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

import org.opengis.annotation.UML;
import org.opengis.geometry.primitive.CurveSegment;

/**
 * The clothoid (or Cornu's spiral), a plane curve whose curvature is a fixed function of its
 * length. In suitably chosen co-ordinates it is given by Fresnel's integrals:
 *
 * 
(TODO: paste the equation here) This geometry is mainly used as a transition
 * curve between curves of type straight line/circular arc or circular arc/circular arc. With this
 * curve type it is possible to achieve a C2-continous transition between the above mentioned curve
 * types. One formula for the clothoid is A² = R×t
 * where A is a constant, R is the varying radius of curvature along the curve
 * and t is the length along the curve and given in the Fresnel integrals.
 *
 * @version ISO 19107
 * @author Martin Desruisseaux (IRD)
 * @since GeoAPI 2.0
 */
@UML(identifier = "GM_Clothoid", specification = ISO_19107)
public interface Clothoid extends CurveSegment {
    /**
     * Returns an affine mapping that places the curve defined by the Fresnel Integrals into the
     * coordinate reference system of this object.
     */
    @UML(identifier = "refLocation", obligation = MANDATORY, specification = ISO_19107)
    AffinePlacement getReferenceLocation();

    /** Gives the value for A in the equations above. */
    @UML(identifier = "scaleFactor", obligation = MANDATORY, specification = ISO_19107)
    double getScaleFactor();

    /**
     * Returns the arc length distance from the inflection point that will be the {@linkplain
     * #getStartPoint start point} for this curve segment. This shall be lower limit t
     * used in the Fresnel integral and is the value of the constructive parameter of this curve
     * segment at its start point. The start parameter can be either positive or negative. The
     * parameter t acts as a constructive parameter.
     *
     * NOTE: If 0 lies between the {@linkplain #getStartConstructiveParam start constructive
     * parameter} and {@linkplain #getEndConstructiveParam end constructive parameter} of the
     * clothoid, then the curve goes through the clothoid's inflection point, and the direction of
     * its radius of curvature, given by the second derivative vector, changes sides with respect to
     * the tangent vector. The term "length" for the parameter {@code t} is applicable only in the
     * parameter space, and its relation to arc length after use of the placement, and with respect
     * to the coordinate reference system of the curve is not deterministic.
     */
    @UML(identifier = "startParameter", obligation = MANDATORY, specification = ISO_19107)
    double getStartConstructiveParam();

    /**
     * Returns the arc length distance from the inflection point that will be the {@linkplain
     * #getEndPoint end point} for this curve segment. This shall be upper limit t used
     * in the Fresnel integral and is the constructive parameter of this curve segment at its end
     * point. The end constructive param can be either positive or negative.
     */
    @UML(identifier = "endParameter", obligation = MANDATORY, specification = ISO_19107)
    double getEndConstructiveParam();
}