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Communication Dans Un Congrès Année : 2016

Computation of the normal vector to a digital plane by sampling signicant points

Résumé

Digital planes are sets of integer points located between two parallel planes. We present a new algorithm that computes the normal vector of a digital plane given only a predicate is a point x in the digital plane or not. In opposition with the algorithm presented in [7], the algorithm is fully local and does not explore the plane. Furthermore its worst-case complexity bound is O(ω), where ω is the arithmetic thickness of the digital plane. Its only restriction is that the algorithm must start just below a Bezout point of the plane in order to return the exact normal vector. In practice, our algorithm performs much better than the theoretical bound, with an average behavior close to O(log ω). We show further how this algorithm can be used to analyze the geometry of arbitrary digital surfaces, by computing normals and identifying convex, concave or saddle parts of the surface.
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Dates et versions

hal-01621492 , version 1 (23-10-2017)

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Jacques-Olivier Lachaud, Xavier Provençal, Tristan Roussillon. Computation of the normal vector to a digital plane by sampling signicant points. 19th IAPR International Conference on Discrete Geometry for Computer Imagery, Apr 2016, Nantes, France. pp.194-205, ⟨10.1007/978-3-319-32360-2_15⟩. ⟨hal-01621492⟩
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