How to rotate an object in Java 3D?

Question

I have a Cone I drew in Java 3D with the following code:

Cone cone = new Cone(2f, 3f);

Transform3D t3d = new Transform3D();
TransformGroup coneTransform = new TransformGroup(t3d);
coneTransform.setCapability(TransformGroup.ALLOW_TRANSFORM_WRITE);

t3d.setTranslation(new Vector3f(0f,0f,0f);
coneTransform.setTransform(t3d);
coneTransform.addChild(cone);

this.addChild(coneTransform);

Suppose I have the cone sitting at point (1,1,1) and I want the tip of the cone to point down an imaginary line running through (0,0,0) and (1,1,1)... how can I do this?

Here's an example of what I've been trying:

Transform3D t3d = new Transform3D();  

Vector3f direction = new Vector3f(1,2,1);    

final double angleX = direction.angle(new Vector3f(1,0,0));
final double angleY = direction.angle(new Vector3f(0,1,0));
final double angleZ = direction.angle(new Vector3f(0,0,1));

t3d.rotX(angleX);
t3d.rotY(angleY);
t3d.rotZ(angleZ);

t3d.setTranslation(direction);

coneTransform.setTransform(t3d);

Thanks in advance for all help!

Answer 1

I finally figured out what I wanted to do by using Quaternions, which I learned about here: http://www.cs.uic.edu/~jbell/Courses/Eng591_F1999/outline_2.html Here's my solution.

Creating the cone:

 private void attachCone(float size) {
        Cone cone = new Cone(size, size* 2);

        // The group for rotation
        arrowheadRotationGroup = new TransformGroup();
        arrowheadRotationGroup.
             setCapability(TransformGroup.ALLOW_TRANSFORM_WRITE);
        arrowheadRotationGroup.addChild(cone);

        // The group for positioning the cone
        arrowheadPositionGroup = new TransformGroup();
        arrowheadPositionGroup. 
              setCapability(TransformGroup.ALLOW_TRANSFORM_WRITE);
        arrowheadPositionGroup.addChild(arrowheadRotationGroup);

        super.addChild(arrowheadPositionGroup);
    }

Now, when I want to rotate the cone to point in a certain direction specified as the vector from the point (0,0,0) to (direction.x, direction.y, direction.z), I use:

private final Vector3f yAxis = new Vector3f(0f, 1f, 0f);
private Vector3f direction; 

private void rotateCone() {
        // Get the normalized axis perpendicular to the direction 
        Vector3f axis = new Vector3f();
        axis.cross(yAxis, direction);
        axis.normalize();

        // When the intended direction is a point on the yAxis, rotate on x
        if (Float.isNaN(axis.x) && Float.isNaN(axis.y) && Float.isNaN(axis.z)) 
        {
            axis.x = 1f;
            axis.y = 0f;
            axis.z = 0f;
        }
        // Compute the quaternion transformations
        final float angleX = yAxis.angle(direction);
        final float a = axis.x * (float) Math.sin(angleX / 2f);
        final float b = axis.y * (float) Math.sin(angleX / 2f);
        final float c = axis.z * (float) Math.sin(angleX / 2f);
        final float d = (float) Math.cos(angleX / 2f);

        Transform3D t3d = new Transform3D();
        Quat4f quat = new Quat4f(a, b, c, d);
        t3d.set(quat);
        arrowheadRotationGroup.setTransform(t3d);

        Transform3D translateToTarget = new Transform3D();
        translateToTarget.setTranslation(this.direction);
        arrowheadPositionGroup.setTransform(translateToTarget);
    }