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tex2CurvesTet.m
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tex2CurvesTet.m
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function dataOut = tex2CurvesTet(dataIn, res, boundaryOff, snapVertIdx)
% Trace the isolines of a texture parametrization to generate a truss
% layout
%
% Input
% dataIn: struct with the mesh description (dataIn.V, dataIn.T) and the
% parametrization (dataIn.u, dataIn.v, dataIn.w)
% res: the resolution parameter (`rho` in the paper)
% boundaryOff: If true, then does not trace boundary elements
% snapVertIdx: Optional. Set of indices into dataIn.V to snap the truss
% layout vertices to. That is, a truss node will lie on each of the indexed
% vertices
% Single-character abbreviations:
% (U, V, W): the three texture coordinates
% F: Faces (triangles)
% T: Simplices (tris for 2D, tets for 3D)
% E: Edges
% P: Vertices/positions/points
% I: integer
% (X, Y, Z): the three world coordinates
% B: Domain boundary
if nargin < 3
boundaryOff = false;
end
if nargin < 4
snapVertIdx = [];
end
DONOTTRACEINTERNAL = false; % removes both nodes and elements
DONOTTRACEBOUNDARY = boundaryOff; % removes elements only
P = dataIn.V;
T = sort(dataIn.T, 2);
% get F from T by enumerating all 4 choices on each tet, and then
% taking a set union by removing duplicates
choice = nchoosek(1:4, 3);
F = unique(sort([...
T(:, choice(1, :));...
T(:, choice(2, :));...
T(:, choice(3, :));...
T(:, choice(4, :))...
], 2), 'rows');
% Get E from T
E = edges(T);
nP = size(P, 1);
nT = size(T, 1);
nF = size(F, 1);
nE = size(E, 1);
tex = dataIn.u;
adjacency = adjacency_list(E);
tex = 1 + snapGridToVertices(P, T, tex, res, snapVertIdx);
epsLarge = 1e-7;
epsSmall = 1e-10;
oneRingMax = [cellfun(@(x) max(tex(x, 1)), adjacency),...
cellfun(@(x) max(tex(x, 2)), adjacency), ...
cellfun(@(x) max(tex(x, 3)), adjacency)];
texRound = round(tex);
idxTexInt = abs(texRound-tex) < epsSmall;
idxTexLocalMax = tex > oneRingMax - epsLarge;
tex(idxTexInt & ~idxTexLocalMax) = ...
tex(idxTexInt & ~idxTexLocalMax) - epsLarge;
tex(idxTexInt & idxTexLocalMax) = ...
tex(idxTexInt & idxTexLocalMax) + epsLarge;
U = tex(:, 1);
V = tex(:, 2);
W = tex(:, 3);
clear tex;
[~, E_F1] = ismember(F(:, [1, 2]), E, 'rows');
[~, E_F2] = ismember(F(:, [2, 3]), E, 'rows');
[~, E_F3] = ismember(F(:, [1, 3]), E, 'rows');
E_F = [E_F1, E_F2, E_F3];
[~, F_T1] = ismember(T(:, [1 2 3]), F, 'rows');
[~, F_T2] = ismember(T(:, [1 2 4]), F, 'rows');
[~, F_T4] = ismember(T(:, [1 3 4]), F, 'rows');
[~, F_T3] = ismember(T(:, [2 3 4]), F, 'rows');
F_T = [F_T1, F_T2, F_T3, F_T4];
isFBoundary = is_boundary_facet(F, T);
F_E = cellfun(...
@(x) find(isFBoundary & (E_F1 == x | E_F2 == x | E_F3 == x)),...
num2cell((1:nE)'),...
