Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation

Multivariate interpolation

In numerical analysis, multivariate interpolation or spatial interpolation is interpolation on functions of more than one variable.The function to be interpolated is known at given points and the interpolation problem consist of yielding values at arbitrary points .-Regular grid:For function...

 in one or more dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s.

Interpolation

Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....

 is the problem of approximating the value for a non-given point in some space when given some colors of points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping

Mipmap

In 3D computer graphics texture filtering, MIP maps are pre-calculated, optimized collections of images that accompany a main texture, intended to increase rendering speed and reduce aliasing artifacts. They are widely used in 3D computer games, flight simulators and other 3D imaging systems. The...

) in real-time

Real-time computing

In computer science, real-time computing , or reactive computing, is the study of hardware and software systems that are subject to a "real-time constraint"— e.g. operational deadlines from event to system response. Real-time programs must guarantee response within strict time constraints...

 3D rendering

3D rendering

3D rendering is the 3D computer graphics process of automatically converting 3D wire frame models into 2D images with 3D photorealistic effects on a computer.-Rendering methods:...

 to select color values for a textured

Texture filtering

In computer graphics, texture filtering or texture smoothing is the method used to determine the texture color for a texture mapped pixel, using the colors of nearby texels . Mathematically, texture filtering is a type of anti-aliasing, but it filters out high frequencies from the texture fill...

 surface.

Connection to Voronoi diagram

For a given set of points in space, a Voronoi diagram

Voronoi diagram

In mathematics, a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space, determined by distances to a specified family of objects in the space...

is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbour interpolation, by assigning the function value at the given point to all the points inside the cell. The figures on the right side show by colour the shape of the cells.