bd_tree.cpp

c++实现的KNN库:建立高维度的K-d tree,实现K邻域搜索

												// repeat for high side
		ANNcoord gap_lo = inner_box.lo[i] - bnd_box.lo[i];
		if (gap_lo < max_length*BD_GAP_THRESH)
			inner_box.lo[i] = bnd_box.lo[i];	// no - expand
		else shrink_ct++;						// yes - shrink this side
	}

	if (shrink_ct >= BD_CT_THRESH)				// did we shrink enough sides?
		 return SHRINK;
	else return SPLIT;
}

//----------------------------------------------------------------------
//	tryCentroidShrink - Attempt a centroid shrink
//
//	We repeatedly apply the splitting rule, always to the larger subset
//	of points, until the number of points decreases by the constant
//	fraction BD_FRACTION.  If this takes more than dim*BD_MAX_SPLIT_FAC
//	splits for this to happen, then we shrink to the final inner box
//	Otherwise we split.
//----------------------------------------------------------------------

const float	BD_MAX_SPLIT_FAC = 0.5;		// maximum number of splits allowed
const float	BD_FRACTION = 0.5;			// ...to reduce points by this fraction
										// ...This must be < 1.

ANNdecomp tryCentroidShrink(			// try a centroid shrink
	ANNpointArray		pa,				// point array
	ANNidxArray			pidx,			// point indices to store in subtree
	int					n,				// number of points
	int					dim,			// dimension of space
	const ANNorthRect	&bnd_box,		// current bounding box
	ANNkd_splitter		splitter,		// splitting procedure
	ANNorthRect			&inner_box)		// inner box if shrinking (returned)
{
	int n_sub = n;						// number of points in subset
	int n_goal = (int) (n*BD_FRACTION); // number of point in goal
	int n_splits = 0;					// number of splits needed
										// initialize inner box to bounding box
	annAssignRect(dim, inner_box, bnd_box);

	while (n_sub > n_goal) {			// keep splitting until goal reached
		int cd;							// cut dim from splitter (ignored)
		ANNcoord cv;					// cut value from splitter (ignored)
		int n_lo;						// number of points on low side
										// invoke splitting procedure
		(*splitter)(pa, pidx, inner_box, n_sub, dim, cd, cv, n_lo);
		n_splits++;						// increment split count

		if (n_lo >= n_sub/2) {			// most points on low side
			inner_box.hi[cd] = cv;		// collapse high side
			n_sub = n_lo;				// recurse on lower points
		}
		else {							// most points on high side
			inner_box.lo[cd] = cv;		// collapse low side
			pidx += n_lo;				// recurse on higher points
			n_sub -= n_lo;
		}
	}
    if (n_splits > dim*BD_MAX_SPLIT_FAC)// took too many splits
		return SHRINK;					// shrink to final subset
	else
		return SPLIT;
}

//----------------------------------------------------------------------
//	selectDecomp - select which decomposition to use
//----------------------------------------------------------------------

ANNdecomp selectDecomp(			// select decomposition method
	ANNpointArray		pa,				// point array
	ANNidxArray			pidx,			// point indices to store in subtree
	int					n,				// number of points
	int					dim,			// dimension of space
	const ANNorthRect	&bnd_box,		// current bounding box
	ANNkd_splitter		splitter,		// splitting procedure
	ANNshrinkRule		shrink,			// shrinking rule
	ANNorthRect			&inner_box)		// inner box if shrinking (returned)
{
	ANNdecomp decomp = SPLIT;			// decomposition

	switch (shrink) {					// check shrinking rule
	case ANN_BD_NONE:					// no shrinking allowed
		decomp = SPLIT;
		break;
	case ANN_BD_SUGGEST:				// author's suggestion
	case ANN_BD_SIMPLE:					// simple shrink
		decomp = trySimpleShrink(
				pa, pidx,				// points and indices
				n, dim,					// number of points and dimension
				bnd_box,				// current bounding box
				inner_box);				// inner box if shrinking (returned)
		break;
	case ANN_BD_CENTROID:				// centroid shrink
		decomp = tryCentroidShrink(
				pa, pidx,				// points and indices
				n, dim,					// number of points and dimension
				bnd_box,				// current bounding box
				splitter,				// splitting procedure
				inner_box);				// inner box if shrinking (returned)
		break;
	default:
		annError("Illegal shrinking rule", ANNabort);
	}
	return decomp;
}