'UniformOutput', false);
clear E_F1 E_F2 E_F3;
clear F_T1 F_T2 F_T3 F_T4;
% Points of intersection between an edge and an integral isosurface
PUI_E = cell(nE, 1);
PVI_E = PUI_E;
PWI_E = PUI_E;
% Values of the possibly non-integral tex-coordinates on these points
VonPUI_E = PUI_E;
WonPUI_E = PUI_E;
UonPVI_E = PUI_E;
WonPVI_E = PUI_E;
UonPWI_E = PUI_E;
VonPWI_E = PUI_E;
% Values of the integral tex-coordinates on these points
UI_E = cell(nE, 1);
VI_E = UI_E;
WI_E = UI_E;
% Points of intersection between integral isocurves (curves with two
% integral tex-coordiantes) and faces (tris)
PUVI_F = cell(nF, 1);
PVWI_F = PUVI_F;
PWUI_F = PUVI_F;
% Values of the third tex-coordinate on these points
WonPUVI_F = PUVI_F;
UonPVWI_F = PUVI_F;
VonPWUI_F = PUVI_F;
% Values of the integral tex-coordinates on these points
U_UVI_F = PUVI_F;
V_UVI_F = PUVI_F;
V_VWI_F = PUVI_F;
W_VWI_F = PUVI_F;
W_WUI_F = PUVI_F;
U_WUI_F = PUVI_F;
allocSize = 2*1e6;
% For final output: nodes (graph vertices)
node = zeros(allocSize, 3);
nodeSize = 0;
% node properties
nodeIsBoundary = false(allocSize, 1);
nodeUI = int32(-ones(allocSize, 1));
nodeVI = nodeUI;
nodeWI = nodeUI;
nodeU = -inf(allocSize, 1);
nodeV = nodeU;
nodeW = nodeU;
nodeSizeTillPrevFace = zeros(nF, 1);
nodeSizeTillPrevTet = zeros(nT, 1);
% stores the edge idx for nodes lying on edges
E_node = int32(zeros(allocSize, 1));
% face idx for nodes lying on faces
F_node = E_node;
T_node = E_node;
isEBoundary = false(nE, 1);
for i=1:3
isEBoundary(E_F(isFBoundary, i)) = true;
end
% For final output: elements (graph edges)
elem = zeros(2*allocSize, 2);
elemSize = 0;
boundaryAngleCosine_E = ones(nE, 1);
for i = 1:nE
if isEBoundary(i)
a = E(i, 1);
b = E(i, 2);
edge = P(a, :) - P(b, :);
faces = F_E{i};
c1 = setdiff(F(faces(1), :), E(i, :));
c2 = setdiff(F(faces(2), :), E(i, :));
n1 = cross(edge, P(c1, :) - P(b, :));
n2 = cross(P(c2, :) - P(b, :), edge);
boundaryAngleCosine_E(i) = dot(n1, n2)/(norm(n1) * norm(n2));
end
end
isEBCurved = boundaryAngleCosine_E < 0.9; % is E on a curved part of the boundary
disp(['# of boundary edges: ' num2str(sum(isEBCurved))]);
isPBoundary = false(nP, 1);
isPBoundary(E(isEBoundary, 1)) = true;
isPBoundary(E(isEBoundary, 2)) = true;
EBCurved = E(isEBCurved, :);
numIncidentEBCurved_P = accumarray(EBCurved(:), 1);
numIncidentEBCurved_P = [numIncidentEBCurved_P; zeros(nP - max(EBCurved(:)), 1)];
boundaryAngleCosine_P = ones(nP, 1);
for i = 1:nP
if isPBoundary(i) && numIncidentEBCurved_P(i) >= 2
neighbours = adjacency{i}(isPBoundary(adjacency{i}));
n1 = -1;
n2 = -1;
for n = neighbours
v = sort([i, n]);
% find the sharp edge {i, n}
if numel(find(E(:, 1)==v(1) & E(:, 2)==v(2) & isEBCurved))
if (n1 == -1)
n1 = n;
else
n2 = n;
break;
end
end
end
vec1 = P(i, :) - P(n1, :);
vec2 = P(n2, :) - P(i, :);
boundaryAngleCosine_P(i) = dot(vec1, vec2)/(norm(vec1) * norm(vec2));
end
end
isPBCurved = boundaryAngleCosine_P < 0.5; % is P on a highly curved part of the boundary
numPBCurved = sum(isPBCurved);
disp(['# of boundary corners: ' num2str(numPBCurved)]);
for i = 1:nE
% disp(['Edge # ' num2str(i)]);
edge = E(i, :);
% find points on intersections b/w integral u-isosurfaces and edges
