Subversion Repositories hibernate-spatial

/*
 * $Id: Circle.java 200 2010-03-31 19:52:12Z maesenka $
 *
 * This file is part of Hibernate Spatial, an extension to the
 * hibernate ORM solution for geographic data.
 *
 * Copyright © 2007-2010 Geovise BVBA
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 * For more information, visit: http://www.hibernatespatial.org/
 */
package org.hibernatespatial;


import com.vividsolutions.jts.geom.Coordinate;
import com.vividsolutions.jts.geom.PrecisionModel;

import java.util.ArrayList;
import java.util.List;

/**
 * This class provides operations for handling the usage of Circles and arcs in
 * Geometries.
 * <p/>
 * Date: Oct 15, 2007
 *
 * @author Tom Acree
 */
public class Circle {
    private Coordinate center = new Coordinate(0.0, 0.0);

    private double radius = 0;

    private PrecisionModel precisionModel = new PrecisionModel();

    // Constructors **********************************************************

    /**
     * Creates a circle whose center is at the origin and whose radius is 0.
     */
    protected Circle() {
    }

    /**
     * Create a circle with a defined center and radius
     *
     * @param center The coordinate representing the center of the circle
     * @param radius The radius of the circle
     */
    public Circle(Coordinate center, double radius) {
        this.center = center;
        this.radius = radius;
    }

    /**
     * Create a circle using the x/y coordinates for the center.
     *
     * @param xCenter The x coordinate of the circle's center
     * @param yCenter The y coordinate of the circle's center
     * @param radius  the radius of the circle
     */
    public Circle(double xCenter, double yCenter, double radius) {
        this(new Coordinate(xCenter, yCenter), radius);
    }

    /**
     * Creates a circle based on bounding box. It is possible for the user of
     * this class to pass bounds to this method that do not represent a square.
     * If this is the case, we must force the bounding rectangle to be a square.
     * To this end, we check the box and set the side of the box to the larger
     * dimension of the rectangle
     *
     * @param xLeft
     * @param yUpper
     * @param xRight
     * @param yLower
     */
    public Circle(double xLeft, double yUpper, double xRight, double yLower) {
        double side = Math.min(Math.abs(xRight - xLeft), Math.abs(yLower
                - yUpper));
        this.center.x = Math.min(xRight, xLeft) + side / 2;
        this.center.y = Math.min(yUpper, yLower) + side / 2;
        this.radius = side / 2;
    }

    /**
     * Three point method of circle construction. All three points must be on
     * the circumference of the circle.
     *
     * @param point1
     * @param point2
     * @param point3
     */
    public Circle(Coordinate point1, Coordinate point2, Coordinate point3) {
        initThreePointCircle(point1, point2, point3);
    }

    /**
     * Three point method of circle construction. All three points must be on
     * the circumference of the circle.
     *
     * @param x1
     * @param y1
     * @param x2
     * @param y2
     * @param x3
     * @param y3
     */
    public Circle(double x1, double y1, double x2, double y2, double x3,
                  double y3) {
        this(new Coordinate(x1, y1), new Coordinate(x2, y2), new Coordinate(x3,
                y3));
    }

    /**
     * shift the center of the circle by delta X and delta Y
     */
    public void shift(double deltaX, double deltaY) {
        this.center.x = this.center.x + deltaX;
        this.center.y = this.center.y + deltaY;
    }

    /**
     * Move the circle to a new center
     */
    public void move(double x, double y) {
        this.center.x = x;
        this.center.y = y;
    }

    /**
     * Defines the circle based on three points. All three points must be on on
     * the circumference of the circle, and hence, the 3 points cannot be have
     * any pair equal, and cannot form a line. Therefore, each point given is
     * one radius measure from the circle's center.
     *
     * @param p1 A point on the desired circle
     * @param p2 A point on the desired circle
     * @param p3 A point on the desired circle
     */
    private void initThreePointCircle(Coordinate p1, Coordinate p2,
                                      Coordinate p3) {
        double a13, b13, c13;
        double a23, b23, c23;
        double x = 0., y = 0., rad = 0.;

