Class Name: PointTransformation Class Name: ListTransformation

• transformations that transform a list of points at a time • transformations that determine the accuracy of transformed points In any implementation of this model, these 3 groups shall be handled as units, either implementing all of the operations in a group or none of them. Stereotype: interface Associations: from 1 SpatialReferenceByCoordinates in association: source to 1 SpatialReferenceByCoordinates in association: target used by 0.. ConcatenatedTransformation Attributes: transformationName: Name This attribute is the identifier of this coordinate transformation. domainOfValidity: GM_Object The domainOfValidity attribute is a geometry that defines the geographical or image region where this Coordinate Transformation object is appropriate to use. The coordinate reference system of this geometry may be the source, target, or any standard coordinate reference system. When image coordinates are the source SpatialReferenceByCoordinates, the coordinate reference system will usually be the image coordinates reference system. This OGC geometry object supports the GM_Object interface. The GM_Object interface, as described in Topic 1: Feature Geometry, includes operations that will check whether or not a specified point or geometry is spatially within the domain of this GM_Object. Operations: inverse : CoordinateTransformation This operation returns another CoordinateTransformation object that reverses the actions of this CoordinateTransformation object. The target of the inverse transformation is the source of the original, and the source of the inverse transformation is the target of the original. Using the original transform followed by the inverse transform will result in an identity map on the source coordinate space, when allowances for error are made.

4.1.21. Class Name: PointTransformation

Package Class Belongs to: Coordinate Transform Documentation: This interface class defines coordinate transformation operations that transform single point position coordinates between two different coordinate reference systems. Superclass: none Stereotype: interface Associations: none Attributes: none Operations: transform point: CoordinatePoint: CoordinatePoint This operation transforms the coordinates of one point given in the source coordinate system to the coordinates of the same point in the target coordinate system. derivativeMatrix point: CoordinatePoint: Matrix This operation determines the matrix of partial derivatives of the transformation result coordinates with respect to the input coordinates, at the specified position in the source coordinate reference system. This matrix is the multi-dimensional equivalent of a derivative or a tangent. The Open GIS Abstract Specification Page 29 Volume 16: Image Coordinate Transformation Services 00-116.doc

4.1.22. Class Name: ListTransformation

Package Class Belongs to: Coordinate Transform Documentation: This interface class defines coordinate transformation operations that transform a list of point position coordinates for each call, between two different coordinate reference systems. The list can contain one or more points. Superclass: none Stereotype: interface Associations: none Attributes: none Operations: transform points: Sequence CoordinatePoint: Sequence CoordinatePoint This operation transforms the coordinates of a list of one or more points given in the source coordinate system to the corresponding list of positions in the target coordinate system. The returned list contains the same number of points in the same order as the input list no densification is performed. derivativeMatrix points: Sequence CoordinatePoint: Sequence Matrix This operation determines matrices of the partial derivatives of the transformation result coordinates with respect to the input coordinates. Each matrix is the multi-dimensional equivalent of a derivative or a tangent. This operation is similar to the corresponding operation in the PointTransformation Interface, but works on a specified list of positions in the source coordinate reference system.

4.1.23. Class Name: TransformationWithAccuracy