[U12, p1Idx] = sort([U(edge(1)), U(edge(2))]);
edge = edge(p1Idx);
p1 = P(edge(1), :);
p2 = P(edge(2), :);
v1 = V(edge(1));
v2 = V(edge(2));
w1 = W(edge(1));
w2 = W(edge(2));
UI_E{i} = integersOpen(U12(1), U12(2));
alphaU = (UI_E{i} - U12(1)) / (U12(2) - U12(1));
PUI_E{i} = (1 - alphaU)*p1 + alphaU*p2;
VonPUI_E{i} = (1 - alphaU)*v1 + alphaU*v2;
WonPUI_E{i} = (1 - alphaU)*w1 + alphaU*w2;
% if edge is on the boundary, add these points to nodes
if isEBoundary(i)
n = numel(alphaU);
nodeIdx = nodeSize + (1:n);
node(nodeIdx, :) = PUI_E{i};
nodeUI(nodeIdx) = UI_E{i};
nodeU(nodeIdx) = UI_E{i};
nodeV(nodeIdx) = VonPUI_E{i};
nodeW(nodeIdx) = WonPUI_E{i};
E_node(nodeIdx) = i;
nodeIsBoundary(nodeIdx) = true;
nodeSize = nodeSize + n;
end
% do the same for integral v-isosurfaces
[V12, p1Idx] = sort([V(edge(1)), V(edge(2))]);
edge = edge(p1Idx);
p1 = P(edge(1), :);
p2 = P(edge(2), :);
u1 = U(edge(1));
u2 = U(edge(2));
w1 = W(edge(1));
w2 = W(edge(2));
VI_E{i} = integersOpen(V12(1), V12(2));
alphaV = (VI_E{i} - V12(1)) / (V12(2) - V12(1));
PVI_E{i} = (1 - alphaV)*p1 + alphaV*p2;
UonPVI_E{i} = (1 - alphaV)*u1 + alphaV*u2;
WonPVI_E{i} = (1 - alphaV)*w1 + alphaV*w2;
if isEBoundary(i)
n = numel(alphaV);
nodeIdx = nodeSize + (1:n);
node(nodeIdx, :) = PVI_E{i};
nodeVI(nodeIdx) = VI_E{i};
nodeU(nodeIdx) = UonPVI_E{i};
nodeV(nodeIdx) = VI_E{i};
nodeW(nodeIdx) = WonPVI_E{i};
E_node(nodeIdx) = i;
nodeIsBoundary(nodeIdx) = true;
nodeSize = nodeSize + n;
end
% finally, do this for integral w-isosurfaces
[W12, p1Idx] = sort([W(edge(1)), W(edge(2))]);
edge = edge(p1Idx);
p1 = P(edge(1), :);
p2 = P(edge(2), :);
u1 = U(edge(1));
u2 = U(edge(2));
v1 = V(edge(1));
v2 = V(edge(2));
WI_E{i} = integersOpen(W12(1), W12(2));
alphaW = (WI_E{i} - W12(1)) / (W12(2) - W12(1));
PWI_E{i} = (1 - alphaW)*p1 + alphaW*p2;
UonPWI_E{i} = (1 - alphaW)*u1 + alphaW*u2;
VonPWI_E{i} = (1 - alphaW)*v1 + alphaW*v2;
if isEBoundary(i)
n = numel(alphaW);
nodeIdx = nodeSize + (1:n);
node(nodeIdx, :) = PWI_E{i};
nodeWI(nodeIdx) = WI_E{i};
nodeU(nodeIdx) = UonPWI_E{i};
nodeV(nodeIdx) = VonPWI_E{i};
nodeW(nodeIdx) = WI_E{i};
E_node(nodeIdx) = i;
nodeIsBoundary(nodeIdx) = true;
nodeSize = nodeSize + n;
end
end
% disp('# boundary edges:');
% disp(elemSize);
% State of final graph so far:
% node-> all nodes lying on boundary edges
% elem-> empty
for i=1:nF
nodeSizeTillPrevFace(i) = nodeSize;
% look at all U-lines on all faces, and find intersection points with
% V-lines and with W-lines. For boundary faces, also build the
% connectivity graph by adding elements forming the U-lines
% disp(['Face # ' num2str(i)]);
% disp('U-lines');
for j=1:3
e1 = E_F(i, mod(j+1, 3)+1);
e2 = E_F(i, mod(j+2, 3)+1);
minUI = max(min(UI_E{e1}), min(UI_E{e2}));
maxUI = min(max(UI_E{e1}), max(UI_E{e2}));
% idx into UIonE{e1} and UIonE{e2}
[~, shift1] = ismember(minUI, UI_E{e1});
if isempty(shift1)
shift1 = 0;
end
idx1 = shift1 + (0:maxUI-minUI);
[~, shift2] = ismember(minUI, UI_E{e2});
if isempty(shift2)
shift2 = 0;
end
idx2 = shift2 + (0:maxUI-minUI);
for k=1:numel(idx1)
% We have to interpolate b/w the vertices at idx1(k)
% position in PUI_E{e1} and idx2(k) in PUI_E{e2}.