        // begin pre-calculations for linear system reduction
        a13 = 2 * (p1.x - p3.x);
        b13 = 2 * (p1.y - p3.y);
        c13 = (p1.y * p1.y - p3.y * p3.y) + (p1.x * p1.x - p3.x * p3.x);
        a23 = 2 * (p2.x - p3.x);
        b23 = 2 * (p2.y - p3.y);
        c23 = (p2.y * p2.y - p3.y * p3.y) + (p2.x * p2.x - p3.x * p3.x);
        // test to be certain we have three distinct points passed
        double smallNumber = 0.01;
        if ((Math.abs(a13) < smallNumber && Math.abs(b13) < smallNumber)
                || (Math.abs(a13) < smallNumber && Math.abs(b13) < smallNumber)) {
            // // points too close so set to default circle
            x = 0;
            y = 0;
            rad = 0;
        } else {
            // everything is acceptable do the y calculation
            y = (a13 * c23 - a23 * c13) / (a13 * b23 - a23 * b13);
            // x calculation
            // choose best formula for calculation
            if (Math.abs(a13) > Math.abs(a23)) {
                x = (c13 - b13 * y) / a13;
            } else {
                x = (c23 - b23 * y) / a23;
            }
            // radius calculation
            rad = Math.sqrt((x - p1.x) * (x - p1.x) + (y - p1.y) * (y - p1.y));
        }
        this.center.x = x;
        this.center.y = y;
        this.radius = rad;
    }

    public Coordinate getCenter() {
        return this.center;
    }

    public double getRadius() {
        return this.radius;
    }

    /**
     * Given 2 points defining an arc on the circle, interpolates the circle
     * into a collection of points that provide connected chords that
     * approximate the arc based on the tolerance value. The tolerance value
     * specifies the maximum distance between a chord and the circle.
     *
     * @param x1        x coordinate of point 1
     * @param y1        y coordinate of point 1
     * @param x2        x coordinate of point 2
     * @param y2        y coordinate of point 2
     * @param x3        x coordinate of point 3
     * @param y3        y coordinate of point 3
     * @param tolerence maximum distance between the center of the chord and the outer
     *                  edge of the circle
     * @return an ordered list of Coordinates representing a series of chords
     *         approximating the arc.
     */
    public static Coordinate[] linearizeArc(double x1, double y1, double x2,
                                            double y2, double x3, double y3, double tolerence) {
        Coordinate p1 = new Coordinate(x1, y1);
        Coordinate p2 = new Coordinate(x2, y2);
        Coordinate p3 = new Coordinate(x3, y3);
        return new Circle(p1, p2, p3).linearizeArc(p1, p2, p3, tolerence);
    }

    /**
     * Given 2 points defining an arc on the circle, interpolates the circle
     * into a collection of points that provide connected chords that
     * approximate the arc based on the tolerance value. This method uses a
     * tolerence value of 1/100 of the length of the radius.
     *
     * @param x1 x coordinate of point 1
     * @param y1 y coordinate of point 1
     * @param x2 x coordinate of point 2
     * @param y2 y coordinate of point 2
     * @param x3 x coordinate of point 3
     * @param y3 y coordinate of point 3
     * @return an ordered list of Coordinates representing a series of chords
     *         approximating the arc.
     */
    public static Coordinate[] linearizeArc(double x1, double y1, double x2,
                                            double y2, double x3, double y3) {
        Coordinate p1 = new Coordinate(x1, y1);
        Coordinate p2 = new Coordinate(x2, y2);
        Coordinate p3 = new Coordinate(x3, y3);
        Circle c = new Circle(p1, p2, p3);
        double tolerence = 0.01 * c.getRadius();
        return c.linearizeArc(p1, p2, p3, tolerence);
    }

    /**
     * Given a circle defined by the 3 points, creates a linearized
     * interpolation of the circle starting and ending on the first coordinate.
     * This method uses a tolerence value of 1/100 of the length of the radius.
     *
     * @param x1 x coordinate of point 1
     * @param y1 y coordinate of point 1
     * @param x2 x coordinate of point 2
     * @param y2 y coordinate of point 2
     * @param x3 x coordinate of point 3
     * @param y3 y coordinate of point 3
     * @return an ordered list of Coordinates representing a series of chords
     *         approximating the arc.
     */
    public static Coordinate[] linearizeCircle(double x1, double y1, double x2,
                                               double y2, double x3, double y3) {
        Coordinate p1 = new Coordinate(x1, y1);
        Coordinate p2 = new Coordinate(x2, y2);
        Coordinate p3 = new Coordinate(x3, y3);
        Circle c = new Circle(p1, p2, p3);
        double tolerence = 0.01 * c.getRadius();
        return c.linearizeArc(p1, p2, p1, tolerence);
    }

