gridpunten

Gridpunten, Dutch for grid points, are the discrete points arranged on a grid within a coordinate space. They form the nodes of a lattice that covers a domain and are defined by their coordinates, typically produced by sampling or partitioning the space. They serve as reference locations for storing values and performing calculations.

In a uniform Cartesian grid, gridpunten have coordinates (i h_x, j h_y) in two dimensions, where i and j are integers and h_x, h_y are the spacings along the x and y axes. In one dimension the points are i h, and in three dimensions they are (i h_x, j h_y, k h_z). Gridpunten can also be non-uniform, with spacings that vary across the domain, or part of an unstructured grid where connectivity between points is irregular.

Applications of gridpunten include sampling continuous fields, numerical approximation, and data storage. They are central to finite difference methods, where derivatives are approximated at gridpunten; finite element methods, where values are associated with nodes; and finite volume methods, where fluxes are computed at cell faces that relate to gridpunten. Outside numerical analysis, gridpunten underpin raster graphics, digital elevation models, and geographic information systems, where each gridpunt may hold a value such as image intensity or altitude.

Variations include structured grids with regular connectivity and unstructured grids with irregular connectivity. Adaptive mesh refinement adds or relocates gridpunten to resolve regions with higher detail. Gridpunten thus provide a versatile framework for representing and computing on discrete approximations of continuous spaces.