular Column with N Edges

general syntax:

object{ Column_N (N, Radius, Height)
        texture{ ... ... }
      } // end of object ------------

Here N >2 = the number of edges,
Radius = means the half width and
Height is the total height of the column.

Sample:

#include "shapes_lo.inc"
object{ Column_N (14, 1.8, 1.30 )
        texture { pigment{color rgb<1,1,1>}
                  finish {ambient 0.05
                          diffuse 0.95
                          phong 1}
                } // end of texture
      } // end of object ------------------

Regular Pyramid with N Edges
also truncated

general syntax:

object{ Pyramid_N (N, Radius1, Radius2, Height)
        texture{ ... ... }
      } // end of object ------------

Here N >2 = the number of edges,
Radius1 = means the half base width,
Radius2 = means the half top width and
Height is the total height of the pyramid.
If we choose Radius2 = 0 the pyramid will not be truncated.

Sample:

#include "shapes_lo.inc"
object{ Pyramid_N (14, 1.8, 1.30, 1.00 )
        texture { pigment{color rgb<1,1,1>}
                  finish {ambient 0.05
                          diffuse 0.95
                          phong 1}
                } // end of texture
      } // end of object ------------------

Macros in detail

To show how it works we start with the Pyramid_N macro :

//--------------------------------------------------------- Pyramid_N macro #macro Pyramid_N (N, Radius1, Radius2, Height) //------------------------------------------------------------------------- #local D= 0.00001; intersection{ #local Nr = 0; // start #local EndNr = N; // end #while (Nr < EndNr) // linear prism in z-direction: prism { -2.00 ,2.00 , 5 // from z1, to z2 , number of points (first = last) <-2.00, 0.00>, < 1.00, 0.00>, < 0.00+Radius2/Radius1,1.00>, <-2.00,1.00>, <-2.00, 0.00> rotate<-90,0,0> scale<1,1,-1> //turns prism in z direction! scale <Radius1+Nr*D,Height+Nr*D,Radius1+Nr*D> rotate<0,Nr * 360/EndNr,0> } // end of prism ---------------------------------------------------- #local Nr = Nr + 1; // next Nr #end // ---------------- end of loop } // end of intersection #end // ------------------------------------------------------ end of macro

If we start this macro with N = 1 the result will be a degenerated intersection out of just one prism.
So all we have to do is turn around the y axis these elements by 360/N and intersect them all:

Samples one prism Samples intersection of prisms

N = 1, Radius1 = 1.70, Radius2 = 1.10, Height= 1.50 N = 11, Radius1 = 1.70, Radius2 = 1.10, Height= 1.50

A Column with N edges is nothing else than a truncated pyramid with top radius = base radius, so the following macro will work together with the above macro:

//--------------------------------------------- Column_N macro
#macro Column_N  (N, Radius, Height )
//------------------------------------------------------------
object{ Pyramid_N (N, Radius, Radius, Height )
      }
#end // ---------------------------------------- end of  macro

N = 3, Radius = 1.00, Height= 0.50

N = 14, Radius = 1.80, Height= 1.30

N = 7, Radius = 2.00, Height= 1.00

N = 7, Radius1 = 2.00, Height= 1.00

POV-Ray Raytracer Descriptions and Examples by Friedrich A. Lohmüller

These shapes are definded as "macro" in my include file "shapes_lo.inc":

Column_N
A column with N edges

Pyramid_N
A pyramid with N edges

POV-Ray Raytracer Descriptions and Examples by Friedrich A. Lohmüller

These shapes are definded as "macro" in my include file "shapes_lo.inc":

Column_NA column with N edges

Pyramid_NA pyramid with N edges

Column_N
A column with N edges

Pyramid_N
A pyramid with N edges