Module org.apache.sis.referencing
Package org.apache.sis.referencing.operation.transform

Class AbstractMathTransform

Object
FormattableObject
AbstractMathTransform
All Implemented Interfaces:
Parameterized, Lenient­Comparable, Math­Transform
Direct Known Subclasses:
Abstract­Math­Transform​.Inverse, Abstract­Math­Transform1D, Abstract­Math­Transform2D, Datum­Shift­Transform, Ellipsoid­To­Centric­Transform, Pass­Through­Transform, Wraparound­Transform
public abstract class AbstractMathTransform extends FormattableObject implements MathTransform, Parameterized, LenientComparable
Provides a default implementation for most methods required by the Math­Transform interface. A Math­Transform is an object that actually does the work of applying a formula to coordinate values. The math transform does not know or care how the coordinates relate to positions in the real world. For example if an affine transform scales z values by a factor of 1000, then it could be converting metres to millimetres, or it could be converting kilometres to metres.

Abstract­Math­Transform provides a convenient base class from which Math­Transform implementations can be easily derived. It also defines a few additional SIS-specific methods for convenience of performance. The simplest way to implement this abstract class is to provide an implementation for the following methods only:

However, more performance may be gained by overriding the other transform(…) methods as well.

Immutability and thread safety

All Apache SIS implementations of Math­Transform are immutable and thread-safe. It is highly recommended that third-party implementations be immutable and thread-safe too. This means that unless otherwise noted in the javadoc, Math­Transform instances can be shared by many objects and passed between threads without synchronization.

Serialization

Math­Transform may or may not be serializable, at implementation choices. Most Apache SIS implementations are serializable, but the serialized objects are not guaranteed to be compatible with future SIS versions. Serialization should be used only for short term storage or RMI between applications running the same SIS version.
Since:
0.5
See Also:

  • Constructor Details

    • AbstractMathTransform

      protected AbstractMathTransform()
      Constructor for subclasses.

  • Method Details

    • getSourceDimensions

      public abstract int getSourceDimensions()
      Returns the number of dimensions of input points.
      Specified by:
      get­Source­Dimensions in interface Math­Transform
      Returns:
      the number of dimensions of input points.
      See Also:

    • getTargetDimensions

      public abstract int getTargetDimensions()
      Returns the number of dimensions of output points.
      Specified by:
      get­Target­Dimensions in interface Math­Transform
      Returns:
      the number of dimensions of output points.
      See Also:

    • getDomain

      public Optional<Envelope> getDomain(DomainDefinition criteria) throws TransformException
      Returns the ranges of coordinate values which can be used as inputs. They are limits where the transform is mathematically and numerically applicable. This is not the domain of validity for which a coordinate reference system has been defined, because this method ignores "real world" considerations such as datum and country boundaries.

      This method is for allowing callers to crop their data for removing areas that may cause numerical problems. For example, results of Mercator projection tend to infinity when the latitude value approaches a pole. For avoiding data structures with unreasonably large values or Double​.Na­N, we commonly crop data to some arbitrary maximal latitude value (typically 80 or 84°) before projection. Those limits are arbitrary, the transform does not become suddenly invalid after a limit. The Domain­Definition gives some controls on the criteria for choosing a limit.

      Many transforms, in particular all affine transforms, have no mathematical limits. Consequently, the default implementation returns an empty value. Again it does not mean that the coordinate operation has no geospatial domain of validity, but the latter is not the purpose of this method. This method is (for example) for preventing a viewer to crash when attempting to render a world-wide image.

      Callers do not need to search through transform steps. SIS implementation of concatenated transforms do that automatically.

      Parameters:
      criteria - controls the definition of transform domain.
      Returns:
      estimation of a domain where this transform is considered numerically applicable.
      Throws:
      Transform­Exception - if the domain cannot be estimated.
      Since:
      1.3
      See Also:

    • getParameterDescriptors

      public ParameterDescriptorGroup getParameterDescriptors()
      Returns the parameter descriptors for this math transform, or null if unknown.

      Relationship with ISO 19111

      This method is similar to Operation­Method​.get­Parameters(), except that typical Math­Transform implementations return parameters in standard units (usually metres or decimal degrees).
      Specified by:
      get­Parameter­Descriptors in interface Parameterized
      Returns:
      the parameter descriptors for this math transform, or null if unspecified.
      See Also:

    • getParameterValues

      public ParameterValueGroup getParameterValues()
      Returns the parameter values for this math transform, or null if unknown. This is not necessarily the parameters that the user specified at construction time, since implementations may have applied normalizations.

