On some unknown results related to the nontrivial properties of ordinary triangles. Part 1

Вестник КРАУНЦ. Физико-математические науки ◽

10.26117/2079-6641-2021-37-4-216-234 ◽

2021 ◽

pp. 216-234

Author(s):

Б.П. Федоров ◽

C.Б. Богданова ◽

С.О. Гладков

Keyword(s):

Depth Perception

В работе приведено подробное решение множества оригинальных задач, сформулированых в свое время Б. П. Федоровым, и относящихся к разнообразным нетривиальным свойствам евклидовых треугольников. При изложении материала используется некоторая общепринятая, но не слишком распространенная в современных учебниках по геометрии терминология, необходимая для понимания и более углубленного восприятия описанных в работе задач. In this paper, it was given a detailed solution of many original problems, formulated by Fedorov B. P. some time ago. These problems belong to the various nontrivial properties of Euclidean triangles. When presenting the material, it has been used some universally accepted, but not very popular in modern textbooks on geometry terminology, which is nesessary for understanding and in-depth perception of the problems described in the paper.

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Three-dimensional image analysis and visualization in confocal light microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146631 ◽

1993 ◽

Vol 51 ◽

pp. 158-159

Author(s):

J. K. Samarabandu ◽

R. Acharya ◽

D. R. Pareddy ◽

P. C. Cheng

Keyword(s):

Depth Perception ◽

Computer Graphic ◽

Three Dimensional ◽

Cellular Organization ◽

Data Set ◽

Computational Burden ◽

Interactive Operation ◽

Cell Organization ◽

Confocal Images ◽

3D Digitization

In the study of cell organization in a maize meristem, direct viewing of confocal optical sections in 3D (by means of 3D projection of the volumetric data set, Figure 1) becomes very difficult and confusing because of the large number of nucleus involved. Numerical description of the cellular organization (e.g. position, size and orientation of each structure) and computer graphic presentation are some of the solutions to effectively study the structure of such a complex system. An attempt at data-reduction by means of manually contouring cell nucleus in 3D was reported (Summers et al., 1990). Apart from being labour intensive, this 3D digitization technique suffers from the inaccuracies of manual 3D tracing related to the depth perception of the operator. However, it does demonstrate that reducing stack of confocal images to a 3D graphic representation helps to visualize and analyze complex tissues (Figure 2). This procedure also significantly reduce computational burden in an interactive operation.

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