void ShellingOrderModule::callLeftmost(const Graph &G,
ShellingOrder &order,
adjEntry adj)
{
List<ShellingOrderSet> partition;
doCall(G,adj,partition);
order.initLeftmost(G,partition);
}
void PlanarDrawLayout::doCall(
const Graph &G,
adjEntry adjExternal,
GridLayout &gridLayout,
IPoint &boundingBox,
bool fixEmbedding)
{
// require to have a planar graph without multi-edges and self-loops;
// planarity is checked below
OGDF_ASSERT(isSimple(G) && isLoopFree(G));
// handle special case of graphs with less than 3 nodes
if(G.numberOfNodes() < 3)
{
node v1, v2;
switch(G.numberOfNodes())
{
case 0:
boundingBox = IPoint(0,0);
return;
case 1:
v1 = G.firstNode();
gridLayout.x(v1) = gridLayout.y(v1) = 0;
boundingBox = IPoint(0,0);
return;
case 2:
v1 = G.firstNode();
v2 = G.lastNode ();
gridLayout.x(v1) = gridLayout.y(v1) = gridLayout.y(v2) = 0;
gridLayout.x(v2) = 1;
boundingBox = IPoint(1,0);
return;
}
}
// we make a copy of G since we use planar biconnected augmentation
GraphCopySimple GC(G);
if(fixEmbedding) {
PlanarAugmentationFix augmenter;
augmenter.call(GC);
} else {
// augment graph planar biconnected
m_augmenter.get().call(GC);
// embed augmented graph
PlanarModule pm;
bool isPlanar = pm.planarEmbed(GC);
if(isPlanar == false)
OGDF_THROW_PARAM(PreconditionViolatedException, pvcPlanar);
}
// compute shelling order
m_computeOrder.get().baseRatio(m_baseRatio);
ShellingOrder order;
m_computeOrder.get().call(GC,order,adjExternal);
// compute grid coordinates for GC
NodeArray<int> x(GC), y(GC);
computeCoordinates(GC,order,x,y);
boundingBox.m_x = x[order(1,order.len(1))];
boundingBox.m_y = 0;
node v;
forall_nodes(v,GC)
if(y[v] > boundingBox.m_y) boundingBox.m_y = y[v];
// copy coordinates from GC to G
forall_nodes(v,G) {
node vCopy = GC.copy(v);
gridLayout.x(v) = x[vCopy];
gridLayout.y(v) = y[vCopy];
}
void PlanarStraightLayout::doCall(
const Graph &G,
adjEntry adjExternal,
GridLayout &gridLayout,
IPoint &boundingBox,
bool fixEmbedding)
{
// require to have a planar graph without multi-edges and self-loops;
// planarity is checked below
OGDF_ASSERT(isSimple(G) && isLoopFree(G));
// handle special case of graphs with less than 3 nodes
if(G.numberOfNodes() < 3)
{
node v1, v2;
switch(G.numberOfNodes())
{
case 0:
boundingBox = IPoint(0,0);
return;
case 1:
v1 = G.firstNode();
gridLayout.x(v1) = gridLayout.y(v1) = 0;
boundingBox = IPoint(0,0);
return;
case 2:
v1 = G.firstNode();
v2 = G.lastNode ();
gridLayout.x(v1) = gridLayout.y(v1) = gridLayout.y(v2) = 0;
gridLayout.x(v2) = 1;
boundingBox = IPoint(1,0);
return;
}
}
// we make a copy of G since we use planar biconnected augmentation
GraphCopySimple GC(G);
if(fixEmbedding) {
// determine adjacency entry on external face of GC (if required)
if(adjExternal != 0) {
edge eG = adjExternal->theEdge();
edge eGC = GC.copy(eG);
adjExternal = (adjExternal == eG->adjSource()) ? eGC->adjSource() : eGC->adjTarget();
}
PlanarAugmentationFix augmenter;
augmenter.call(GC);
} else {
adjExternal = 0;
// augment graph planar biconnected
m_augmenter.get().call(GC);
// embed augmented graph
m_embedder.get().call(GC,adjExternal);
}
// compute shelling order with shelling order module
m_computeOrder.get().baseRatio(m_baseRatio);
ShellingOrder order;
m_computeOrder.get().callLeftmost(GC,order,adjExternal);
// compute grid coordinates for GC
NodeArray<int> x(GC), y(GC);
computeCoordinates(GC,order,x,y);
boundingBox.m_x = x[order(1,order.len(1))];
boundingBox.m_y = 0;
node v;
forall_nodes(v,GC)
if(y[v] > boundingBox.m_y) boundingBox.m_y = y[v];
// copy coordinates from GC to G
forall_nodes(v,G) {
node vCopy = GC.copy(v);
gridLayout.x(v) = x[vCopy];
gridLayout.y(v) = y[vCopy];
}
void PlanarDrawLayout::computeCoordinates(const Graph &G,
ShellingOrder &order,