% UI_E{e1/2} and VonUI_E{e1/2} follow the same indexing
k1 = idx1(k);
k2 = idx2(k);
ePair = [e1 e2];
P12 = [PUI_E{e1}(k1, :); PUI_E{e2}(k2, :)];
u = UI_E{e1}(k1); % U is the same for both
V12 = [VonPUI_E{e1}(k1); VonPUI_E{e2}(k2)];
W12 = [WonPUI_E{e1}(k1); WonPUI_E{e2}(k2)];
% point with smaller v or w is at alpha = 0
if abs(diff(V12)) > abs(diff(W12))
[~, idxSort] = sort(V12);
sorter = 2;
else
[~, idxSort] = sort(W12);
sorter = 3;
end
V12 = V12(idxSort);
P12 = P12(idxSort, :);
ePair = ePair(idxSort);
W12 = W12(idxSort);
if V12(1) > V12(2)
rangeV = integersHalfOpen(V12(2), V12(1));
alphaV = (rangeV - V12(2)) / (V12(1) - V12(2));
alphaV = 1 - alphaV;
else
rangeV = integersHalfOpen(V12(1), V12(2));
alphaV = (rangeV - V12(1)) / diff(V12);
end
if W12(1) > W12(2)
rangeW = integersHalfOpen(W12(2), W12(1));
alphaW = (rangeW - W12(2)) / (W12(1) - W12(2));
alphaW = 1 - alphaW;
else
rangeW = integersHalfOpen(W12(1), W12(2));
alphaW = (rangeW - W12(1)) / diff(W12);
end
nvi = numel(alphaV);
viNodes = (1 - alphaV)*P12(1, :) + alphaV*P12(2, :);
w_vi = (1 - alphaV)*W12(1) + alphaV*W12(2);
PUVI_F{i} = [PUVI_F{i}; viNodes];
U_UVI_F{i} = [U_UVI_F{i}; repmat(u, nvi, 1)];
V_UVI_F{i} = [V_UVI_F{i}; rangeV];
WonPUVI_F{i} = [WonPUVI_F{i}; w_vi];
nodeIdx_v = nodeSize + (1:nvi)';
node(nodeIdx_v, :) = viNodes;
nodeUI(nodeIdx_v) = u;
nodeVI(nodeIdx_v) = rangeV;
nodeU(nodeIdx_v) = u;
nodeV(nodeIdx_v) = rangeV;
nodeW(nodeIdx_v) = w_vi;
F_node(nodeIdx_v) = i;
nwi = numel(alphaW);
wiNodes = (1 - alphaW)*P12(1, :) + alphaW*P12(2, :);
v_wi = (1 - alphaW)*V12(1) + alphaW*V12(2);
PWUI_F{i} = [PWUI_F{i}; wiNodes];
U_WUI_F{i} = [U_WUI_F{i}; repmat(u, nwi, 1)];
W_WUI_F{i} = [W_WUI_F{i}; rangeW];
VonPWUI_F{i} = [VonPWUI_F{i}; v_wi];
nodeIdx_w = nodeSize + nvi + (1:nwi)';
node(nodeIdx_w, :) = wiNodes;
nodeUI(nodeIdx_w) = u;
nodeWI(nodeIdx_w) = rangeW;
nodeU(nodeIdx_w) = u;
nodeV(nodeIdx_w) = v_wi;
nodeW(nodeIdx_w) = rangeW;
F_node(nodeIdx_w) = i;
% add elements on the boundary
if isFBoundary(i)
% find existing nodes on edges
e1NodeIdx = find(E_node==ePair(1) & nodeUI==u);
e2NodeIdx = find(E_node==ePair(2) & nodeUI==u);
% combine vars for vi and wi and sort by v
v = [double(rangeV); v_wi];
w = [w_vi; double(rangeW)];
nodeIdx = [nodeIdx_v; nodeIdx_w];
n = nvi + nwi;
if sorter==2
[~, sortIdx] = sort(v);
else
[~, sortIdx] = sort(w);
end
nodeIdx = nodeIdx(sortIdx);
nodeIsBoundary(nodeIdx) = true;
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
e1NodeIdx, nodeIdx(1);
nodeIdx(end), e2NodeIdx];
elemSize = elemSize + 2;
else
% otherwise, just add the elem connecting the two boundary
% nodes
elem(elemSize + 1, :) = [e1NodeIdx, e2NodeIdx];
elemSize = elemSize + 1;
end
end
nodeSize = nodeSize + nvi + nwi;
end
end
% Repeat for V-lines now. But we now have to search for UV points
% in the existing set of nodes. VW points have still not been
% inserted into the nodeset, which we'll do now. Similar to
% U-line processing, we have to insert boundary elements as well.
