Approximation of isosurface in the Marching Cube: ambiguity problem
Sergey V. Matveyev · 1994
The purpose of the present article is the consideration of the problem of ambiguity over the faces arising in the Marching Cube algorithm. The article shows that for unambiguous choice of the sequence of the points of intersection of the isosurface with edges confining the face it is su#cient to sort them along one of the coordinates. It also presents the solution of this problem inside the cube. The graph theory methods are used to approximate the isosurface inside the cell. Introduction Let there be a rectilinear volume grid whose nodes contain the values of the function F ijk = F (x, y, z). The problem is to approximate the isosurface S # = {(x, y, z):F (x, y, z)=#}. (1) In the MC algorithm [1], [2] the isosurface is approximated sequentially in all cells comprising the volume grid and intersecting the specified surface. In this case the coordinates of the points of of edges intersecting the isosurface are computed. Then the part of the surface intersecting the given cell is c...