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SFCOctTreePoint.m
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SFCOctTreePoint.m
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function [LT, visitOrder] = SFCOctTreePoint(Vlvls, OT, blockSizeFactor, minBlockSize)
LT = [];
visitOrder = [];
Idim = size(Vlvls{1});
global Isize;
Isize = Idim(1);
global Vs;
Vs = Vlvls;
global Tree;
Tree = OT;
global bsFactor;
bsFactor = blockSizeFactor;
global minBlkSize;
minBlkSize = minBlockSize;
%% the mode of octree: 1 -- Volume Octree; 2 -- Point Octree
global modeOCT;
modeOCT = OT.mode;
% get nodes
Itl = [1,1,1];
Ibr = [Idim(1),Idim(2),Idim(3)];
outFace = 2; % should use a flexible out edge!!! Going out to the left face
entryPix = [1,1,1];
% SHOULD use encoding of the 3D hamCycle version!
% node configuration:
% p6 p7
% /| /|
% p1 p2|
% | p5-|p8
% p4---p3
% face configuration
%
% /|F3 /
% |----|F4|
% | F1 | /z
% |----|/
% F1: Front
% F2: Left
% F3: Top
% F4: Right
% F5: Bottom
% F6: Back
lvl = length(Vlvls);
if size(Vlvls{end},1)<=4 % have to use hamPath
ePix = getEquivPixAtLvl(entryPix, 1, lvl);
% choose the best outEdge
minCost = realmax;
for toFace = 1:6
[tLTv, tVO, tExitPix] = linearizeHamPath3D(Vlvls{end}, ePix, toFace);
cost = norm(gradient(tLTv)',1); % amaximum absolute row sum
if cost < minCost
minCost = cost;
topLTv = tLTv;
topVisitOrder = tVO;
outFace = toFace;
exitPix = tExitPix;
end
end
else % could use hamCycle
[topLTv, topVisitOrder] = SFCmine3D(Vlvls{end});
topLTv = topLTv(:,1);
end
topLvlBlockSize = lvlToNodeSize(lvl);
topLT(:,1) = topLTv;
topLT(:,2) = repmat(topLvlBlockSize,length(topLTv),1);
inFace =2; % left
lastVal = -1;
lastPos = [0 0 0];
LT = [];
visitOrder = topVisitOrder;
idInsert = 1;
for i= 1:length(topVisitOrder)
entryN = topVisitOrder(i,:);
if i == length(topVisitOrder)
exitN = [1,1,0]; % a virtual node for the last element
else
exitN = topVisitOrder(i+1,:);
end
[Itl,Ibr] = getNodeExtent(entryN, lvl);
dir = exitN - entryN;
if i ~= length(topVisitOrder) && norm(dir) > 1
warning('Error: Distance between two nodes in path is greater than 1!');
disp(i);
return;
end
if i > 1
switch outFace
case 1 % front
inFace = 6; % back
case 2 % left
inFace = 4; % right
case 3 % top
inFace = 5; % bottom
case 4 % right
inFace = 2; % left
case 5 % bottom
inFace = 3; % top
case 6
end
end
if dir(3) == -1% 5<-bottom
outFace = 5;
elseif dir(3) == 1 % 3<-top
outFace = 3;
else
if dir(1) == 1
outFace = 4; %4<- right
elseif dir(1) == -1
outFace = 2; %2<- left
else
if dir(2) == 1
outFace = 6; %6 <- back
else
outFace = 1; %1 <- front
end
end
end
LTzz = topLT(i,:);
vOzz = topVisitOrder(i,:);
% if Itl(1)==65 && Itl(2) == 65
strProg = sprintf('Progress: top level block %i of %i', i, length(topVisitOrder));
disp(strProg);
[epix, LTzz, vOzz] = refine3D(inFace, outFace, Itl, Ibr, lastVal, lastPos);
% end
lastVal = LTzz(end,:);
lastPos = vOzz(end,:);
% set return parameters
% idInsert = length(LTzz(:,1)) + idInsert - 1; %length(LT) - length(topLT) + i + 1;
if i > 1
LT = [LT; LTzz];
visitOrder = [visitOrder; vOzz];
else
LT = LTzz;
% LT = [LTzz;topLT(i+1:end,:)];
visitOrder = vOzz;
end
% disp(LT);
end
end
