/**
* Return a midpoint of a helix, calculated from three positions of three adjacent subunit
* centers.
*
* @param p1 center of first subunit
* @param p2 center of second subunit
* @param p3 center of third subunit
* @return midpoint of helix
*/
private Point3d getMidPoint(Point3d p1, Point3d p2, Point3d p3) {
Vector3d v1 = new Vector3d();
v1.sub(p1, p2);
Vector3d v2 = new Vector3d();
v2.sub(p3, p2);
Vector3d v3 = new Vector3d();
v3.add(v1);
v3.add(v2);
v3.normalize();
// calculat the total distance between to subunits
double dTotal = v1.length();
// calculate the rise along the y-axis. The helix axis is aligned with y-axis,
// therfore, the rise between subunits is the y-distance
double rise = p2.y - p1.y;
// use phythagorean theoremm to calculate chord length between two subunit centers
double chord = Math.sqrt(dTotal * dTotal - rise * rise);
// System.out.println("Chord d: " + dTotal + " rise: " + rise + "chord: " + chord);
double angle = helixLayers.getByLargestContacts().getAxisAngle().angle;
// using the axis angle and the chord length, we can calculate the radius of the helix
// http://en.wikipedia.org/wiki/Chord_%28geometry%29
double radius = chord / Math.sin(angle / 2) / 2; // can this go to zero?
// System.out.println("Radius: " + radius);
// project the radius onto the vector that points toward the helix axis
v3.scale(radius);
v3.add(p2);
// System.out.println("Angle: " +
// Math.toDegrees(helixLayers.getByLowestAngle().getAxisAngle().angle));
Point3d cor = new Point3d(v3);
return cor;
}
private Vector3d orthogonalize(Vector3d vector1, Vector3d vector2) {
double dot = vector1.dot(vector2);
Vector3d ref = new Vector3d(vector2);
// System.out.println("p.r: " + dot);
// System.out.println("Orig refVector: " + referenceVector);
if (dot < 0) {
vector2.negate();
}
if (Math.abs(dot) < 0.00001) {
System.out.println("HelixAxisAligner: Warning: reference axis parallel");
}
vector2.cross(vector1, vector2);
// System.out.println("Intermed. refVector: " + vector2);
vector2.normalize();
// referenceVector.cross(referenceVector, principalRotationVector);
vector2.cross(vector1, vector2);
vector2.normalize();
if (ref.dot(vector2) < 0) {
vector2.negate();
}
// System.out.println("Mod. refVector: " + vector2);
return vector2;
}
/**
* Returns a transformation matrix that rotates refPoints to match coordPoints
*
* @param refPoints the points to be aligned
* @param referenceVectors
* @return
*/
private Matrix4d alignAxes(Vector3d[] axisVectors, Vector3d[] referenceVectors) {
Matrix4d m1 = new Matrix4d();
AxisAngle4d a = new AxisAngle4d();
Vector3d axis = new Vector3d();
// calculate rotation matrix to rotate refPoints[0] into coordPoints[0]
Vector3d v1 = new Vector3d(axisVectors[0]);
Vector3d v2 = new Vector3d(referenceVectors[0]);
double dot = v1.dot(v2);
if (Math.abs(dot) < 0.999) {
axis.cross(v1, v2);
axis.normalize();
a.set(axis, v1.angle(v2));
m1.set(a);
// make sure matrix element m33 is 1.0. It's 0 on Linux.
m1.setElement(3, 3, 1.0);
} else if (dot > 0) {
// parallel axis, nothing to do -> identity matrix
m1.setIdentity();
} else if (dot < 0) {
// anti-parallel axis, flip around x-axis
m1.set(flipX());
}
// apply transformation matrix to all refPoints
m1.transform(axisVectors[0]);
m1.transform(axisVectors[1]);
// calculate rotation matrix to rotate refPoints[1] into coordPoints[1]
v1 = new Vector3d(axisVectors[1]);
v2 = new Vector3d(referenceVectors[1]);
Matrix4d m2 = new Matrix4d();
dot = v1.dot(v2);
if (Math.abs(dot) < 0.999) {
axis.cross(v1, v2);
axis.normalize();
a.set(axis, v1.angle(v2));
m2.set(a);
// make sure matrix element m33 is 1.0. It's 0 on Linux.
m2.setElement(3, 3, 1.0);
} else if (dot > 0) {
// parallel axis, nothing to do -> identity matrix
m2.setIdentity();
} else if (dot < 0) {
// anti-parallel axis, flip around z-axis
m2.set(flipZ());
}
// apply transformation matrix to all refPoints
m2.transform(axisVectors[0]);
m2.transform(axisVectors[1]);
// combine the two rotation matrices
m2.mul(m1);
// the RMSD should be close to zero
Point3d[] axes = new Point3d[2];
axes[0] = new Point3d(axisVectors[0]);
axes[1] = new Point3d(axisVectors[1]);
Point3d[] ref = new Point3d[2];
ref[0] = new Point3d(referenceVectors[0]);
ref[1] = new Point3d(referenceVectors[1]);
if (SuperPosition.rmsd(axes, ref) > 0.1) {
System.out.println(
"Warning: AxisTransformation: axes alignment is off. RMSD: "
+ SuperPosition.rmsd(axes, ref));
}
return m2;
}