RE: cross-sections of 3D objects

```Hi Bill,

Thanks for the pointer.  I did try the method that you suggested of using
IsoContour to get a single iso-line to represent the intersection of a 3D
surface and a plane.  However, iso-line doesn't seem to properly capture the
cross-section.  For example, when I tried to cut a sphere with a plane having
a normal vector of <0,1,0>, the iso-line at times showed a distorted diamond
and other times nothing at all depending on the position of the plane along
the y-axis.  Initially I thought this was occurring because we are setting the
base contour = d (from ax+by+cz=d and in my case the equation reduces to y =
d), only a few points computed from domain Set of the manifold dimension=2
Gridded3Dset can actually be used for the contour.  In other words, maybe the
plane wasn't "catching" the points I have used for the 3D shape.

So the next thing I tried was to generate my shape with the Gridded3DSet by
moving along the y-axis.  I would create the sphere by drawing circles as I
move up the y-axis incrementally.  Now, in theory if I set the base contour
equal to one of the y increment that I used to construct sphere, the iso-line
should be a circle, but the same problem described above persisted.

I am not sure where the problem might be or maybe I didn't code it properly.
I have included the piece of code in case you would like to take a look.

John

float a = 0.f;
float b = 1.f;
float c = 0.f;
if (p == null) p = new RealType("plane", null, null);
FunctionType pfunction = new FunctionType(xyz, p);
FlatField fplane = new FlatField(pfunction, set);
float[][] set_samples = set.getSamples(true); //getting domain samples
from the 3D shape.
float[][] p_samples = new float[Mfold*Mfold];

//Computing ax+by+cz = d
for(int i=0;i<p_samples.length;i++)
{
p_samples[i] =
a*set_samples[i]+b*set_samples[i]+c*set_samples[i];
}

fplane.setSamples(p_samples);

display2D = new DisplayImplJ2D("display1");

// Get display's graphics mode control and draw scales
GraphicsModeControl dispGMC = (GraphicsModeControl)
display2D.getGraphicsModeControl();
dispGMC.setScaleEnable(true);

ScalarMap tempzMap = new ScalarMap( z,    Display.YAxis );
ScalarMap tempxMap = new ScalarMap( x, Display.XAxis );
ScalarMap tempIsoMap = new ScalarMap( p,  Display.IsoContour );
ScalarMap tempRGBMap = new ScalarMap( p,  Display.RGB );

// The ContourControl
// Note that we get the control from the IsoContour map
ContourControl isoControl = (ContourControl) tempIsoMap.getControl();
// Define some parameters for contour lines
float interval = 100.f;  // interval between lines
float lowValue = -100.f;   // lowest value
float highValue = 100.f;    // highest value
float base = p_samples; //  starting at this base value

System.out.println("base = "+base);
System.out.println("set_samples = "+set_samples); //the y values
of the 3D shape.
//the above lines give the same value.

// ...and set the lines with the method
isoControl.setContourInterval(interval, lowValue, highValue, base);
isoControl.enableLabels(true);

// Create a data reference and set the FlatField as our data
DataReference p_ref = new DataReferenceImpl("p_ref");
p_ref.setData( fplane );

>===== Original Message From Bill Hibbard <billh@xxxxxxxxxxxxx> ====
>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

```