      Normalized and contextual parameters

      Most Apache SIS implementations of map projections perform their calculations on an ellipsoid having a semi-major axis length of 1. In such cases, the group returned by this method contains a "semi_major" parameter with a value of 1. If the real axis length is desired, we need to take in account the context of this math transform, i.e. the scales and offsets applied before and after this transform. This information is provided by get­Contextual­Parameters().
      Specified by:
      get­Parameter­Values in interface Parameterized
      Returns:
      the parameter values for this math transform, or null if unspecified. Note that those parameters may be normalized (e.g. represent a transformation of an ellipsoid of semi-major axis length of 1).
      See Also:

    • getContextualParameters

      protected ContextualParameters getContextualParameters()
      Returns the parameters for a sequence of normalize → this → denormalize transforms (optional operation). Subclasses can override this method if they choose to split their computation in linear and non-linear parts. Such split is optional: it can leads to better performance (because SIS can concatenate efficiently consecutive linear transforms), but should not change significantly the result (ignoring differences in rounding errors). If a split has been done, then this Math­Transform represents only the non-linear step and Apache SIS needs this method for reconstructing the parameters of the complete transform.
      Returns:
      the parameter values for the sequence of normalize → this → denormalize transforms, or null if unspecified. Callers should not modify the returned parameters, since modifications (if allowed) will generally not be reflected back in this Math­Transform.
      Since:
      0.6

    • isIdentity

      public boolean isIdentity()
      Tests whether this transform does not move any points. The default implementation always returns false.
      Specified by:
      is­Identity in interface Math­Transform

    • transform

      public DirectPosition transform(DirectPosition ptSrc, DirectPosition ptDst) throws TransformException
      Transforms the specified pt­Src and stores the result in pt­Dst. The default implementation performs the following steps: This method does not update the associated Coordinate­Reference­System value.
      Specified by:
      transform in interface Math­Transform
      Parameters:
      pt­Src - the coordinate tuple to be transformed.
      pt­Dst - the coordinate tuple that stores the result of transforming pt­Src, or null.
      Returns:
      the coordinate tuple after transforming pt­Src and storing the result in pt­Dst, or a newly created point if pt­Dst was null.
      Throws:
      Mismatched­Dimension­Exception - if pt­Src or pt­Dst doesn't have the expected dimension.
      Transform­Exception - if the point cannot be transformed.

    • transform

      public abstract Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws TransformException
      Transforms a single coordinate tuple in an array, and optionally computes the transform derivative at that location. Invoking this method is conceptually equivalent to running the following: 
      Matrix derivative = null;
if (derivate) {
    double[] coordinates = Arrays.copyOfRange(srcPts, srcOff, srcOff + getSourceDimensions());
    derivative = this.derivative(new GeneralDirectPosition(coordinates));
}
this.transform(srcPts, srcOff, dstPts, dstOff, 1);                   // May overwrite srcPts.
return derivative;
      However, this method provides two advantages:
      • It is usually easier to implement for Abstract­Math­Transform subclasses. The default transform(double[], int, double[], int, int) method implementation will invoke this method in a loop, taking care of the iteration strategy depending on the argument value.
      • When both the transformed point and its derivative are needed, this method may be significantly faster than invoking the transform and derivative methods separately because many internal calculations are the same. Computing those two information in a single step can help to reduce redundant calculation.

      Note for implementers

      The source and destination may overlap. Consequently, implementers must read all source coordinate values before to start writing the transformed coordinates in the destination array.
      Parameters:
      src­Pts - the array containing the source coordinates (cannot be null).
      src­Off - the offset to the point to be transformed in the source array.
      dst­Pts - the array into which the transformed coordinates is returned. May be the same than src­Pts. May be null if only the derivative matrix is desired.
      dst­Off - the offset to the location of the transformed point that is stored in the destination array.
      derivate - true for computing the derivative, or false if not needed.
      Returns:
      the matrix of the transform derivative at the given source position, or null if the derivate argument is false.
      Throws:
      Transform­Exception - if the point cannot be transformed or if a problem occurred while calculating the derivative.
      See Also:

    • transform

      public void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws TransformException
      Transforms a list of coordinate tuples. This method is provided for efficiently transforming many points. The supplied array of coordinate values will contain packed coordinate values.

