public static double[] invertBilinear(Vec4 U, Vec4 X, Vec4 Y, Vec4 Z, Vec4 W) {
    Vec4 s1 = W.subtract3(X);
    Vec4 s2 = Z.subtract3(Y);
    Vec4 UminX = U.subtract3(X);
    Vec4 UminY = U.subtract3(Y);
    Vec4 normal = Z.subtract3(X).cross3(W.subtract3(Y));

    double A = s1.cross3(s2).dot3(normal);
    double B = s2.cross3(UminX).dot3(normal) - s1.cross3(UminY).dot3(normal);
    double C = UminX.cross3(UminY).dot3(normal);

    double descriminant = B * B - 4d * A * C;
    if (descriminant < 0) return null;
    descriminant = Math.sqrt(descriminant);

    double beta = B > 0 ? (-B - descriminant) / (2d * A) : 2d * C / (-B + descriminant);

    Vec4 Sbeta1 = Vec4.mix3(beta, X, W);
    Vec4 Sbeta2 = Vec4.mix3(beta, Y, Z);

    double alpha =
        U.subtract3(Sbeta1).dot3(Sbeta2.subtract3(Sbeta1)) / Sbeta2.subtract3(Sbeta1).dotSelf3();

    return new double[] {alpha, beta};
  }
Ejemplo n.º 2
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  /**
   * Compute the positions of the arrow head of the graphic's legs.
   *
   * @param dc Current draw context
   * @param base Position of the arrow's starting point.
   * @param tip Position of the arrow head tip.
   * @param arrowLength Length of the arrowhead as a fraction of the total line length.
   * @param arrowAngle Angle of the arrow head.
   * @return Positions required to draw the arrow head.
   */
  protected List<Position> computeArrowheadPositions(
      DrawContext dc, Position base, Position tip, double arrowLength, Angle arrowAngle) {
    // Build a triangle to represent the arrowhead. The triangle is built from two vectors, one
    // parallel to the
    // segment, and one perpendicular to it.

    Globe globe = dc.getGlobe();

    Vec4 ptA = globe.computePointFromPosition(base);
    Vec4 ptB = globe.computePointFromPosition(tip);

    // Compute parallel component
    Vec4 parallel = ptA.subtract3(ptB);

    Vec4 surfaceNormal = globe.computeSurfaceNormalAtPoint(ptB);

    // Compute perpendicular component
    Vec4 perpendicular = surfaceNormal.cross3(parallel);

    double finalArrowLength = arrowLength * parallel.getLength3();
    double arrowHalfWidth = finalArrowLength * arrowAngle.tanHalfAngle();

    perpendicular = perpendicular.normalize3().multiply3(arrowHalfWidth);
    parallel = parallel.normalize3().multiply3(finalArrowLength);

    // Compute geometry of direction arrow
    Vec4 vertex1 = ptB.add3(parallel).add3(perpendicular);
    Vec4 vertex2 = ptB.add3(parallel).subtract3(perpendicular);

    return TacticalGraphicUtil.asPositionList(globe, vertex1, vertex2, ptB);
  }
Ejemplo n.º 3
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  /**
   * Determine the positions that make up the arrowhead.
   *
   * @param dc Current draw context.
   * @param startPosition Position of the arrow's base.
   * @param endPosition Position of the arrow head tip.
   * @return Positions that define the arrowhead.
   */
  protected List<Position> computeArrowheadPositions(
      DrawContext dc, Position startPosition, Position endPosition) {
    Globe globe = dc.getGlobe();

    // Arrowhead looks like this:
    //                  _
    //        A\         | 1/2 width
    // ________B\       _|
    // Pt. 1    /
    //        C/
    //         | |
    //      Length

    Vec4 p1 = globe.computePointFromPosition(startPosition);
    Vec4 pB = globe.computePointFromPosition(endPosition);

    // Find vector in the direction of the arrow
    Vec4 vB1 = p1.subtract3(pB);

    double arrowLengthFraction = this.getArrowLength();

    // Find the point at the base of the arrowhead
    Vec4 arrowBase = pB.add3(vB1.multiply3(arrowLengthFraction));

