Package com.kuka.math.geometry

This package contains interfaces and implementations for basic linear algebra and geometric concepts.

See:
Description

Interface Summary

IRotation	Abstract representation of a rotation in 3-dimensional space.
ITransformation	Represents a transformation in 3-dimensional space.

Class Summary

AbstractRotation	Abstract representation of a rotation in 3-dimensional space.
AbstractTransformation	Represents a transformation in 3-dimensional space.
AxisAngleRotation	Immutable representation of a spatial rotation in axis-angle form.
EulerZyxRotation	Immutable representation of a spatial rotation as Z-Y-X Euler angles, which are the same as X-Y-Z fixed angles.
MathUtils	Utility class providing static helper methods for the mathematical classes.
Matrix	Immutable representation of a 3x3 matrix.
MatrixBuilder	A mutable builder class for matrices.
MatrixRotation	Immutable representation of a spatial rotation in matrix form.
MatrixTransformation	Immutable implementation of a spatial transformation in matrix form, that is the rotation part and the vector part of the homogeneous transformation matrix.
Point3D	Immutable representation of a 3-dimensional point.
Rotation	Immutable representation of a spatial rotation as Z-Y-X Euler angles and/or 3x3 rotation matrix.
Transformation	An immutable representation of a spatial transformation.
Vector3D	Immutable representation of a 3-element vector consisting of x, y and z elements.
XyzAbcTransformation	Immutable representation of a spatial transformation as a combination of x, y, z translational elements and α, β, γ (resp.

Enum Summary

CoordinateAxis	This enumeration represents the three axes of a Cartesian coordinate system.
CoordinateDirection	This enum specifies the six directions along the three axes of a Cartesian coordinate system.
CoordinatePlane	This enumeration represents the coordinate planes in a Cartesian coordinate system.

Package com.kuka.math.geometry Description

This package contains interfaces and implementations for basic linear algebra and geometric concepts. The focus of this package is on geometric operations in 3-dimensional cartesian space. A good introductory reference is the book by Craig, John J. — Introduction to robotics; advanced mathematical concepts are found for example in Murray, R. et al — A mathematical Introduction to Robotic Manipulation.

Transformations and Rotations
The package provides the classes Transformation and Rotation to describe transformations and rotations in three dimensional geometric space. You can use these classes for general purpose calculations in combination with the rest of the RoboticsAPI. For further information refer to the documentation in Transformation.

Point, Vector, Matrix
To describe a point or a vector in three dimensional space or a 3x3 matrix the package provides the classes Point3D, Vector3D and Matrix.

The following propositions are hold on vectors and points:

1. Sum and difference of vectors are vectors
2. The sum of a vector and a point is a point
3. The difference between two points is a vector
4. The sum of two points is meaningless

Specialized transformations and rotations
The package also provides the interfaces ITransformation and IRotation along with different derived classes, for example XyzAbcTransformation/ MatrixTransformation and EulerZyxRotation/ MatrixRotation. These classes implement specific representations of the geometric types and may be used for performance reasons if a specific representation is needed.

Utility functions
To compare Points, Vectors, Matrices, Rotations and Transformations use MathUtils.

Coordinate axes, coordinate directions and coordinate planes
To simplify the representation and the description of the different axes, axes directions and planes the package provides the enums

• CoordinateAxis
• CoordinateDirection
• CoordinatePlane