scholarly journals REGULAR POLYGONS IN 2D OBJECTS SHAPE DESCRIPTION

2021 ◽  
Vol 4 ◽  
pp. 43-61
Author(s):  
Andrzej Kwinta ◽  
◽  
Joanna Bac-Bronowicz ◽  
1995 ◽  
Vol 5 (12) ◽  
pp. 1539-1550 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
A. Gervois ◽  
J. P. Troadec
Keyword(s):  

1997 ◽  
Vol 7 (10) ◽  
pp. 1181-1189 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
J. P. Troadec ◽  
A. Gervois
Keyword(s):  

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.


2021 ◽  
pp. 0734242X2110450
Author(s):  
Yifeng Li ◽  
Xunpeng Qin ◽  
Zhenyuan Zhang ◽  
Huanyu Dong

Transport and separation processes of solid waste can only be modelled successfully with discrete element methods in case the shape of the particles can be described accurately. The existing techniques for morphological data acquisition, such as computed tomography, laser scanning technique, optical interferometer, stereo photography and structured light technique, are laborious and require a large amount of realistic solid waste samples. Therefore, there is a pressing need for an alternative method to describe the shape of solid waste particles and to generate multiple variations of particles with almost similar shapes. In this paper, a new method to describe solid waste particles is proposed that is frequency-based and uses spherical harmonics (SHs). Additionally, a new shape generation method is introduced that uses the shape description of a single particle to generate an array of related shapes based on a probability density function with a dimensionless control factor η. The newly proposed methods were successfully applied to describe the complex shapes of pieces of metal and plastic scrap. The shapes of these pieces of scrap can be described adequately with 15° of SH expansion and the overall divergence is within 0.1 mm. Five different values for η were tested, which generated shapes with the same distribution as the original particle. Rising levels of η cause the morphological variation of the generated particles to increase. These new methods improve the modelling of transportation and separation processes.


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