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Fundamentals
Published in Michael Hann, The Grammar of Pattern, 2019
A regular polygon is a closed, two-dimensional figure bounded by equal-length, straight lines (Rich 1963, p. 7, Hann 2012, p. 5) and with equal interior angles. The number of regular polygons is (in principle) infinite. Where sides are not of equal length, and interior angles differ, then the word ‘regular’ is not used. Triangles of various kinds, quadrilaterals (such as squares and other four-sided figures such as rectangles), pentagons and hexagons, etc. are examples of polygons. All polygons are formed by sides (or lines), vertices (the points where adjacent sides meet) and angles (between adjacent sides). Often, polygons, either on their own or in combination, act as compositional frameworks underpinning and guiding the placement of components of a visual statement. Occasionally the word ‘convex’ is added to denote a polygon with all interior angles less than 180° and all vertices pointing outwards from the interior of the figure. The concern here is with regular convex polygons of the types used as unit cells for tilings or grids. Various regular convex polygons (from a three-sided equilateral triangle to a regular ten-sided decagon) are presented in Figure 2.1. As the number of sides (or number of connecting lines) increases, the polygon's shape becomes progressively like a circle (Jacobs 1974, p. 499).
Model
Published in Jordan Meadows, Vehicle Design, 2017
An alternate method for constructing surfaces digitally is based on polygon modeling. Other software packages such as Maya provide powerful capability for modeling surfaces this way. Rather than generating a network of curves and splines, this method of digital modeling is developed from mesh data created with polygons. Polygon models are a collection of vertices, edges, and faces organized to approximate and represent a surface. Whereas NURBS-based principles were developed as an outgrowth from old-world shipbuilding and coachbuilding with splines, polygon models are more akin to figurative sculpting. The principles of such are derived from model-making techniques developed in the entertainment industry to create surfaces with immense nuance and detail. However, they do have a difficult time representing a curved surface with typical automotive refinement.
Hardware Implementation of the Image Recognition System Based on Parallel Shift Technology
Published in Stepan Bilan, Sergey Yuzhakov, Image Processing and Pattern Recognition, 2018
Hardware implementation allows implementation of an image shift without first calculating the coordinates of the image pixel shift. Analysis of the examined coatings showed that there are only three types of lattices that are built on the basis of regular polygons that makes it possible to form a dense mosaic field. Such regular polygons include triangles, quadrilaterals and hexagons. Use of other grids of regular polygons does not make it possible to form a discrete plane densely. Other forms of coverage with different forms of cells do not allow the shift of images without loss of information.
Optimization design method for noise barrier tunnel junction on merging lanes using quad meshes
Published in Journal of Asian Architecture and Building Engineering, 2022
A polygon mesh is a collection of vertices, edges, and faces, representing complex objects in computer graphics. It uses a combination of simple polygon cells with triangles and quadrangles being the most common. Polygon meshes can be represented using various methods: face-vertex meshes (FV mesh) are the most common mesh representation using a set of faces and vertices. Mesh faces consist of the indices of the mesh vertices combined in the counterclockwise direction. The mesh vertices with two or more identical coordinates generated by the contact of mesh faces can be welded into a single mesh vertex. In other words, one mesh vertex is shared by one or more mesh faces, and the geometry is represented even when it moves because face connectivity is maintained.
Digital Twinning remote laboratories for online practical learning
Published in Production & Manufacturing Research, 2022
C. Palmer, B. Roullier, M. Aamir, F. McQuade, Leonardo Stella, A. Anjum, U. Diala
The Geometry Pipeline provides 3-D equipment model representations for the equipment items and virtual environment in the form of FBX files (Autodesk, 2021). The hierarchy of the FBX file is defined as follows: At the root level, the file contains one or more objects. Each object may either contain other objects or meshes (but not both). A mesh is a three-dimensional, polygonal representation of a piece of geometry, made up of sets of vertices and faces. Meshes are always leaf nodes within an FBX. As well as potentially containing meshes and other objects, each object contains a transform. This is a set of vectors representing the position, rotation and scale of the object relative to its parent.
Simulation analysis on the coupler behaviour and its influence on the braking safety of locomotive
Published in Vehicle System Dynamics, 2018
Ruiming Zou, Shihui Luo, Weihua Ma
Polygonal modelling is a common way of modelling, consisting of vertices and polygons geometrically, where vertex is determined by coordinates in Euclidean space while the polygon is created out of vertices. The geometry of the model can be determined by topological relationship of all polygons.