/*
* (non-Javadoc)
*
* @see math.geom2d.OrientedCurve2D#windingAngle(math.geom2d.Point2D)
*/
public double windingAngle(Point2D point) {
Point2D p1 = point(0);
Point2D p2 = point(abs(angleExtent));
// compute angle of point with extreme points
double angle1 = Angle2D.horizontalAngle(point, p1);
double angle2 = Angle2D.horizontalAngle(point, p2);
// test on which 'side' of the arc the point lie
boolean b1 = (new StraightLine2D(p1, p2)).isInside(point);
boolean b2 = ellipse.isInside(point);
if (angleExtent > 0) {
if (b1 || b2) { // inside of ellipse arc
if (angle2 > angle1) return angle2 - angle1;
else return 2 * PI - angle1 + angle2;
} else { // outside of ellipse arc
if (angle2 > angle1) return angle2 - angle1 - 2 * PI;
else return angle2 - angle1;
}
} else {
if (!b1 || b2) {
if (angle1 > angle2) return angle2 - angle1;
else return angle2 - angle1 - 2 * PI;
} else {
if (angle1 > angle2) return angle2 - angle1 + 2 * PI;
else return angle2 - angle1;
}
}
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Curve2D#position(math.geom2d.Point2D)
*/
public double position(Point2D point) {
double angle = Angle2D.horizontalAngle(ellipse.center(), point);
if (this.containsAngle(angle))
if (angleExtent > 0) return Angle2D.formatAngle(angle - startAngle);
else return Angle2D.formatAngle(startAngle - angle);
// If the point is not contained in the arc, return NaN.
return Double.NaN;
}
/** Returns a new CircleArc2D. t0 and t1 are position on circle. */
public CircleArc2D subCurve(double t0, double t1) {
double startAngle, extent;
if (this.direct) {
startAngle = t0;
extent = Angle2D.formatAngle(t1 - t0);
} else {
extent = -Angle2D.formatAngle(t1 - t0);
startAngle = Angle2D.formatAngle(-t0);
}
return new CircleArc2D(this, startAngle, extent);
}
/** Returns a new EllipseArc2D. */
public EllipseArc2D subCurve(double t0, double t1) {
// convert position to angle
t0 = Angle2D.formatAngle(startAngle + t0);
t1 = Angle2D.formatAngle(startAngle + t1);
// check bounds of angles
if (!Angle2D.containsAngle(startAngle, startAngle + angleExtent, t0, angleExtent > 0))
t0 = startAngle;
if (!Angle2D.containsAngle(startAngle, startAngle + angleExtent, t1, angleExtent > 0))
t1 = angleExtent;
// create new arc
return new EllipseArc2D(ellipse, t0, t1, angleExtent > 0);
}
public double project(Point2D point) {
double angle = ellipse.project(point);
// Case of an angle contained in the ellipse arc
if (this.containsAngle(angle)) {
if (angleExtent > 0) return Angle2D.formatAngle(angle - startAngle);
else return Angle2D.formatAngle(startAngle - angle);
}
// return either 0 or T1, depending on which extremity is closer.
double d1 = this.firstPoint().distance(point);
double d2 = this.lastPoint().distance(point);
return d1 < d2 ? 0 : abs(angleExtent);
}
/**
* Computes the projection position of the point on the circle, by computing angle with
* horizonrtal
*/
public double project(Point2D point) {
double xp = point.x() - this.xc;
double yp = point.y() - this.yc;
// compute angle
return Angle2D.horizontalAngle(xp, yp);
}
/**
* Computes the radical axis of the two circles.
*
* @since 0.11.1
* @return the radical axis of the two circles.
* @throws IllegalArgumentException if the two circles have same center
*/
public static StraightLine2D radicalAxis(Circle2D circle1, Circle2D circle2) {
// extract center and radius of each circle
double r1 = circle1.radius();
double r2 = circle2.radius();
Point2D p1 = circle1.center();
Point2D p2 = circle2.center();
// compute horizontal angle of joining line
double angle = Angle2D.horizontalAngle(p1, p2);
// distance between centers
double dist = p1.distance(p2);
if (dist < Shape2D.ACCURACY) {
throw new IllegalArgumentException("Input circles must have distinct centers");
}
// position of the radical axis on the joining line
double d = (dist * dist + r1 * r1 - r2 * r2) * .5 / dist;
// pre-compute trigonometric functions
double cot = Math.cos(angle);
double sit = Math.sin(angle);
// compute parameters of the line
double x0 = p1.x() + d * cot;
double y0 = p1.y() + d * sit;
double dx = -sit;
double dy = cot;
// update state of current line
return new StraightLine2D(x0, y0, dx, dy);
}
/** @deprecated replaced by circlesIntersections(Circle2D, Circle2D) (0.11.1) */
@Deprecated
public static Collection<Point2D> getIntersections(Circle2D circle1, Circle2D circle2) {
ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);
// extract center and radius of each circle
Point2D center1 = circle1.center();
Point2D center2 = circle2.center();
double r1 = circle1.radius();
double r2 = circle2.radius();
double d = Point2D.distance(center1, center2);
// case of no intersection
if (d < abs(r1 - r2) || d > (r1 + r2)) return intersections;
// Angle of line from center1 to center2
double angle = Angle2D.horizontalAngle(center1, center2);
// position of intermediate point
double d1 = d / 2 + (r1 * r1 - r2 * r2) / (2 * d);
Point2D tmp = Point2D.createPolar(center1, d1, angle);
