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In  and  have been proved that covariogramand orientation-dependent chord length distribution function of a triangle and an ellipse depends on maximal chord t max (u) in direction u. In this paper a necessary condition for orientation-dependent chord length distribution function as a function of maximal chord is obtained. A class of parallelo...
The paper considers a random segment L(ω) in R n with fixed direction and length that intersects a given bounded convex body D ⊂ R n . We obtain a relationship between the covariogram of D and the distribution of the random variable |L| — the length of L ∩ D. A relationship between the distribution of |L| and the orientation-dependent chord length...
In this paper we obtain the explicit forms of the covariogram and the orientation-dependent chord length distribution function for any parallelogram. The explicit form of the chord length distribution function for a parallelogram is also obtained.
The paper considers the problem of recognition of triangles by orientation-dependent chord length distribution. The following results are obtained: 1. The explicit form of the covariogram and orientation-dependent chord length distribution function for a triangle. 2. The explicit form for the chord length distribution function for a triangle. 3. Th...