/* 
Torus to mug morphing animation, by Lucas Vieira - January 17, 2007 - 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: [[:File:Mug_and_Torus_morph.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>*0.8
	look_at <0,0,0>
	//rotate -45*y
}

#declare dist = 0.2;
light_source {
	<0,0,0>, 1
	//translate <-3,5,-5>*1
	translate 5*y
	translate -5*z
	translate 2*x
}


#declare a = 1;

// Cylinders for the mug shape
#declare C_a = function { pow(x / a,2)   pow(z / a,2)-1.5 }
#declare C_b = function { pow(x / a,2)   pow(z / a,2)-1.2 }
#declare B_b = function { (y 1.3) }


// Torus (handle and the morphing target)
#declare R = 1; #declare r = 0.22;
#declare T_a = function { pow(R - sqrt(pow(x,2)   pow(y,2)),2)   pow(z,2) - pow(r,2) }
#declare R2 = 1; #declare r2 = 0.5;
#declare T_b = function { pow(R2 - sqrt(pow(x,2)   pow(y,2)),2)   pow(z,2) - pow(r2,2) }

// Hollow mug (concave)
#declare Mug = function { min(min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))),max(T_a(x-1,y,z),-C_a(x,y,z))) }

// Solid mug (cylinder with handle, convex)
#declare Mug2 = function { min(C_a(x,y,z),max(T_a(x-1,y,z),-C_a(x,y,z))) }


#declare c = 0.5;

// Linear to smooth interpolation
#declare Int = pow(sin(clock*pi/2),2);


// Functions for the mug parts, left as backups.
// max(C_a(x,y,z),B_b(x,y,z)) bottom
// max(C_a(x,y,z),-C_b(x,y,z)) sides
// min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))) bottom sides
// max(T_a(x-1,y,z),-C_a(x,y,z)) handle
// min(min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))),max(T_a(x-1,y,z),-C_a(x,y,z))) full mug
  	

// Render as isosurface or CSG.
// Isosurface is used in the transitional states.
#declare RenderIsosurface = 0;
#if (RenderIsosurface)
union {
	isosurface {
		function {
			// Add previously defined object functions using Int and (1-Int) as to generate the smooth transition
	    	//Mug2(x,y,z)*(1-Int)  
			Mug(x,y,z)
			//T_b(x-1,y,z)*Int
		}
	  	contained_by { box { -<3,1.5,3>, <3,1.5,3> } }
		accuracy 0.001
		max_gradient 5 // 10
		//rotate -90*x
	}
	cylinder {
		<0,-1.3 Int*2.8,0>, <0,-1.5,0>, sqrt(1.5)
	}
	pigment {
  		color rgb <0.6,0.8,1> transmit 0.1
	}
	finish {
		specular 0.5
		roughness 0.01
		ambient 0.2
	}
}
#else
union {
	difference {
		cylinder {
			-1.5*y, 1.5*y, sqrt(1.5)
		}
		cylinder {
			-2*y, 2*y, sqrt(1.2)
		}
	}
	difference {
		torus {
			R, r
			rotate 90*x
			translate x
		}
		cylinder {
			-1.5*y, 1.5*y, sqrt(1.5)
		}
	}
	cylinder {
		<0,0-0.25 Int*(1.5 0.25),0>, <0,-1.5,0>, sqrt(1.5)
	}
	pigment {
  		color rgb <0.6,0.8,1> transmit 0.1
	}
	finish {
		specular 0.5
		roughness 0.01
		ambient 0.2
	}
}
#end

/* END OF FILE */