RE: cross-sections of 3D objects

Hi John,

It sounds like your 'sphere' Set has too few samples. Try
a more densely sampled sphere.

Good luck,
Bill

On Mon, 27 May 2002, johnyao wrote:

> 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.
> Thanks in advance for any comments.
>
> 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[1][Mfold[0]*Mfold[1]];
>
>     //Computing ax+by+cz = d
>     for(int i=0;i<p_samples[0].length;i++)
>     {
>         p_samples[0][i]
> a*set_samples[0][i]+b*set_samples[1][i]+c*set_samples[2][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 );
>
>     // Add maps to display
>
>     display2D.addMap( tempzMap );
>     display2D.addMap( tempxMap );
>
>     display2D.addMap( tempIsoMap );
>     display2D.addMap( tempRGBMap );
>
>     // 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[0][400]; //  starting at this base value
>
>     System.out.println("base = "+base);
>     System.out.println("set_samples = "+set_samples[1][400]); //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 );
>
>     // Add reference to display
>     display2D.addReference( p_ref );
>
>
> >===== 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
>
>