#local _Pi = 3.141592654;

#macro involute_point (r_theta) <r_theta.u/cos(r_theta.v), tan(r_theta.v)-r_theta.v> #end
#macro make_2d_point (r_theta) <r_theta.u*sin(r_theta.v), r_theta.u*cos(r_theta.v)> #end
#macro make_3d_point (r_theta) <r_theta.u*sin(r_theta.v), 0, r_theta.u*cos(r_theta.v)> #end
#macro rotate_point (r_theta, _angle) <r_theta.u, r_theta.v + _angle> #end
#macro find_involute_angle (bc, r) 
 	#if (r/bc >= 1) 
    acos(bc/r) 
  #else 0
  #end
#end
#macro find_angle(bc, r) 
 	#if (r/bc >= 1) 
    involute_point(<bc, acos(bc/r)>).v
  #else 0
  #end
#end

#macro scale_point (r_theta) <
  (fake_th*(pd+(r_theta.u-pd)*cos(back_cone_angle)))
  /(th-(r_theta.u-pd)*sin(back_cone_angle)), 
  r_theta.v> #end


#local end_angle = (find_involute_angle (1, 1.2));
#local step = end_angle / 10;

//#local i = 0;
//#while (i <= end_angle)
//#local i = i + step;
//sphere { make_3d_point(rotate_point(involute_point(<1,i>), 0)), .003 pigment { color rgb < 0, 1, 1> } }
//#end

camera {
//	fisheye
	angle .02
//   orthographic
//	up <0,3,0>
//  right<0,6,0>
	location <0, 2000, 1>
	look_at <0, 0, 1>
}

light_source { <0, 30, 10> color rgb <1, 1, 1> }


#local th = 1;

#local quality_involute = 10;
#local pa = 14.5;
#local pd = 1;
#local mdl = 0.0625;
#local n = 32;

#local bc = pd * cos(pa*_Pi/180);
#local od = pd + mdl;
#local rd = pd - 1.157*mdl;
#local cp = (2*_Pi)/n;

#local pd_cone_angle   = atan2(pd,th);
#local back_cone_angle = (_Pi/2)-pd_cone_angle;

#local lrd = rd-pd;

#local fake_th = th-lrd*sin(back_cone_angle);
#local fake_rd = pd+lrd*cos(back_cone_angle);
#local fake_pd = (fake_th*pd)/th;

#local fake_od = scale_point(<od,0>).u;
#local fake_bc = scale_point(<bc,0>).u;


#local involute_begin         = (find_involute_angle(bc, rd));
#local involute1_offset       = (-find_angle(bc, pd)-(cp/4));
#local involute_length        = (find_involute_angle(bc, od));
#local circle_offset_val      = (find_angle(bc,od));
#local involute_step          = ((involute_length-involute_begin)/(quality_involute));

#local involute2_offset       = -(involute1_offset);
#render concat("\r\n involute_begin:    ", str(involute_begin, 5,5), "")
#render concat("\r\n involute1_offset:  ", str(involute1_offset,5,5), "")
#render concat("\r\n involute_length:   ", str(involute_length,5,5), "")
#render concat("\r\n circle_offset_val: ", str(circle_offset_val,5,5), "")
#render concat("\r\n involute_step:     ", str(involute_step,5,5), "")
#render concat("\r\n involute2_offset:  ", str(involute2_offset,5,5), "\r\n")

//#declare angle_to_turn = (involute2_offset-(find_angle(bc, pd)))*180/_Pi;

prism {
linear_spline
conic_sweep
0, fake_th,

(quality_involute*2+2 +4)
#local current_pigment = <0, 0, 1>;
#local numbers = (quality_involute*2+2 +4);

#local color_offset = <0, (1/numbers), -(1/numbers)>

// -------------------- left involute
  #local i = 0;
  #while (i < quality_involute)
    #local i = i + 1;
    #local theta = i*involute_step;//+involute_begin;