function faceId = outDirToFace(outdir)
if outdir(3) == -1% 5<-bottom
faceId = 5;
elseif outdir(3) == 1 % 3<-top
faceId = 3;
else
if outdir(1) == 1
faceId = 4; %4<- right
elseif outdir(1) == -1
faceId = 2; %2<- left
else
if outdir(2) == 1
faceId = 6; %6 <- back
else
faceId = 1; %1 <- front
end
end
end
end
function faceId = inDirToFace(indir)
if indir(3) == 1% 3<-top
faceId = 3;
elseif indir(3) == -1
faceId = 5;% 5<-bottom
else
if indir(1) == 1
faceId = 2; %2<- left
elseif indir(1) == -1
faceId = 4; %4<- right
else
if indir(2) == 1
faceId = 1; %1 <- front
else
faceId = 6; %6 <- back
end
end
end
end
function [exitPix, LTinout, VOinout, posInOrg] = refine3D(inFace, outFace, blockmin, blockmax, lastVal, lastNode)
global Vs;
global Isize;
% global LT;
VOinout = [];
LTinout = [];
exitPix = [];
posInOrg = [];
blkSize = blockmax - blockmin + 1;
[Lfine, Lcoarse] = getLvlsInBlock3D(blockmin, blockmax);
%% Get the starting position of the current block
if lastNode(1) == 0 && lastNode(2) == 0 && lastNode(3) == 0
tblockmin = blockmin;
tblockmax = blockmax;
else
lastL = log2(lastVal(2)) + 1;
currL = log2(blockmax(1)-blockmin(1)+1)+1;
%% need to think the correct version: The first node to be visited should have the same level as the last node
if lastL < currL && Lcoarse < lastL % the last node has a smaller size than the current one
lastLen = lastVal(2);
switch inFace
case 1 % front: y is fixed
tblockmin(2) = blockmin(2);
tblockmin(1) = max(blockmin(1), lastNode(1));
tblockmin(3) = max(blockmin(3),lastNode(3));
tblockmax(2) = blockmin(2) + lastLen - 1;
tblockmax(1) = tblockmin(1) + lastLen - 1;
tblockmax(3) = tblockmin(3) + lastLen - 1;
case 4 % right: x is fixed
tblockmin(1) = blockmax(1) - lastLen + 1;
tblockmin(2) = max(blockmin(2), lastNode(2));
tblockmin(3) = max(blockmin(3),lastNode(3));
tblockmax(1) = tblockmin(1) + lastLen - 1;
tblockmax(2) = tblockmin(2) + lastLen - 1;
tblockmax(3) = tblockmin(3) + lastLen - 1;
case 6 % back: y is fixed
tblockmin(2) = blockmax(2) - lastLen + 1;
tblockmin(1) = max(blockmin(1), lastNode(1));
tblockmin(3) = max(blockmin(3),lastNode(3));
tblockmax(2) = blockmax(2);
tblockmax(1) = tblockmin(1) + lastLen - 1;
tblockmax(3) = tblockmin(3) + lastLen - 1;
case 2 % left: x is fixed
tblockmin(1) = blockmin(1);
tblockmin(2) = max(blockmin(2),lastNode(2));
tblockmin(3) = max(blockmin(3),lastNode(3));
% tblockmax(3) =
tblockmax(1) = blockmax(1);
tblockmax(2) = tblockmin(2)+lastLen - 1; % lastVal(2) := edge length
tblockmax(3) = tblockmin(3) + lastLen - 1;
case 5 % bottom: z is fixed
tblockmin(3) = blockmin(3);
tblockmin(2) = max(blockmin(2), lastNode(2));
tblockmin(1) = max(blockmin(1), lastNode(1));
tblockmax(2) = tblockmin(2) + lastLen - 1;
tblockmax(1) = tblockmin(1) + lastLen - 1;
tblockmax(3) = tblockmin(3) + lastLen - 1;
case 3 % top: z is fixed
tblockmin(3) = blockmax(3) - lastLen + 1;
tblockmin(2) = max(blockmin(2), lastNode(2));
tblockmin(1) = max(blockmin(1), lastNode(1));
tblockmax(2) = tblockmin(2) + lastLen - 1;
tblockmax(1) = tblockmin(1) + lastLen - 1;
tblockmax(3) = tblockmin(3) + lastLen - 1;
end
if tblockmin(1) < blockmin(1) || tblockmin(2) < blockmin(2) || tblockmin(3) < blockmin(3) ||...
