예제 #1
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  /** @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;
  }
예제 #2
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  /**
   * 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);
  }
예제 #3
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  /**
   * 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);
  }
예제 #4
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 @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);
 }
예제 #5
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  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;
  }
예제 #6
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  /**
   * 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;
  }
예제 #7
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  /**
   * 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;
  }
예제 #8
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  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;
  }
예제 #9
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  /**
   * 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);
  }
예제 #10
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  /**
   * 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);
  }
예제 #11
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  /**
   * 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;
  }
예제 #12
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  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);
  }
예제 #13
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 /** 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);
 }
예제 #14
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 public double distance(double x, double y) {
   return abs(Point2D.distance(xc, yc, x, y) - r);
 }
예제 #15
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 public double distance(Point2D point) {
   return abs(Point2D.distance(xc, yc, point.x(), point.y()) - r);
 }
예제 #16
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 /*
  * (non-Javadoc)
  *
  * @see math.geom2d.Shape2D#distance(math.geom2d.Point2D)
  */
 public double distance(Point2D point) {
   return distance(point.x(), point.y());
 }
예제 #17
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 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);
 }
예제 #18
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 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);
 }
예제 #19
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 public double signedDistance(Point2D point) {
   return signedDistance(point.x(), point.y());
 }
예제 #20
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 /**
  * 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;
 }
예제 #21
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 /*
  * (non-Javadoc)
  *
  * @see java.awt.Shape#contains(Point2D)
  */
 public boolean contains(Point2D point) {
   return contains(point.x(), point.y());
 }
예제 #22
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 /** 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());
 }
예제 #23
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 /** Create a new circle with specified point center and radius */
 public Circle2D(Point2D center, double radius) {
   this(center.x(), center.y(), radius, true);
 }
예제 #24
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 public double signedDistance(Point2D p) {
   return signedDistance(p.x(), p.y());
 }
예제 #25
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 /*
  * (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);
 }
예제 #26
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 public boolean isInside(Point2D p) {
   return signedDistance(p.x(), p.y()) < 0;
 }
예제 #27
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  /* (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);
  }