/*  Villarceau circles 2.0, by Lucas Vieira - October 2, 2006 - Coded in: POV-Ray 3.6 License: Public Domain   Info ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Author user page: http://en.wikipedia.org/wiki/User:LucasVB The final animation at Wikimedia Commons: http://commons.wikimedia.org/wiki/Image:Villarceau_circles.gif   Notes ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Several modifications were done for each part of the animation and I didn't keep them all here. So if you wish to reproduce the animation, you'll have to play with this code quite a bit. :)   */  background { color rgb 1 }  global_settings { 	assumed_gamma 1.5 }  camera { 	orthographic 	location <0,4,-5>*0.75 	look_at <0,0,0> 	rotate 5*y // slight camera angle so the cutting plane doesn't look too boring 	//rotate 90*y // debug rotation }  light_source { 	<0,0,0>, 1 	translate <-5,5,0>*1 	shadowless // makes everything softer, because shading comes entirely from the surface normal 	           // this removes specular reflections, but I thought it looked a lot better }   //Several rotation codes used for various parts of the animation.  //#declare rotation = (-95*sin(clock*pi/2))*y; // 360*clock*y; #declare rotation = -90*y; //#declare rotation = (-85 * sin(clock*pi/2))*y;   //Bottom half-torus #if (1) difference { 	difference { 		torus { 			1, 0.5 		} 		torus { 			1, 0.499 			pigment { 				image_map { 					//surface inside the torus 					png "checker2.png" // 1024x512 checkered image, with 64x64 cells. 					interpolate 4 					map_type 5 					//transmit all 1-sin(clock*pi/2) 					//transmit all 0.85 				} 			} 		} 	} 	box {    -3*<1,0,1>, <1,1,1>*3 		rotate degrees(asin(0.5-0.001))*z 	} 	pigment { 		image_map { 			png "checker.png" // 1024x512 checkered image, with 64x64 cells. 			interpolate 4 			map_type 5 			//transmit all 1-sin(clock*pi/2) 			//transmit all 0.85 		} 	} 	finish { 		specular 0.5 		roughness 0.01 		ambient 0.5 	} 	rotate rotation } #end   //Top half-torus (the one discarded during the animation) //Notice it doesn't have an inner surface like the other half  #if (0) intersection { 	difference { 		torus { 			1, 0.5 		} 		torus { 			1, 0.499 		} 	} 	box {    -3*<1,0,1>, <1,1,1>*3 		rotate degrees(asin(0.5-0.001))*z 	} 	pigment { 		image_map { 			png "checker.png" // 1024x512 checkered image, with 64x64 cells. 			interpolate 4 			map_type 5 			//transmit all 1-sin(clock*pi/2) // Fades it away while moving to the left (see below) 			//transmit all 0.85 		} 	} 	finish { 		specular 0.5 		roughness 0.01 		ambient 0.5 	} 	//translate -x*0.5*sin(clock*pi/2) // Moves this part to the left. Should be enabled along with the fade code above 	rotate rotation } #end  //Cutting plane #if (0) box { 	<1.8,0.001,1.8>, -<1.8,0.001,1.8> 	pigment { 		color rgb <1,0.8,0.5> 		//transmit 1-sin(clock*pi/2)*0.4 		//transmit 0.6+0.4*sin(clock*pi/2) 		transmit 0.6 	} 	finish { 		specular 0.5 		roughness 0.01 		ambient 0.3 	} 	//translate 3.5*x - sin(clock*pi/2)*3.5*x 	rotate degrees(asin(0.5-0.001))*z } #end  //The Villarceau circles #if (0) union { 	torus { 		1, 0.01 		translate 0.5*z 	} 	torus { 		1, 0.01 		translate -0.5*z 	} 	pigment { 		color rgb <1,0,0> 		//transmit clock 	} 	finish { 		ambient 1 	} 	no_shadow 	rotate degrees(asin(0.5-0.001))*z 	rotate -85*y } #end  /* END OF FILE */