tblockmax(1) > blockmax(1)|| tblockmax(2) > blockmax(2) || tblockmax(3) > blockmax(3)
tblockmin = blockmin;
tblockmax = blockmax;
disp('Potential Erroneous Case');
disp(inFace);
end
else
tblockmin = blockmin;
tblockmax = blockmax;
end
end
[inFaceNodes, outFaceNodes] = getInoutFaceNodes(tblockmin, tblockmax, inFace, outFace);
doOneLevelFiner = false;
forceRefine = false;
posInOrg = false;
% check levels in the block
% if Lcoarse - Lfine >= 6
% disp(Lcoarse-Lfine);
% warning('danger! too many levels!');
% end
if Lfine == Lcoarse % only one level in the block
% if blockSize == blockSize @ L
if blkSize(1) == lvlToNodeSize(Lfine)
% get value from Lcoarse == Lfine
blockminInBlock = getEquivPixAtLvl(blockmin, 1, Lfine);
blockrbInBlock = getEquivPixAtLvl(blockmax, 1, Lfine);
% LT = Vs{Lfine}(blockmin(1):blockmax(1), blockmin(2):blockmax(2),:);
%replace item
LTinout(:,1) = Vs{Lfine}(blockminInBlock(1):blockrbInBlock(1),...
blockminInBlock(2):blockrbInBlock(2),blockminInBlock(3):blockrbInBlock(3),:);
LTinout(:,2) = repmat(blkSize(1),length(LTinout),1);
VOinout = blockmin;
posInOrg = true;
else
if blkSize(1) > 4
% forceRefine = true; % force the block to be smaller than 8*8
% should we limit the 3D block to be smaller than 4*4*4?
doOneLevelFiner = true;
else
ePix = findBestEntry(inFaceNodes, Lfine, lastVal);
blockminInBlock = getEquivPixAtLvl(blockmin, 1, Lfine);
blockrbInBlock = getEquivPixAtLvl(blockmax, 1, Lfine);
ePixInBlock = ePix - blockminInBlock + [1,1,1];
if blockrbInBlock == blockminInBlock
visitOrderK = blockminInBlock;
LTK = Vs{Lfine}(blockminInBlock(1),blockminInBlock(2),blockminInBlock(3),:);
exitPix = ePixInBlock;
else
% hamPath 3D
[LTK, visitOrderK, exitPix] = linearizeHamPath3D(Vs{Lfine}(blockminInBlock(1):blockrbInBlock(1),...
blockminInBlock(2):blockrbInBlock(2),blockminInBlock(3):blockrbInBlock(3)), ePixInBlock, outFace);
% [LTK, visitOrderK, exitPix] = linearizeHamPath(Vs{Lfine}(blockminInBlock(1):blockrbInBlock(1),...
% blockminInBlock(2):blockrbInBlock(2)),...
% ePixInBlock, outEdge);
end
if isempty(LTK)
disp('Something went wrong in hamPath generation for the block.');
end
LTinout(:,1) = LTK;
LTinout(:,2) = repmat(lvlToNodeSize(Lfine),length(LTinout),1);
visitOrderKOrg = getEquivPixAtLvl(visitOrderK - [1,1,1], Lcoarse, 1) + blockmin;
VOinout = visitOrderKOrg;
posInOrg = true;
end
end
else
doOneLevelFiner = true;
end
if doOneLevelFiner % more than one levels in the block
% work with a level finer
if forceRefine
if blkSize(1) <= 4
forceRefine = false;
LL = Lcoarse;
else
LL = Lcoarse;
solvableBlkSize = blkSize;
% make sure that a finer level has block size equal to or smaller than 4*4
while solvableBlkSize(1) > 4
LL = LL + 1;
solvableBlkSize(1) = solvableBlkSize(1)/2;
end
end
else
LL = Lcoarse;
end
ePix = findBestEntry(inFaceNodes, LL, lastVal);
blockminInBlock = getEquivPixAtLvl(blockmin, 1, LL);
blockrbInBlock = getEquivPixAtLvl(blockmax, 1, LL);
ePixInBlock = ePix - blockminInBlock + [1,1,1];
% if forceRefine % force one level finer to avoid large blocks for hamPath
% [LTc, vOc, ePixc] = linearizeHamPath(Vs{LL}(blockminInBlock(1):blockrbInBlock(1),...
