I'm working on my first scientific visualization "job" in these days; it's a computational fluid dynamics simulation, which has to be displayed to make some inference.Instead of importing datas into VTK, I loaded them into my 3D framework. And it was a fail, because of three conceptual errors:
- my engine was written to display polygons; instead, we have ~3000 point samples which have to be manipulated in different ways
- datas were in double precision! all my framework used to be in floating point, and the loss of data was unacceptable
- a single point dispersed in a sea is not recognizable; its impossible to make inferences. Therefore, I thought it could be nice to partition data in sets, and display a convex hull of similar points.
Convex envelopes
Given a set of points, a convex hull is the minimum convex boundary which contains them.
There exist many algorythms for computing it, by my choice fall on Jarvins' March: also called "the gift wrapping algorythm", consists in... well... rotating around your set trying to keep your sheeps inside the corral!
- the algorythm starts choosing a single point which surely lies on the hull (p0 in the image)
- you trace a vector from your point to any other point in your set
- [important] you compute the angle formed by an axis and the previously traced vectors, and you pick the minimum one by using the arcotangent.
- now you have the second point and iterate from 2; on step 3 you'll naturally won't pick just the minimum, but you'll check that the new angle is greater than the last one
Going back to the CFD job, I used the convex hull to display the set of points featuring the highest values. Well, the first screenshot shows how useless it is: the points are too far, and this representation, again, does not help us in any way. Probably, a better way could be to keep together the closest points, using some kind of "distance" function. I'll work on it.