% disp('V-lines');
nodeSearchFilter = false(allocSize, 1);
nodeSearchFilter(nodeSizeTillPrevFace(i)+1 : nodeSize) = true;
for j=1:3
e1 = E_F(i, mod(j+1, 3)+1);
e2 = E_F(i, mod(j+2, 3)+1);
minVI = max(min(VI_E{e1}), min(VI_E{e2}));
maxVI = min(max(VI_E{e1}), max(VI_E{e2}));
% idx into UIonE{e1} and UIonE{e2}
[~, shift1] = ismember(minVI, VI_E{e1});
if isempty(shift1)
shift1 = 0;
end
idx1 = shift1 + (0:maxVI-minVI);
[~, shift2] = ismember(minVI, VI_E{e2});
if isempty(shift2)
shift2 = 0;
end
idx2 = shift2 + (0:maxVI-minVI);
for k=1:numel(idx1)
% We have to interpolate b/w the vertices at idx1(k)
% position in PUI_E{e1} and idx2(k) in PUI_E{e2}.
% UI_E{e1/2} and VonUI_E{e1/2} follow the same indexing
k1 = idx1(k);
k2 = idx2(k);
ePair = [e1 e2];
P12 = [PVI_E{e1}(k1, :); PVI_E{e2}(k2, :)];
v = VI_E{e1}(k1); % V is the same for both
U12 = [UonPVI_E{e1}(k1); UonPVI_E{e2}(k2)];
W12 = [WonPVI_E{e1}(k1); WonPVI_E{e2}(k2)];
% point with smaller U is at alpha = 0
if abs(diff(U12)) > abs(diff(W12))
[~, idxSort] = sort(U12);
sorter = 1;
else
[~, idxSort] = sort(W12);
sorter = 3;
end
U12 = U12(idxSort);
P12 = P12(idxSort, :);
ePair = ePair(idxSort);
W12 = W12(idxSort);
if W12(1) > W12(2)
rangeW = integersHalfOpen(W12(2), W12(1));
alphaW = (rangeW - W12(2)) / (W12(1) - W12(2));
alphaW = 1 - alphaW;
else
rangeW = integersHalfOpen(W12(1), W12(2));
alphaW = (rangeW - W12(1)) / diff(W12);
end
localNodeSearchFilter = nodeSearchFilter &...
