mappingtransform

Mapping transform is a general term used in mathematics, computer science, and data processing to describe a rule that assigns every element of one domain to an element of another. It is often represented as a function f: X -> Y and can be used to change coordinates, feature representations, or data values. In geometry and computer graphics, mapping transforms relocate points, directions, or textures from one space to another. Common operations include translation, rotation, scaling, and perspective projection, frequently combined into a single transform for efficiency.

Types include linear transforms, represented by a matrix, affine transforms combining linear transformation and translation, and projective transforms that model perspective. Nonlinear mapping transforms include polynomial, radial basis, or spline-based mappings. In data science, mapping transforms often refer to feature engineering steps that map input features to new representations that are more suitable for modeling, such as normalization, encoding, or kernel mappings.

Properties: depending on the spaces and the rule, a mapping transform can be injective, surjective, bijective, or neither; many practical transforms are designed to be invertible within a chosen domain. They are composable: applying two transforms in sequence yields a single combined transform.

Applications: coordinate system changes in engineering, image and video processing for remapping pixels or textures, geographic information systems for coordinate reference frame conversions, robotics and computer vision for pose estimation, and machine learning for feature extraction.

See also: transform, mapping, affine transform, coordinate transformation, projective transform.