/*
* 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 org.opengis.geometry.primitive.CurveSegment;
import org.opengis.annotation.UML;
import static org.opengis.annotation.Obligation.*;
import static org.opengis.annotation.Specification.*;
/**
* 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:
*
* <P><center>(TODO: paste the equation here)</center></P>
*
* 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 <var>A</var><sup>2</sup> = <var>R</var>×<var>t</var>
* where <var>A</var> is a constant, <var>R</var> is the varying radius of curvature along
* the curve and <var>t</var> is the length along the curve and given in the Fresnel integrals.
*
*
* @source $URL: http://svn.osgeo.org/geotools/trunk/modules/library/opengis/src/main/java/org/opengis/geometry/coordinate/Clothoid.java $
* @version <A HREF="http://www.opengeospatial.org/standards/as">ISO 19107</A>
* @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 <var>A</var> 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 <var>t</var> 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 <var>t</var>
* acts as a constructive parameter.
*
* <P>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.</P>
*/
@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 <var>t</var> 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();
}