Компьютерное построение трехмерных выпуклых тел произвольных форм

Translated title of the contribution: Computer-aided construction of three-dimensional convex bodies of arbitrary shapes

Quan Mu, Boris A. Kargin, Evgeniya G. Kablukova

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Cirrus clouds consist of ice crystals of various shapes, sizes, and orientations. In the numerical study of the radiation characteristics of cirrus clouds, simplified crystal forms likes regular polyhedra (for example, prisms with hexagonal bases) are often used. To study the optical properties of irregularly shaped ice crystals, a number of authors of the previously constructed models in which, for example, a part of the crystal is cut off by a random plane, or the angle between some crystal faces changes randomly. In this paper, it is proposed to use the convex hull of randomly generated or user-specified points in three-dimensional space as a model for irregularly shaped ice crystals. A method for modeling three-dimensional convex polyhedra with a random arrangement of vertices is presented, which is based on the incremental and the directed edges algorithms. Each face of the modeled convex polyhedron is triangular. By stretching and squeezing, as well as an appropriate choice of the distribution function of random points in space, the resulting polyhedra can simulate the irregular shapes of ice cloud crystals. As a result of the algorithm execution, the number of vertices, their coordinates are saved, and for each face of the polyhedron, the sequence of vertices is ordered to make their vector product corresponds to the right-hand rule and determines the direction of the outer normal. These models of three-dimensional convex bodies of various sizes and irregular shapes are designed to calculate the attenuation coefficients and the scattering phase functions of optical radiation by cloud crystals using the ray tracing method. The paper presents a visualization of crystals modeled according to the given algorithm, and the dependence of the number of vertices and faces of the polyhedron on the number of generated random points. The program code is written in C++ using the OpenGL library.

Translated title of the contributionComputer-aided construction of three-dimensional convex bodies of arbitrary shapes
Original languageRussian
Article number4
Pages (from-to)54-61
Number of pages8
JournalJournal of Computational Technologies
Issue number2
Publication statusPublished - 2022



State classification of scientific and technological information



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