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Cellular Networks
Published in Mahbub Hassan, Wireless and Mobile Networking, 2022
As shown in Fig. 5, three options for tessellation are considered: equilateral triangle, square, and regular hexagon. Hexagon has the largest area among the three; hence it is typically used for modeling cellular networks.
Orthogonal Expansions in Curvilinear Coordinates
Published in Gregory S. Chirikjian, Alexander B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, 2021
Gregory S. Chirikjian, Alexander B. Kyatkin
A regular tessellation is a division of a surface (or space) into congruent regular polygons (polyhe-dra in the three-dimensional case, and polytopes in higher dimensional cases). Our current discussion is restricted to tessellations of surfaces, in particular the plane and sphere.
Linear Model Analysis of Real-Time Rendering
Published in Wong Gabriyel, Wang Jianliang, Real-Time Rendering: Computer Graphics with Control Engineering, 2017
In this research, we focus on exploiting a current trend in hardware technology that provides fine resolution in geometry control, known as tessellation. Since geometry is the primitive construct of any object in 3D space, it becomes a natural choice as one of the modelling variables in our framework. In brief, tessellation is the process of sub-dividing surfaces into smaller shapes with the objective of generating higher resolution information of the 3D model. Tessellation, also known as a sub division technique, is a well researched field in computer graphics and had been adopted widely in many interactive rendering applications because of the visual acuity it provides. However, only recently has graphics hardware provided sufficient support for tessellation-based techniques in applications [30].
Study of in-plane wave propagation in 2-D polycrystalline microstructure
Published in Mechanics of Advanced Materials and Structures, 2022
Manas Kumar Padhan, Mira Mitra
The microstructure of polycrystalline materials is generated by tessellation. Tessellation is the method of partitioning the 2-D space into small non-overlapping regions of convex polygon, which represents the microstructure of a material. Although several methods are available to represent a random polycrystalline microstructure, Voronoi tessellation is widely used [39, 40]. Voronoi tessellation works on nucleation and growth, where a set of points called nucleation points are randomly generated on an area A0. These randomly generated points share the area among themselves by considering the neighboring points near the nuclei. Neighboring points are selected by ensuring a constant growth of radius in each direction from the nuclei and the growth ceases when the boundary of two nuclei touches.
Unveiling students’ explorations of tessellations with Scratch through mathematical aesthetics
Published in International Journal of Mathematical Education in Science and Technology, 2022
Kenan Gökdağ, Meriç Özgeldi, İlker Yakın
In the first activity, students were asked to create regular tessellations with triangle, square, pentagon, hexagon, heptagon, octagon, nonagon, and decagon by using Scratch. All students created tessellations and realized that triangles, squares, and regular hexagons are the only regular polygons that will tessellate. The arrangement of Scratch code blocks showed their explorations on looking for appealing tessellation structure. In this activity, students first discovered the rule of calculating one external angle in a regular polygon (i.e. 360/n). Figure 2 shows the code blocks students used to create regular tessellations.