      Example

      If the source dimension is 3, then the coordinates will be packed in this order: (x₀,y₀,z₀, x₁,y₁,z₁ …).

      Implementation note

      The default implementation invokes transform(double[], int, double[], int, boolean) in a loop, using an iteration strategy determined from the arguments for iterating over the points. For creating a more efficient implementation, see Iteration­Strategy javadoc for a method skeleton.
      Specified by:
      transform in interface Math­Transform
      Parameters:
      src­Pts - the array containing the source point coordinates.
      src­Off - the offset to the first point to be transformed in the source array.
      dst­Pts - the array into which the transformed point coordinates are returned. May be the same than src­Pts.
      dst­Off - the offset to the location of the first transformed point that is stored in the destination array.
      num­Pts - the number of point objects to be transformed.
      Throws:
      Transform­Exception - if a point cannot be transformed. Some implementations will stop at the first failure, wile some other implementations will fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform to this.

    • transform

      public void transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) throws TransformException
      Transforms a list of coordinate tuples. The default implementation delegates to transform(double[], int, double[], int, int) using a temporary array of doubles.

      Implementation note

      See Iteration­Strategy javadoc for a method skeleton.
      Specified by:
      transform in interface Math­Transform
      Parameters:
      src­Pts - the array containing the source point coordinates.
      src­Off - the offset to the first point to be transformed in the source array.
      dst­Pts - the array into which the transformed point coordinates are returned. May be the same than src­Pts.
      dst­Off - the offset to the location of the first transformed point that is stored in the destination array.
      num­Pts - the number of point objects to be transformed.
      Throws:
      Transform­Exception - if a point cannot be transformed. Some implementations will stop at the first failure, wile some other implementations will fill the un-transformable points with Float​.Na­N values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform to this.

    • transform

      public void transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts) throws TransformException
      Transforms a list of coordinate tuples. The default implementation delegates to transform(double[], int, double[], int, int) using a temporary array of doubles.
      Specified by:
      transform in interface Math­Transform
      Parameters:
      src­Pts - the array containing the source point coordinates.
      src­Off - the offset to the first point to be transformed in the source array.
      dst­Pts - the array into which the transformed point coordinates are returned.
      dst­Off - the offset to the location of the first transformed point that is stored in the destination array.
      num­Pts - the number of point objects to be transformed.
      Throws:
      Transform­Exception - if a point cannot be transformed. Some implementations will stop at the first failure, wile some other implementations will fill the untransformable points with Float.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform to this.

    • transform

      public void transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws TransformException
      Transforms a list of coordinate tuples. The default implementation delegates to transform(double[], int, double[], int, int) using a temporary array of doubles if necessary.
      Specified by:
      transform in interface Math­Transform
      Parameters:
      src­Pts - the array containing the source point coordinates.
      src­Off - the offset to the first point to be transformed in the source array.
      dst­Pts - the array into which the transformed point coordinates are returned.
      dst­Off - the offset to the location of the first transformed point that is stored in the destination array.
      num­Pts - the number of point objects to be transformed.
      Throws:
      Transform­Exception - if a point cannot be transformed. Some implementations will stop at the first failure, wile some other implementations will fill the untransformable points with Double.NaN values, continue and throw the exception only at end. Implementations that fall in the latter case should set the last completed transform to this.

    • derivative

      public Matrix derivative(DirectPosition point) throws TransformException
      Gets the derivative of this transform at a point. The default implementation performs the following steps:
      Specified by:
      derivative in interface Math­Transform
      Parameters:
      point - the coordinate tuple where to evaluate the derivative.
      Returns:
      the derivative at the specified point (never null).
      Throws:
      Null­Pointer­Exception - if the derivative depends on coordinates and point is null.
      Mismatched­Dimension­Exception - if point does not have the expected dimension.
      Transform­Exception - if the derivative cannot be evaluated at the specified point.

    • inverse

      public MathTransform inverse() throws NoninvertibleTransformException
      Returns the inverse transform of this object. The default implementation returns this if this transform is an identity transform, or throws an exception otherwise. Subclasses should override this method.

