// Sphere of Torii - The math doesn't work :(
// Peter Houston  <houston.graphics@iname.com>

#version 3.1;

#include "colors.inc"

global_settings
{
  assumed_gamma 1.0
}

// ----------------------------------------
camera
{
  location  <0.0, .5, -3.5>
  direction 1.5*z
  right     4/3*x
  look_at   <0.0, 0.0,  0.0>
}

sky_sphere
{
  pigment
  {
    gradient y
    color_map { [0.0 color blue 0.6] [1.0 color rgb 1] }
  }
}

light_source
{
  0*x // light's position (translated below)
  color red 1.0  green 1.0  blue 1.0  // light's color
  translate <-30, 30, -30>
}

// ----------------------------------------
plane { y, -1 pigment {color rgb <0.7,0.5,0.3>}}

#macro Rotate_Torus ( X , Y , Z )

// Calculate angle of rotation on the Y Axis

#declare LengthP=sqrt((Z*Z)+(X*X));
#declare YTan=tan(Z/X);
#declare YRotAngle=atan2(YTan,1);

// Calculate angle of Rotation on the Z Azis

#declare ZTan=tan(LengthP/(1-Y));
#declare ZRotAngle=atan2(ZTan,1);
torus {0.15, 0.015
		translate <0,1,0>
		rotate y*-YTan//YRotAngle
		rotate z*-ZTan//ZRotAngle
		pigment {Red}
}

// Marker for reference these should end up in the centre of the torii
sphere {<X,Y,Z>,.05 pigment {Yellow}}
#end 



#declare Torus_Ball_Eighth =
union {
//	joints
	Rotate_Torus ( 0.0000000000, 1.0000000000, 0.0000000000 )
	Rotate_Torus ( 0.0000000000, 0.9807852804, 0.1950903220 )
	Rotate_Torus ( 0.1950903220, 0.9807852804, 0.0000000000 )
	Rotate_Torus ( 0.0000000000, 0.9238795325, 0.3826834324 )
	Rotate_Torus ( 0.1987568534, 0.9596829823, 0.1987568534 )
	Rotate_Torus ( 0.3826834324, 0.9238795325, 0.0000000000 )
	Rotate_Torus ( 0.0000000000, 0.8314696123, 0.5555702330 )
	Rotate_Torus ( 0.2088465989, 0.8903200345, 0.4046150446 )
	Rotate_Torus ( 0.0000000000, 0.7071067812, 0.7071067812 )
	Rotate_Torus ( 0.2113248654, 0.7886751346, 0.5773502692 )
   	Rotate_Torus ( 0.4082482905, 0.8164965809, 0.4082482905 )
   	Rotate_Torus ( 0.4046150446, 0.8903200345, 0.2088465989 )
   	Rotate_Torus ( 0.5555702330, 0.8314696123, 0.0000000000 )
	Rotate_Torus ( 0.5773502692, 0.7886751346, 0.2113248654 )
	Rotate_Torus ( 0.7071067812, 0.7071067812, 0.0000000000 )
	Rotate_Torus ( 0.0000000000, 0.5555702330, 0.8314696123 )
   	Rotate_Torus ( 0.2113248654, 0.5773502692, 0.7886751346 )
	Rotate_Torus ( 0.0000000000, 0.3826834324, 0.9238795325 )
	Rotate_Torus ( 0.2088465989, 0.4046150446, 0.8903200345 )
	Rotate_Torus ( 0.4082482905, 0.4082482905, 0.8164965809 )
	Rotate_Torus ( 0.0000000000, 0.1950903220, 0.9807852804 )
	Rotate_Torus ( 0.1987568534, 0.1987568534, 0.9596829823 )
	Rotate_Torus ( 0.0000000000, 0.0000000000, 1.0000000000 )
	Rotate_Torus ( 0.1950903220, 0.0000000000, 0.9807852804 )
	Rotate_Torus ( 0.3826834324, 0.0000000000, 0.9238795325 )
	Rotate_Torus ( 0.4046150446, 0.2088465989, 0.8903200345 )
	Rotate_Torus ( 0.5773502692, 0.2113248654, 0.7886751346 )
	Rotate_Torus ( 0.5555702330, 0.0000000000, 0.8314696123 )
	Rotate_Torus ( 0.7071067812, 0.0000000000, 0.7071067812 )
	Rotate_Torus ( 0.7886751346, 0.5773502692, 0.2113248654 )
	Rotate_Torus ( 0.8314696123, 0.5555702330, 0.0000000000 )
	Rotate_Torus ( 0.8164965809, 0.4082482905, 0.4082482905 )
	Rotate_Torus ( 0.8903200345, 0.4046150446, 0.2088465989 )
	Rotate_Torus ( 0.9238795325, 0.3826834324, 0.0000000000 )
	Rotate_Torus ( 0.7886751346, 0.2113248654, 0.5773502692 )
	Rotate_Torus ( 0.8903200345, 0.2088465989, 0.4046150446 )
	Rotate_Torus ( 0.8314696123, 0.0000000000, 0.5555702330 )
	Rotate_Torus ( 0.9238795325, 0.0000000000, 0.3826834324 )
	Rotate_Torus ( 0.9596829823, 0.1987568534, 0.1987568534 )
	Rotate_Torus ( 0.9807852804, 0.1950903220, 0.0000000000 )
	Rotate_Torus ( 0.9807852804, 0.0000000000, 0.1950903220 )
	Rotate_Torus ( 1.0000000000, 0.0000000000, 0.0000000000 )
	Rotate_Torus ( 0.6396021491, 0.4264014327, 0.6396021491 )
	Rotate_Torus ( 0.6396021491, 0.6396021491, 0.4264014327 )
	Rotate_Torus ( 0.4264014327, 0.6396021491, 0.6396021491 )
}



#declare Torus_Ball_Hemisphere = 
union {
	object { Torus_Ball_Eighth }
	object { Torus_Ball_Eighth rotate <0, 90, 0> }
	object { Torus_Ball_Eighth rotate <0, 180, 0> }
	object { Torus_Ball_Eighth rotate <0, 270, 0> }
}


#declare Torus_Ball = 
union {
	object { Torus_Ball_Hemisphere }
	object { Torus_Ball_Hemisphere rotate <180, 0, 0> }
}


//object {Torus_Ball_Eighth}
object {Torus_Ball}