Rotate around specific point in Java3D

Question

I have an application, where all scene objects are loaded from .obj files (they are exported from Blender). And I need to rotate one of this objects around specific point. Currently, I have the following code:

public void rotateTo() {
    // translate to origin, rotate, translate back

    Vector3f origin = new Vector3f();
    Vector3f pivot = new Vector3f(.0f, .5f, .0f);

    this.getTransform(this.transform);
    this.transform.get(origin);

    double angle = -Math.PI / 2;
    double newX = origin.getX() + Math.cos(angle) * (pivot.getX() - origin.getX()) - Math.sin(angle) * (pivot.getY() - origin.getY());
    double newY = origin.getY() + Math.sin(angle) * (pivot.getX() - origin.getX()) + Math.cos(angle) * (pivot.getY() - origin.getY());

    this.transform.set(new Vector3f((float)newX, (float)newY, .0f), 0.15f);
    this.setTransform(this.transform);

    this.transform.set(origin, 0.15f);
    this.setTransform(this.transform);

}

Where this refers to TransformGroup object, that I need to rotate, and this.transform refers to Transform3D object.

But this method doesn't work as I expected. I have also tried this and this solutions, but they also didn't work for me.

I think, maybe, try to perform this manipulation with the help of GeometryArray, but I can't understand, how to do this. Also, I can try to export my objects with different origin points, but it's not clean solution, I think, because then I would need to move them to right positions with code.

Here's my object:

I'm trying to rotate it around green point, but in all cases it rotates around red point, or doesn't rotate at all, or translates to some point without rotation.

P.S. I know, that Java3D is an old library and can use more powerful tools, but it's my university professor's requirement and I can't refuse using it.

Answer 1

Composition of transformations can be achieved using matrix multiplication. Below is an example that rotates a cube 180° about the X axis with the pivot at the centre of its top face.

There are three steps as mentioned in the question: translate so that the pivot is at the origin, rotate, and translate back. Comment out steps to see what is happening.

• With all steps commented out, the box appears at the centre with its red side facing forward.

• Uncomment the first step. The box shifts down so its top is at the centre of the screen.

• Uncomment the second step. The box rotates about the X axis (the left-right axis, through the top of the box). The green side now faces forward, and the bottom of the box is now at the centre of the screen.

• Uncomment the third step. The box shifts up, and the overall effect is that it rotated about a left-right axis through its top face.

The application of a transformation T to a vector v is defined as T*v in Java 3D, so the composition of two transformations T and U where T is to be done first and U is to be done second is U*T. Note how the order is reversed. In general, the composition of the transformations T1, T2, ..., Tn where T1 is done first and Tn is done last is Tn*...*T2*T1.

This can be expressed in Java 3D using the following pattern:

Transform3D t1 = ..., t2 = ..., t3 = ...;
// first do t1, then t2, then t3
Transform3D all = new Transform3D(); // all = identity
all.mul(t1, all); // all = t1 * all
all.mul(t2, all); // all = t2 * all
all.mul(t3, all); // all = t3 * all
// now all == t3 * t2 * t1

Methods such as Transform3D.set(Vector3d,double) and TransformGroup.setTransform() overwrite the existing transformation rather than compose with it, which is one of the reasons your code does not work.

I found the article http://www.developer.com/java/other/article.php/3717101/Understanding-Transforms-in-Java-3D.htm helpful.

// based on http://www.java3d.org/starting.html
import com.sun.j3d.utils.geometry.ColorCube;
import com.sun.j3d.utils.universe.SimpleUniverse;
import javax.media.j3d.*;
import javax.vecmath.*;

public class Demo
{
  public Demo() {
    SimpleUniverse universe = new SimpleUniverse();
    BranchGroup group = new BranchGroup();
    group.addChild(createModel());
    universe.getViewingPlatform().setNominalViewingTransform();
    universe.addBranchGraph(group);
  }

  Node createModel() {
    double radius = 0.3;
    ColorCube cube = new ColorCube(radius);
    // rotation of cube about the center of the top face
    // i.e. the point (x=0, y=radius, z=0)
    Transform3D transform = new Transform3D();
    // step 1: translate cube down so that (0, radius, 0) is at the origin
    Transform3D translate1 = new Transform3D();
    translate1.setTranslation(new Vector3d(0.0, -radius, 0.0));
    transform.mul(translate1, transform);
    // step 2: rotate cube about X axis by 180 degrees
    Transform3D rotate = new Transform3D();
    rotate.rotX(Math.PI);
    transform.mul(rotate, transform);
    // step 3: translate cube back up
    Transform3D translate2 = new Transform3D();
    translate2.setTranslation(new Vector3d(0.0, +radius, 0.0));
    transform.mul(translate2, transform);
    // create a TransformGroup
    TransformGroup tg = new TransformGroup();
    tg.setTransform(transform);
    tg.addChild(cube);
    return tg;
  }

  public static void main(String[] args) {
    new Demo();
  }
}