Ordered list of labels for all the axes of this CRS. The gml:axisAbbrev value should be used for these axis labels, after spaces and forbiddden characters are removed. When the srsName attribute is included, this attribute is optional. When the srsName attribute is omitted, this attribute shall also be omitted.

The "srsDimension" is the length of coordinate sequence (the number of entries in the list). This dimension is specified by the coordinate reference system. When the srsName attribute is omitted, this attribute shall be omitted.

In general this reference points to a CRS instance of gml:CoordinateReferenceSystemType (see coordinateReferenceSystems.xsd). For well known references it is not required that the CRS description exists at the location the URI points to. If no srsName attribute is given, the CRS must be specified as part of the larger context this geometry element is part of, e.g. a geometric element like point, curve, etc. It is expected that this attribute will be specified at the direct position level only in rare cases.

Ordered list of unit of measure (uom) labels for all the axes of this CRS. The value of the string in the gml:catalogSymbol should be used for this uom labels, after spaces and forbiddden characters are removed. When the axisLabels attribute is included, this attribute shall also be included. When the axisLabels attribute is omitted, this attribute shall also be omitted.

Source

<element name="vectorAtStart" type="gml:VectorType"><annotation><documentation>"vectorAtStart" is the unit tangent vector at the start point of the spline.</documentation></annotation></element>

Ordered list of labels for all the axes of this CRS. The gml:axisAbbrev value should be used for these axis labels, after spaces and forbiddden characters are removed. When the srsName attribute is included, this attribute is optional. When the srsName attribute is omitted, this attribute shall also be omitted.

The "srsDimension" is the length of coordinate sequence (the number of entries in the list). This dimension is specified by the coordinate reference system. When the srsName attribute is omitted, this attribute shall be omitted.

In general this reference points to a CRS instance of gml:CoordinateReferenceSystemType (see coordinateReferenceSystems.xsd). For well known references it is not required that the CRS description exists at the location the URI points to. If no srsName attribute is given, the CRS must be specified as part of the larger context this geometry element is part of, e.g. a geometric element like point, curve, etc. It is expected that this attribute will be specified at the direct position level only in rare cases.

Ordered list of unit of measure (uom) labels for all the axes of this CRS. The value of the string in the gml:catalogSymbol should be used for this uom labels, after spaces and forbiddden characters are removed. When the axisLabels attribute is included, this attribute shall also be included. When the axisLabels attribute is omitted, this attribute shall also be omitted.

Source

<element name="vectorAtEnd" type="gml:VectorType"><annotation><documentation>"vectorAtEnd" is the unit tangent vector at the end point of the spline.</documentation></annotation></element>

Cubic splines are similar to line strings in that they are a sequence of segments each with its own defining function. A cubic spline uses the control points and a set of derivative parameters to define a piecewise 3rd degree polynomial interpolation. Unlike line-strings, the parameterization by arc length is not necessarily still a polynomial. The function describing the curve must be C2, that is, have a continuous 1st and 2nd derivative at all points, and pass through the controlPoints in the order given. Between the control points, the curve segment is defined by a cubic polynomial. At each control point, the polynomial changes in such a manner that the 1st and 2nd derivative vectors are the same from either side. The control parameters record must contain vectorAtStart, and vectorAtEnd which are the unit tangent vectors at controlPoint[1] and controlPoint[n] where n = controlPoint.count. Note: only the direction of the vectors is relevant, not their length.

The attribute "interpolation" specifies the curve interpolation mechanism used for this segment. This mechanismuses the control points and control parameters to determine the position of this curve segment. For a CubicSpline the interpolation is fixed as "cubicSpline".

The attribute "numDerivativesInterior" specifies the type of continuity that is guaranteed interior to the curve. The default value of "0" means simple continuity, which is a mandatory minimum level of continuity. This level is referred to as "C 0 " in mathematical texts. A value of 1 means that the function and its first derivative are continuous at the appropriate end point: "C 1 " continuity. A value of "n" for any integer means the function and its first n derivatives are continuous: "C n " continuity.NOTE: Use of these values is only appropriate when the basic curve definition is an underdetermined system. For example, line string segments cannot support continuity above C 0 , since there is no spare control parameter to adjust the incoming angle at the end points of the segment. Spline functions on the other hand often have extra degrees of freedom on end segments that allow them to adjust the values of the derivatives to support C 1 or higher continuity.