% blockminInBlock(2):blockrbInBlock(2)), ePixInBlock, outEdge);
% end
if ~forceRefine
szInBlock = blockrbInBlock-blockminInBlock + 1;
if szInBlock(1) > 4
forceRefine = true;
LL = Lcoarse;
solvableBlkSize = szInBlock;
% make sure that a finer level has block size equal to or smaller than 4*4
while solvableBlkSize(1) > 4
LL = LL + 1;
solvableBlkSize(1) = solvableBlkSize(1)/2;
end
ePix = findBestEntry(inFaceNodes, LL, lastVal);
blockminInBlock = getEquivPixAtLvl(blockmin, 1, LL);
blockrbInBlock = getEquivPixAtLvl(blockmax, 1, LL);
ePixInBlock = ePix - blockminInBlock + [1,1,1];
end
end
[LTc, vOc, ePixc] = linearizeHamPath3D(Vs{LL}(blockminInBlock(1):blockrbInBlock(1),...
blockminInBlock(2):blockrbInBlock(2),blockminInBlock(3):blockrbInBlock(3)), ePixInBlock, outFace);
% [LTc, vOc, ePixc] = linearizeHamPath(Vs{LL}(blockminInBlock(1):blockrbInBlock(1),...
% blockminInBlock(2):blockrbInBlock(2)), ePixInBlock, outEdge);
% convert back to the original (finest level)
if(size(vOc,2) ~= 2)
disp('caution!');
end
vOcOrg = getEquivPixAtLvl(vOc - [1,1,1], LL, 1) + blockmin;
cblockSize = 2^ (LL - 1);
cInFace = inFace; % adopt the inEdge of the coarser level
cOutFace = outFace; % adopt the outEdge of the coarser level
LTc(:,1) = LTc;
LTc(:,2) = repmat(cblockSize,length(LTc),1);
LTz = [];
VOz = [];
for i = 1:length(vOcOrg)
cblockmin = vOcOrg(i,:);
shouldRef = needRefine(cblockmin, cblockSize);
if forceRefine
shouldRef = true;
end
if shouldRef
entryN = vOc(i,:);
% updateEdges();
if i ~= length(vOc)
% try every possible direction?
%TODO: Choose the right direction!
exitN = vOc(i+1,:);
outdir = exitN - entryN;
if norm(outdir) > 1
warning('Error: Distance between two nodes in path is greater than 1!');
return;
end
% get edge id
cOutFace = outDirToFace(outdir);
else
cOutFace = outFace;
end
if i > 1
inDir = vOc(i,:) - vOc(i-1,:);
cInFace = inDirToFace(inDir);
end
% get in, out edges from Nc
cblockmax = cblockmin + [cblockSize-1,cblockSize-1,cblockSize-1];
% [NcInEdge, NcOutEdge] = getInoutEdgeNodes(cblockmin, cblockmax,...
% cInEdge, cOutEdge);
if isempty(VOz)
tlastNode = lastNode;
tlastVal = lastVal;
else
tlastNode = VOz(end,:);
tlastVal = LTz(end,:);
end
[ePixNc, LTNc, vOzc, posConverted] = refine3D(cInFace, cOutFace,...
