Patent ID: 11887330
Assignee: KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY
Field: Computer technology (Electrical engineering)
Classification: CPC G | IPC G

Claim 4:
5. The method of claim 1, wherein the estimating of the position of the nearest point extending from the plurality of pointing rays comprises obtaining a solution of a vector x defined by the following equations using a Least Square Method (LSM):, x
  =
  
   
    
     (
     
      
       A
       T
      
      ⁢
      A
     
     )
    
    
     -
     1
    
   
   ⁢
   
    A
    T
   
   ⁢
   b
  
 

 
  A
  =
  
   [
   
    
     
      1
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         x
         ⁢
         1
        
       
      
     
     
      0
     
     
      0
     
     
       
     
     
      0
     
    
    
     
      0
     
     
      1
     
     
      0
     
     
      
       -
       
        u
        
         y
         ⁢
         1
        
       
      
     
     
      0
     
     
      0
     
     
       
     
     
      0
     
    
    
     
      0
     
     
      0
     
     
      1
     
     
      
       -
       
        u
        
         z
         ⁢
         1
        
       
      
     
     
      0
     
     
      0
     
     
       
     
     
      0
     
    
    
     
      1
     
     
      0
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         x
         ⁢
         2
        
       
      
     
     
      0
     
     
       
     
     
      0
     
    
    
     
      0
     
     
      1
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         y
         ⁢
         2
        
       
      
     
     
      0
     
     
      …
     
     
      0
     
    
    
     
      0
     
     
      0
     
     
      1
     
     
      0
     
     
      
       -
       
        u
        
         z
         ⁢
         2
        
       
      
     
     
      0
     
     
       
     
     
      0
     
    
    
     
      1
     
     
      0
     
     
      0
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         x
         ⁢
         3
        
       
      
     
     
       
     
     
      0
     
    
    
     
      0
     
     
      1
     
     
      0
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         y
         ⁢
         3
        
       
      
     
     
       
     
     
      0
     
    
    
     
      0
     
     
      0
     
     
      1
     
     
      0
     
     
      0
     
     
      
       -
       
        u
        
         z
         ⁢
         3
        
       
      
     
     
       
     
     
      0
     
    
    
     
       
     
     
       
     
     
       
     
     
      ⋮
     
     
       
     
     
       
     
     
      ⋱
     
     
      ⋮
     
    
    
     
      1
     
     
      0
     
     
      0
     
     
      0
     
     
      0
     
     
      0
     
     
       
     
     
      
       -
       
        u
        xn
       
      
     
    
    
     
      0
     
     
      1
     
     
      0
     
     
      0
     
     
      
        
       0
      
     
     
      0
     
     
      
       …
        
      
     
     
      
       -
       
        u
        yn
       
      
     
    
    
     
      0
     
     
      0
     
     
      1
     
     
      0
     
     
      0
     
     
      0
     
     
       
     
     
      
       -
       
        u
        zn
       
      
     
    
   
   ]
  
 

 
  x
  =
  
   [
   
    
     
      x
     
    
    
     
      y
     
    
    
     
      z
     
    
    
     
      
       a
       1
      
     
    
    
     
      
       a
       2
      
     
    
    
     
      
       a
       3
      
     
    
    
     
      ⋮
     
    
    
     
      
       a
       n
      
     
    
   
   ]
  
 

 
  b
  =
  
   [
   
    
     
      
       x
       1
      
     
    
    
     
      
       y
       1
      
     
    
    
     
      
       z
       1
      
     
    
    
     
      
       x
       2
      
     
    
    
     
      
       y
       2
      
     
    
    
     
      
       z
       2
      
     
    
    
     
      
       x
       3
      
     
    
    
     
      
       y
       3
      
     
    
    
     
      
       z
       3
      
     
    
    
     
      ⋮
     
    
    
     
      
       x
       n
      
     
    
    
     
      
       y
       n
      
     
    
    
     
      
       z
       n
      
     
    
   
   ]
  
 

where uxn, uyn, and uzn denote x, y, and z components in an orthogonal coordinate system of a gesture-direction vector un used to configure an n-th pointing ray, x, y, and z are variables indicating x, y, and z components in an orthogonal coordinate system of the nearest point, and xn, yn, and zn denote x, y, and z components in an orthogonal coordinate system of a head position Pn of a user used to configure the n-th pointing ray.