Re: matrix projection control

Hi Christian,

> does anyone know where  I can find  the definition of the 16 coefficients of
> the matrix of a projection control?

DisplayImplJ3D uses the 4 x 4 matrices defined by Java3D,
which are described in:

under Section 8.1.29 on Transform3D and Appendix A.2 on matrices.

The easy way to manipulate these matrices is using two static
methods of visad.java3d.MouseBehaviorJ3D:

  public static double[] static_multiply_matrix(double[] a, double[] b);

  public static double[] static_make_matrix(double rotx, double roty, double 
         double scale, double transx, double transy, double transz);

The first multiplies two 4 x 4 matrices appropriately to compose
their view transforms, the second constructs a 4 x 4 matrix with
the given rotation angles (in degrees and around the various axes),
scale, and translations.

The only way to figure this out is to experiment with these.
See visad/examples/Test57 for a simple example.

> I am looking also for an example of drawing and animating trajectories
> of particles in 3d.

There are no current examples that I am aware of, but it is
certainly feasible.  The Aeri example at:

analyzes wind data to generate "flags" that are a little like

A set of trajectories are a set of 1-D paths through 4-D space-time,
but for an animated display you'd want a 1-D sub-path at each time
step.  This would be a FieldImpl with MathType:

  (time -> Set(x, y, z))

displayed with ScalarMaps:

  time -> Animation
  x -> XAxis
  y -> YAxis
  z -> ZAxis

and where the Sets are UnionSets of Gridded3DSets with manifold
dimension = 1 (analogous to map outlines which are UnionSets
of Gridded2DSets with manifold dimension = 1).  Each Gridded3DSet
with manifold dimension = 1 would be the trajectory of one
particle, taken over a time interval:

  [current_time - trajectory_length, current_time]

and the UnionSet would be taken over the set of particles.
Note that current_time is just the time sample of the FieldImpl
(time -> Set(x, y, z)), and trajectory_length is just the time
interval represented by the instantaneous display of a

The system does need an example of such a trajectory display.
If you'd like to contribute one that would be great, otherwise
one of these days we will add one.

Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI  53706
hibbard@xxxxxxxxxxxxxxxxx  608-263-4427  fax: 608-263-6738