camera { orthographic  right x * 5.6 / 2 up y * 5.6 location <1, 0, -3> 
look_at <1, -2.8, 0> }
light_source { <0, 100, 0> rgb 1 } 
background { rgb z }  
  
union {       
                               
   isosurface {
         
      function { y - cos(2 * x - 1) + 0.01 } 
      
      open
      
      max_gradient 5            
              
      contained_by { box { 0 1 } }
                     
      pigment { color rgb 1 }               
      
   }
   
                                    
   
   text { ttf "timrom" "Isosurface" 0.1 0 pigment { color rgb 0 } scale 
0.25 translate <1.1, 1, 0>}
                               
   translate <0, -1.1, 0>
      
   no_shadow
}   
   
         
union {       
                               
   height_field {
         
      function 10, 10 { cos(2 * x - 1) } 
                     
      pigment { color rgb 1 } 
            
   }
   
   
   
   text { ttf "timrom" "Heightfield" 0.1 0 pigment { color rgb 0 } scale 
0.25 translate <1.1, 1, 0>}   
                              
   translate < 0, -2.2, 0>
   
   no_shadow
} 

union {     

   height_field {
         
      function 10, 10 { cos(2 * x - 1) }  
      
      smooth        
      
      pigment { color rgb 1 }   
      
   }
   
  
   
   text { ttf "timrom" "Smooth HF" 0.1 0 pigment { color rgb 0 } scale 
0.25 translate <1.1, 1, 0>}       
                                         
   translate < 0, -3.3, 0>
   
   no_shadow
}  

union {   
   
   mesh2 {      
      
      vertex_vectors {
                  
         9 * 9
                
         #local YC = 0;
         #while (YC <= 8) 
         
            #local XC = 0;
            #while (XC <= 8)
                  
               #local X = XC / 8;
               #local Y = YC / 8;                              
               
               <X, cos(2 * X - 1), Y>
                                                                   
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
               
      }  
      
               
      face_indices {  
                                            
         8 * 8 * 2
                
         #local YC = 0;
         #while (YC < 8) 
                                                 
            #local XC = 0;
            #while (XC < 8)
                                          
               <YC * 9 + XC, YC * 9 + XC + 1, (YC + 1) * 9 + XC>
               <(YC + 1) * 9 + XC + 1, (YC + 1) * 9 + XC, YC * 9 + XC + 
1>                           
                              
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
           
      }      
      
                                         
      pigment { color rgb 1 }      
      
   }
   
  
   
   text { ttf "timrom" "Mesh" 0.1 0 pigment { color rgb 0 } scale 0.25 
translate <1.1, 1, 0>}      
                              
   translate < 0, -4.4, 0>

   no_shadow
}   
   
union {   
   
   mesh2 {      
      
      vertex_vectors {
                  
         9 * 9
                
         #local YC = 0;
         #while (YC <= 8) 
         
            #local XC = 0;
            #while (XC <= 8)
                  
               #local X = XC / 8;
               #local Y = YC / 8;                              
               
               <X, cos(2 * X - 1), Y>
                                                                   
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
               
      }  
      
      normal_vectors {
             
        
         9 * 9
                
         #local YC = 0;
         #while (YC <= 8) 
         
            #local XC = 0;
            #while (XC <= 8)
                  
               #local X = XC / 8;
               #local Y = YC / 8;                              
               
               vcross( // Thanks to Warp for math and Trevor Quayle for 
explanation                                                    
               <1, -2 * sin(2 * X - 1), 0>, // for "1" in x go 
"gradient" up
               <0, 0, 1>)                   // for "1" in z go 
"gradient" up               
                                                                   
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
               
      }   
         
      face_indices {  
                                            
         8 * 8 * 2
                
         #local YC = 0;
         #while (YC < 8) 
                                                 
            #local XC = 0;
            #while (XC < 8)
                                          
               <YC * 9 + XC, YC * 9 + XC + 1, (YC + 1) * 9 + XC>
               <(YC + 1) * 9 + XC + 1, (YC + 1) * 9 + XC, YC * 9 + XC + 
1>                           
                              