NodeArray<int> &x,
NodeArray<int> &y)
{
// let c_1,...,c_q be the the current contour, then
// next[c_i] = c_i+1, prev[c_i] = c_i-1
NodeArray<node> next(G), prev(G);
// upper[v] = w means x-coord. of v is relative to w
// (abs. x-coord. of v = x[v] + abs. x-coord of w)
NodeArray<node> upper(G,nullptr);
// maximal rank of a neighbour
NodeArray<int> maxNeighbour(G,0);
// internal nodes (nodes not on contour)
BoundedStack<node> internals(G.numberOfNodes());
for(node v : G.nodes)
{
for(adjEntry adj : v->adjEdges) {
int r = order.rank(adj->twinNode());
if (r > maxNeighbour[v])
maxNeighbour[v] = r;
}
}
// initialize contour with base
const ShellingOrderSet &V1 = order[1];
node v1 = V1[1];
node v2 = V1[V1.len()];
node rightSide = v2;
int i;
for (i = 1; i <= V1.len(); ++i)
{
y[V1[i]] = 0;
x[V1[i]] = (i == 1) ? 0 : 1;
if (i < V1.len())
next[V1[i]] = V1[i+1];
if (i > 1)
prev[V1[i]] = V1[i-1];
}
prev[v1] = next[v2] = nullptr;
// process shelling order from bottom to top
for (int k = 2; k <= order.length(); k++)
{
// Referenz auf aktuelle Menge Vk (als Abk?rzung)
const ShellingOrderSet &Vk = order[k]; // Vk = { z_1,...,z_l }
int l = Vk.len();
node z1 = Vk[1];
node cl = Vk.left(); // left vertex
node cr = Vk.right(); // right vertex
bool isOuter;
if (m_sideOptimization && cr == rightSide && maxNeighbour[cr] <= k)
{
isOuter = true;
rightSide = Vk[l];
} else
isOuter = false;
// compute relative x-distance from c_i to cl for i = l+1, ..., r
int sum = 0;
for (node v = next[cl]; v != cr; v = next[v]) {
sum += x[v];
x[v] = sum;
}
x[cr] += sum;
int eps = (maxNeighbour [cl] <= k && k > 2) ? 0 : 1;
int x_cr, y_z;
if (m_sizeOptimization)
{
int yMax;
if (isOuter)
{
yMax = max(y[cl]+1-eps,
y[cr] + ((x[cr] == 1 && eps == 1) ? 1 : 0));
for (node v = next[cl]; v != cr; v = next[v]) {
if (x[v] < x[cr]) {
int y1 = (y[cr]-y[v])*(eps-x[cr])/(x[cr]-x[v])+y[cr];
if (y1 >= yMax)
yMax = 1+y1;
}
}
for (node v = cr; v != cl; v = prev[v]) {
if (y[prev[v]] > y[v] && maxNeighbour[v] >= k) {
if (yMax <= y[v] + x[v] - eps) {
eps = 1;
yMax = y[v] + x[v];
}
break;
}
}
x_cr = max(x[cr]-eps-l+1, (y[cr] == yMax) ? 1 : 0);
y_z = yMax;
} else {
// yMax = max { y[c_i] | l <= i <= r }
yMax = y[cl] - eps;
for (node v = cr; v != cl; v = prev[v]) {
if (y[v] > yMax)
yMax = y[v];
}
int offset = max (yMax-x[cr]+l+eps-y[cr],
(y[prev[cr]] > y[cr]) ? 1 : 0);
y_z = y[cr] + x[cr] + offset - l + 1 - eps;
x_cr = y_z - y[cr];
}
} else {
y_z = y[cr] + x[cr] + 1 - eps;
x_cr = y_z - y[cr];
}
node alpha = cl;
for (node v = next[cl];
maxNeighbour[v] <= k-1 && order.rank(v) <= order.rank(prev[v]);
v = next[v])
{
if (order.rank (v) < order.rank (alpha))
alpha = v;
if (v == cr)
break;
}
node beta = prev[cr];
for (node v = prev[cr];
maxNeighbour[v] <= k-1 && order.rank(v) <= order.rank(next[v]);
v = prev[v])
{
if (order.rank (v) <= order.rank (beta))
beta = v;
if (v == cl)
break;
}
for (i = 1; i <= l; ++i) {
x[Vk[i]] = 1;
y[Vk[i]] = y_z;
}
x[z1] = eps;
for (node v = alpha; v != cl; v = prev [v]) {
upper[v] = cl;
internals.push (v);
}
for (node v = next [beta]; v != cr; v = next [v]) {
upper[v] = cr;
x [v] -= x[cr];
internals.push (v);
}
for (node v = beta; v != alpha; v = prev[v]) {
upper[v] = z1;
x [v] -= x[z1];
internals.push (v);
}
x[cr] = x_cr;
// update contour after insertion of z_1,...,z_l
for (i = 1; i <= l; i++) {
if (i < l)
next[Vk[i]] = Vk[i+1];
if (i > 1)
prev[Vk[i]] = Vk[i-1];
}
next [cl] = z1;
next [Vk[l]] = cr;
prev [cr] = Vk[l];
prev [z1] = cl;
}
// compute final x-coordinates for the nodes on the (final) contour
int sum = 0;
for (node v = v1; v != nullptr; v = next[v])
x [v] = (sum += x[v]);
// compute final x-coordinates for the internal nodes
while (!internals.empty()) {
node v = internals.pop();
x[v] += x[upper[v]];
}
}