Hi, Cliff!
> Nice work, both on cline and superell!
Thank you!
> Those are some impressive
> pictures of the superell raytraces. It's probably worthwhile to take
> a couple minutes to upload a few pictures of the cline as well - you
> can show the implicit and the brep raytraces from a couple different
> views, and make a note that the differences are expected and due to
> the view-dependent nature of the cline primitive.
Good idea. Images will be uploaded tomorrow.
> I've been thinking a little about the dsp - I suspect the main reason
> it is so slow is the (very) large number of control points that result
> from inserting all of the grid points into the bezier surface. There
> may be a way to get a reasonable fit without such a large control
> point count:
> 1. the first thing to try is to identify all local maximum and minimum
> points in the dsp grid, and insert just those into the bezier surface.
> I.e. for each grid point, check that all of its surrounding points
> are either all greater or all less than that point. That
> categorization can be made in a single pass over the grid - the
> comparison of the two heights should be computationally cheap, so
> repeating checks (i.e. former neighbor point is checked again against
> the old center point not that the neighbor is the center) as you
> raster your way across the grid shouldn't be a big deal.
> 2. if that doesn't produce an accurate enough surface, the next
> refinement is to make another pass and insert all points which have a
> "large" delta height with one or more of their neighboring points.
> The heuristic here would be to find the min and max heights in the dsp
> grid, and have some "threshold" value for the deltas based on the
> relative size of the current max-neighbor delta and the overall max
> delta.
> With any luck, some form of those two selection methods can produce an
> accurate enough smooth surface without the huge control point count.
I also think that the reason for the slow raytracing is the large number of
control points (and thus high degree) on the Bezier Surface. I haven't tried
your method mentioned above yet, but it sounds quite reasonable. I also
consider methods reducing the order of Bezier curves (and thus Bezier
surfaces), as there are lots of algorithms on this topic, trying to represent a
high degree Bezier curve with a reduced degree curve as accurately as possible.
One simple approach can be found at:
http://www.yamnuska.ca/geek/degreeReductionBezier.pdf .
Cheers!
Wu
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