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The Hexagonal Efficient Coordinate System (HECS), formerly known as Array Set Addressing (ASA), is a coordinate system for hexagonal grids that allows hexagonally sampled images to be efficiently stored and processed on digital systems. HECS represents the hexagonal grid as a set of two interleaved rectangular sub-arrays, which can be addressed ...
In 2018, Eric Weiss showed how to fully represent an image as a hypervector. A vector could contain information about all the objects in the image, including properties such as color, position, and size. [2] In 2023, Abbas Rahimi et al., used HDC with neural networks to solve Raven's progressive matrices. [2]
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
In 1985, Joseph O'Rourke published a cubic-time algorithm to find the minimum-volume enclosing box of a 3-dimensional point set. O'Rourke's approach uses a 3-dimensional rotating calipers technique, and is based on lemmas characterizing the minimum enclosing box:
Honeycomb point set as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. Vectors and are primitive translation vectors.. The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1]
In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula.
For a simple graph with vertex set U = {u 1, …, u n}, the adjacency matrix is a square n × n matrix A such that its element A ij is 1 when there is an edge from vertex u i to vertex u j, and 0 when there is no edge. [1]
Computational speed is restricted by the file sizes of 3D images, which are significantly larger than 2D images. For example, an 8-bit (1024x1024) pixel 2D image has a file size of 1 MB, while an 8-bit (1024x1024x1024) voxel 3D image has a file size of 1 GB. This can be partially offset using parallel computing. [13] [14]