cblockmin, cblockmax, tlastVal, tlastNode);
% , LTc(i,:), vOc(i,:)
if posConverted
vOzcOrg = vOzc;
else
vOzcOrg = vOzc;
% if vOzc(1)*2^(LL-1)<Isize && vOzc(2)*2^(LL-1)< Isize && vOzc(3)*2^(LL-1) < Isize
% vOzcOrg = getEquivPixAtLvl(vOzc - [1,1,1], LL, 1) + blockmin;
% else
% vOzcOrg = vOzc;
% end
end
% replace LTNc, vOc items:
if i > 1
% keep the last i+1:end items
LTz = [LTz; LTNc];
% VOz = [VOz(1:idInsert-1,:); vOzc(1:end,:); vOc(i+1:end,:)];
VOz = [VOz; vOzcOrg];
else
% LTz = [LTNc(1:end,:); LTc(i+1:end,:)];
LTz = LTNc;
% VOz = [vOzc(1:end,:); vOc(i+1:end,:)];
VOz = vOzcOrg;
end
posInOrg = true;
else
if i > length(LTc)
disp('index out of bound!');
return;
end
LTz = [LTz;LTc(i,:)];
VOz = [VOz;vOcOrg(i,:)];
end
if i == length(vOc)
if shouldRef
exitPix = ePixNc;
else
exitPix = ePixc;
end
end
end
LTinout = LTz;
VOinout = VOz;
end
% need to convert BACK to locations in the finest level
exitPix = VOinout(end,:);
end
function [Ptl, Pbr] = getNodeExtent(nodePos, lvl)
blkSize = lvlToNodeSize(lvl);
Ptl = (nodePos-1) .*blkSize + 1;
Pbr = Ptl + [blkSize-1,blkSize-1,blkSize-1];
end
% get block levels
function [Lfine, Lcoarse] = getLvlsInBlock3D(blocktl, blockbr)
global Vs;
FS = Vs{1};
global Tree;
global bsFactor;
global minBlkSize;
% get sub image
% subFS = FS(blocktl(1):blockbr(1),blocktl(2):blockbr(2),blocktl(3):blockbr(3));
% find all nodes within the subimage
% TODO:
lvls = [];
blks = [];
blkSize = blockbr - blocktl + [1 1 1];
% blkSize = blockbr - blocktl;
octBlkSize = blkSize(1);
octBlktl = (blocktl - [1 1 1]);
octBlkbr = octBlktl + octBlkSize;
[binNos,minD,maxD] = Tree.rangeQuery([octBlktl octBlkbr]);
% for i = 1:Tree.BinCount
% boundsToCheck = Tree.BinBoundaries(i,:);
% hasChildren = find(Tree.BinParents == i,1);
% if isempty(hasChildren)
% if boundsToCheck(1) >= octBlktl(1) && boundsToCheck(2)>=octBlktl(2) && boundsToCheck(3)>=octBlktl(3)...
% && boundsToCheck(4) <= octBlkbr(1) &&...
% boundsToCheck(5) <= octBlkbr(2) && boundsToCheck(6) <= octBlkbr(3)
% % has to be leaf node!!!
% lvls(end+1,:) = Tree.BinDepths(i);
% blks(end+1,:) = boundsToCheck;
% end
% end
% end
%% NOTE: The OcTree library uses 0 for coarsest level !!!! Other parts of our method uses an inverted level notation!!!
% check min/max nodes within the sub volume
% [SBr, SBc, SBv] = find(subFS);
if isempty(binNos) % In fact, this should not happen
% if isempty(lvls)
Lfine = int16(ceil(nodeSizeToLvl(octBlkSize(1))));%size(Vs,1);%1;
Lcoarse = Lfine;%size(Vs,1);%1;
else
% maxD = max(lvls);
% minD = min(lvls);
Lfine = convertOctLvlToSFCLvl(maxD, Tree.DepthMax);% size(Vs,1) - (max(lvls)) + 1;
Lcoarse = convertOctLvlToSFCLvl(minD,Tree.DepthMax); %size(Vs,1) - (min(lvls)) + 1;
end
end
function [inFaceNodes, outFaceNodes] = getInoutFaceNodes(blockmin, blockmax, inFace, outFace)
P4 = blockmin;
P7 = blockmax;
P1 = [blockmin(1),blockmin(2),blockmax(3)];
P2 = [blockmax(1),blockmin(2),blockmax(3)];
P3 = [blockmax(1),blockmin(2),blockmin(3)];
P5 = [blockmin(1),blockmax(2),blockmin(3)];
P6 = [blockmin(1),blockmax(2),blockmax(3)];
