public Vector2D tangent(double t) {
// format between min and max admissible values
t = min(max(0, t), abs(angleExtent));
// compute tangent vector depending on position
if (angleExtent < 0) {
// need to invert vector for indirect arcs
return ellipse.tangent(startAngle - t).times(-1);
} else {
return ellipse.tangent(startAngle + t);
}
}
/** Returns the curvature of the ellipse arc. Curvature is negative if the arc is indirect. */
public double curvature(double t) {
// convert position to angle
if (angleExtent < 0) t = startAngle - t;
else t = startAngle + t;
double kappa = ellipse.curvature(t);
return this.isDirect() ? kappa : -kappa;
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Shape2D#signedDistance(math.geom2d.Point2D)
*/
public double signedDistance(double x, double y) {
boolean direct = angleExtent >= 0;
double dist = distance(x, y);
Point2D point = new Point2D(x, y);
boolean inside = ellipse.isInside(point);
if (inside) return angleExtent > 0 ? -dist : dist;
Point2D p1 = point(startAngle);
double endAngle = startAngle + angleExtent;
Point2D p2 = point(endAngle);
boolean onLeft = (new StraightLine2D(p1, p2)).isInside(point);
if (direct && !onLeft) return dist;
if (!direct && onLeft) return -dist;
Ray2D ray = new Ray2D(p1, -sin(startAngle), cos(startAngle));
boolean left1 = ray.isInside(point);
if (direct && !left1) return dist;
if (!direct && left1) return -dist;
ray = new Ray2D(p2, -sin(endAngle), cos(endAngle));
boolean left2 = ray.isInside(point);
if (direct && !left2) return dist;
if (!direct && left2) return -dist;
if (direct) return -dist;
else return dist;
}
/*
* (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#intersections(math.geom2d.LinearShape2D)
*/
public Collection<Point2D> intersections(LinearShape2D line) {
// check point contained in it
ArrayList<Point2D> array = new ArrayList<Point2D>();
for (Point2D point : ellipse.intersections(line)) if (contains(point)) array.add(point);
return array;
}
/*
* (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;
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Curve2D#point(double, math.geom2d.Point2D)
*/
public Point2D point(double t) {
// check bounds
t = max(t, 0);
t = min(t, abs(angleExtent));
// convert position to angle
if (angleExtent < 0) t = startAngle - t;
else t = startAngle + t;
// return corresponding point
return ellipse.point(t);
}
@Override
public String toString() {
Point2D center = ellipse.center();
return String.format(
Locale.US,
"EllipseArc2D(%7.2f,%7.2f,%7.2f,%7.2f,%7.5f,%7.5f,%7.5f)",
center.x(),
center.y(),
ellipse.r1,
ellipse.r2,
ellipse.theta,
startAngle,
angleExtent);
}
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);
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Shape2D#transform(math.geom2d.AffineTransform2D)
*/
public EllipseArc2D transform(AffineTransform2D trans) {
// transform supporting ellipse
Ellipse2D ell = ellipse.transform(trans);
// ensure ellipse is direct
if (!ell.isDirect()) ell = ell.reverse();
// Compute position of end points on the transformed ellipse
double startPos = ell.project(this.firstPoint().transform(trans));
double endPos = ell.project(this.lastPoint().transform(trans));
// Compute the new arc
boolean direct = !(angleExtent > 0 ^ trans.isDirect());
return new EllipseArc2D(ell, startPos, endPos, direct);
}
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);
}
