//                       Spiral Test File                  december 2010

//                           By J.J.Frank

#declare Major_Radius = 1;
#declare Minor_X_Radius = 0.7;
#declare Minor_Y_Radius = 0.1;
#declare Speed = -1;
#declare Turns = 5.5;


//CONTROL SECTION        
#declare Major_Radius = ((Major_Radius != 0) ? abs(Major_Radius) : 
1);
#declare Minor_X_Radius = ((Minor_X_Radius != 0) ? 
abs(Minor_X_Radius) : 0.1);
#declare Minor_Y_Radius = ((Minor_Y_Radius != 0) ? 
abs(Minor_Y_Radius) : 0.01);
#declare Speed = ((Speed != 0) ? Speed : 1);
#declare Turns = ((Turns != 0) ? abs(Turns) : 1);

//INTERNAL PARAMETERS
#if (Speed>0)
  #declare Up = true;                          // Up = 
anti-clockwise
#else
  #declare Up = false;
  #declare Speed = abs(Speed);
#end
#declare Ellipticity = Minor_X_Radius / Minor_Y_Radius;       // POLY 
8
#declare Slope       = Speed / 4;                             // POLY 
8
#declare A2          = Minor_X_Radius * Minor_X_Radius;       // POLY 
8
#declare P2          = Slope * Slope;                         // POLY 
8
#declare R2          = Major_Radius * Major_Radius;           // POLY 
8
#declare T2          = Ellipticity * Ellipticity;             // POLY 
8
#declare Phi         = degrees(atan2(Slope,1));               // 
Clipping
#declare Thick       = ((Minor_X_Radius > Minor_Y_Radius) ? 	// 
Clipping
                         Minor_X_Radius : Minor_Y_Radius);
#declare Long        = Major_Radius * sqrt(1 + P2);           // 
Clipping
#declare High        = Slope * Major_Radius;                  // 
Building
#declare IntTurns    = int(Turns);              	            // 
Building
#declare Fraction    = Turns - IntTurns;                      // 
Building

/**/
// *******angle 45*************************************
camera { location < 2, 5.5, -5*1 >
         look_at  < 0.1, 5.5-2,   0 > 
         angle 45}  

/*
// *******angle 15***************************************
camera { location < 2, 5.5, -5*3.75>
         look_at  < 0.1, 5.5-2,   0 > 
         angle 15}    
*/
/*
// *******angle 05**************************************
camera { location < 2, 5.5, -5*14 >
         look_at  < 0.1, 5.5-2,   0 > 
         angle 5}
// ******************************************************
*/
// *************************** Poly 8 **********************************