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
           
      }      
      
      normal_indices {  
                                            
         8 * 8 * 2
                
         #local YC = 0;
         #while (YC < 8) 
                                                 
            #local XC = 0;
            #while (XC < 8)
                                          
               <YC * 9 + XC, YC * 9 + XC + 1, (YC + 1) * 9 + XC>
               <(YC + 1) * 9 + XC + 1, (YC + 1) * 9 + XC, YC * 9 + XC + 
1>                           
                              
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
           
      }      
      
                              
      pigment { color rgb 1 }      
      
   }
   
  
   
   text { ttf "timrom" "Smo. Mesh" 0.1 0 pigment { color rgb 0 } scale 
0.25 translate <1.1, 1, 0>}      
                              
   translate < 0, -5.5, 0>

   no_shadow
}   

union {   
   
   mesh2 {      
      
      vertex_vectors {
                  
         9 * 9
                
         #local YC = 0;
         #while (YC <= 8) 
         
            #local XC = 0;
            #while (XC <= 8)
                  
               #local X = XC / 8;
               #local Y = YC / 8;                              
               
               <X, cos(2 * X - 1), Y>
                                                                   
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
               
      }
                  
      normal_vectors {
             
        
         9 * 9
                
         #local YC = 0;
         #while (YC <= 8) 
         
            #local XC = 0;
            #while (XC <= 8)
                  
               #local X = XC / 8;
               #local Y = YC / 8;    
               
               #local Xnext = (XC + 1) / 8;
               #local Ynext = (YC + 1) / 8;     
               
               #local Xprev = (XC - 1) / 8;
               #local Yprev = (YC - 1) / 8;                            
   
                     
               #local N = <0, 0, 0>;                       
               
               #local P = <X, cos(2 * X - 1), Y>;    
                                                                         
                                          
               #local P_0 = <Xnext, cos(2 * Xnext - 1), Y>; 
               #local V_0 = P_0 - P;   
               
               #local P_1 = <X, cos(2 * X - 1), Ynext>;                
                                                           
               #local V_1 = P_1 - P;        
               
               #local P_2 = <Xprev, cos(2 * Xprev - 1), Y>; 
               #local V_2 = P_2 - P;                         
                              
               #local P_3 = <X, cos(2 * X - 1), Yprev>;
               #local V_3 = P_3 - P;    
                                                                         
    
               #if (XC < 8 & YC < 8)
                             
                  #local N = N + vcross(V_0, V_1);                     
        
                  
               #end 
               
               #if (YC < 8 & XC > 0)
                 
                  #local N = N + vcross(V_1, V_2);  
                  
               #end
               
               #if (XC > 0 & YC > 0)   
                             
                  #local N = N + vcross(V_2, V_3);
                  
               #end 
               
               #if (YC > 0 & XC < 8)     
               
                  #local N = N + vcross(V_3, V_0);
               
               #end
               
               N
                                                                   
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
               
      }   
         
      face_indices {  
                                            
         8 * 8 * 2
                
         #local YC = 0;
         #while (YC < 8) 
                                                 
            #local XC = 0;
            #while (XC < 8)
                                          
               <YC * 9 + XC, YC * 9 + XC + 1, (YC + 1) * 9 + XC>
               <(YC + 1) * 9 + XC + 1, (YC + 1) * 9 + XC, YC * 9 + XC + 
1>                           
                              
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
           
      }      
      
      normal_indices {  
                                            
         8 * 8 * 2
                
         #local YC = 0;
         #while (YC < 8) 
                                                 
            #local XC = 0;
            #while (XC < 8)
                                          
               <YC * 9 + XC, YC * 9 + XC + 1, (YC + 1) * 9 + XC>
               <(YC + 1) * 9 + XC + 1, (YC + 1) * 9 + XC, YC * 9 + XC + 
1>                           
                              
               #local XC = XC + 1;
            #end
         
            #local YC = YC + 1;
         #end 
           
      }      
      
                              
      pigment { color rgb 1 }      
      
   }
   
  
   
   text { ttf "timrom" "SM appr." 0.1 0 pigment { color rgb 0 } scale 
0.25 translate <1.1, 1, 0>}    
                              
   translate < 0, -6.6, 0>

   no_shadow
}