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A one-to-one correspondence between the infinitesimal motions of bar-jointframeworks in $\mathbb{R}^d$ and those in $\mathbb{S}^d$ is a classicalobservation by Pogorelov, and further connections among different rigiditymodels in various different spaces have been extensively studied. In thispaper, we shall extend this line of research to include the infinitesimalrigidity of frameworks consisting of points and hyperplanes. This enables us tounderstand correspondences between point-hyperplane rigidity, classicalbar-joint rigidity, and scene analysis.  Among other results, we derive a combinatorial characterization of graphsthat can be realized as infinitesimally rigid frameworks in the plane with agiven set of points collinear. This extends a result by Jackson and Jord\'{a}n,which deals with the case when three points are collinear.

Point-hyperplane frameworks, slider joints, and rigidity preserving transformations