nodeVI==v & nodeUI>=0;
rangeU = nodeUI(localNodeSearchFilter);
nui = numel(rangeU);
nodeIdx_u = find(localNodeSearchFilter);
% sort the searched list
[rangeU, sortIdx] = sort(rangeU);
nodeIdx_u = nodeIdx_u(sortIdx);
w_ui = nodeW(nodeIdx_u);
nwi = numel(alphaW);
wiNodes = (1 - alphaW)*P12(1, :) + alphaW*P12(2, :);
u_wi = (1 - alphaW)*U12(1) + alphaW*U12(2);
PVWI_F{i} = [PVWI_F{i}; wiNodes];
V_VWI_F{i} = [V_VWI_F{i}; repmat(v, nwi, 1)];
W_VWI_F{i} = [W_VWI_F{i}; rangeW];
UonPVWI_F{i} = [UonPVWI_F{i}; u_wi];
nodeIdx_w = nodeSize + (1:nwi)';
node(nodeIdx_w, :) = wiNodes;
nodeVI(nodeIdx_w) = v;
nodeWI(nodeIdx_w) = rangeW;
nodeU(nodeIdx_w) = u_wi;
nodeV(nodeIdx_w) = v;
nodeW(nodeIdx_w) = rangeW;
F_node(nodeIdx_w) = i;
% add elements on the boundary
if isFBoundary(i)
% find existing nodes on edges
e1NodeIdx = find(E_node==ePair(1) & nodeVI==v);
e2NodeIdx = find(E_node==ePair(2) & nodeVI==v);
% combine vars for ui and wi and sort by u
u = [double(rangeU); u_wi];
w = [w_ui; double(rangeW)];
nodeIdx = [nodeIdx_u; nodeIdx_w];
n = nui + nwi;
if sorter==1
[~, sortIdx] = sort(u);
else
[~, sortIdx] = sort(w);
end
nodeIdx = nodeIdx(sortIdx);
nodeIsBoundary(nodeIdx_w) = true;
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
e1NodeIdx, nodeIdx(1);
nodeIdx(end), e2NodeIdx];
elemSize = elemSize + 2;
else
% otherwise, just add the elem connecting the two boundary
% nodes
elem(elemSize + 1, :) = [e1NodeIdx, e2NodeIdx];
elemSize = elemSize + 1;
end
end
nodeSize = nodeSize + nwi;
end
end
% Finally for W-lines. Now, we don't need to insert any new nodes.
% disp('W-lines');
nodeSearchFilter(nodeSizeTillPrevFace(i)+1 : nodeSize) = true;
for j=1:3
e1 = E_F(i, mod(j+1, 3)+1);
e2 = E_F(i, mod(j+2, 3)+1);
minWI = max(min(WI_E{e1}), min(WI_E{e2}));
maxWI = min(max(WI_E{e1}), max(WI_E{e2}));
% idx into UIonE{e1} and UIonE{e2}
[~, shift1] = ismember(minWI, WI_E{e1});
if isempty(shift1)
shift1 = 0;
end
idx1 = shift1 + (0:maxWI-minWI);
[~, shift2] = ismember(minWI, WI_E{e2});
if isempty(shift2)
shift2 = 0;
end
idx2 = shift2 + (0:maxWI-minWI);
for k=1:numel(idx1)
% We have to interpolate b/w the vertices at idx1(k)
% position in PUI_E{e1} and idx2(k) in PUI_E{e2}.
% UI_E{e1/2} and VonUI_E{e1/2} follow the same indexing
k1 = idx1(k);
k2 = idx2(k);
ePair = [e1 e2];
w = WI_E{e1}(k1); % W is the same for both
U12 = [UonPWI_E{e1}(k1); UonPWI_E{e2}(k2)];
V12 = [VonPWI_E{e1}(k1); VonPWI_E{e2}(k2)];
% point with smaller U or V is at alpha = 0
if abs(diff(U12)) > abs(diff(V12))
[~, idxSort] = sort(U12);
sorter = 1;
else
[~, idxSort] = sort(V12);
sorter = 2;
end
ePair = ePair(idxSort);
localNodeSearchFilter = nodeSearchFilter &...
nodeWI==w & nodeUI>=0;
rangeU = nodeUI(localNodeSearchFilter);
nodeIdx_u = find(localNodeSearchFilter);
nui = numel(rangeU);
% sort the searched lists
[rangeU, sortIdx] = sort(rangeU);
nodeIdx_u = nodeIdx_u(sortIdx);
v_ui = nodeV(nodeIdx_u);
localNodeSearchFilter = nodeSearchFilter &...
