/*
* GeoTools - The Open Source Java GIS Toolkit
* http://geotools.org
*
* (C) 2011, Open Source Geospatial Foundation (OSGeo)
* (C) 2003-2005, Open Geospatial Consortium Inc.
*
* All Rights Reserved. http://www.opengis.org/legal/
*/
package org.opengis.geometry.coordinate;
import java.util.List;
import org.opengis.geometry.primitive.CurveInterpolation;
import org.opengis.annotation.UML;
import static org.opengis.annotation.Obligation.*;
import static org.opengis.annotation.Specification.*;
/**
* Cubic splines.
* 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. Splines have two
* parameterizations that are used in this specification, the defining one (constructive
* parameter) and the one that has been reparameterized by arc length to satisfy the requirements
* in {@link GenericCurve}.
* <p>
* The function describing the curve must be C<sup>2</sup>, that is, have a continuous
* 1<sup>st</sup> and 2<sup>nd</sup> derivative at all points, and pass through the
* {@linkplain #getControlPoints control points} 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 1<sup>st</sup> and 2<sup>nd</sup> derivative vectors are
* the same from either side. The control parameters record must contain
* {@link #getVectorAtStart vectorAtStart}, and {@link #getVectorAtEnd vectorAtEnd}
* which are the unit tangent vectors at {@code controlPoint[0]} and <code>controlPoint[n]</coded>
* where <var>n</var> = {@code controlPoint.length-1}.
*
*
* @source $URL: http://svn.osgeo.org/geotools/branches/2.7.x/modules/library/opengis/src/main/java/org/opengis/geometry/coordinate/CubicSpline.java $
* @version <A HREF="http://www.opengeospatial.org/standards/as">ISO 19107</A>
* @author Martin Desruisseaux (IRD)
* @since GeoAPI 2.0
*/
@UML(identifier="GM_CubicSpline", specification=ISO_19107)
public interface CubicSpline extends PolynomialSpline {
/**
* The interpolation mechanism for a {@code CubicSpline}
* is {@link CurveInterpolation#CUBIC_SPLINE CUBIC_SPLINE}.
*/
@UML(identifier="interpolation", obligation=MANDATORY, specification=ISO_19107)
CurveInterpolation getInterpolation();
/**
* The values used for the initial derivative.
* The restriction on {@code vectorAtStart} and {@code vectorAtEnd} reduce these
* sequences to a single tangent vector each. Consequently, the {@linkplain List#size size}
* of the returned list is 1.
*/
@UML(identifier="vectorAtStart", obligation=MANDATORY, specification=ISO_19107)
List/*double[]*/ getVectorAtStart();
/**
* The values used for the final derivative.
* The restriction on {@code vectorAtStart} and {@code vectorAtEnd} reduce these
* sequences to a single tangent vector each. Consequently, the {@linkplain List#size size}
* of the returned list is 1.
*/
@UML(identifier="vectorAtEnd", obligation=MANDATORY, specification=ISO_19107)
List/*double[]*/ getVectorAtEnd();
}