Geometric Transforms

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

Geometric Object Transformations

(RefLink[GeometricTransformation, paclet:ref/GeometricTransformation]) — apply any transformation function to geometric objects

Rotation Matrices in 3D

(RefLink[EulerMatrix, paclet:ref/EulerMatrix]) — axis-oriented rotations in the current frame (intrinsic rotations)

(RefLink[RollPitchYawMatrix, paclet:ref/RollPitchYawMatrix]) — axis-oriented rotations in the global frame (extrinsic rotations)

(RefLink[EulerAngles, paclet:ref/EulerAngles]), (RefLink[RollPitchYawAngles, paclet:ref/RollPitchYawAngles]) — gives angles from rotation matrices

Transformation Matrices in nD

(RefLink[RotationMatrix, paclet:ref/RotationMatrix]) — rotations in any number of dimensions

(RefLink[ScalingMatrix, paclet:ref/ScalingMatrix]) — stretch or shrink along any direction

(RefLink[TransformationMatrix, paclet:ref/TransformationMatrix]) — the matrix representation of a transformation function

Symbolic Transformation Functions in nD

(RefLink[TransformationFunction, paclet:ref/TransformationFunction]) — general symbolic representation of transformations

(RefLink[Composition, paclet:ref/Composition]) — symbolic composition of transformation functions

(RefLink[InverseFunction, paclet:ref/InverseFunction]) — inverse of transformation functions

Transformation Functions from Points

(RefLink[FindGeometricTransform, paclet:ref/FindGeometricTransform]) — find affine or linear fractional transform between point sets

Algebraic Structure

(RefLink[FiniteGroupData, paclet:ref/FiniteGroupData]) — properties of finite groups