implicit surfaces, aka blob mesh, and metaballs. PART II

So as we can see in a previous post (if we read comments) there where some concerns about my proposals validity. MainlyDelt0r raised some valid questions. therefore i have been struggling to improve my initial idea, and here is what i came up with. Now, its still has some flows. and questions. but its for u to judge, sins i have no clue about maths, and here its quite important, i mean the math.

so the idea is this.

A. we have a mesh. *(base mesh) which we will use to to determine where the “blobs” appear.

B. we will get the normals of each vertex.

c. then the slicing planes should be generated. (here u can look at my old post or drawings beneath)

here comes the first problem. what i want to find out – is there a way to limit this “slice plane’s ” effect. here no one will understand me, so lets have a look at the picture:

Here we have a blob mesh, and a slice tool. the white plane is a slice plane, and green line is outline which is generated. the problem is that the green outline goes out of boundaries of slice plane, and correct me if iam wrong but iam sure algorithm behind this procedure works this way. so what we would like to have here would look like this:

Ok how to do it ? i have no clue. It might require rewriting all algorithms behind this operation, or doing it old way, and then subtracting unneeded parts. which is probably easier.

so now lets imagine our slicing works like we want it, and lets move on.

so in order to understand my “hand” drawings here is another diagram for explanation:

so this diagram shows a mesh we will be thinking about. in next drawings i draw only 3 vertexis out of this mesh. In this image we can also see averaged normals (left)cos normally each plane is plane :) so all 4 vertexies should like in image on right. but we can get average values.

you can enlarge this image to see better. but the idea is to make planes for each vertex separately.

so here as well we have problems. first of all we would want to arrange planes so the would make a “continuity” i mean they would go like this: /\/\/\/\/\/\ shit i have no idea how to explane…. look at the drawings again. chm…. please tell me if anyone understands what i am talking about ? ah? anyone?

so and last step would be to “weld” vertexies who are very close to each other.

again i wonder how easy it would be to make so many “restricted” planes for slicing.

but from what i understand, if it would work it could improve mesh topology or?

Are you thinking of something like this, except on the isosurface?

http://en.wikipedia.org/wiki/Voronoi_diagram

hey nick, i will look in to it very soon, thanks for comment. and for others here is an interesting read :

http://www.cs.cmu.edu/~aw/pdf/particles-reprint.pdf