#local current_pigment = current_pigment + color_offset;
//sphere { 
  make_2d_point(scale_point(rotate_point(involute_point(<bc,theta>), involute1_offset))), 
//.003 pigment { color rgb current_pigment } }

  #end            
// -------------------- outer points
  #local theta = involute1_offset+circle_offset_val;
#local current_pigment = current_pigment + color_offset;
//sphere { 
  make_2d_point(scale_point(<od,theta>)),
// .003 pigment { color rgb current_pigment } }

#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<sqrt(od*od+od*abs(sin(theta))), 0>)),
// .003 pigment { color rgb current_pigment } }

  #local theta = -(involute1_offset+circle_offset_val);
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<od,theta>)), 
//.003 pigment { color rgb current_pigment } }
// -------------------- right involute
  #local i = quality_involute;
  #while (i >= 0)
    #local theta = i*(involute_step+involute_begin);

#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(rotate_point(involute_point(<bc,theta>),involute1_offset)))*<-1,1>, //*<-1,1,1> 
//.003 pigment { color rgb current_pigment } }

    #local i = i - 1;
  #end                  
// -------------------- inside points         
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<rd,involute2_offset>)), 
//.003 pigment { color rgb current_pigment } }
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<rd,involute1_offset>))
//.003 
pigment { color rgb <0,1,0> }

translate <0,-.00001,0> }

// test
//}


#local _Pi = 3.141592654;

#local scale_factor = 1000;                               
                               
#macro involute_point (r_theta) <r_theta.u/cos(r_theta.v), tan(r_theta.v)-r_theta.v> #end
//#macro make_2d_point (r_theta) <r_theta.u*sin(r_theta.v), r_theta.u*cos(r_theta.v)> #end
#macro make_2d_point (r_theta) <r_theta.u*sin(r_theta.v)*scale_factor, r_theta.u*cos(r_theta.v)*scale_factor> #end

//#macro make_3d_point (r_theta) <r_theta.u*sin(r_theta.v), 0, r_theta.u*cos(r_theta.v)> #end
#macro make_3d_point (r_theta) <r_theta.u*sin(r_theta.v)*scale_factor, 0, r_theta.u*cos(r_theta.v)*scale_factor> #end

#macro rotate_point (r_theta, _angle) <r_theta.u, r_theta.v + _angle> #end
#macro find_involute_angle (bc, r) 
 	#if (r/bc >= 1) 
    acos(bc/r) 
  #else 0
  #end
#end
#macro find_angle(bc, r) 
 	#if (r/bc >= 1) 
    involute_point(<bc, acos(bc/r)>).v
  #else 0
  #end
#end

#macro scale_point (r_theta) <
  (fake_th*(pd+(r_theta.u-pd)*cos(back_cone_angle)))
  /(th-(r_theta.u-pd)*sin(back_cone_angle)), 
  r_theta.v> #end


#local end_angle = (find_involute_angle (1, 1.2));
#local step = end_angle / 10;

//#local i = 0;
//#while (i <= end_angle)
//#local i = i + step;
//sphere { make_3d_point(rotate_point(involute_point(<1,i>), 0)), .003 pigment { color rgb < 0, 1, 1> } }
//#end

camera {
//	fisheye
	angle .02
//   orthographic
//	up <0,3,0>
//  right<0,6,0>
	location <0, 2000, 1>
	look_at <0, 0, 1>
}

light_source { <0, 30, 10> color rgb <1, 1, 1> }




#local th = 1;

#local quality_involute = 10;
#local pa = 14.5;
#local pd = 1;
#local mdl = 0.0625;
#local n = 32;

#local bc = pd * cos(pa*_Pi/180);
#local od = pd + mdl;
#local rd = pd - 1.157*mdl;
#local cp = (2*_Pi)/n;

#local pd_cone_angle   = atan2(pd,th);
#local back_cone_angle = (_Pi/2)-pd_cone_angle;

