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This geoLatte-geom library offers a geometry model that conforms to the OGC Simple Features for SQL
specification.
/*
* This file is part of Hibernate Spatial, an extension to the
* hibernate ORM solution for spatial (geographic) data.
*
* Copyright © 2007-2012 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
*/
package org.geolatte.geom;
import java.util.ArrayList;
import java.util.List;
import com.vividsolutions.jts.geom.Coordinate;
import com.vividsolutions.jts.geom.PrecisionModel;
//TODO -- verify code, and place in utility class
/**
* This class provides operations for handling the usage of Circles and arcs in
* Geometries.
*
*
* @author Tom Acree
*/
public class Circle {
private static final double TWO_PI = Math.PI * 2;
private Coordinate center = new Coordinate( 0.0, 0.0 );
private double radius;
// Constructors **********************************************************
private PrecisionModel precisionModel = new PrecisionModel();
/**
* 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 The leftmost x coordinate
* @param yUpper The uppermost y coordinate
* @param xRight The rightmost x coordinate
* @param yLower The lowest y coordinate
*/
public Circle(double xLeft, double yUpper, double xRight, double yLower) {
final 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 The first point
* @param point2 The second point
* @param point3 The third point
*/
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 The x coordinate of the first point
* @param y1 The y coordinate of the first point
* @param x2 The x coordinate of the second point
* @param y2 The y coordinate of the second point
* @param x3 The x coordinate of the third point
* @param y3 The y coordinate of the third point
*/
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 )
);
}
/**
* 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) {
final Coordinate p1 = new Coordinate( x1, y1 );
final Coordinate p2 = new Coordinate( x2, y2 );
final 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) {
final Coordinate p1 = new Coordinate( x1, y1 );
final Coordinate p2 = new Coordinate( x2, y2 );
final Coordinate p3 = new Coordinate( x3, y3 );
final Circle c = new Circle( p1, p2, p3 );
final 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) {
final Coordinate p1 = new Coordinate( x1, y1 );
final Coordinate p2 = new Coordinate( x2, y2 );
final Coordinate p3 = new Coordinate( x3, y3 );
final Circle c = new Circle( p1, p2, p3 );
final double tolerence = 0.01 * c.getRadius();
return c.linearizeArc( p1, p2, p1, tolerence );
}
/**
* 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) {
final 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 );
}
}
/**
* Shifts the center of the circle by delta X and delta Y
*
* @param deltaX The shift along the X-coordinate axis
* @param deltaY The shift along the Y-coordinate axis
*/
public void shift(double deltaX, double deltaY) {
this.center.x = this.center.x + deltaX;
this.center.y = this.center.y + deltaY;
}
/**
* Moves the circle to a new center
*
* @param x The x coordinate of the new center
* @param y The y coordinate of the 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, y, rad;
// 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 );
// testsuite-suite to be certain we have three distinct points passed
final 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 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) {
final Arc arc = createArc( p1, p2, p3 );
final List result = linearizeInternal( null, arc, tolerence );
return result.toArray( new Coordinate[result.size()] );
}
private List linearizeInternal(List coordinates, Arc arc, double tolerence) {
if ( coordinates == null ) {
coordinates = new ArrayList();
}
final double arcHt = arc.getArcHeight();
if ( Double.compare( arcHt, tolerence ) <= 0 ) {
final int lastIndex = coordinates.size() - 1;
final 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
final Arc[] splits = arc.split();
linearizeInternal( coordinates, splits[0], tolerence );
linearizeInternal( coordinates, splits[1], tolerence );
}
return coordinates;
}
@Override
public boolean equals(Object o) {
if ( this == o ) {
return true;
}
if ( o == null || getClass() != o.getClass() ) {
return false;
}
final 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;
}
@Override
public int hashCode() {
int result;
long temp;
result = center.hashCode();
temp = radius != +0.0d ? Double.doubleToLongBits( radius ) : 0L;
result = 31 * result + (int) ( temp ^ ( temp >>> 32 ) );
return result;
}
@Override
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) {
final double dx = p.x - this.center.x;
final 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;
}
/**
* Returns the coordinate on the circle at the specified angle
*
* @param angle The angle
*
* @return Coordinate
*/
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 );
}
/**
* Returns the distance the point is from the center of the circle
*
* @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 ) );
}
/**
* Creates an arc through the specified points
*
* @param p1 The first point
* @param p2 The second point
* @param p3 The third point
*
* @return The {@code Arc} through the three points
*/
public Arc createArc(Coordinate p1, Coordinate p2, Coordinate p3) {
return new Arc( p1, p2, p3 );
}
/**
* An arc, or circle segment
*/
public class Arc {
private Coordinate p1, p2;
private double arcAngle;
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 );
final double midPtAngle = getAngle( midPt );
// determine the direction
final 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() {
final Coordinate chordCenterPt = this.getChordCenterPoint();
final double dist = distanceFromCenter( chordCenterPt );
if ( this.arcAngle > Math.PI ) {
return Circle.this.radius + dist;
}
else {
return Circle.this.radius - dist;
}
}
/**
* Returns the center of this {@code Arc}
*
* @return the center of this {@code Arc}
*/
public Coordinate getChordCenterPoint() {
final double centerX = this.p1.x + ( this.p2.x - this.p1.x ) / 2;
final double centerY = this.p1.y + ( this.p2.y - this.p1.y ) / 2;
return new Coordinate( centerX, centerY );
}
/**
* Splits this {@code Arc} at the mid point
*
* @return an array of two {@code Arc}s
*/
public Arc[] split() {
final int directionFactor = isClockwise() ? -1 : 1;
final double angleOffset = directionFactor * ( this.arcAngle / 2 );
final double midAngle = this.p1Angle + angleOffset;
final Coordinate newMidPoint = getPoint( midAngle );
final Arc arc1 = new Arc( this.p1, newMidPoint, isClockwise() );
final 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;
}
@Override
public String toString() {
return "P1: " + this.p1 + " P2: " + this.p2 + " clockwise: " + this.clockwise;
}
}
}
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