# Geometric Transforms

The Wolfram Language's symbolic architecture and sophisticated mathematical capabilities allow it to take a uniquely high-level approach to geometric transformationssupporting complete geometric, matrix, and functional representations in any number of dimensions, whether for mechanical systems, computer graphics, or pure mathematics.

### Geometric Object Transformations

GeometricTransformation apply any transformation function to geometric objects

### Rotation Matrices in 3D

EulerMatrix axis-oriented rotations in the current frame (intrinsic rotations)

RollPitchYawMatrix axis-oriented rotations in the global frame (extrinsic rotations)

gives angles from rotation matrices

### Transformation Matrices in nD

RotationMatrix rotations in any number of dimensions

ScalingMatrix stretch or shrink along any direction

TransformationMatrix the matrix representation of a transformation function

### Symbolic Transformation Functions in nD

TransformationFunction general symbolic representation of transformations

Composition symbolic composition of transformation functions

InverseFunction inverse of transformation functions

### Transformation Functions from Points

FindGeometricTransform find affine or linear fractional transform between point sets

### Algebraic Structure

FiniteGroupData properties of finite groups