    /**
     * Given 2 points defining an arc on the circle, interpolates the circle
     * into a collection of points that provide connected chords that
     * approximate the arc based on the tolerance value. The tolerance value
     * specifies the maximum distance between a chord and the circle.
     *
     * @param p1        begin coordinate of the arc
     * @param p2        any other point on the arc
     * @param p3        end coordinate of the arc
     * @param tolerence maximum distance between the center of the chord and the outer
     *                  edge of the circle
     * @return an ordered list of Coordinates representing a series of chords
     *         approximating the arc.
     */
    public Coordinate[] linearizeArc(Coordinate p1, Coordinate p2,
                                     Coordinate p3, double tolerence) {
        Arc arc = createArc(p1, p2, p3);
        List<Coordinate> result = linearizeInternal(null, arc, tolerence);
        return result.toArray(new Coordinate[result.size()]);
    }

    private List<Coordinate> linearizeInternal(List<Coordinate> coordinates,
                                               Arc arc, double tolerence) {
        if (coordinates == null) {
            coordinates = new ArrayList<Coordinate>();
        }
        double arcHt = arc.getArcHeight();
        if (Double.compare(arcHt, tolerence) <= 0) {
            int lastIndex = coordinates.size() - 1;
            Coordinate lastCoord = lastIndex >= 0 ? coordinates.get(lastIndex)
                    : null;

            if (lastCoord == null || !arc.getP1().equals2D(lastCoord)) {
                coordinates.add(arc.getP1());
                coordinates.add(arc.getP2());
            } else {
                coordinates.add(arc.getP2());
            }

        } else {
            // otherwise, split
            Arc[] splits = arc.split();
            linearizeInternal(coordinates, splits[0], tolerence);
            linearizeInternal(coordinates, splits[1], tolerence);
        }
        return coordinates;
    }

    public boolean equals(Object o) {
        if (this == o) {
            return true;
        }
        if (o == null || getClass() != o.getClass()) {
            return false;
        }
        Circle circle = (Circle) o;

        if (Double.compare(circle.radius, this.radius) != 0) {
            return false;
        }
        if (this.center != null ? !this.center.equals2D(circle.center)
                : circle.center != null) {
            return false;
        }
        return true;
    }

    public String toString() {
        return "Circle with Radius = " + this.radius
                + " and a center at the coordinates (" + this.center.x + ", "
                + this.center.y + ")";
    }

    /**
     * Returns the angle of the point from the center and the horizontal line
     * from the center.
     *
     * @param p a point in space
     * @return The angle of the point from the center of the circle
     */
    public double getAngle(Coordinate p) {
        double dx = p.x - this.center.x;
        double dy = p.y - this.center.y;
        double angle;

        if (dx == 0.0) {
            if (dy == 0.0) {
                angle = 0.0;
            } else if (dy > 0.0) {
                angle = Math.PI / 2.0;
            } else {
                angle = (Math.PI * 3.0) / 2.0;
            }
        } else if (dy == 0.0) {
            if (dx > 0.0) {
                angle = 0.0;
            } else {
                angle = Math.PI;
            }
        } else {
            if (dx < 0.0) {
                angle = Math.atan(dy / dx) + Math.PI;
            } else if (dy < 0.0) {
                angle = Math.atan(dy / dx) + (2 * Math.PI);
            } else {
                angle = Math.atan(dy / dx);
            }
        }
        return angle;
    }

    public Coordinate getPoint(final double angle) {
        double x = Math.cos(angle) * this.radius;
        x = x + this.center.x;
        x = this.precisionModel.makePrecise(x);

        double y = Math.sin(angle) * this.radius;
        y = y + this.center.y;
        y = this.precisionModel.makePrecise(y);
        return new Coordinate(x, y);
    }

    /**
     * @param p A point in space
     * @return The distance the point is from the center of the circle
     */
    public double distanceFromCenter(Coordinate p) {
        return Math.abs(this.center.distance(p));
    }

    public Arc createArc(Coordinate p1, Coordinate p2, Coordinate p3) {
        return new Arc(p1, p2, p3);
    }

    /**
     * Returns an angle between 0 and 2*PI. For example, 4*PI would get returned
     * as 2*PI since they are equivalent.
     *
     * @param angle an angle in radians to normalize
     * @return an angle between 0 and 2*PI
     */
    public static double normalizeAngle(double angle) {
        double maxRadians = 2 * Math.PI;
        if (angle >= 0 && angle <= maxRadians) {
            return angle;
        }
        if (angle < 0) {
            return maxRadians - Math.abs(angle);
        } else {
            return angle % maxRadians;
        }
    }

