Plane-probing algorithms have become fundamental tools to locally capture arithmetical and geometrical properties of digital surfaces (boundaries of a connected set of voxels), and especially normal vector information. On a digital plane, the overall idea is to consider a local pattern, a triangle, that is expanded starting from a point of interest using simple probes of the digital plane with a predicate "Is a point x in the digital plane?". Challenges in plane-probing methods are to design an algorithm that terminates on a triangle with several geometrical properties: its normal vector should match with the expected one for digital plane (correctness), the triangle should be as compact as possible (acute or right angles only), and probes should be as close as possible to the source point (locality property). In addition, we also wish to minimize the number of iterations or probes during the computations. Existing methods provide correct outputs but only experimental evidence for these properties. In this paper, we present a new plane-probing algorithm that is theoretically correct on digital planes, and with better experimental compactness and locality than existing solutions. Additional properties of this new approach also suggest that theoretical proofs of the aforementioned geometrical properties could be achieved.