//----------------------------------------------------------------------
//	rbd_tree - recursive procedure to build a bd-tree
//
//		This is analogous to rkd_tree, but for bd-trees.  See the
//		procedure rkd_tree() in kd_split.cpp for more information.
//
//		If the number of points falls below the bucket size, then a
//		leaf node is created for the points.  Otherwise we invoke the
//		procedure selectDecomp() which determines whether we are to
//		split or shrink.  If splitting is chosen, then we essentially
//		do exactly as rkd_tree() would, and invoke the specified
//		splitting procedure to the points.  Otherwise, the selection
//		procedure returns a bounding box, from which we extract the
//		appropriate shrinking bounds, and create a shrinking node.
//		Finally the points are subdivided, and the procedure is
//		invoked recursively on the two subsets to form the children.
//----------------------------------------------------------------------

ANNkd_ptr rbd_tree(				// recursive construction of bd-tree
	ANNpointArray		pa,				// point array
	ANNidxArray			pidx,			// point indices to store in subtree
	int					n,				// number of points
	int					dim,			// dimension of space
	int					bsp,			// bucket space
	ANNorthRect			&bnd_box,		// bounding box for current node
	ANNkd_splitter		splitter,		// splitting routine
	ANNshrinkRule		shrink)			// shrinking rule
{
	ANNdecomp decomp;					// decomposition method

	ANNorthRect inner_box(dim);			// inner box (if shrinking)

	if (n <= bsp) {						// n small, make a leaf node
		if (n == 0)						// empty leaf node
			return KD_TRIVIAL;			// return (canonical) empty leaf
		else							// construct the node and return
			return new ANNkd_leaf(n, pidx); 
	}
	
	decomp = selectDecomp(				// select decomposition method
				pa, pidx,				// points and indices
				n, dim,					// number of points and dimension
				bnd_box,				// current bounding box
				splitter, shrink,		// splitting/shrinking methods
				inner_box);				// inner box if shrinking (returned)
	
	if (decomp == SPLIT) {				// split selected
		int cd;							// cutting dimension
		ANNcoord cv;					// cutting value
		int n_lo;						// number on low side of cut
										// invoke splitting procedure
		(*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo);

		ANNcoord lv = bnd_box.lo[cd];	// save bounds for cutting dimension
		ANNcoord hv = bnd_box.hi[cd];

		bnd_box.hi[cd] = cv;			// modify bounds for left subtree
		ANNkd_ptr lo = rbd_tree(		// build left subtree
				pa, pidx, n_lo,			// ...from pidx[0..n_lo-1]
				dim, bsp, bnd_box, splitter, shrink);
		bnd_box.hi[cd] = hv;			// restore bounds

		bnd_box.lo[cd] = cv;			// modify bounds for right subtree
		ANNkd_ptr hi = rbd_tree(		// build right subtree
				pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1]
				dim, bsp, bnd_box, splitter, shrink);
		bnd_box.lo[cd] = lv;			// restore bounds
										// create the splitting node
		return new ANNkd_split(cd, cv, lv, hv, lo, hi);
	}
	else {								// shrink selected
		int n_in;						// number of points in box
		int n_bnds;						// number of bounding sides

		annBoxSplit(					// split points around inner box
				pa,						// points to split
				pidx,					// point indices
				n,						// number of points
				dim,					// dimension
				inner_box,				// inner box
				n_in);					// number of points inside (returned)

		ANNkd_ptr in = rbd_tree(		// build inner subtree pidx[0..n_in-1]
				pa, pidx, n_in, dim, bsp, inner_box, splitter, shrink);
		ANNkd_ptr out = rbd_tree(		// build outer subtree pidx[n_in..n]
				pa, pidx+n_in, n - n_in, dim, bsp, bnd_box, splitter, shrink);

		ANNorthHSArray bnds = NULL;		// bounds (alloc in Box2Bnds and
										// ...freed in bd_shrink destroyer)

		annBox2Bnds(					// convert inner box to bounds
				inner_box,				// inner box
				bnd_box,				// enclosing box
				dim,					// dimension
				n_bnds,					// number of bounds (returned)
				bnds);					// bounds array (modified)

										// return shrinking node
		return new ANNbd_shrink(n_bnds, bnds, in, out);
	}
}