Restoring a Triangle on a Plane by Three Projections

In this paper, we consider the following problem. On the plane, a triangle Δ ABC and three straight lines l 1 , l 2 , and l 3 in the general position are given; the locations of the straight lines are unknown. One must restore the triangle Δ ABC by the known lengths of the sides of the triangles Δ A...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 276; no. 6; pp. 751 - 758
Main Authors Kurkina, M. V., Semenov, S. P., Slavsky, V. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2023
Springer
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Straight lines
small-angle computed tomography
51N20
triangle
65D18
97G70
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Summary:In this paper, we consider the following problem. On the plane, a triangle Δ ABC and three straight lines l 1 , l 2 , and l 3 in the general position are given; the locations of the straight lines are unknown. One must restore the triangle Δ ABC by the known lengths of the sides of the triangles Δ A 1 B 1 C 1 , Δ A 2 B 2 C 2 , and Δ A 3 B 3 C 3 , which are the projections of the triangle Δ ABC onto the lines l 1 , l 2 , and l 3 . Similar problems and their multidimensional generalizations are of interest in the theory of computer images.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06798-z