    Vec4 normal = globe.computeSurfaceNormalAtPoint(arrowBase);

    // Compute the length of the arrowhead
    double arrowLength = vB1.getLength3() * arrowLengthFraction;
    double arrowHalfWidth = arrowLength * this.getArrowAngle().tanHalfAngle();

    // Compute a vector perpendicular to the segment and the normal vector
    Vec4 perpendicular = vB1.cross3(normal);
    perpendicular = perpendicular.normalize3().multiply3(arrowHalfWidth);

    // Find points A and C
    Vec4 pA = arrowBase.add3(perpendicular);
    Vec4 pC = arrowBase.subtract3(perpendicular);

    return TacticalGraphicUtil.asPositionList(globe, pA, pB, pC);
  }
Ejemplo n.º 4
0
  /**
   * Compute points on either side of a line segment. This method requires a point on the line, and
   * either a next point, previous point, or both.
   *
   * @param point Center point about which to compute side points.
   * @param prev Previous point on the line. May be null if {@code next} is non-null.
   * @param next Next point on the line. May be null if {@code prev} is non-null.
   * @param leftPositions Left position will be added to this list.
   * @param rightPositions Right position will be added to this list.
   * @param halfWidth Distance from the center line to the left or right lines.
   * @param globe Current globe.
   */
  protected void generateParallelPoints(
      Vec4 point,
      Vec4 prev,
      Vec4 next,
      List<Position> leftPositions,
      List<Position> rightPositions,
      double halfWidth,
      Globe globe) {
    if ((point == null) || (prev == null && next == null)) {
      String message = Logging.getMessage("nullValue.PointIsNull");
      Logging.logger().severe(message);
      throw new IllegalArgumentException(message);
    }
    if (leftPositions == null || rightPositions == null) {
      String message = Logging.getMessage("nullValue.PositionListIsNull");
      Logging.logger().severe(message);
      throw new IllegalArgumentException(message);
    }
    if (globe == null) {
      String message = Logging.getMessage("nullValue.GlobeIsNull");
      Logging.logger().severe(message);
      throw new IllegalArgumentException(message);
    }

    Vec4 offset;
    Vec4 normal = globe.computeSurfaceNormalAtPoint(point);

    // Compute vector in the direction backward along the line.
    Vec4 backward = (prev != null) ? prev.subtract3(point) : point.subtract3(next);

    // Compute a vector perpendicular to segment BC, and the globe normal vector.
    Vec4 perpendicular = backward.cross3(normal);

    double length;
    // If both next and previous points are supplied then calculate the angle that bisects the angle
    // current, next, prev.
    if (next != null && prev != null && !Vec4.areColinear(prev, point, next)) {
      // Compute vector in the forward direction.
      Vec4 forward = next.subtract3(point);

      // Calculate the vector that bisects angle ABC.
      offset = forward.normalize3().add3(backward.normalize3());
      offset = offset.normalize3();

      // Compute the scalar triple product of the vector BC, the normal vector, and the offset
      // vector to
      // determine if the offset points to the left or the right of the control line.
      double tripleProduct = perpendicular.dot3(offset);
      if (tripleProduct < 0) {
        offset = offset.multiply3(-1);
      }

      // Determine the length of the offset vector that will keep the left and right lines parallel
      // to the control
      // line.
      Angle theta = backward.angleBetween3(offset);
      if (!Angle.ZERO.equals(theta)) length = halfWidth / theta.sin();
      else length = halfWidth;
    } else {
      offset = perpendicular.normalize3();
      length = halfWidth;
    }
    offset = offset.multiply3(length);

    // Determine the left and right points by applying the offset.
    Vec4 ptRight = point.add3(offset);
    Vec4 ptLeft = point.subtract3(offset);

    // Convert cartesian points to geographic.
    Position posLeft = globe.computePositionFromPoint(ptLeft);
    Position posRight = globe.computePositionFromPoint(ptRight);

    leftPositions.add(posLeft);
    rightPositions.add(posRight);
  }