Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Geometric Shapes in POV-Ray
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Geometric Shapes
   Overview

Objects in "shapes3.inc"
- Segment_of_CylinderRing
- Segment_of_Torus
- Segment_of_Object
- Egg
- Egg_Shape
- Facetted_Egg
- Facetted_Egg_Shape
>Facetted_Sphere
- Ring_Sphere
- Column_N
- Column_N_AB
- Pyramid_N
- Pyramid_N_AB
- Round_Pyramid_N_out
- Round_Pyramid_N_in
- Round_Cylinder_Tube
- Rounded_Tube_AB
- Rounded_Tube
- Round_N_Tube_Polygon
- Round_Conic_Torus
- Round_Conic_Prism
- Half_Hollowed_Rounded_Cyl1
- Half_Hollowed_Rounded_Cyl2

 
                               
Geometric object definded in my include file "shapes3.inc" (formerly "shapes_lo.inc").
Facetted_Sphere
Facetted_Sphere
general syntax:
object{ Facetted_Sphere(
             Quarter_Meridian_Segments,
             Equatorial_Segments
           ) //------------------------
        texture{ ... }
      } // end of object --------------
Quarter_Meridian_Segments =
      number of segments in one quarter of a meridian,
Equatorial_Segments =
      number of segments along the equator.
The radius of the outline is scaled to 1 unit.
Example:
#include "shapes3.inc"
object{ Facetted_Sphere (6, 16 )
        texture{ pigment{ color rgb<1,1,1>}
                 finish { phong 0.1}
               } // end texture
        scale<1,1,1> rotate<0,0,0>
        translate< 0, 1, 0>
      } // end of object ------------------
Here some variations of that macro:
Facetted_Spheres
Variations of "Facetted_Sphere(...)"

Macro in detail
This is realisized by an intersection of prisms with a sphere-like faccetted outline at one end:
Facetted_Sphere
Facetted_Sphere
Facetted_Sphere - 1 prism element of the intersection
Facetted_Sphere (6, 12 ) = intersection of 12 prism elements
// ----------------------- macro Facetted_Sphere()
#macro Facetted_Sphere( Quarter_Meridian_Segments,
                        Equatorial_Segments
                      ) //------------------------

#local Facets_Silhouette =
 prism {
   -2 ,2 ,
   2*Quarter_Meridian_Segments+4
   < -2,-1.00 >,

   #local Nr    = -Quarter_Meridian_Segments;
   #local EndNr =  Quarter_Meridian_Segments;
   #while (Nr < EndNr+1)
     #local Angle_degrees = Nr* 90/EndNr;
     #local Angle_radians = radians(Angle_degrees);
   < cos(Angle_radians) , sin(Angle_radians)>,

   #local Nr = Nr + 1 ;
   #end
   < -2, 1 >,
   < -2,-1 >
 //turns prism in z direction:
 rotate<-90,0,0> scale<1,1,-1>
 } // end of prism object -------------------------

intersection{
 #local Nr = 0;                  // start
 #local EndNr = Equatorial_Segments; // end
 #while (Nr < EndNr)

 object{ Facets_Silhouette
         rotate<0,Nr * 360/EndNr,0>
       } //------------------------------

 #local Nr = Nr + 1;    // next Nr
 #end // ---------------  end of loop

} // end of intersection

#end //--------------- end of macro Facetted_Sphere()

© Friedrich A. Lohmüller, 2013
www.f-lohmueller.de