The attribute "numDerivativesAtEnd" specifies the type of continuity between this curve segment and its successor. If this is the last curve segment in the curve, one of these values, as appropriate, is ignored. The default value of "0" means simple continuity, which is a mandatory minimum level of continuity. This level is referred to as "C 0 " in mathematical texts. A value of 1 means that the function and its first derivative are continuous at the appropriate end point: "C 1 " continuity. A value of "n" for any integer means the function and its first n derivatives are continuous: "C n " continuity.NOTE: Use of these values is only appropriate when the basic curve definition is an underdetermined system. For example, line string segments cannot support continuity above C 0 , since there is no spare control parameter to adjust the incoming angle at the end points of the segment. Spline functions on the other hand often have extra degrees of freedom on end segments that allow them to adjust the values of the derivatives to support C 1 or higher continuity.

The attribute "numDerivativesAtStart" specifies the type of continuity between this curve segment and its predecessor. If this is the first curve segment in the curve, one of these values, as appropriate, is ignored. The default value of "0" means simple continuity, which is a mandatory minimum level of continuity. This level is referred to as "C 0 " in mathematical texts. A value of 1 means that the function and its first derivative are continuous at the appropriate end point: "C 1 " continuity. A value of "n" for any integer means the function and its first n derivatives are continuous: "C n " continuity.NOTE: Use of these values is only appropriate when the basic curve definition is an underdetermined system. For example, line string segments cannot support continuity above C 0 , since there is no spare control parameter to adjust the incoming angle at the end points of the segment. Spline functions on the other hand often have extra degrees of freedom on end segments that allow them to adjust the values of the derivatives to support C 1 or higher continuity.

Source

<complexType name="SimpleCubicSplineType"><annotation><documentation>Cubic splines are similar to line strings in that they are a sequence of segments each with its own defining function. A cubic spline uses the control points and a set of derivative parameters to define a piecewise 3rd degree polynomial interpolation. Unlike line-strings, the parameterization by arc length is not necessarily still a polynomial. The function describing the curve must be C2, that is, have a continuous 1st and 2nd derivative at all points, and pass through the controlPoints in the order given. Between the control points, the curve segment is defined by a cubic polynomial. At each control point, the polynomial changes in such a manner that the 1st and 2nd derivative vectors are the same from either side. The control parameters record must contain vectorAtStart, and vectorAtEnd which are the unit tangent vectors at controlPoint[1] and controlPoint[n] where n = controlPoint.count. Note: only the direction of the vectors is relevant, not their length.</documentation></annotation><complexContent><extension base="gml:AbstractCurveSegmentType"><sequence><annotation><documentation>Unlike in gml:CubicSplineType, positions can only be specified in one way: inlined using gml:posList. The number of direct positions in the list must be at least three.</documentation></annotation><element ref="gml:posList"/><element name="vectorAtStart" type="gml:VectorType"><annotation><documentation>"vectorAtStart" is the unit tangent vector at the start point of the spline.</documentation></annotation></element><element name="vectorAtEnd" type="gml:VectorType"><annotation><documentation>"vectorAtEnd" is the unit tangent vector at the end point of the spline.</documentation></annotation></element></sequence><attribute name="interpolation" type="gml:CurveInterpolationType" fixed="cubicSpline"><annotation><documentation>The attribute "interpolation" specifies the curve interpolation mechanism used for this segment. This mechanism uses the control points and control parameters to determine the position of this curve segment. For a CubicSpline the interpolation is fixed as "cubicSpline".</documentation></annotation></attribute><attribute name="degree" type="integer" fixed="3"><annotation><documentation>The degree for a cubic spline is "3".</documentation></annotation></attribute></extension></complexContent></complexType>

The attribute "interpolation" specifies the curve interpolation mechanism used for this segment. This mechanismuses the control points and control parameters to determine the position of this curve segment. For a CubicSpline the interpolation is fixed as "cubicSpline".

<attribute name="interpolation" type="gml:CurveInterpolationType" fixed="cubicSpline"><annotation><documentation>The attribute "interpolation" specifies the curve interpolation mechanism used for this segment. This mechanism uses the control points and control parameters to determine the position of this curve segment. For a CubicSpline the interpolation is fixed as "cubicSpline".</documentation></annotation></attribute>

<attribute name="degree" type="integer" fixed="3"><annotation><documentation>The degree for a cubic spline is "3".</documentation></annotation></attribute>