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Annotations
Attributes
Diagrams
Instances
Properties
Source
Used by
Element womlcore:CubicBSplineType / womlcore:bezier
Namespace http://xml.fmi.fi/namespace/woml/core/2011/06/15
Diagram
Diagram index19.tmp#id80 index1328.tmp#id250 index1336.tmp#id249
Type womlcore:CubicBezierSegmentPropertyType
Properties
content: complex
minOccurs: 1
maxOccurs: unbounded
Model womlcore:CubicBezierSegment
Children womlcore:CubicBezierSegment
Instance
<womlcore:bezier xlink:actuate="" xlink:arcrole="" xlink:href="" nilReason="" gml:remoteSchema="" xlink:role="" xlink:show="" xlink:title="" xlink:type="simple">
  <womlcore:CubicBezierSegment>{1,1}</womlcore:CubicBezierSegment>
</womlcore:bezier>
Attributes
QName Type Fixed Default Use Annotation
gml:remoteSchema anyURI optional
nilReason gml:NilReasonType optional
xlink:actuate restriction of string optional
The 'actuate' attribute is used to communicate the desired timing 
of traversal from the starting resource to the ending resource; 
it's value should be treated as follows:
onLoad - traverse to the ending resource immediately on loading 
         the starting resource 
onRequest - traverse from the starting resource to the ending 
            resource only on a post-loading event triggered for 
            this purpose 
other - behavior is unconstrained; examine other markup in link 
        for hints 
none - behavior is unconstrained
xlink:arcrole anyURI optional
xlink:href anyURI optional
xlink:role anyURI optional
xlink:show restriction of string optional
The 'show' attribute is used to communicate the desired presentation 
of the ending resource on traversal from the starting resource; it's 
value should be treated as follows: 
new - load ending resource in a new window, frame, pane, or other 
      presentation context
replace - load the resource in the same window, frame, pane, or 
          other presentation context
embed - load ending resource in place of the presentation of the 
        starting resource
other - behavior is unconstrained; examine other markup in the 
        link for hints 
none - behavior is unconstrained
xlink:title string optional
xlink:type string simple optional
Source
<element name="bezier" type="womlcore:CubicBezierSegmentPropertyType" minOccurs="1" maxOccurs="unbounded"/>
Schema location http://xml.fmi.fi/schema/woml/core/2011/06/15/woml-common-geometry.xsd
Complex Type womlcore:CubicBSplineType
Namespace http://xml.fmi.fi/namespace/woml/core/2011/06/15
Annotations
A cubic B-spline is continuously a piecewise composition of 1 or more Bézier curves of degree 3 (cubic).
Each of these cubic Bézier curves is defined by four points: two knots which define the start and the end
points of the curve (segment), and two inner Bézier points which the curve usually does not
pass through.
                
The "beginKnot" element must be included in the first segment. If there are more than one 
Bézier curve (segments) in the B-spline curve, 
the first knot ("beginKnot") of the next Bézier must be the same point as 
the last knot ("endKnot") previous Bézier to guarantee B-spline curve 
continuity. It is recommended that the "beginKnot" is omitted from
all segments but the first one. If it's given in the segments following
the first one, it's value should be ignored and the value of "endKnot" of 
the previous segment used instead. 
                
If the B-spline is to differentiable (not have sharp bends) at the knots, the inner Bézier points on both 
sides of the knot must be colinear. This condition can be explicitly said be adding the attribute 
"numDerivativeInterior" with value "1". It's also possible for a cubic B-spline curve to twice differentiable
at the knots. This requires further conditions on the positioning of the inner Bézier points. If the entire
curve is twice differentiable at all points, we may give the attribute "numDerivativeInterior" the value "2".
                
It should be noted, that B-splines cannot always be properly projected to another map projections. Projection of
a Bézier curve may lead into a rational function instead of a polynomial one. If a re-projection of
a B-spline curve is necessary, it may be easiest to first interpolate the B-spline into a line string, and then 
re-project the line string points. However, this technique is useful for display only: it may be impossible to
fit the points of the transformed line string back to a B-spline. For this reason the applications should always
edit the B-spline only in the same projection where it was originally defined.
Diagram
Diagram index176.tmp#id245 index176.tmp#id246 index176.tmp#id247 index176.tmp#id244 index647.tmp#id248
Type extension of gml:AbstractCurveSegmentType
Type hierarchy
Used by
Model womlcore:bezier+
Children womlcore:bezier
Attributes
QName Type Fixed Default Use Annotation
numDerivativeInterior integer 0 optional
numDerivativesAtEnd integer 0 optional
numDerivativesAtStart integer 0 optional
Source
<complexType name="CubicBSplineType">
  <annotation>
    <documentation>A cubic B-spline is continuously a piecewise composition of 1 or more Bézier curves of degree 3 (cubic). Each of these cubic Bézier curves is defined by four points: two knots which define the start and the end points of the curve (segment), and two inner Bézier points which the curve usually does not pass through. The "beginKnot" element must be included in the first segment. If there are more than one Bézier curve (segments) in the B-spline curve, the first knot ("beginKnot") of the next Bézier must be the same point as the last knot ("endKnot") previous Bézier to guarantee B-spline curve continuity. It is recommended that the "beginKnot" is omitted from all segments but the first one. If it's given in the segments following the first one, it's value should be ignored and the value of "endKnot" of the previous segment used instead. If the B-spline is to differentiable (not have sharp bends) at the knots, the inner Bézier points on both sides of the knot must be colinear. This condition can be explicitly said be adding the attribute "numDerivativeInterior" with value "1". It's also possible for a cubic B-spline curve to twice differentiable at the knots. This requires further conditions on the positioning of the inner Bézier points. If the entire curve is twice differentiable at all points, we may give the attribute "numDerivativeInterior" the value "2". It should be noted, that B-splines cannot always be properly projected to another map projections. Projection of a Bézier curve may lead into a rational function instead of a polynomial one. If a re-projection of a B-spline curve is necessary, it may be easiest to first interpolate the B-spline into a line string, and then re-project the line string points. However, this technique is useful for display only: it may be impossible to fit the points of the transformed line string back to a B-spline. For this reason the applications should always edit the B-spline only in the same projection where it was originally defined.</documentation>
  </annotation>
  <complexContent>
    <extension base="gml:AbstractCurveSegmentType">
      <sequence>
        <element name="bezier" type="womlcore:CubicBezierSegmentPropertyType" minOccurs="1" maxOccurs="unbounded"/>
      </sequence>
    </extension>
  </complexContent>
</complexType>
Schema location http://xml.fmi.fi/schema/woml/core/2011/06/15/woml-common-geometry.xsd