/**
* Returns the result of rotating a matrix about a given unit vector by a given angle.
*
* @param matrix initial matrix
* @param unitvect vector to rotate around, must be normalised
* @param angle rotation angle in radians
* @return rotated matrix
*/
private static double[] rotateAround(double[] matrix, double[] unitvec, double angle) {
assert Math.abs(
(unitvec[0] * unitvec[0] + unitvec[1] * unitvec[1] + unitvec[2] * unitvec[2]) - 1)
< 1e6;
double[] rm = Matrices.fromPal(new Pal().Dav2m(Matrices.mult(unitvec, angle)));
return Matrices.mmMult(matrix, rm);
}
/**
* Takes X,Y,Z normalised coordinate ranges and tries to work out the ranges in projected plane
* coordinates they represent for a given rotation matrix. The determination is approximate.
*
* @param vxyzRanges 3-element array giving ranges of normalised X,Y,Z data coordinates
* @param rot 9-element rotation matrix to be applied before projection
* @return 2-element array giving plane coordinate X and Y ranges covered by the supplied data
* coordinate ranges
*/
private Range[] readProjectedRanges(Range[] vxyzRanges, double[] rot) {
double[] vxBounds = vxyzRanges[0].getBounds();
double[] vyBounds = vxyzRanges[1].getBounds();
double[] vzBounds = vxyzRanges[2].getBounds();
double[] r3 = new double[3];
Range pxRange = new Range();
Range pyRange = new Range();
/* Iterate over each corner of the cuboid represented by the XYZ
* ranges, and use each of these corners (actually, their projection
* on the unit sphere surface) as sample points to mark out the
* limits of X and Y projected position ranges.
* This is pretty rough, but should provide an overestimate of the
* actual X, Y ranges (I think?). The smaller the range in XYZ
* the better the estimate. */
Point2D.Double point = new Point2D.Double();
for (int jx = 0; jx < 2; jx++) {
r3[0] = vxBounds[jx];
for (int jy = 0; jy < 2; jy++) {
r3[1] = vyBounds[jy];
for (int jz = 0; jz < 2; jz++) {
r3[2] = vzBounds[jz];
double[] s3 = Matrices.normalise(Matrices.mvMult(rot, r3));
if (project(s3[0], s3[1], s3[2], point)) {
pxRange.submit(point.x);
pyRange.submit(point.y);
}
}
}
}
return new Range[] {pxRange, pyRange};
}
/**
* Attempts to return a rotation matrix corresponding to moving the plane between two cursor
* positions, with a given initial rotation matrix in effect.
*
* @param rot0 initial rotation matrix
* @param pos0 initial projected position
* @param pos1 destination projected position
* @return destination rotation matrix, or null
* @see Projection#projRotate
*/
private double[] genericRotate(double[] rot0, Point2D.Double pos0, Point2D.Double pos1) {
double[] rv0 = new double[3];
if (unproject(pos0, rv0)
&& getSkyviewProjecter().validPosition(new double[] {pos1.x, pos1.y})) {
double[] unrot0 = Matrices.invert(rot0);
double[] ru0 = Matrices.mvMult(unrot0, rv0);
return getRotation(ru0, pos1, rot0);
} else {
return null;
}
}
private static double[] getRotation(double[] rv0, Point2D.Double pos1, double[] rot0) {
boolean reflect = isReflected(rot0);
final double fr = reflect ? -1 : +1;
final double rx = rv0[0];
final double ry = rv0[1];
final double rz = rv0[2];
final double px = pos1.x;
final double py = pos1.y;
// Use algebra from verticalRotate matrix.
double delta0 = Math.atan2(-rot0[2], rot0[8]);
double alpha0 = Math.atan2(-rot0[3], rot0[4] * fr);
// Find alpha and delta rotation angles which put the given vector
// at the target screen position.
double alpha =
new Solver() {
double[] derivs(double a) {
double sa = Math.sin(a);
double ca = Math.cos(a);
return new double[] {
-sa * rx + ca * ry * fr - px, -ca * rx - sa * ry * fr,
};
}
}.solve(alpha0);
if (Double.isNaN(alpha)) {
return null;
}
final double ca = Math.cos(alpha);
final double sa = Math.sin(alpha);
double delta =
new Solver() {
double[] derivs(double d) {
double sd = Math.sin(d);
double cd = Math.cos(d);
return new double[] {
sd * (ca * rx + sa * ry * fr) + cd * rz - py, cd * (ca * rx + sa * ry * fr) - sd * rz,
};
}
}.solve(delta0);
if (Double.isNaN(delta)) {
return null;
}
double[] rot1 = verticalRotate(delta, alpha, reflect);
if (Matrices.mvMult(rot1, rv0)[0] >= 0 && Matrices.mvMult(rot1, RZ)[2] > 0) {
return rot1;
} else {
return null;
}
}
/**
* Works out the rotation matrix to use to center the positions represented by Cartesian
* coordinate ranges on the plot surface. Null may be returned if there is no appropriate
* rotation.
*
* @return 9-element rotation matrix or null.
*/
private static double[] getRangeRotation(Range[] vxyzRanges, boolean reflect) {
double[] center = new double[3];
for (int id = 0; id < 3; id++) {
double[] bounds = vxyzRanges[id].getBounds();
double mid = 0.5 * (bounds[0] + bounds[1]);
if (Double.isNaN(mid)) {
return null;
}
assert mid >= -1.001 && mid <= +1.001;
center[id] = mid;
}
if (Matrices.mod(center) < 0.3) {
return null;
}
center = Matrices.normalise(center);
return rotateToCenter(center, reflect);
}
@Override
public double[] cursorRotate(double[] rot0, Point2D.Double pos0, Point2D.Double pos1) {
/* Attempt the rotation that transforms a point from one
* projected plane position to another. */
double[] rot1 = genericRotate(rot0, pos0, pos1);
if (rot1 != null) {
return rot1;
}
/* That may fail because one or other of the supplied points is
* not in the projection region. In that case do something
* that feels like dragging the sphere around.
* This rotation could be improved. It is algebraically messy,
* and it also does not transition smoothly from the genericRotate
* case, though perhaps that's not possible in general. */
else {
boolean reflect = isReflected(rot0);
double fr = reflect ? -1 : +1;
double phi = (pos1.x - pos0.x);
double psi = (pos1.y - pos0.y);
double[] rm = rot0;
double[] sightvec = Matrices.mvMult(Matrices.invert(rm), new double[] {1, 0, 0});
double[] hvec = Matrices.normalise(Matrices.cross(sightvec, RZ));
rm = rotateAround(rm, hvec, -psi);
rm = rotateAround(rm, RZ, -phi * fr);
if (Matrices.mvMult(rm, RZ)[2] >= 0) {
return rm;
} else {
double delta = Math.atan2(-rm[2], rm[8]);
double alpha = Math.atan2(-rm[3], rm[4] * fr);
delta = Math.min(+0.5 * Math.PI, delta);
delta = Math.max(-0.5 * Math.PI, delta);
return verticalRotate(delta, alpha, reflect);
}
}
}
/**
* Indicates whether a rotation matrix represents reflected coordinates.
*
* @param rotmat rotation matrix
* @return true if determinant is less than 0
*/
private static boolean isReflected(double[] rotmat) {
return Matrices.det(rotmat) < 0;
}