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Consider a stationary Boolean model $X$ with convex grains in ${ℝ}^d$ and let any exposed lower tangent point of $X$ be shifted towards the hyperplane $N_0=\{x\in {ℝ}^d:x_1=0\}$ by the length of the part of the segment between the point and its projection onto the $N_0$ covered by $X$. The resulting point process in the halfspace (the Laslett’s transform of $X$) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie [Cressie])...