  Environmental contours are widely used as basis for design of structures
exposed to environmental loads. The basic idea of the method is to decouple the
environmental description from the structural response. This is done by
establishing an envelope of environmental conditions, such that any structure
tolerating loads on this envelope will have a failure probability smaller than
a prescribed value. Specifically, given an $n$-dimensional random variable
$\mathbf{X}$ and a target probability of failure $p_{e}$, an environmental
contour is the boundary of a set $\mathcal{B} \subset \mathbb{R}^{n}$ with the
following property: For any failure set $\mathcal{F} \subset \mathbb{R}^{n}$,
if $\mathcal{F}$ does not intersect the interior of $\mathcal{B}$, then the
probability of failure, $P(\mathbf{X} \in \mathcal{F})$, is bounded above by
$p_{e}$. As is common for many real-world applications, we work under the
assumption that failure sets are convex.
  In this paper, we show that such environmental contours may be regarded as
boundaries of Voronoi cells. This geometric interpretation leads to new
theoretical insights and suggests a simple novel construction algorithm that
guarantees the desired probabilistic properties. The method is illustrated with
examples in two and three dimensions, but the results extend to environmental
contours in arbitrary dimensions. Inspired by the Voronoi-Delaunay duality in
the numerical discrete scenario, we are also able to derive an analytical
representation where the environmental contour is considered as a
differentiable manifold, and a criterion for its existence is established.
