/**
   * Get a "good" initial viewer transform. The viewer transform is chosen such that for the first
   * source,
   *
   * <ul>
   *   <li>the XY plane is aligned with the screen plane,
   *   <li>the <em>z = dim_z / 2</em> slice is shown,
   *   <li>centered and scaled such that the full <em>dim_x</em> by <em>dim_y</em> is visible.
   * </ul>
   *
   * @param viewerWidth width of the viewer display
   * @param viewerHeight height of the viewer display
   * @param state the {@link ViewerState} containing at least one source.
   * @return proposed initial viewer transform.
   */
  public static AffineTransform3D initTransform(
      final int viewerWidth,
      final int viewerHeight,
      final boolean zoomedIn,
      final ViewerState state) {
    final int cX = viewerWidth / 2;
    final int cY = viewerHeight / 2;

    final Source<?> source = state.getSources().get(state.getCurrentSource()).getSpimSource();
    final int timepoint = state.getCurrentTimepoint();
    if (!source.isPresent(timepoint)) return new AffineTransform3D();

    final AffineTransform3D sourceTransform = new AffineTransform3D();
    source.getSourceTransform(timepoint, 0, sourceTransform);

    final Interval sourceInterval = source.getSource(timepoint, 0);
    final double sX0 = sourceInterval.min(0);
    final double sX1 = sourceInterval.max(0);
    final double sY0 = sourceInterval.min(1);
    final double sY1 = sourceInterval.max(1);
    final double sZ0 = sourceInterval.min(2);
    final double sZ1 = sourceInterval.max(2);
    final double sX = (sX0 + sX1 + 1) / 2;
    final double sY = (sY0 + sY1 + 1) / 2;
    final double sZ = (sZ0 + sZ1 + 1) / 2;

    final double[][] m = new double[3][4];

    // rotation
    final double[] qSource = new double[4];
    final double[] qViewer = new double[4];
    Affine3DHelpers.extractApproximateRotationAffine(sourceTransform, qSource, 2);
    LinAlgHelpers.quaternionInvert(qSource, qViewer);
    LinAlgHelpers.quaternionToR(qViewer, m);

    // translation
    final double[] centerSource = new double[] {sX, sY, sZ};
    final double[] centerGlobal = new double[3];
    final double[] translation = new double[3];
    sourceTransform.apply(centerSource, centerGlobal);
    LinAlgHelpers.quaternionApply(qViewer, centerGlobal, translation);
    LinAlgHelpers.scale(translation, -1, translation);
    LinAlgHelpers.setCol(3, translation, m);

    final AffineTransform3D viewerTransform = new AffineTransform3D();
    viewerTransform.set(m);

    // scale
    final double[] pSource = new double[] {sX1 + 0.5, sY1 + 0.5, sZ};
    final double[] pGlobal = new double[3];
    final double[] pScreen = new double[3];
    sourceTransform.apply(pSource, pGlobal);
    viewerTransform.apply(pGlobal, pScreen);
    final double scaleX = cX / pScreen[0];
    final double scaleY = cY / pScreen[1];
    final double scale;
    if (zoomedIn) scale = Math.max(scaleX, scaleY);
    else scale = Math.min(scaleX, scaleY);
    viewerTransform.scale(scale);

    // window center offset
    viewerTransform.set(viewerTransform.get(0, 3) + cX, 0, 3);
    viewerTransform.set(viewerTransform.get(1, 3) + cY, 1, 3);
    return viewerTransform;
  }