org.apache.sis.referencing.operation.transform

Interface LinearTransform

All Superinterfaces:

MathTransform

public interface LinearTransform
extends MathTransform

A usually affine, or otherwise a projective transform, which convert coordinates using only linear equations. A projective transform is capable of mapping an arbitrary quadrilateral into another arbitrary quadrilateral, while preserving the straightness of lines. In the special case where the transform is affine, the parallelism of lines in the source is preserved in the output.

Such a coordinate transformation can be represented by a matrix of arbitrary size, which is given by the getMatrix() method. The relationship between matrix size and transform dimensions is as below:

• The number of columns in the matrix is equal to the number of source dimensions plus 1
• The number of rows in the matrix is equal to the number of target dimensions plus 1.

Affine transform

In most cases the transform in affine. For such transforms, the last matrix row contains only zero values except in the last column, which contains 1. For example a conversion from projected coordinates (metres) to display coordinates (pixel) can be done as below:

Projective transform

If the last matrix row does not met the above constraints, then the transform is not affine. A projective transform can be used as a generalization of affine transforms. In such case the computation performed by SIS is similar to PerspectiveTransform in Java Advanced Imaging. For example a square matrix of size 4×4 is used for transforming three-dimensional coordinates. The transformed points (x',y',z') are computed as below:

$$\left[\begin{array}{c}x\text{'}\\ y\text{'}\\ z\text{'}\end{array}\right]=\left[\begin{array}{c}u/t\\ v/t\\ w/t\end{array}\right]$$

where u, v, w and t are obtained by

$$\left[\begin{array}{c}u\\ v\\ w\\ t\end{array}\right]=\left[\begin{array}{cccc}{m}_{00}& m_{01}& m_{02}& m_{03}\\ m_{10}& m_{11}& m_{12}& m_{13}\\ m_{20}& m_{21}& m_{22}& m_{23}\\ m_{30}& m_{31}& m_{32}& m_{33}\end{array}\right]\times \left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]$$

Instantiation

The easiest way to instantiate a LinearTransform is to use the MathTransforms.linear(Matrix) convenience method.

Since:

0.4

See Also:

MathTransforms.linear(Matrix), LinearTransformBuilder, AffineTransform, Affine transformation on MathWorld

Defined in the sis-referencing module

Method Summary

Methods

Modifier and Type	Method and Description
Matrix	getMatrix() Returns the coefficients of this linear transform as a matrix.
boolean	isAffine() Returns true if this transform is affine.

Methods inherited from interface MathTransform

derivative, getSourceDimensions, getTargetDimensions, inverse, isIdentity, toWKT, transform, transform, transform, transform, transform

Method Detail

isAffine

boolean isAffine()

Returns true if this transform is affine. An affine transform preserves parallelism.

Returns:

true if this transform is affine.

Since:

0.6

See Also:

MatrixSIS.isAffine()

getMatrix

Matrix getMatrix()

Returns the coefficients of this linear transform as a matrix. Converting a coordinate with this MathTransform is equivalent to multiplying the returned matrix by a vector containing the ordinate values with an additional 1 in the last row. See LinearTransform class Javadoc for more details.

Returns:

The coefficients of this linear transform as a matrix.

See Also:

MathTransforms.getMatrix(MathTransform)