#declare Spiral_Shape = object { poly { 8
// 165 factors
/*  x^8         */   <  1
/*  x^7.y       */   ,  0
/*  x^7.z       */   ,  0
/*  x^7         */   ,  0
/*  x^6.y^2     */   ,  2*T2
/*  x^6.y.z     */   ,  0
/*  x^6.y       */   ,  0
/*  x^6.z^2     */   ,  4
/*  x^6.z       */   ,  0
/*  x^6         */   ,  -2*((1-P2*T2)*R2+A2)
/*  x^5.y^3     */   ,  0
/*  x^5.y^2.z   */   ,  0
/*  x^5.y^2     */   ,  0
/*  x^5.y.z^2   */   ,  0
/*  x^5.y.z     */   ,  0
/*  x^5.y       */   ,  -8*R2*Slope*T2
/*  x^5.z^3     */   ,  0
/*  x^5.z^2     */   ,  0
/*  x^5.z       */   ,  0
/*  x^5         */   ,  0
/*  x^4.y^4     */   ,  T2*T2
/*  x^4.y^3.z   */   ,  0
/*  x^4.y^3     */   ,  0
/*  x^4.y^2.z^2 */   ,  6*T2
/*  x^4.y^2.z   */   ,  0
/*  x^4.y^2     */   ,  2*T2*((1-P2*T2)*R2-A2)
/*  x^4.y.z^3   */   ,  0
/*  x^4.y.z^2   */   ,  0
/*  x^4.y.z     */   ,  0
/*  x^4.y       */   ,  0
/*  x^4.z^4     */   ,  6
/*  x^4.z^3     */   ,  0
/*  x^4.z^2     */   ,  -2*((3-2*P2*T2)*R2+3*A2)
/*  x^4.z       */   ,  0
/*  x^4         */   ,  ((1+P2*T2)*R2-A2)*((1+P2*T2)*R2-A2)
/*  x^3.y^5     */   ,  0
/*  x^3.y^4.z   */   ,  0
/*  x^3.y^4     */   ,  0
/*  x^3.y^3.z^2 */   ,  0
/*  x^3.y^3.z   */   ,  0
/*  x^3.y^3     */   ,  0
/*  x^3.y^2.z^3 */   ,  0
/*  x^3.y^2.z^2 */   ,  0
/*  x^3.y^2.z   */   ,  0
/*  x^3.y^2     */   ,  0
/*  x^3.y.z^4   */   ,  0
/*  x^3.y.z^3   */   ,  0
/*  x^3.y.z^2   */   ,  -16*R2*Slope*T2
/*  x^3.y.z     */   ,  0
/*  x^3.y       */   ,  0
/*  x^3.z^5     */   ,  0
/*  x^3.z^4     */   ,  0
/*  x^3.z^3     */   ,  0
/*  x^3.z^2     */   ,  0
/*  x^3.z       */   ,  0
/*  x^3         */   ,  0
/*  x^2.y^6     */   ,  0
/*  x^2.y^5.z   */   ,  0
/*  x^2.y^5     */   ,  0
/*  x^2.y^4.z^2 */   ,  2*T2*T2
/*  x^2.y^4.z   */   ,  0
/*  x^2.y^4     */   ,  0
/*  x^2.y^3.z^3 */   ,  0
/*  x^2.y^3.z^2 */   ,  0
/*  x^2.y^3.z   */   ,  0
/*  x^2.y^3     */   ,  0
/*  x^2.y^2.z^4 */   ,  6*T2
/*  x^2.y^2.z^3 */   ,  0
/*  x^2.y^2.z^2 */   ,  2*T2*((2-P2*T2)*R2-2*A2)
/*  x^2.y^2.z   */   ,  0
/*  x^2.y^2     */   ,  0
/*  x^2.y.z^5   */   ,  0
/*  x^2.y.z^4   */   ,  0
/*  x^2.y.z^3   */   ,  0
/*  x^2.y.z^2   */   ,  0
/*  x^2.y.z     */   ,  0
/*  x^2.y       */   ,  0
/*  x^2.z^6     */   ,  4
/*  x^2.z^5     */   ,  0
/*  x^2.z^4     */   ,  -2*((3-P2*T2)*R2+3*A2)
/*  x^2.z^3     */   ,  0
/*  x^2.z^2     */   ,  2*(R2-A2)*((1+P2*T2)*R2-A2)
/*  x^2.z       */   ,  0
/*  x^2         */   ,  0
/*  x.y^7       */   ,  0
/*  x.y^6.z     */   ,  0
/*  x.y^6       */   ,  0
/*  x.y^5.z^2   */   ,  0
/*  x.y^5.z     */   ,  0
/*  x.y^5       */   ,  0
/*  x.y^4.z^3   */   ,  0
/*  x.y^4.z^2   */   ,  0
/*  x.y^4.z     */   ,  0
/*  x.y^4       */   ,  0
/*  x.y^3.z^4   */   ,  0
/*  x.y^3.z^3   */   ,  0
/*  x.y^3.z^2   */   ,  0
/*  x.y^3.z     */   ,  0
/*  x.y^3       */   ,  0
/*  x.y^2.z^5   */   ,  0
/*  x.y^2.z^4   */   ,  0
/*  x.y^2.z^3   */   ,  0
/*  x.y^2.z^2   */   ,  0
/*  x.y^2.z     */   ,  0
/*  x.y^2       */   ,  0
/*  x.y.z^6     */   ,  0
/*  x.y.z^5     */   ,  0
/*  x.y.z^4     */   ,  -8*R2*Slope*T2
/*  x.y.z^3     */   ,  0
/*  x.y.z^2     */   ,  0
/*  x.y.z       */   ,  0
/*  x.y         */   ,  0
/*  x.z^7       */   ,  0
/*  x.z^6       */   ,  0
/*  x.z^5       */   ,  0
/*  x.z^4       */   ,  0
/*  x.z^3       */   ,  0
/*  x.z^2       */   ,  0
/*  x.z         */   ,  0
/*  x           */   ,  0
/*  y^8         */   ,  0
/*  y^7.z       */   ,  0
/*  y^7         */   ,  0
/*  y^6.z^2     */   ,  0
/*  y^6.z       */   ,  0
/*  y^6         */   ,  0
/*  y^5.z^3     */   ,  0
/*  y^5.z^2     */   ,  0
/*  y^5.z       */   ,  0
/*  y^5         */   ,  0
/*  y^4.z^4     */   ,  T2*T2
/*  y^4.z^3     */   ,  0
/*  y^4.z^2     */   ,  0
/*  y^4.z       */   ,  0
/*  y^4         */   ,  0
/*  y^3.z^5     */   ,  0
/*  y^3.z^4     */   ,  0
/*  y^3.z^3     */   ,  0
/*  y^3.z^2     */   ,  0
/*  y^3.z       */   ,  0
/*  y^3         */   ,  0
/*  y^2.z^6     */   ,  2*T2
/*  y^2.z^5     */   ,  0
/*  y^2.z^4     */   ,  2*T2*(R2-A2)
/*  y^2.z^3     */   ,  0
/*  y^2.z^2     */   ,  0
/*  y^2.z       */   ,  0
/*  y^2         */   ,  0
/*  y.z^7       */   ,  0
/*  y.z^6       */   ,  0
/*  y.z^5       */   ,  0
/*  y.z^4       */   ,  0
/*  y.z^3       */   ,  0
/*  y.z^2       */   ,  0
/*  y.z         */   ,  0
/*  y           */   ,  0
/*  z^8         */   ,  1
/*  z^7         */   ,  0
/*  z^6         */   ,  -2*(R2+A2)
/*  z^5         */   ,  0
/*  z^4         */   ,  (R2-A2)*(R2-A2)
/*  z^3         */   ,  0
/*  z^2         */   ,  0
/*  z           */   ,  0
/*  C           */   ,  0.0001  >    sturm    }    // end poly
} // end object

// With C = 0 you can get a system break (in 1997 with version 3.1).