// Add the 2 intersection points
double h = sqrt(r1 * r1 - d1 * d1);
intersections.add(Point2D.createPolar(tmp, h, angle + PI / 2));
intersections.add(Point2D.createPolar(tmp, h, angle - PI / 2));
return intersections;
}
/* (non-Javadoc)
* @see math.geom2d.GeometricObject2D#almostEquals(math.geom2d.GeometricObject2D, double)
*/
public boolean almostEquals(GeometricObject2D obj, double eps) {
if (this == obj) return true;
if (!(obj instanceof EllipseArc2D)) return false;
EllipseArc2D arc = (EllipseArc2D) obj;
// test whether supporting ellipses have same support
if (abs(ellipse.xc - arc.ellipse.xc) > eps) return false;
if (abs(ellipse.yc - arc.ellipse.yc) > eps) return false;
if (abs(ellipse.r1 - arc.ellipse.r1) > eps) return false;
if (abs(ellipse.r2 - arc.ellipse.r2) > eps) return false;
if (abs(ellipse.theta - arc.ellipse.theta) > eps) return false;
// test if angles are the same
if (!Angle2D.equals(startAngle, arc.startAngle)) return false;
if (!Angle2D.equals(angleExtent, arc.angleExtent)) return false;
return true;
}
public Box2D boundingBox() {
// first get ending points
Point2D p0 = firstPoint();
Point2D p1 = lastPoint();
// get coordinate of ending points
double x0 = p0.x();
double y0 = p0.y();
double x1 = p1.x();
double y1 = p1.y();
// initialize min and max coords
double xmin = min(x0, x1);
double xmax = max(x0, x1);
double ymin = min(y0, y1);
double ymax = max(y0, y1);
// precomputes some values
Point2D center = ellipse.center();
double xc = center.x();
double yc = center.y();
double endAngle = startAngle + angleExtent;
boolean direct = angleExtent >= 0;
// check cases arc contains one maximum
if (Angle2D.containsAngle(startAngle, endAngle, PI / 2 + ellipse.theta, direct))
ymax = max(ymax, yc + ellipse.r1);
if (Angle2D.containsAngle(startAngle, endAngle, 3 * PI / 2 + ellipse.theta, direct))
ymin = min(ymin, yc - ellipse.r1);
if (Angle2D.containsAngle(startAngle, endAngle, ellipse.theta, direct))
xmax = max(xmax, xc + ellipse.r2);
if (Angle2D.containsAngle(startAngle, endAngle, PI + ellipse.theta, direct))
xmin = min(xmin, xc - ellipse.r2);
// return a bounding with computed limits
return new Box2D(xmin, xmax, ymin, ymax);
}
/** Specify parameters of supporting ellipse, bounding angles and flag for direct ellipse. */
public EllipseArc2D(
double xc,
double yc,
double a,
double b,
double theta,
double start,
double end,
boolean direct) {
this.ellipse = new Ellipse2D(xc, yc, a, b, theta);
this.startAngle = start;
this.angleExtent = Angle2D.formatAngle(end - start);
if (!direct) this.angleExtent = this.angleExtent - PI * 2;
}
/**
* Computes the intersections points between two circles or circular shapes.
*
* @param circle1 an instance of circle or circle arc
* @param circle2 an instance of circle or circle arc
* @return a collection of 0, 1 or 2 intersection points
*/
public static Collection<Point2D> circlesIntersections(Circle2D circle1, Circle2D circle2) {
// extract center and radius of each circle
Point2D center1 = circle1.center();
Point2D center2 = circle2.center();
double r1 = circle1.radius();
double r2 = circle2.radius();
double d = Point2D.distance(center1, center2);
// case of no intersection
if (d < abs(r1 - r2) || d > (r1 + r2)) return new ArrayList<Point2D>(0);
// Angle of line from center1 to center2
double angle = Angle2D.horizontalAngle(center1, center2);
if (d == abs(r1 - r2) || d == (r1 + r2)) {
Collection<Point2D> r = new ArrayList<>(1);
r.add(Point2D.createPolar(center1, r1, angle));
return r;
}
// position of intermediate point
double d1 = d / 2 + (r1 * r1 - r2 * r2) / (2 * d);
Point2D tmp = Point2D.createPolar(center1, d1, angle);
// distance between intermediate point and each intersection
double h = sqrt(r1 * r1 - d1 * d1);
// create empty array
ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);
// Add the 2 intersection points
Point2D p1 = Point2D.createPolar(tmp, h, angle + PI / 2);
intersections.add(p1);
Point2D p2 = Point2D.createPolar(tmp, h, angle - PI / 2);
intersections.add(p2);
return intersections;
}
public double position(Point2D point) {
double angle = Angle2D.horizontalAngle(xc, yc, point.x(), point.y());
if (direct) return Angle2D.formatAngle(angle - theta);
else return Angle2D.formatAngle(theta - angle);
}
/**
* Returns the ellipse arc which refers to the reversed parent ellipse, with same start angle, and
* with opposite angle extent.
*/
public EllipseArc2D reverse() {
double newStart = Angle2D.formatAngle(startAngle + angleExtent);
return new EllipseArc2D(ellipse, newStart, -angleExtent);
}
/** Returns the angle associated with the given position */
public double getAngle(double position) {
if (position < 0) position = 0;
if (position > abs(angleExtent)) position = abs(angleExtent);
if (angleExtent < 0) position = -position;
return Angle2D.formatAngle(startAngle + position);
}
public boolean containsAngle(double angle) {
return Angle2D.containsAngle(startAngle, startAngle + angleExtent, angle, angleExtent > 0);
}