#local lrd = rd-pd;

#local fake_th = th-lrd*sin(back_cone_angle);
#local fake_rd = pd+lrd*cos(back_cone_angle);
#local fake_pd = (fake_th*pd)/th;

#local fake_od = scale_point(<od,0>).u;
#local fake_bc = scale_point(<bc,0>).u;

#render concat("\r\n quality_involute:    ", str(involute_begin, 5,5), "")
#render concat("\r\n pa:  ", str(involute1_offset,5,5), "")
#render concat("\r\n pd:   ", str(involute_length,5,5), "")
#render concat("\r\n mdl: ", str(circle_offset_val,5,5), "")
#render concat("\r\n n:     ", str(involute_step,5,5), "")
#render concat("\r\n involute2_offset:  ", str(involute2_offset,5,5), "\r\n")



#local involute_begin         = (find_involute_angle(bc, rd));
#local involute1_offset       = (-find_angle(bc, pd)-(cp/4));
#local involute_length        = (find_involute_angle(bc, od));
#local circle_offset_val      = (find_angle(bc,od));
#local involute_step          = ((involute_length-involute_begin)/(quality_involute));

#local involute2_offset       = -(involute1_offset);
#render concat("\r\n involute_begin:    ", str(involute_begin, 5,5), "")
#render concat("\r\n involute1_offset:  ", str(involute1_offset,5,5), "")
#render concat("\r\n involute_length:   ", str(involute_length,5,5), "")
#render concat("\r\n circle_offset_val: ", str(circle_offset_val,5,5), "")
#render concat("\r\n involute_step:     ", str(involute_step,5,5), "")
#render concat("\r\n involute2_offset:  ", str(involute2_offset,5,5), "\r\n")




prism {
linear_spline
linear_sweep
0, fake_th,

(quality_involute*2+2 +4)
#local current_pigment = <0, 0, 1>;
#local numbers = (quality_involute*2+2 +4);

#local color_offset = <0, (1/numbers), -(1/numbers)>

// -------------------- left involute
  #local i = 0;
  #while (i < quality_involute)
    #local i = i + 1;
    #local theta = i*involute_step;//+involute_begin;

#local current_pigment = current_pigment + color_offset;
//sphere { 
  make_2d_point(scale_point(rotate_point(involute_point(<bc,theta>), involute1_offset))), 
//.003 pigment { color rgb current_pigment } }

  #end            
// -------------------- outer points
  #local theta = involute1_offset+circle_offset_val;
#local current_pigment = current_pigment + color_offset;
//sphere { 
  make_2d_point(scale_point(<od,theta>)),
// .003 pigment { color rgb current_pigment } }

#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<sqrt(od*od+od*abs(sin(theta))), 0>)),
// .003 pigment { color rgb current_pigment } }

  #local theta = -(involute1_offset+circle_offset_val);
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<od,theta>)), 
//.003 pigment { color rgb current_pigment } }
// -------------------- right involute
  #local i = quality_involute;
  #while (i >= 0)
    #local theta = i*(involute_step+involute_begin);

#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(rotate_point(involute_point(<bc,theta>),involute1_offset)))*<-1,1>, //*<-1,1,1> 
//.003 pigment { color rgb current_pigment } }

    #local i = i - 1;
  #end                  
// -------------------- inside points         
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<rd,involute2_offset>)), 
//.003 pigment { color rgb current_pigment } }
#local current_pigment = current_pigment + color_offset;
//sphere { 
make_2d_point(scale_point(<rd,involute1_offset>))
//.003 
scale <1/scale_factor,1,1/scale_factor>
pigment { color rgb <0,0,1> }

translate <0,0,0> }

// test
//}













cylinder { <0,0,0>, <0,-.1,0>, 
	make_2d_point(scale_point(<rd,0>)).v
	scale <1/scale_factor,1,1/scale_factor>
	pigment { color rgb <1, 0, 0> } }