    /**
     * Returns the angle between the angles a1 and a2 in radians. Angle is
     * calculated in the counterclockwise direction.
     *
     * @param a1 first angle
     * @param a2 second angle
     * @return the angle between a1 and a2 in the clockwise direction
     */
    public static double subtractAngles(double a1, double a2) {
        if (a1 < a2) {
            return a2 - a1;
        } else {
            return TWO_PI - Math.abs(a2 - a1);
        }
    }

    private static final double TWO_PI = Math.PI * 2;

    public class Arc {
        private Coordinate p1, p2;

        private double arcAngle; // angle in radians

        private double p1Angle;

        private double p2Angle;

        private boolean clockwise;

        private Arc(Coordinate p1, Coordinate midPt, Coordinate p2) {
            this.p1 = p1;
            this.p2 = p2;
            this.p1Angle = getAngle(p1);
            // See if this arc covers the whole circle
            if (p1.equals2D(p2)) {
                this.p2Angle = TWO_PI + this.p1Angle;
                this.arcAngle = TWO_PI;
            } else {
                this.p2Angle = getAngle(p2);
                double midPtAngle = getAngle(midPt);

                // determine the direction
                double ccDegrees = Circle.subtractAngles(this.p1Angle,
                        midPtAngle)
                        + Circle.subtractAngles(midPtAngle, this.p2Angle);

                if (ccDegrees < TWO_PI) {
                    this.clockwise = false;
                    this.arcAngle = ccDegrees;
                } else {
                    this.clockwise = true;
                    this.arcAngle = TWO_PI - ccDegrees;
                }
            }
        }

        private Arc(Coordinate p1, Coordinate p2, boolean isClockwise) {
            this.p1 = p1;
            this.p2 = p2;
            this.clockwise = isClockwise;
            this.p1Angle = getAngle(p1);
            if (p1.equals2D(p2)) {
                this.p2Angle = TWO_PI + this.p1Angle;
            } else {
                this.p2Angle = getAngle(p2);
            }
            determineArcAngle();
        }

        private void determineArcAngle() {
            double diff;
            if (this.p1.equals2D(this.p2)) {
                diff = TWO_PI;
            } else if (this.clockwise) {
                diff = this.p1Angle - this.p2Angle;
            } else {
                diff = this.p2Angle - this.p1Angle;
            }
            this.arcAngle = Circle.normalizeAngle(diff);
        }

        /**
         * given a an arc defined from p1 to p2 existing on this circle, returns
         * the height of the arc. This height is defined as the distance from
         * the center of a chord defined by (p1, p2) and the outer edge of the
         * circle.
         *
         * @return the arc height
         */
        public double getArcHeight() {
            Coordinate chordCenterPt = this.getChordCenterPoint();
            double dist = distanceFromCenter(chordCenterPt);
            if (this.arcAngle > Math.PI) {
                return Circle.this.radius + dist;
            } else {
                return Circle.this.radius - dist;
            }
        }

        public Coordinate getChordCenterPoint() {
            double centerX = this.p1.x + (this.p2.x - this.p1.x) / 2;
            double centerY = this.p1.y + (this.p2.y - this.p1.y) / 2;
            return new Coordinate(centerX, centerY);
        }

        public Arc[] split() {
            int directionFactor = isClockwise() ? -1 : 1;
            double angleOffset = directionFactor * (this.arcAngle / 2);

            double midAngle = this.p1Angle + angleOffset;
            Coordinate newMidPoint = getPoint(midAngle);

            Arc arc1 = new Arc(this.p1, newMidPoint, isClockwise());
            Arc arc2 = new Arc(newMidPoint, this.p2, isClockwise());
            return new Arc[]{arc1, arc2};
        }

        public Coordinate getP1() {
            return this.p1;
        }

        public Coordinate getP2() {
            return this.p2;
        }

        public double getArcAngle() {
            return this.arcAngle;
        }

        public double getArcAngleDegrees() {
            return Math.toDegrees(this.arcAngle);
        }

        public double getP1Angle() {
            return this.p1Angle;
        }

        public double getP2Angle() {
            return this.p2Angle;
        }

        public boolean isClockwise() {
            return this.clockwise;
        }

        public String toString() {
            return "P1: " + this.p1 + " P2: " + this.p2 + " clockwise: " + this.clockwise;
        }
    }

}