/** @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;
}
/**
* 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);
}
@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;
}
/**
* Transforms this circle by an affine transform. If the transformed shape is a circle (ellipse
* with equal axis lengths), returns an instance of Circle2D. The resulting ellipse is direct if
* this ellipse and the transform are either both direct or both indirect.
*/
public EllipseShape2D transform(AffineTransform2D trans) {
// When the transform is not a similarity, should switch to EllipseArc
// computation
if (!AffineTransform2D.isSimilarity(trans)) {
return this.asEllipse().transform(trans);
}
// If transform is a similarity, the result is a circle
Point2D center = this.center().transform(trans);
Point2D p1 = this.firstPoint().transform(trans);
boolean direct = !this.direct ^ trans.isDirect();
Circle2D result = new Circle2D(center, center.distance(p1), direct);
return result;
}
/**
* Computes intersections of a circle with a line. Returns an array of Point2D, of size 0, 1 or 2
* depending on the distance between circle and line. If there are 2 intersections points, the
* first one in the array is the first one on the line.
*
* @return a collection of intersection points
* @since 0.11.1
*/
public static Collection<Point2D> lineCircleIntersections(
LinearShape2D line, CircularShape2D circle) {
// initialize array of points (maximum 2 intersections)
ArrayList<Point2D> intersections = new ArrayList<Point2D>(2);
// extract parameters of the circle
Circle2D parent = circle.supportingCircle();
Point2D center = parent.center();
double radius = parent.radius();
// Compute line perpendicular to the test line, and going through the
// circle center
StraightLine2D perp = StraightLine2D.createPerpendicular(line, center);
// Compute distance between line and circle center
Point2D inter = perp.intersection(new StraightLine2D(line));
if (inter == null) {
throw new RuntimeException(
"Could not compute intersection point when computing line-cicle intersection");
}
double dist = inter.distance(center);
// if the distance is the radius of the circle, return the
// intersection point
if (abs(dist - radius) < Shape2D.ACCURACY) {
if (line.contains(inter) && circle.contains(inter)) intersections.add(inter);
return intersections;
}
// compute angle of the line, and distance between 'inter' point and
// each intersection point
double angle = line.horizontalAngle();
double d2 = sqrt(radius * radius - dist * dist);
// Compute position and angle of intersection points
Point2D p1 = Point2D.createPolar(inter, d2, angle + Math.PI);
Point2D p2 = Point2D.createPolar(inter, d2, angle);
// add points to the array only if they belong to the line
if (line.contains(p1) && circle.contains(p1)) intersections.add(p1);
if (line.contains(p2) && circle.contains(p2)) intersections.add(p2);
// return the result
return intersections;
}
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;
}
/**
* Creates a circle containing 3 points.
*
* @deprecated replaced by createCircle(Point2D, Point2D, Point2D) (0.11.1)
*/
@Deprecated
public static Circle2D create(Point2D p1, Point2D p2, Point2D p3) {
if (Point2D.isColinear(p1, p2, p3)) throw new ColinearPoints2DException(p1, p2, p3);
// create two median lines
StraightLine2D line12 = StraightLine2D.createMedian(p1, p2);
StraightLine2D line23 = StraightLine2D.createMedian(p2, p3);
// check medians are not parallel
assert !AbstractLine2D.isParallel(line12, line23)
: "If points are not colinear, medians should not be parallel";
// Compute intersection of the medians, and circle radius
Point2D center = AbstractLine2D.getIntersection(line12, line23);
double radius = Point2D.distance(center, p2);
// return the created circle
return new Circle2D(center, radius);
}
/**
* Computes the circumscribed circle of the 3 input points.
*
* @return the circle that contains the three input points
* @throws ColinearPoints2DException if the 3 points are colinear
*/
public static Circle2D circumCircle(Point2D p1, Point2D p2, Point2D p3) {
// Computes circum center, possibly throwing ColinearPoints2DException
Point2D center = circumCenter(p1, p2, p3);
// compute radius
double radius = Point2D.distance(center, p2);
// return the created circle
return new Circle2D(center, radius);
}
/**
* 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 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);
}
/** 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);
}
public double distance(double x, double y) {
return abs(Point2D.distance(xc, yc, x, y) - r);
}
public double distance(Point2D point) {
return abs(Point2D.distance(xc, yc, point.x(), point.y()) - r);
}
/*
* (non-Javadoc)
*
* @see math.geom2d.Shape2D#distance(math.geom2d.Point2D)
*/
public double distance(Point2D point) {
return distance(point.x(), point.y());
}
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(double x, double y) {
if (direct) return Point2D.distance(xc, yc, x, y) - r;
else return r - Point2D.distance(xc, yc, x, y);
}
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;
}
/*
* (non-Javadoc)
*
* @see java.awt.Shape#contains(Point2D)
*/
public boolean contains(Point2D point) {
return contains(point.x(), point.y());
}
/** 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());
}
/** 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 math.geom2d.Shape2D#distance(double, double)
*/
public double distance(double x, double y) {
Point2D p = point(project(new Point2D(x, y)));
return p.distance(x, y);
}
public boolean isInside(Point2D p) {
return signedDistance(p.x(), p.y()) < 0;
}
/* (non-Javadoc)
* @see math.geom2d.circulinear.CirculinearCurve2D#transform(math.geom2d.transform.CircleInversion2D)
*/
public CircleLine2D transform(CircleInversion2D inv) {
// Extract inversion parameters
Point2D center = inv.center();
Point2D c1 = this.center();
// If circles are concentric, creates directly the new circle
if (center.distance(c1) < Shape2D.ACCURACY) {
double r0 = inv.radius();
double r2 = r0 * r0 / this.r;
return new Circle2D(center, r2, this.direct);
}
// line joining centers of the two circles
StraightLine2D centersLine = new StraightLine2D(center, c1);
// get the two intersection points with the line joining the circle centers
Collection<Point2D> points = this.intersections(centersLine);
if (points.size() < 2) {
throw new RuntimeException(
"Intersection of circle with line through center has less than 2 points");
}
Iterator<Point2D> iter = points.iterator();
Point2D p1 = iter.next();
Point2D p2 = iter.next();
// If the circle contains the inversion center, it transforms into a
// straight line
if (this.distance(center) < Shape2D.ACCURACY) {
// choose the intersection point that is not the center
double dist1 = center.distance(p1);
double dist2 = center.distance(p2);
Point2D p0 = dist1 < dist2 ? p2 : p1;
// transform the point, and return the perpendicular
p0 = p0.transform(inv);
return StraightLine2D.createPerpendicular(centersLine, p0);
}
// For regular cases, the circle transforms into an other circle
// transform the two extreme points of the circle,
// resulting in a diameter of the new circle
p1 = p1.transform(inv);
p2 = p2.transform(inv);
// compute center and diameter of transformed circle
double diam = p1.distance(p2);
c1 = Point2D.midPoint(p1, p2);
// create the transformed circle
boolean direct = !this.isDirect() ^ this.isInside(inv.center());
return new Circle2D(c1, diam / 2, direct);
}
