Java – Angle between two 3D vectors

I have a series of vertices (pink) that I want to rotate so that one edge of the pattern of vertices matches with the edge of the triangle (white).

To do this, I first create two vectors to represent the edges: floretAB and triangleAB (green). I then find the cross product of the two to get an axis around which I can rotate the vertices (red).

I then get the angle between the two vectors, and use that, with the rotation axis to create a quaternion. Finally, I rotate all the vertices around the quaternion.

Before rotation

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What rotation should produce

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However, although the vertices correctly rotate around the quaternion, the angle is not coming out correct, as illustrated here:

This is the code I'm using to get the angle between the two vectors. I don't understand what I'm doing wrong:

double[] cross = new double[3];
crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross);
double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ);
double crossMag = Math.sqrt(cross[0]*cross[0] + cross[1]*cross[1] + cross[2]*cross[2]);
double angle = Math.atan2(crossMag, dot);

public static double dotProduct(double vector1X,double vector1Y,double vector1Z,double vector2X,double vector2Y,double vector2Z){

    return vector1X*vector2X + vector1Y*vector2Y + vector1Z*vector2Z;

}

public static void crossProduct(double vector1X,double vector1Y,double vector1Z,double vector2X,double vector2Y,double vector2Z, double[] outputArray){

    outputArray[0] = vector1Y*vector2Z - vector1Z*vector2Y;     
    outputArray[1] = vector1Z*vector2X - vector1X*vector2Z;
    outputArray[2] = vector1X*vector2Y - vector1Y*vector2X;

}

Any help with this would be most appreciated as it is really bugging me.

Thanks, James

Edit: Here is the rest of the code:

        // get floret p1,p2 vector
    // get triangle p1,p2 vector
    Vector3D floretAB = new Vector3D(florets3D[0], florets3D[7]);
    // get triangle p1,p2 vector
    Vector3D triangleAB = new Vector3D(triangle[0], triangle[1]);

    // get rotation axis (cross) and angle (dot)

    /*
    double[] cross = new double[3];
    crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross);
    double dotMag = floretAB.getMagnitude() * triangleAB.getMagnitude();
    double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ) / dotMag;
    double angle = Math.acos(dot);
    */

    double[] cross = new double[3];
    crossProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ, cross);
    double dot = dotProduct(floretAB.mX, floretAB.mY, floretAB.mZ, triangleAB.mX, triangleAB.mY, triangleAB.mZ);
    double crossMag = Math.sqrt(cross[0]*cross[0] + cross[1]*cross[1] + cross[2]*cross[2]);
    double angle = Math.atan2(crossMag, dot);

    // rotate floret so p1,p2 vector matches with triangle p1,p2 vector     
    double[] newVerts = new double[3];
    Quaternion quat = new Quaternion(cross[0], cross[1], cross[2], angle);
    for(int i = 0;i<numfloretVerts;i++){
        Vertex3D vert = florets3D[i];
        quat.RotateVector(vert.getmX(), vert.getmY(), vert.getmZ(), newVerts);
        vert.setmX(newVerts[0]);
        vert.setmY(newVerts[1]);
        vert.setmZ(newVerts[2]);
    }

_

public class Vector3D {

public double mX;
public double mY;
public double mZ;

public Vertex3D point;

/**
 * Constructs a vector from two points. The new vector is normalised
 * 
 * @param point1
 * @param point2
 */
public Vector3D(Vertex3D point1, Vertex3D point2){
    mX = point2.getmX() - point1.getmX();
    mY = point2.getmY() - point1.getmY();
    mZ = point2.getmZ() - point1.getmZ();
    normalise();
    point = point1;
}

/**
 * Normalises the vector
 */
public void normalise(){
    double magnitude = Math.sqrt(mX*mX + mY*mY + mZ*mZ);
    if(magnitude!=0){
        mX /= magnitude;
        mY /= magnitude;
        mZ /= magnitude;
    }
}

/**
 * 
 * @return the magnitude of the vector
 */
public double getMagnitude(){
    return Math.sqrt(mX*mX + mY*mY + mZ*mZ);
}

}

_

public class Quaternion {

private static final double TOLERANCE = 0.00001f;

double w;
double x;
double y;
double z;

public Quaternion(double axisX, double axisY, double axisZ, double angleInRadians){
    setAxisAngle(axisX, axisY, axisZ, angleInRadians);      
}

public void Normalise(){

    // Don't normalize if we don't have to
    double mag2 = w * w + x * x + y * y + z * z;
    if (Math.abs(mag2) > TOLERANCE && Math.abs(mag2 - 1.0f) > TOLERANCE) {
        double mag = (double) Math.sqrt(mag2);
        w /= mag;
        x /= mag;
        y /= mag;
        z /= mag;
    }

}

public void getConjugate(double[] outputArray){

    outputArray[0] = w;
    outputArray[1] = -x;
    outputArray[2] = -y;
    outputArray[3] = -z;

}

public void Multiply(double[] aq, double[] rq, double[] outputArray){

    outputArray[0] = aq[0] * rq[0] - aq[1] * rq[1] - aq[2] * rq[2] - aq[3] * rq[3];
    outputArray[1] = aq[0] * rq[1] + aq[1] * rq[0] + aq[2] * rq[3] - aq[3] * rq[2];
    outputArray[2] = aq[0] * rq[2] + aq[2] * rq[0] + aq[3] * rq[1] - aq[1] * rq[3];
    outputArray[3] = aq[0] * rq[3] + aq[3] * rq[0] + aq[1] * rq[2] - aq[2] * rq[1];

}

private double[] vecQuat = new double[4];
private double[] resQuat = new double[4];
private double[] thisQuat = new double[4];

private double[] conj = new double[4];

/**
 * Rotates a vector (or point) around this axis-angle
 * 
 * @param vectorX the x component of the vector (or point)
 * @param vectorY the y component of the vector (or point)
 * @param vectorZ the z component of the vector (or point)
 * @param outputArray the array in which the results will be stored
 */
public void RotateVector(double vectorX, double vectorY, double vectorZ, double[] outputArray){

    vecQuat[0] = 0.0f;
    vecQuat[1] = vectorX;
    vecQuat[2] = vectorY;
    vecQuat[3] = vectorZ;

    thisQuat[0] = w;
    thisQuat[1] = x;
    thisQuat[2] = y;
    thisQuat[3] = z;

    getConjugate(conj);
    Multiply(vecQuat,conj,resQuat);
    Multiply(thisQuat,resQuat,vecQuat);

    outputArray[0] = vecQuat[1];
    outputArray[1] = vecQuat[2];
    outputArray[2] = vecQuat[3];

}

/**
 * set Quaternion by providing axis-angle form
 */
public void setAxisAngle(double axisX, double axisY, double axisZ, double angleInRadians){
    w = (double) Math.cos( angleInRadians/2);
    x = (double) (axisX * Math.sin( angleInRadians/2 ));
    y = (double) (axisY * Math.sin( angleInRadians/2 ));
    z = (double) (axisZ * Math.sin( angleInRadians/2 ));

    Normalise();
}
}