/*
 *    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.primitive;

import java.util.List;
import org.opengis.geometry.coordinate.GenericCurve;
import org.opengis.annotation.Association;
import org.opengis.annotation.UML;

import static org.opengis.annotation.Obligation.*;
import static org.opengis.annotation.Specification.*;


/**
 * Curve with a positive orientation. {@code Curve} is
 * a descendent subtype of {@link Primitive} through {@link OrientablePrimitive}. It is the basis
 * for 1-dimensional geometry. A curve is a continuous image of an open interval and so could be
 * written as a parameterized function such as
 *
 * <code>c(t):(a, b) → E<sup>n</sup></code>
 *
 * where "t" is a real parameter and E<sup>n</sup> is Euclidean space of dimension <var>n</var>
 * (usually 2 or 3, as determined by the coordinate reference system). Any other parameterization
 * that results in the same image curve, traced in the same direction, such as any linear shifts
 * and positive scales such as
 *
 * <code>e(t) = c(a + t(b-a)):(0,1) → E<sup>n</sup></code>,
 *
 * is an equivalent representation of the same curve. For the sake of simplicity, {@code Curve}s
 * should be parameterized by arc length, so that the parameterization operation inherited from
 * {@link GenericCurve} will be valid for parameters between 0 and the length of the curve.
 * <p>
 * Curves are continuous, connected, and have a measurable length in terms of the coordinate system.
 * The orientation of the curve is determined by this parameterization, and is consistent with the
 * tangent function, which approximates the derivative function of the parameterization and shall
 * always point in the "forward" direction. The parameterization of the reversal of the curve defined
 * by
 *
 * <code>c(t):(a, b) → E<sup>n</sup></code>
 *
 * would be defined by a function of the form
 *
 * <code>s(t) = c(a + b - t):(a, b) → E<sup>n</sup></code>.
 *
 * <p>
 * A curve is composed of one or more curve segments. Each curve segment within a curve may be
 * defined using a different interpolation method. The curve segments are connected to one another,
 * with the end point of each segment except the last being the start point of the next segment in
 * the segment list.
 *
 *
 * @source $URL: http://svn.osgeo.org/geotools/trunk/modules/library/opengis/src/main/java/org/opengis/geometry/primitive/Curve.java $
 * @version <A HREF="http://www.opengeospatial.org/standards/as">ISO 19107</A>
 * @author Martin Desruisseaux (IRD)
 * @since GeoAPI 1.0
 *
 * @see PrimitiveFactory#createCurve
 */
@UML(identifier="GM_Curve", specification=ISO_19107)
public interface Curve extends OrientableCurve, GenericCurve {
    /**
     * Lists the components {@linkplain CurveSegment curve segments} of {@code Curve}, each
     * of which defines the direct position of points along a portion of the curve. The order of
     * the {@linkplain CurveSegment curve segments} is the order in which they are used to trace
     * this {@code Curve}. For a particular parameter interval, the {@code Curve} and
     * {@link CurveSegment} agree.
     *
     * @return The list of curve segments. Should never be {@code null} neither empty.
     *
     * @see CurveSegment#getCurve
     * @see Surface#getPatches
     * @issue http://jira.codehaus.org/browse/GEO-63
     */
    @Association("Segmentation")
    @UML(identifier="segment", obligation=MANDATORY, specification=ISO_19107)
    List<? extends CurveSegment> getSegments();

    /**
     * Returns the orientable curves associated with this curve.
     *
     * @return The orientable curves as an array of length 2.
     *
     * @see OrientableCurve#getPrimitive
     * @issue http://jira.codehaus.org/browse/GEO-63
     */
    @Association("Oriented")
    @UML(identifier="proxy", obligation=MANDATORY, specification=ISO_19107)
    OrientableCurve[] getProxy();
}