//HALF TURN BUILDING BLOCK
#if ((IntTurns >=1) | (Fraction >= 0.5))       // Only when it is 
needed.
  #declare HalfSpiral = object {
    Spiral_Shape                               
    #if ((Long - Thick - 0.000001) > 0 )       // Then the inner 
cylinder is
      clipped_by {                             //  possible.
          plane { ((Up = true) ? -z : z), 0 } }   // Front or back 
half.
    #else  //#if ((Long - Thick - 0.000001) > 0 )
      clipped_by {
          plane { ((Up = true) ? -z : z), 0 } } 
    #end  //#else ((Long - Thick - 0.000001) > 0 )
    bounded_by { clipped_by }                      // Saves lots of 
render time.
  } // end object HalfSpiral
#end  //#If ((IntTurns >=1) | (Fraction >= 0.5))

//COMPLETE TURN BUILDING BLOCK       
#if (IntTurns >=1)                                 // Only when it is 
needed.
  #declare OneSpiral = 
    union { object { HalfSpiral translate  High * y }
            object { HalfSpiral rotate 180 * y
                                translate  3 * High * y }  }
#end

//PARTIAL TURN BUILDING BLOCK
#if ((Fraction > 0) & (Fraction != 0.5))           // Only when it is 
needed.
  #declare PartSpiral = object {
    Spiral_Shape
    #if ((Long - Thick - 0.000001) > 0 )
      clipped_by {
          plane { (Up = true ? -z : z), 0 } 
          plane { (Up = true ? z : -z) , 0 
                  rotate ((Fraction > 0.5) ? (Fraction - 0.5) : 
Fraction) * 
                         (Up = true ? 360 : -360) * -y } } 
    #else  //#if ((Long - Thick - 0.000001) > 0 )
      clipped_by {
          plane { (Up = true ? -z : z), 0 }
          plane { (Up = true ? z : -z) , 0 
                  rotate ((Fraction > 0.5) ? (Fraction - 0.5) : 
Fraction) *
                         (Up = true ? 360 : -360) * -y } } 
    #end  //#else ((Long - Thick - 0.000001) > 0 )
    bounded_by { clipped_by } 
  } // end object PartSpiral 
#end //#if ((Fraction > 0) & (Fraction != 0.5))

//BUILDING OF THE SPIRAL
#declare Count = 0;
#if (IntTurns >= 1)                             // >= 1 complete 
turn.
  #declare Spiral = OneSpiral;                   // First complete 
turn.
  #declare Count = Count + 4;
  #while (Count < (IntTurns * 4) )              // More complete turns.
    #declare Spiral = union {
      object { Spiral }
      object { OneSpiral  translate Count * High * y } }
    #declare Count = Count + 4;
  #end  //#while (Count < (IntTurns * 4) )
  #if (Fraction>0)                              // Fractional turn.
    #declare Spiral = union {
      object { Spiral }                         // What we already had 
build.
      #if (Fraction>=0.5)
        object { HalfSpiral translate (Count + 1) * High * y }   // « 
turn.
      #end  //#if (Fraction>=0.5)
      #if (Fraction != 0.5)                      // Fractional turn.
        object { PartSpiral
                 translate (Count + (Fraction > 0.5 ? 3 : 1) ) * High * 
y
                 rotate (Fraction > 0.5 ? 180 : 0) * y }
      #end  //#if (Fraction != 0.5)
      } // end union
  #end  //#if (Fraction>0)
#else  //#if (IntTurns >= 1)                     // < 1 complete turn.
  #if (Fraction>=0.5)                            // >= 0.5 turn.
    #declare Spiral = union {
      object { HalfSpiral translate High * y }   // « turn.
      #if (Fraction > 0.5)                       // Fractional turn.
        object { PartSpiral
                 translate 3 * High * y 
                 rotate 180 * y }
      #end  //#if (Fraction > 0.5)
    } //end union
  #else  //#if (Fraction>=0.5)                    // < 0.5 turn.
      #declare Spiral =
        object { PartSpiral                       // Fractional turn.
                 translate High * y }
  #end  //#else (Fraction>=0.5)
#end  //#else (IntTurns >= 1)

// end of spiral.inc
#declare Spiral1 = Spiral

#include "colors.inc"

object { Spiral1 pigment { checker scale 0.1 } }
object { plane { y, 0 } pigment { color Yellow } }

light_source { <  100,  100, -100 > color White }  // 
rechts,boven,achter
light_source { < -100,  100, -100 > color White }  // links,boven,achter
light_source { < -100,  100,  100 > color White }  // links,boven,voor
light_source { <  100,  100,  100 > color White }  // rechts,boven,voor