/**
* 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;
}
/**
* 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;
}
/**
* 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;
}
/**
* Computes intersections of the circle with a line. Return 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.
*/
public Collection<Point2D> intersections(LinearShape2D line) {
return Circle2D.lineCircleIntersections(line, this);
}
/**
* Returns the intersection points with another circle. The result is a collection with 0, 1 or 2
* points.
*/
public Collection<Point2D> intersections(Circle2D circle) {
return Circle2D.circlesIntersections(this, circle);
}