nodeWI==w & nodeVI>=0;
nodeIdx_v = find(localNodeSearchFilter);
nvi = numel(nodeIdx_v);
% sort V-lists by U-values as well
[u_vi, sortIdx] = sort(nodeU(nodeIdx_v));
nodeIdx_v = nodeIdx_v(sortIdx);
rangeV = nodeV(nodeIdx_v);
% add elements on the boundary
if isFBoundary(i)
% find existing nodes on edges
e1NodeIdx = find(E_node==ePair(1) & nodeWI==w);
e2NodeIdx = find(E_node==ePair(2) & nodeWI==w);
% combine vars for ui and vi and sort by u
u = [double(rangeU); u_vi];
v = [v_ui; double(rangeV)];
nodeIdx = [nodeIdx_u; nodeIdx_v];
n = nui + nvi;
if sorter==1
[~, sortIdx] = sort(u);
else
[~, sortIdx] = sort(v);
end
nodeIdx = nodeIdx(sortIdx);
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
e1NodeIdx, nodeIdx(1);
nodeIdx(end), e2NodeIdx];
elemSize = elemSize + 2;
% otherwise, just add the elem connecting the two boundary
% nodes
else
elem(elemSize + 1, :) = [e1NodeIdx, e2NodeIdx];
elemSize = elemSize + 1;
end
end
end
end
end
numBNode = nodeSize;
% State of final graph so far:
% node-> all nodes lying on faces (tris)
% elem-> all elems on the boundary
% includes extra nodes/elems which need to be collapsed (later)
% for each tet, we have the nodes on the bounding faces
% first, we iterate over each (unordered) pair of these bounding faces
% Then, for each such pair, we iterate over each (unordered) pair of
% tex-coordinates. We move between the two faces along each integral
% isoline of this pair, and find the intersections with the isoplane of
% the third tex-coordinate.
for i=1:nT
% disp(['Tet # ' num2str(i)]);
f_choice = nchoosek(1:4, 2);
nodeSizeTillPrevTet(i) = nodeSize;
% First, UV-lines. This will find ALL the internal nodes and
% also all the elems lying on UV-lines
% disp('UV-lines');
for j=1:size(f_choice, 1)
f1 = F_T(i, f_choice(j, 1));
f2 = F_T(i, f_choice(j, 2));
idx1 = (1:numel(U_UVI_F{f1}))';
for k1 = 1:numel(idx1)
u = U_UVI_F{f1}(k1);
v = V_UVI_F{f1}(k1);
k2 = find(U_UVI_F{f2} == u & V_UVI_F{f2} == v);
if isempty(k2)
continue;
end
fPair = [f1 f2]';
P12 = [PUVI_F{f1}(k1, :); PUVI_F{f2}(k2, :)];
W12 = [WonPUVI_F{f1}(k1); WonPUVI_F{f2}(k2)];
[W12, idxSort] = sort(W12);
P12 = P12(idxSort, :);
fPair = fPair(idxSort);
range = integersOpen(W12(1), W12(2));
alpha = (range - W12(1)) / diff(W12);
n = numel(alpha);
allNodes = (1 - alpha)*P12(1, :) + alpha*P12(2, :);
% find existing nodes on faces
f1NodeIdx = find(F_node==fPair(1) & nodeUI==u & nodeVI==v);
f2NodeIdx = find(F_node==fPair(2) & nodeUI==u & nodeVI==v);
% add the internal nodes first
nodeIdx = nodeSize + (1:n)';
node(nodeIdx, :) = allNodes;
nodeUI(nodeIdx) = u;
nodeVI(nodeIdx) = v;
nodeWI(nodeIdx) = range;
nodeU(nodeIdx) = u;
nodeV(nodeIdx) = v;
nodeW(nodeIdx) = range;
T_node(nodeIdx) = i;
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
f1NodeIdx, nodeIdx(1);...
nodeIdx(end), f2NodeIdx];
elemSize = elemSize + 2;
else
% otherwise, just add the elem connecting the two nodes
% on the faces f1 and f2
elem(elemSize + 1, :) = [f1NodeIdx, f2NodeIdx];
elemSize = elemSize + 1;
end
nodeSize = nodeSize + n;
end
end
nodeSearchFilter = false(allocSize, 1);
nodeSearchFilter(nodeSizeTillPrevTet(i)+1 : nodeSize) = true;
% Then, trace out the elems on VW-lines. Note that the nodes
% are already there.
% disp('VW-lines');
for j=1:size(f_choice, 1)
f1 = F_T(i, f_choice(j, 1));
f2 = F_T(i, f_choice(j, 2));
idx1 = (1:numel(V_VWI_F{f1}))';
for k1 = 1:numel(idx1)
v = V_VWI_F{f1}(k1);
w = W_VWI_F{f1}(k1);
k2 = find(V_VWI_F{f2} == v & W_VWI_F{f2} == w, 1);
if isempty(k2)
continue;
end
U12 = [UonPVWI_F{f1}(k1); UonPVWI_F{f2}(k2)];
fPair = [f1 f2]';
[~, sortIdx] = sort(U12);
fPair = fPair(sortIdx);
localNodeSearchFilter = nodeSearchFilter &...
