Koordinatmapping

Koordinatmapping is the transformation of coordinates from one reference frame or coordinate system to another. It takes a point described in one set of coordinates and produces a corresponding point in another system, enabling translation, rotation, scaling, or projection of positions. It is a foundational idea in mathematics, computer graphics, GIS, and engineering.

Mappings can be linear, affine, projective, or nonlinear. Linear mappings are described by matrices and preserve straight lines; affine mappings add translation to linear mappings. Projective mappings use homogeneous coordinates to model perspective effects, which is essential for rendering and vision tasks.

Common applications include converting between world space and camera or screen space in graphics; mapping texture coordinates onto 3D surfaces (UV mapping); transforming geographic coordinates to planar map coordinates via projections in GIS; and mapping joint or sensor coordinates to physical positions in robotics.

Implementation often relies on transformation matrices and homogeneous coordinates to combine multiple operations—such as rotation, scaling, and translation—into a single step. In digital data, coordinate mapping may require interpolation or resampling when changing resolution or alignment.

Key challenges include distortion from non-linear mappings, loss of information in projections, and numerical errors in computations. The choice of mapping depends on which properties to preserve (angles, areas, distances) and on the geometry and precision requirements of the application.