More precise clipping with implicit functions

[Bill Lorensen]

The vtkLinearSubdivisionFilter splits each triangle into 4 triangles. It was added to vtk on Oct 11, 1999.

Bill

At 12:29 PM 1/22/00 +1200, david.pont at forestresearch.co.nz wrote:


>John,
>      I too have wrangled with this problem. I have implemented a 'naive' class
>to treat polydata as an implicit function, allowing clipping/cutting with truly
>arbitrary geometry. But the relative resolution of the datasets, one to clip or
>cut with, versus the other to be clipped or cut, causes the same type of
>problems you are having. This is a result of the fact that implicit functions
>are only evaluated at each point in the dataset to be operated on. On review
>this is entirely logical, but leaves us with behaviour which at face value is
>unexpected. The more dense the points in the target dataset, the more faithfully
>it can interact with the geometry of the implicit function. In our case we are
>sampling an implicit function (which can have 'infinite' resolution) at very low
>resolution.
>
>
>To date the only (dumb) solution I have thought of is to increase the
>resolution/point density of the target dataset. In my case, and yours it seems,
>the data set is polygonal. I thought about first passing the dataset through a
>triange filter and then a recursive algorithm which takes each triangle and
>subdivides it into smaller triangles until a user specified threshhold (maximum
>edge length) is reached. In your case your large square polygon would be
>fractured into small triangles (maximum edge length something like the radius of
>your implicit sphere might be satisfactory?) and these new points would interact
>with the small sphere as 'expected'. This is rather pathological behaviour in
>the world of geometry, the reverse of decimation, and may make very large
>datasets (rather slowly too!). Actually your case suggests one improvement,
>restrict activity the a user specified 'bounds', no point making lots of little
>triangles outside the region of interest. By the way I do recall an announcement
>about 'subdivision surfaces' which sounded like they might be useful for this
>type of thing?, probably just wishful thinking on my part?
>
>So this one has had me thinking for quite a while, if you have any insights let
>me know.
>
>      regards
>           Dave Pont




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