P8 = [blockmax(1),blockmax(2),blockmin(3)];
switch inFace
case 1 %front P1,P2,P3,P4
inFaceNodes(1,:) = P1;
inFaceNodes(2,:) = P2;
inFaceNodes(3,:) = P3;
inFaceNodes(4,:) = P4;
case 2 %left P1,P4,P5,P6
inFaceNodes(1,:) = P1;
inFaceNodes(2,:) = P4;
inFaceNodes(3,:) = P5;
inFaceNodes(4,:) = P6;
case 3 %top P1,P2,P7,P6
inFaceNodes(1,:) = P1;
inFaceNodes(2,:) = P2;
inFaceNodes(3,:) = P7;
inFaceNodes(4,:) = P6;
case 4 %right P2,P3,P8,P7
inFaceNodes(1,:) = P2;
inFaceNodes(2,:) = P3;
inFaceNodes(3,:) = P8;
inFaceNodes(4,:) = P7;
case 5 %bottom P4,P3,P8,P5
inFaceNodes(1,:) = P4;
inFaceNodes(2,:) = P3;
inFaceNodes(3,:) = P8;
inFaceNodes(4,:) = P5;
case 6 %bottom P6,P7,P8,P5
inFaceNodes(1,:) = P6;
inFaceNodes(2,:) = P7;
inFaceNodes(3,:) = P8;
inFaceNodes(4,:) = P5;
end
switch outFace
case 1 %front P1,P2,P3,P4
outFaceNodes(1,:) = P1;
outFaceNodes(2,:) = P2;
outFaceNodes(3,:) = P3;
outFaceNodes(4,:) = P4;
case 2 %left P1,P4,P5,P6
outFaceNodes(1,:) = P1;
outFaceNodes(2,:) = P4;
outFaceNodes(3,:) = P5;
outFaceNodes(4,:) = P6;
case 3 %top P1,P2,P7,P6
outFaceNodes(1,:) = P1;
outFaceNodes(2,:) = P2;
outFaceNodes(3,:) = P7;
outFaceNodes(4,:) = P6;
case 4 %right P2,P3,P8,P7
outFaceNodes(1,:) = P2;
outFaceNodes(2,:) = P3;
outFaceNodes(3,:) = P8;
outFaceNodes(4,:) = P7;
case 5 %bottom P4,P3,P8,P5
outFaceNodes(1,:) = P4;
outFaceNodes(2,:) = P3;
outFaceNodes(3,:) = P8;
outFaceNodes(4,:) = P5;
case 6 %bottom P6,P7,P8,P5
outFaceNodes(1,:) = P6;
outFaceNodes(2,:) = P7;
outFaceNodes(3,:) = P8;
outFaceNodes(4,:) = P5;
end
end
function epix = getEquivPixAtLvl(entryPix, srcLvl, destLvl)
epix = ceil(entryPix ./ double(2^(destLvl-srcLvl)));
end
function blkSize = lvlToNodeSize(lvl)
blkSize = 2^(lvl-1);
end
%find the entry pixel to the block @ level with the lastVal
function epix = findBestEntry(inFaceNodes, level, lastVal)
global Vs;
epix = [];
disp(level);
if isempty(level)
disp('Level error!');
return;
elseif level < 1 || level > size(Vs,1)
disp('Level out of bound');
return;
end
V = Vs{level};
% SV = V(blocktl(1):blockrb(1), blocktl(2):blockrb(2));
% find all pixels along the face inFace
% get min max nodes from the face nodes
nbl = min(inFaceNodes(:,:));
ebl = max(inFaceNodes(:,:));
nb = getEquivPixAtLvl(nbl, 1, level);% level);
eb = getEquivPixAtLvl(ebl, 1, level);% level);
if nb(1) >= eb(1) && nb(2) >= eb(2) && nb(3) >= eb(3)
epix = eb;
return;
end
minDif = realmax;
for z = nb(3):eb(3)
for y = nb(1):eb(1)
for x = nb(2):eb(2)
vdif = abs(V(y,x,z) - lastVal(1));
if vdif < minDif
minDif = vdif;
epix = [y,x,z];
end
end
end
end
end
function lvl = nodeSizeToLvl(nodeSize)
lvl = log2(nodeSize) + 1;
end
function shouldRef = needRefine(blocktl, blockSize)
global modeOCT;
% if modeOCT == 2 % point-based octree
% [Lfine, Lcoarse] = getLvlsInBlock3D(blocktl, blocktl+ [blockSize,blockSize,blockSize]);
% else
[Lfine, Lcoarse] = getLvlsInBlock3D(blocktl, blocktl+ [blockSize,blockSize,blockSize] - [1,1,1]);
% end
Lblk = nodeSizeToLvl(blockSize);
if Lcoarse == Lblk
shouldRef = false;
else
shouldRef = true;
end
end