cpt-city

Lewitt-Kaiser-Bessel

R.M. Lewitt has proposed a radial basis function for the discretization of tomographic problems; the radial dependance of the function is a generalised version of the Kaiser-Bessel window used in signal processing. Here we render the function in two dimensions with POV-Ray, using the Reds_09 colour scheme by Cynthia Brewer.

The script uses a large datafile, lkb3dpov.inc, which is a triangular mesh of the function values.

#include "Reds_09.inc"
#include "colors.inc"

camera {
    up       <0,1,0>
    right    <1.25,0,0> 
    location <28,25,-40>
    angle    4.0
    look_at  <0,0.3,0>
}

background {
    color Gray90
}

/* texture for the included mesh */

#declare PMtext =
texture { 
    pigment { 
        gradient <0, 1, 0>
        translate -0.1
        color_map { Reds_09 }
        scale 1.2
    }
    finish {
        phong 0.02
        phong_size 15
    }
}

light_source {
    <-30,40,-40>
    color White
}

light_source {
    <-30,40,-140>
    color White
}

/* the axes */

cylinder {
  <-2,0,0>,
  <2,0,0>,
  0.0075
  texture { pigment { color Black }}
}

cone {
   <2,0,0>, 0.03
   <2.12,0,0>, 0
   texture { pigment { color Black }}
}

cylinder {
  <0,0,-2>,
  <0,0,2>,
  0.0075
  texture { pigment { color Black }}
}

cone {
   <0,0,2>, 0.03
   <0,0,2.12>, 0
   texture { pigment { color Black }}
}

cylinder {
  <0,0,0>,
  <0,1.5,0>,
  0.0075
  texture { pigment { color Black }}
}

cone {
   <0,1.5,0>, 0.03
   <0,1.62,0>, 0
   texture { pigment { color Black }}
}

#include "lkb3dpov.inc"