Asymptotic number of Z3Δ cells covering C(1) surface on uniform grid and complexity of recursive-partitioning simulation of septal tissue regions

The exact asymptotic computational complexity for a problem of indexing cells on a uniform grid intersecting with a union of C(1) surfaces has been proven. The computational complexity of the recursive partition indexing algorithm, utilized for simulation of septated tissues, is derived and the algorithm is demonstrated as being asymptotically optimal.