File:Blue Trefoil Knot.png

Summary

Description
English: A trefoil knot.
Date
Source Own work
Author Jim.belk

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Category:Self-published work#Blue%20Trefoil%20Knot.pngCategory:PD-self#Blue%20Trefoil%20Knot.png

Source

This image was created using POV-Ray for Windows, version 3.6. The image was rendered to an 1800 x 1800 square, using 0.3 anti-aliasing.

#include "colors.inc"
     
/* Makes a trefoil knot using a hypotrochoid */
    
background { color White }

global_settings { assumed_gamma 1.0}

camera
  {
  location <0, 0, -25>
  right <1,0,0> up <0,1,0>
  look_at  <0, 0, 0>
  angle 5
  }


light_source
  {
  <0, 20, -50>
  color White
  area_light <5, 0, 0>, <0, 5, 0>, 10, 10  /* very slow, decrease 10 to 2 for experiments */
  adaptive 3
  }
  
#declare r_tube = 0.1;
#declare num_steps = 36;
#declare step_size = 1/num_steps;
              

sphere_sweep
  {
  cubic_spline num_steps+3,
  #declare N = -1;
  #while(N <= num_steps + 1)
    #declare theta = 2 * pi * N * step_size;
    <0.3*( 2*sin(2*theta)-sin(theta) ), 0.3*( 2*cos(2*theta)+cos(theta) ), 0.3*sin(3*theta)>, r_tube
    /* uses a hypotrochoid */
    #declare N = N + 1;
  #end
  pigment { color rgb <0,0.25,1> }
  finish          
    {
    ambient 0.15
    diffuse 0.85
    brilliance 2
    phong 0.25
    phong_size 5
    }
  }


plane
  {
  <0,0,-1>, -0.4
  pigment { color White }
  finish
    {
    ambient 0.35
    diffuse 0.65
    }
  }
Category:Blue knots rendered#3%201 Category:Knots and links on transparent background Category:Trefoil knot diagrams with 3-fold rotational symmetry Category:Topological graph theory
Category:Blue knots rendered Category:Created with Persistence of Vision Category:Knots and links on transparent background Category:PD-self Category:Self-published work Category:Topological graph theory Category:Trefoil knot diagrams with 3-fold rotational symmetry