### Abstract

We present a parallel algorithm for the construction of the hyperoctree representing a $d$-dimensional object from a set of $n$ \mbox{$(d-1)$}-dimensional hyperoctrees, representing adjacent crossections of this object. On a $p$-processor SIMD hypercube the time complexity of our algorithm is $O(\frac m p \log p\log n)$, where $m$ is the maximum of input and output size.