Segment_of_Torus

Segment of a Torus

general syntax:

object{ Segment_of_Torus (R_major, R_minor, Segment_Angle)
        texture{ ... ... }
      } // end of object ------------

With:
R_major = the major radius of the torus,
R_minor = the minor radius of the torus,
Segment_Angle = the angle of the segment of the torus.

For reasons of compatibility the old macro "Torus_Segment"
still exists - there the angle was orientated in a righthanded sense!

Samples:

#include "shapes_lo.inc"
object{ Segment_of_Torus( 1.00, 0.25, -145)
        texture { pigment{color rgb<1,0.7,0>}
                  finish {ambient 0.15 diffuse 0.85 phong 1}
                } // end of texture
        rotate<-90,0,0> translate<0,1,0>
      } // end of Segment_of_Torus(...) -----------------------


object{ Segment_of_Torus( 0.60, 0.25, -275)
        texture { pigment{color rgb<1,0.4,0>}
                  finish {ambient 0.15 diffuse 0.85 phong 1}
                } // end of texture
        rotate<0,30,0> translate<0.5,0.3,-0.5>
      } // end of Segment_of_Torus(...) -----------------------

object{ Segment_of_Torus( 0.60, 0.50, -60)
        texture { pigment{color rgb<1,0.2,0>}
                  finish {ambient 0.15 diffuse 0.85 phong 1}
                } // end of texture
        rotate<-90,0,-190> translate<0,1,0>
      } // end of Segment_of_Torus(...) -----------------------

Macro in detail

For this we have to consider two cases:
1. abs(Segment_Angle) <= 180 degrees (just an intersection of the torus and the two boxes) and
2. abs(Segment_Angle) > 180 degrees (an intersection of the torus and the union of the two boxes):

//--------------------------------------------------------Segment_of_Torus macro #macro Segment_of_Torus ( R_major, R_minor, Segment_Angle) //--------------------------------------------------------------------------- #local D = 0.00001; #if (Segment_Angle < 0) #local Negativ_Flag = 1; #local Segment_Angle = -Segment_Angle; #else #local Negativ_Flag = 0; #end #if (Segment_Angle > 360) #local Segment_Angle = mod(Segment_Angle,360); #end intersection{ torus { R_major, R_minor } #if (Segment_Angle > 180) union{ #end // use union! box { <-1,-1,0>,<1,1,1> scale < R_major+R_minor+D, R_minor+D, R_major+R_minor+D> }// end of box box { <-1,-1,-1>,<1,1,0> scale < R_major+R_minor+D, R_minor+D, R_major+R_minor+D> rotate < 0,-Segment_Angle,0 > }// end of box #if (Segment_Angle > 180) } #end // end of union, if union is used! #if (Negativ_Flag = 0) rotate<0, Segment_Angle,0> #end } // end of intersection #end // ----------------------------- end of macro Segment_of_Torus

The following images show how this macro works
(the boxes are visualizised in texture glass):

Segment_of_Torus

abs(Segment_Angle) <= 180 degrees
R_major = 1.00, R_minor = 0.25, Angle = -145 abs(Segment_Angle) > 180 degrees
R_major = 1.00, R_minor = 0.25, Angle = -215

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

This shape is definded as "macro" in my include file "shapes_lo.inc":

Segment_of_Torus

For reasons of compatibility the old macro "Torus_Segment"
still exists - there the angle was orientated in a righthanded sense!

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

This shape is definded as "macro" in my include file "shapes_lo.inc":

Segment_of_Torus

For reasons of compatibility the old macro "Torus_Segment" still exists - there the angle was orientated in a righthanded sense!

For reasons of compatibility the old macro "Torus_Segment"
still exists - there the angle was orientated in a righthanded sense!