Function representation

<p>Function Representation (FRep or F-Rep) is used in <a href="/facts/Solid_modeling/12J69aud">solid modeling</a>, volume modeling and <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a>. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications"  as a uniform representation of multidimensional geometric objects (shapes). An object as a point set in multidimensional space is defined by a single continuous real-valued function 
  
    
      
        f
        (
        X
        )
      
    
    {\displaystyle f(X)}
  
 of point coordinates 
  
    
      
        X
        [
        
          x
          
            1
          
        
        ,
        
          x
          
            2
          
        
        ,
        .
        .
        .
        ,
        
          x
          
            n
          
        
        ]
      
    
    {\displaystyle X[x_{1},x_{2},...,x_{n}]}
  
 which is evaluated at the given point by a procedure traversing a tree structure with primitives in the leaves and operations in the nodes of the tree. The points with 
  
    
      
        f
        (
        
          x
          
            1
          
        
        ,
        
          x
          
            2
          
        
        ,
        .
        .
        .
        ,
        
          x
          
            n
          
        
        )
        ≥
        0
      
    
    {\displaystyle f(x_{1},x_{2},...,x_{n})\geq 0}
  
 belong to the object, and the points with 
  
    
      
        f
        (
        
          x
          
            1
          
        
        ,
        
          x
          
            2
          
        
        ,
        .
        .
        .
        ,
        
          x
          
            n
          
        
        )
        <
        0
      
    
    {\displaystyle f(x_{1},x_{2},...,x_{n})<0}
  
 are outside of the object. The point set with 
  
    
      
        f
        (
        
          x
          
            1
          
        
        ,
        
          x
          
            2
          
        
        ,
        .
        .
        .
        ,
        
          x
          
            n
          
        
        )
        =
        0
      
    
    {\displaystyle f(x_{1},x_{2},...,x_{n})=0}
  
 is called an <a href="/facts/Isosurface/kvMHSemB">isosurface</a>.
</p>

Function representation open-in-new

Function representation