nodeVI==v & nodeWI==w & nodeUI>=0;
range = nodeUI(localNodeSearchFilter);
n = numel(range);
nodeIdx = find(localNodeSearchFilter);
%sort the searched lists
[~, sortIdx] = sort(range);
nodeIdx = nodeIdx(sortIdx);
% find existing nodes on faces
f1NodeIdx = find(F_node==fPair(1) & nodeVI==v & nodeWI==w);
f2NodeIdx = find(F_node==fPair(2) & nodeVI==v & nodeWI==w);
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
f1NodeIdx, nodeIdx(1);...
nodeIdx(end), f2NodeIdx];
elemSize = elemSize + 2;
else
% otherwise, just add the elem connecting the two nodes
% on the faces f1 and f2
elem(elemSize + 1, :) = [f1NodeIdx, f2NodeIdx];
elemSize = elemSize + 1;
end
end
end
% Finally, trace out the elems on WU-lines. This works exactly the
% same way as tracing VW-lines.
% disp('WU-lines');
for j=1:size(f_choice, 1)
f1 = F_T(i, f_choice(j, 1));
f2 = F_T(i, f_choice(j, 2));
idx1 = (1:numel(W_WUI_F{f1}))';
for k1 = 1:numel(idx1)
w = W_WUI_F{f1}(k1);
u = U_WUI_F{f1}(k1);
k2 = find(W_WUI_F{f2} == w & U_WUI_F{f2} == u, 1);
if isempty(k2)
continue;
end
V12 = [VonPWUI_F{f1}(k1); VonPWUI_F{f2}(k2)];
fPair = [f1 f2]';
[~, sortIdx] = sort(V12);
fPair = fPair(sortIdx);
localNodeSearchFilter = nodeSearchFilter &...
nodeWI==w & nodeUI==u & nodeVI>=0;
range = nodeVI(localNodeSearchFilter);
n = numel(range);
nodeIdx = find(localNodeSearchFilter);
%sort the searched lists
[~, sortIdx] = sort(range);
nodeIdx = nodeIdx(sortIdx);
% find existing nodes on faces
f1NodeIdx = find(F_node==fPair(1) & nodeWI==w & nodeUI==u);
f2NodeIdx = find(F_node==fPair(2) & nodeWI==w & nodeUI==u);
if n
% add the internal elems
elem(elemSize + (1:n-1), :) = [nodeIdx(1:n-1), nodeIdx(2:n)];
elemSize = elemSize + n-1;
% add two elems if there is any internal node
elem(elemSize + (1:2), :) = [...
f1NodeIdx, nodeIdx(1);...
nodeIdx(end), f2NodeIdx];
elemSize = elemSize + 2;
else
% otherwise, just add the elem connecting the two nodes
% on the faces f1 and f2
elem(elemSize + 1, :) = [f1NodeIdx, f2NodeIdx];
elemSize = elemSize + 1;
end
end
end
end
node(nodeSize+1:end, :) = [];
elem(elemSize+1:end, :) = [];
nodeIsBoundary(nodeSize+1:end) = [];
nodeUI(nodeSize+1:end) = [];
nodeVI(nodeSize+1:end) = [];
nodeWI(nodeSize+1:end) = [];
E_node(nodeSize+1:end) = [];
F_node(nodeSize+1:end) = [];
T_node(nodeSize+1:end) = [];
clear nodeU nodeV nodeW;
disp(['Pre-collapse graph size: (' num2str(nodeSize) ', ' num2str(elemSize) ')']);
% And finally, we need to collapse edges. This is done by
% following isolines emanating from each boundary vertex, and
% collapsing all invalid vertices along a line in one go.
newIdx_node = zeros(nodeSize, 1);
isEBCurved_node = false(nodeSize, 1);
isEBCurved_node(E_node > 0) = isEBCurved(E_node(E_node > 0));
node2 = zeros(nodeSize, 3);
nodeUI2 = -int32(ones(nodeSize, 1));
nodeVI2 = -int32(ones(nodeSize, 1));
nodeWI2 = -int32(ones(nodeSize, 1));
nodeB2 = false(nodeSize, 1);
nodeC2 = false(nodeSize, 1);
oldIdx_node2 = zeros(nodeSize, 1);
elem2 = zeros(elemSize, 2);
elemC2 = false(elemSize, 1);