Re: cross-sections of 3D objects

• To: johnyao <johnyao@xxxxxxxxxxxxxxxxx>
• Subject: Re: cross-sections of 3D objects
• From: Bill Hibbard <billh@xxxxxxxxxxxxx>
• Date: Sat, 25 May 2002 18:29:46 -0500 (CDT)

Hi John,

VisAD doesn't currently include operations for computing
the intersections of surfaces and planes in 3-D. However,
you might hack it as follows. Your plance can be defined by:

  ax + by + cz = d

So define a FlatField with MathType:

  ((x, y, z) -> plane)

and with your mainfold dimension = 2 Gridded3DSet as its
domain Set. Compute the 'plane' value at each sample
location as:

  ax + by + cz

Then create the ScalarMap plane -> IsoContour and set the
base contour = d (with a very large contour interval so you
only get one contour curve). That is, the IsoContour will
be a set of iso-lines on the surface (not an iso-surface),
but you only want one iso-line.

Good luck,
Bill
----------------------------------------------------------
Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI  53706
hibbard@xxxxxxxxxxxxxxxxx  608-263-4427  fax: 608-263-6738
http://www.ssec.wisc.edu/~billh/vis.html


On Sat, 25 May 2002, johnyao wrote:

> Hello,
>
> I have created 3D shapes with the gridded3DSet with manifold dimension=2.
> Therefore, the 3D objects are not solids, but are more like closed surfaces.
> I understand that VisAD can do volume rendering with cross-sections with
> resampling based on several earlier messages including one with sample code by
> Bill.  But I am wondering what's the best way to get a cross-section of my
> shape if they are not true solids with volume.  As a simple example, if a
> cross-section of my sphere is taken, the 2D plane should only show the rim
> (the circumference) of the circle.
>
> I have also tried the following code from one of earlier message to resample:
>
> if (w == null) w = new RealType("testing", null, null);
> float[][] plane2D = new float[3][num*num];
>     int k = 0;
>     for (int i=0; i<num; i++){
>         for (int j=0; j<num; j++){
>             plane2D[0][k] = xmin+(xmax-xmin)*j/(num-1.0f);
>             plane2D[1][k] = ymin+(ymax-ymin)*j/(num-1.0f);
>             plane2D[2][k++] = (float)zplane;
>         }
>     }
> // construct a Gridded3Dset with manifold dimension = 2
> // whose N * N samples lie on a plane at z = zplane
>     Gridded3DSet plane_set = new Gridded3DSet(xyz, plane2D, num, num);
>     FlatField fplane = (FlatField)field.resample(plane_set,
> Data.WEIGHTED_AVERAGE, Data.NO_ERRORS);
>
> However, I got this error message when I ran my program:
>
> VisADProbeMaker:visad.SetException: Gridded3DSet.valueToGrid:
> ManifoldDimension must be 3
>
> I am not sure how this works because the Set in field is a Gridded3DSet with
> manifold dimension of 2.
>
> How should this be done in VisAD?
>
> Thanks very much,
> john
>
>

• References:
  • cross-sections of 3D objects
    • From: johnyao