      Implementation note

      The Abstract­Math­Transform​.Inverse inner class can be used as a base for inverse transform implementations.
      Specified by:
      inverse in interface Math­Transform
      Throws:
      Noninvertible­Transform­Exception

    • tryConcatenate

      protected MathTransform tryConcatenate(boolean applyOtherFirst, MathTransform other, MathTransformFactory factory) throws FactoryException
      Concatenates or pre-concatenates in an optimized way this math transform with the given one, if possible. If an optimization is possible, a new math transform is created to perform the combined transformation. The apply­Other­First value determines the transformation order as bellow:
      • If apply­Other­First is true, then transforming a point p by the combined transform is equivalent to first transforming p by other and then transforming the result by this.
      • If apply­Other­First is false, then transforming a point p by the combined transform is equivalent to first transforming p by this and then transforming the result by other.
      If no optimization is available for the combined transform, then this method returns null. In the latter case, the concatenation will be prepared by Default­Math­Transform­Factory using a generic implementation.

      The default implementation returns the identity transform if the other transform is the inverse of this transform, or returns null otherwise. This method is ought to be overridden by subclasses capable of concatenating some combination of transforms in a special way. Linear­Transform implementations do not need to override this method since matrix multiplications will be handled automatically, and this method does not need to handle the is­Identity() case.

      Parameters:
      apply­Other­First - true if the transformation order is other followed by this, or false if the transformation order is this followed by other.
      other - the other math transform to (pre-)concatenate with this transform.
      factory - the factory which is (indirectly) invoking this method, or null if none.
      Returns:
      the math transforms combined in an optimized way, or null if no such optimization is available.
      Throws:
      Factory­Exception - if an error occurred while combining the transforms.
      Since:
      0.8
      See Also:

    • hashCode

      public final int hashCode()
      Returns a hash value for this transform. This method invokes compute­Hash­Code() when first needed and caches the value for future invocations. Subclasses shall override compute­Hash­Code() instead of this method.
      Overrides:
      hash­Code in class Object
      Returns:
      the hash code value. This value may change between different execution of the Apache SIS library.

    • computeHashCode

      protected int computeHashCode()
      Computes a hash value for this transform. This method is invoked by hash­Code() when first needed.
      Returns:
      the hash code value. This value may change between different execution of the Apache SIS library.

    • equals

      public final boolean equals(Object object)
      Compares the specified object with this math transform for strict equality. This method is implemented as below (omitting assertions): 
      return equals(other, ComparisonMode.STRICT);
      Specified by:
      equals in interface Lenient­Comparable
      Overrides:
      equals in class Object
      Parameters:
      object - the object to compare with this transform.
      Returns:
      true if the given object is a transform of the same class and using the same parameter values.
      Throws:
      Assertion­Error - if assertions are enabled and the objects are equal but their hash codes are different.
      See Also:

    • equals

      public boolean equals(Object object, ComparisonMode mode)
      Compares the specified object with this math transform for equality. Two math transforms are considered equal if, given identical source positions, their transformed positions would be equal or approximately equal. This method may conservatively returns false if unsure.

      The default implementation returns true if the following conditions are met:

      • object is an instance of the same class than this. We require the same class because there is no interface for the various kinds of transform.
      • If the hash code value has already been computed for both instances, their values are the same (opportunist performance enhancement).
      • The contextual parameters are equal according the given comparison mode.
      Specified by:
      equals in interface Lenient­Comparable
      Parameters:
      object - the object to compare with this transform.
      mode - the strictness level of the comparison. Default to STRICT.
      Returns:
      true if the given object is considered equals to this math transform.
      See Also:

    • formatTo

      protected String formatTo(Formatter formatter)
      Formats the inner part of a Well Known Text version 1 (WKT 1) element. The default implementation formats all parameter values returned by get­Parameter­Values(). The parameter group name is used as the math transform name.

      Compatibility note

      Param_MT is defined in the WKT 1 specification only. If the formatter convention is set to WKT 2, then this method silently uses the WKT 1 convention without raising an error (unless this Math­Transform cannot be formatted as valid WKT 1 neither).
      Specified by:
      format­To in class Formattable­Object
      Parameters:
      formatter - the formatter to use.
      Returns:
      the WKT element name, which is "Param_MT" in the default implementation.
      See Also: