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};
}
/**
* 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);
}
/**
* 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);
}
/**
* 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);
}
