private Matrix4d reorientHelix(int index) {
Matrix4d matrix = new Matrix4d();
matrix.setIdentity();
matrix.setRotation(new AxisAngle4d(1, 0, 0, Math.PI / 2 * (index + 1)));
matrix.mul(transformationMatrix);
return matrix;
}
public Point3d calcCenterOfRotation() {
List<Integer> line = getLongestLayerLine();
// can't determine center of rotation if there are only 2 points
// TODO does this ever happen??
if (line.size() < 3) {
return subunits.getCentroid();
}
Point3d centerOfRotation = new Point3d();
List<Point3d> centers = subunits.getOriginalCenters();
// calculate helix mid points for each set of 3 adjacent subunits
for (int i = 0; i < line.size() - 2; i++) {
Point3d p1 = new Point3d(centers.get(line.get(i)));
Point3d p2 = new Point3d(centers.get(line.get(i + 1)));
Point3d p3 = new Point3d(centers.get(line.get(i + 2)));
transformationMatrix.transform(p1);
transformationMatrix.transform(p2);
transformationMatrix.transform(p3);
centerOfRotation.add(getMidPoint(p1, p2, p3));
}
// average over all midpoints to find best center of rotation
centerOfRotation.scale(1 / (line.size() - 2));
// since helix is aligned along the y-axis, with an origin at y = 0, place the center of
// rotation there
centerOfRotation.y = 0;
// transform center of rotation to the original coordinate frame
reverseTransformationMatrix.transform(centerOfRotation);
// System.out.println("center of rotation: " + centerOfRotation);
return centerOfRotation;
}
private static Matrix4d flipZ() {
Matrix4d rot = new Matrix4d();
rot.m00 = -1;
rot.m11 = -1;
rot.m22 = 1;
rot.m33 = 1;
return rot;
}
/* (non-Javadoc)
* @see org.biojava.nbio.structure.quaternary.core.AxisAligner#getGeometicCenterTransformation()
*/
@Override
public Matrix4d getGeometicCenterTransformation() {
run();
Matrix4d geometricCentered = new Matrix4d(reverseTransformationMatrix);
geometricCentered.setTranslation(new Vector3d(getGeometricCenter()));
return geometricCentered;
}
/*
* Modifies the rotation part of the transformation axis for
* a Cn symmetric complex, so that the narrower end faces the
* viewer, and the wider end faces away from the viewer. Example: 3LSV
*/
private void calcZDirection() {
calcBoundaries();
// if the longer part of the structure faces towards the back (-z direction),
// rotate around y-axis so the longer part faces the viewer (+z direction)
if (Math.abs(minBoundary.z) > Math.abs(maxBoundary.z)) {
Matrix4d rot = flipY();
rot.mul(transformationMatrix);
transformationMatrix.set(rot);
}
}
/**
* Sets the value of this axis-angle to the rotational component of the passed matrix. If the
* specified matrix has no rotational component, the value of this AxisAngle4d is set to an angle
* of 0 about an axis of (0,1,0).
*
* @param m1 the matrix4d
*/
public final void set(Matrix4d m1) {
Matrix3d m3d = new Matrix3d();
m1.get(m3d);
x = (float) (m3d.m21 - m3d.m12);
y = (float) (m3d.m02 - m3d.m20);
z = (float) (m3d.m10 - m3d.m01);
double mag = x * x + y * y + z * z;
if (mag > EPS) {
mag = Math.sqrt(mag);
double sin = 0.5 * mag;
double cos = 0.5 * (m3d.m00 + m3d.m11 + m3d.m22 - 1.0);
angle = (float) Math.atan2(sin, cos);
double invMag = 1.0 / mag;
x = x * invMag;
y = y * invMag;
z = z * invMag;
} else {
x = 0.0f;
y = 1.0f;
z = 0.0f;
angle = 0.0f;
}
}
/* (non-Javadoc)
* @see org.biojava.nbio.structure.quaternary.core.AxisAligner#getRotationMatrix()
*/
@Override
public Matrix3d getRotationMatrix() {
run();
Matrix3d m = new Matrix3d();
transformationMatrix.getRotationScale(m);
return m;
}
/**
* Calculates the min and max boundaries of the structure after it has been transformed into its
* canonical orientation.
*/
private void calcBoundaries() {
minBoundary.x = Double.MAX_VALUE;
maxBoundary.x = Double.MIN_VALUE;
minBoundary.y = Double.MAX_VALUE;
maxBoundary.x = Double.MIN_VALUE;
minBoundary.z = Double.MAX_VALUE;
maxBoundary.z = Double.MIN_VALUE;
xzRadiusMax = Double.MIN_VALUE;
Point3d probe = new Point3d();
for (Point3d[] list : subunits.getTraces()) {
for (Point3d p : list) {
probe.set(p);
transformationMatrix.transform(probe);
minBoundary.x = Math.min(minBoundary.x, probe.x);
maxBoundary.x = Math.max(maxBoundary.x, probe.x);
minBoundary.y = Math.min(minBoundary.y, probe.y);
maxBoundary.y = Math.max(maxBoundary.y, probe.y);
minBoundary.z = Math.min(minBoundary.z, probe.z);
maxBoundary.z = Math.max(maxBoundary.z, probe.z);
xzRadiusMax = Math.max(xzRadiusMax, Math.sqrt(probe.x * probe.x + probe.z * probe.z));
}
}
// System.out.println("MinBoundary: " + minBoundary);
// System.out.println("MaxBoundary: " + maxBoundary);
// System.out.println("zxRadius: " + xzRadiusMax);
}
private void calcTransformationBySymmetryAxes() {
Vector3d[] axisVectors = new Vector3d[2];
axisVectors[0] = new Vector3d(principalRotationVector);
axisVectors[1] = new Vector3d(referenceVector);
// y,z axis centered at the centroid of the subunits
Vector3d[] referenceVectors = new Vector3d[2];
referenceVectors[0] = new Vector3d(Z_AXIS);
referenceVectors[1] = new Vector3d(Y_AXIS);
transformationMatrix = alignAxes(axisVectors, referenceVectors);
// combine with translation
Matrix4d combined = new Matrix4d();
combined.setIdentity();
Vector3d trans = new Vector3d(subunits.getCentroid());
trans.negate();
combined.setTranslation(trans);
transformationMatrix.mul(combined);
// for helical geometry, set a canonical view for the Z direction
calcZDirection();
}
private double[] getSubunitZDepth() {
int n = subunits.getSubunitCount();
double[] depth = new double[n];
Point3d probe = new Point3d();
// transform subunit centers into z-aligned position and calculate
// z-coordinates (depth) along the z-axis.
