Dpoints

Dpoints is a term used in geometry and computer science to denote a collection of points in a d-dimensional space. In many contexts, dpoints are abstract data structures that store the coordinates of points as sequences (x1, x2, ..., xd). Each point may also carry optional attributes such as color, intensity, or normal vectors.

Representation: A dpoints object typically includes a dimensionality parameter d and a set of N points, often stored as an array of length N with each entry containing d coordinates. Depending on the application, the coordinates may be integers or real numbers, and points can be dense (all coordinates provided) or sparse (some coordinates stored implicitly).

Usage: Dpoints are widely used in computational geometry, computer graphics, and machine learning for tasks such as clustering, nearest-neighbor search, mesh generation, and point-cloud processing. Algorithms may exploit the structure of dpoints using data structures like k-d trees or ball trees to accelerate distance computations. In dimensionality reduction, a dpoints dataset might be mapped to a lower-dimensional space while preserving pairwise distances as much as possible.

Variants: There is no single universal definition of dpoints; the term is generic and may be used differently in libraries or papers. Some implementations emphasize memory layout (row-major vs column-major), while others focus on streaming updates of the point set.

See also: Point cloud, Point set, k-d tree, Nearest neighbor search, Dimensionality reduction, Euclidean distance.