Patent ID: 7158131

Claim:
An implicit function rendering method of a nonmanifold, characterized in that: (1) an input nonmanifold curved surface is divided along a branch line, broken down into curved surface patches having no branches; (2) numbers i are allocated to the patches in an obtained order, a front and a back of each patch are distinguished from each other, a number i + is given to the front, and a number i − is given to the back; (3) a space is sampled by a lattice point p; and Euclid distance d E (p) to the curved surface and number i(p) of a surface of a nearest point are allocated to the lattice point; (4) for each lattice point p, i(p n ) is determined at six adjacent points p n , and groups of (i(p), i(p n )) where i(p)≠i(p n ) are enumerated; (5) a group of new numbers are substituted for the group of numbers allocated above, but if the numbers which are first i + and i − become the same numbers as a result of the substitution, no substitution is carried out for a combination thereof, whereby numbers are arrayed in order from 0 after said substitution; and (6) in accordance with a substitution table, a region number i(p) is rewritten at each lattice point p, and an implicit volume function of a real value is comprised of the obtained volume region number i(p) and the Euclid distance d E (p) to the surface at each voxel, wherein d E =√{square root over (( x−X ) 2 +( y−Y ) 2 +( z−Z ) 2 )}{square root over (( x−X ) 2 +( y−Y ) 2 +( z−Z ) 2 )}{square root over (( x−X ) 2 +( y−Y ) 2 +( z−Z ) 2 )} where the coordinate (x, y, z) is a lattice point, and the coordinate (X, Y, Z) is the point closest to a curved surface from the lattice point; and (7) rendering and displaying an implicit function curved surface from the implicit volume function of the real value.