for (int i = 0; i < n; i++) {
Point3d p = subunits.getCenters().get(i);
probe.set(p);
transformationMatrix.transform(probe);
depth[i] = probe.z;
}
return depth;
}
/* (non-Javadoc)
* @see org.biojava.nbio.structure.quaternary.core.AxisAligner#getGeometricCenter()
*/
@Override
public Point3d getGeometricCenter() {
run();
Point3d geometricCenter = new Point3d();
Vector3d translation = new Vector3d();
// reverseTransformationMatrix.get(translation);
// TODO does this apply to the helic case?
// calculate adjustment around z-axis and transform adjustment to
// original coordinate frame with the reverse transformation
// Vector3d corr = new Vector3d(0,minBoundary.y+getDimension().y, 0);
// reverseTransformationMatrix.transform(corr);
// geometricCenter.set(corr);
reverseTransformationMatrix.transform(translation);
geometricCenter.add(translation);
return geometricCenter;
}
/**
* 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;
}
private void calcReverseTransformation() {
reverseTransformationMatrix.invert(transformationMatrix);
}
private void calcTransformation() {
calcTransformationBySymmetryAxes();
// make sure this value is zero. On Linux this value is 0.
transformationMatrix.setElement(3, 3, 1.0);
}
/**
* Computes the new transform for this interpolator for a given alpha value.
*
* @param alphaValue alpha value between 0.0 and 1.0
* @param transform object that receives the computed transform for the specified alpha value
* @since Java 3D 1.3
*/
public void computeTransform(float alphaValue, Transform3D transform) {
// compute the current value of u from alpha and the
// determine lower and upper knot points
computePathInterpolation(alphaValue);
// Determine the segment within which we will be interpolating
currentSegmentIndex = this.lowerKnot - 1;
// if we are at the start of the curve
if (currentSegmentIndex == 0 && currentU == 0f) {
iHeading = keyFrames[1].heading;
iPitch = keyFrames[1].pitch;
iBank = keyFrames[1].bank;
iPos.set(keyFrames[1].position);
iScale.set(keyFrames[1].scale);
// if we are at the end of the curve
} else if (currentSegmentIndex == (numSegments - 1) && currentU == 1.0) {
iHeading = keyFrames[upperKnot].heading;
iPitch = keyFrames[upperKnot].pitch;
iBank = keyFrames[upperKnot].bank;
iPos.set(keyFrames[upperKnot].position);
iScale.set(keyFrames[upperKnot].scale);
// if we are somewhere in between the curve
} else {
// Get a reference to the current spline segment i.e. the
// one bounded by lowerKnot and upperKnot
currentSegment = cubicSplineCurve.getSegment(currentSegmentIndex);
// interpolate quaternions
iHeading = currentSegment.getInterpolatedHeading(currentU);
iPitch = currentSegment.getInterpolatedPitch(currentU);
iBank = currentSegment.getInterpolatedBank(currentU);
// interpolate position
currentSegment.getInterpolatedPositionVector(currentU, iPos);
// interpolate position
currentSegment.getInterpolatedScale(currentU, iScale);
// System.out.println("Pos :" + iPos);
}
// Modification by ReubenDB
if (colorRampingInterpolate == true) {
float[] curPos = new float[3];
iPos.get(curPos);
myColorRamp.getColor(curPos[1], histColor);
// System.out.println("SETING COLOR:" + histColor + " CurPos: " + curPos[0] + ", " + curPos[1]
// + ", " + curPos[2]);
objectCA.setColor(histColor);
// System.out.println("CurrentAlpha = " + myAlpha.value());
}
if (timeDisplayInterpolate == true) {
myTimeDisplay.updateDisplayFromAlpha(myAlpha.value());
// System.out.println(myAlpha.value());
}
// Generate a transformation matrix in tMat using interpolated
// heading, pitch and bank
pitchMat.setIdentity();
pitchMat.rotX(-iPitch);
bankMat.setIdentity();
bankMat.rotZ(iBank);
tMat.setIdentity();
tMat.rotY(-iHeading);
tMat.mul(pitchMat);
tMat.mul(bankMat);
// TODO: Vijay - Handle Non-Uniform scale
// Currently this interpolator does not handle non uniform scale
// We cheat by just taking the x scale component
// Scale the transformation matrix
sMat.set((double) iScale.x);
tMat.mul(sMat);
// Set the translation components.
tMat.m03 = iPos.x;
tMat.m13 = iPos.y;
tMat.m23 = iPos.z;
rotation.set(tMat);
// construct a Transform3D from: axis * rotation * axisInverse
transform.mul(axis, rotation);
transform.mul(transform, axisInverse);
}