Question

I have unknown number of objects in 3D Space, I would like to know what is the fastest way to detect if two objects or many objects have a distance less than a threshold between each others.
I think that is an n! problem, but I would like a better way for solving it.

I have tried the following pseudo code, and I need your comment about it.

 for (int y=0; y<blobList.size();y++){
       for (int x =1; x<blobList.size();x++)
       {
           CvPoint *blob_a = new CvPoint();
           CvPoint *blob_b = new CvPoint();
           blob_a->x = blobList[x].second->maxx;
           blob_a->y = blobList[x].second->maxy;
           blob_b->x = blobList[y].second->maxx;
           blob_b->y = blobList[y].second->maxy;

           double dist = distance(blob_a,blob_b);
           cout<< " distance between blob "<<blobList[y].second->label<<"and "<<blobList[x].second->label<<endl;
           cout<<dist<<endl;

           if( dist<ParamMgr.fDistance)
           {

           cout<< " Collision between "<<blobList[y].second->label<<"and "<<blobList[x].second->label<<endl;
           }
           else {
               cout<< " "<<endl;
           }
       }

Answer 1

I can think of three solutions, each with a different time\space tradeoff.

n x n array

If you have a small number n of objects and a distance function D(n₁, n₂), you can compute the distances in advance.

Create a 2D n X n array. In array[i, j] store the result of D(n_i, n_j).

Pros:

• After the initial calculation, the answer for any two objects is given in O(1).
• Simplicity

Cons:

• inefficiency for large data sets
• Can’t easily add new objects on-the-fly

Memoization

Memoize your distance function to remember previous calls.

R-Tree

The standard data structure for storing objects in 2D\3D Objects like Points and Polyhedrons is R-Trees. In short, your objects are grouped into 3D cubes of near-by items. It provides efficient insertion and lookup time of log(n) time, and threshold distance lookup is extremely efficient, especially when the answer is negative.

Quoting the Wikipedia article:

A common real-world usage for an R-tree might be to store … polygons that typical maps
are made of: streets, buildings, outlines of lakes, coastlines, etc.
and then find answers quickly to queries such as “Find all museums
within 2 km of my current location”, “retrieve all road segments
within 2 km of my location”

And:

The key idea of the data structure is to group nearby objects and
represent them with their minimum bounding rectangle in the next
higher level of the tree; the “R” in R-tree is for rectangle.

You have R-Tree implementations in most modern programming languages.