# KUBRIX Technology

Through an Incremental and homeomorphic annealing transformation **Ф**, KUBRIX morphs an input surface mesh into the outer surface mesh of a 3-D multi-block Cartesian grid. Let **ξ(i,j)**, **η(i, j)** and** ζ(i, j)** be the probabilities, at each iteration** i**, that triangle** j** of the input mesh will eventually be orthogonal to directions **x**, **y** and **z**, receptively. At each iteration, Fuzzy-logic and a set of necessary conditions are used to compute **ξ(i+1,j)**, **η(i+1, j)** and** ζ(i+1, j)**, which represent an incremental step in the transformation **Ф**. Morphing is complete when all probabilities converge to **1 **o **0**.

The interior of the stair step mesh is meshed algebraically, then all vertices are transformed back (though inverse of **Ф**) into a mesh that fits inside the initial surface mesh