public java.awt.geom.GeneralPath appendPath(java.awt.geom.GeneralPath path) {
// number of curves to approximate the arc
int nSeg = (int) ceil(abs(angleExtent) / (PI / 2));
nSeg = min(nSeg, 4);
// angular extent of each curve
double ext = angleExtent / nSeg;
// compute coefficient
double k = btan(abs(ext));
for (int i = 0; i < nSeg; i++) {
// position of the two extremities
double ti0 = abs(i * ext);
double ti1 = abs((i + 1) * ext);
// extremity points
Point2D p1 = this.point(ti0);
Point2D p2 = this.point(ti1);
// tangent vectors, multiplied by appropriate coefficient
Vector2D v1 = this.tangent(ti0).times(k);
Vector2D v2 = this.tangent(ti1).times(k);
// append a cubic curve to the path
path.curveTo(
p1.x() + v1.x(), p1.y() + v1.y(), p2.x() - v2.x(), p2.y() - v2.y(), p2.x(), p2.y());
}
return path;
}
/**
* 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);
}
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);
}
@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 java.awt.geom.GeneralPath getGeneralPath() {
// create new path
java.awt.geom.GeneralPath path = new java.awt.geom.GeneralPath();
// move to the first point
Point2D point = this.firstPoint();
path.moveTo((float) point.x(), (float) point.y());
// append the curve
path = this.appendPath(path);
// return the final path
return path;
}
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);
}
public double signedDistance(Point2D point) {
return signedDistance(point.x(), point.y());
}
/**
* Test whether the point is inside the circle. The test is performed by translating the point,
* and re-scaling it such that its coordinates are expressed in unit circle basis.
*/
public boolean isInside(Point2D point) {
double xp = (point.x() - this.xc) / this.r;
double yp = (point.y() - this.yc) / this.r;
return (xp * xp + yp * yp < 1) ^ !direct;
}
/** Create a new circle with specified center, radius and orientation */
public Circle2D(Point2D center, double radius, boolean direct) {
this(center.x(), center.y(), radius, direct);
}
/** Create a new circle with specified point center and radius */
public Circle2D(Point2D center, double radius) {
this(center.x(), center.y(), radius, true);
}
public double signedDistance(Point2D p) {
return signedDistance(p.x(), p.y());
}
/*
* (non-Javadoc)
*
* @see java.awt.Shape#contains(Point2D)
*/
public boolean contains(Point2D point) {
return contains(point.x(), point.y());
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Shape2D#distance(math.geom2d.Point2D)
*/
public double distance(Point2D point) {
return distance(point.x(), point.y());
}
public double distance(Point2D point) {
return abs(Point2D.distance(xc, yc, point.x(), point.y()) - r);
}
/** Returns true if the point p lies on the ellipse, with precision given by Shape2D.ACCURACY. */
public boolean contains(Point2D p) {
return contains(p.x(), p.y());
}
public boolean isInside(Point2D p) {
return signedDistance(p.x(), p.y()) < 0;
}
