toposweep.cpp revision 76addc201c409e81eaaa73fe27cc0f79c4db097c
#include <2geom/toposweep.h>
#include <2geom/path-intersection.h>
#include <2geom/basic-intersection.h>
//using namespace Geom;
namespace Geom {
TopoGraph::Edge &TopoGraph::Vertex::operator[](unsigned ix) {
ix %= degree();
return ix < enters.size() ? enters[ix] : exits[ix - enters.size()];
}
TopoGraph::Edge TopoGraph::Vertex::operator[](unsigned ix) const {
ix %= degree();
return ix < enters.size() ? enters[ix] : exits[ix - enters.size()];
}
void TopoGraph::Vertex::erase(unsigned ix) {
ix %= degree();
if(ix < enters.size())
enters.erase(enters.begin() + ix);
else
exits.erase(exits.begin() + (ix - enters.size()));
}
void TopoGraph::Vertex::insert(unsigned ix, Edge v) {
ix %= degree();
if(ix < enters.size())
enters.insert(enters.begin() + ix, v);
else
exits.insert(exits.begin() + (ix - enters.size()), v);
}
unsigned TopoGraph::Vertex::find_section(boost::shared_ptr<Section> section) const {
unsigned i = 0;
for(; i < degree(); i++)
if((*this)[i].section == section) return i;
return i;
}
TopoGraph::Edge TopoGraph::remove_edge(unsigned ix, unsigned jx) {
Vertex &v = vertices[ix];
if(v.degree()) {
jx %= v.degree();
Edge &ret = v[jx];
v.erase(jx);
v = vertices[ret.other];
if(v.degree()) {
v.erase(v.find_section(ret.section));
return ret;
}
}
assert(0);
return v[0]; // if assert is disabled, return first Edge.
}
void TopoGraph::cannonize() {
std::vector<unsigned> vix;
unsigned ix = 0;
for(unsigned i = 0; i < vertices.size(); i++) {
vix.push_back(ix);
if(vertices[i].degree() != 0) vertices[ix++] = vertices[i];
}
for(unsigned i = 0; i < ix; i++)
for(unsigned j = 0; j < vertices[i].degree(); j++)
vertices[i][j].other = vix[vertices[i][j].other];
}
void TopoGraph::assert_invariants() const {
for(unsigned i = 0; i < vertices.size(); i++) {
for(unsigned j = 0; j < vertices[i].degree(); j++) {
Edge e = vertices[i][j];
assert(e.other != i);
assert(are_near(e.section->fp, vertices[i].avg, tol) || are_near(e.section->tp, vertices[i].avg, tol));
assert(!are_near(e.section->fp, e.section->tp, tol));
assert(e.section.get());
unsigned oix = vertices[e.other].find_section(e.section);
assert(oix != vertices[e.other].degree());
}
}
}
//near predicate utilized in process_splits
template<typename T>
struct NearPredicate { bool operator()(T x, T y) { return are_near(x, y); } };
// ensures that f and t are elements of a vector, sorts and uniqueifies
// also asserts that no values fall outside of f and t
// if f is greater than t, the sort is in reverse
void process_splits(std::vector<double> &splits, double f, double t) {
splits.push_back(f);
std::sort(splits.begin(), splits.end());
while(are_near(splits.back(), t)) splits.erase(splits.end() - 1);
splits.push_back(t);
if(f > t) std::reverse(splits.begin(), splits.end());
//remove any splits which fall outside t / f
while(!splits.empty() && splits.front() != f) splits.erase(splits.begin());
while(!splits.empty() && splits.back() != t) splits.erase(splits.end() - 1);
std::vector<double>::iterator end = std::unique(splits.begin(), splits.end(), NearPredicate<double>());
splits.resize(end - splits.begin());
}
// A little sugar for appending a list to another
template<typename T>
void concatenate(T &a, T const &b) { a.insert(a.end(), b.begin(), b.end()); }
//returns a list of monotonic sections of a path
//TODO: handle saddle points
std::vector<boost::shared_ptr<Section> > mono_sections(PathVector const &ps, Dim2 d) {
std::vector<boost::shared_ptr<Section> > monos;
for(unsigned i = 0; i < ps.size(); i++) {
//TODO: necessary? can we have empty paths?
if(ps[i].size()) {
for(unsigned j = 0; j < ps[i].size(); j++) {
//find the points of 0 derivative
Curve* deriv = ps[i][j].derivative();
std::vector<double> splits = deriv->roots(0, X);
concatenate(splits, deriv->roots(0, Y));
delete deriv;
process_splits(splits, 0, 1);
//split on points of 0 derivative
for(unsigned k = 1; k < splits.size(); k++)
monos.push_back(boost::shared_ptr<Section>(new Section(CurveIx(i,j), splits[k-1], splits[k], ps, d)));
}
}
}
return monos;
}
//finds the t-value on a section, which corresponds to a particular horizontal or vertical line
//d indicates the dimension along which the roots is performed.
//-1 is returned if no root is found
double section_root(Section const &s, PathVector const &ps, double v, Dim2 d) {
std::vector<double> roots = s.curve.get(ps).roots(v, d);
for(unsigned j = 0; j < roots.size(); j++)
if(Interval(s.f, s.t).contains(roots[j])) return roots[j];
return -1;
}
bool SectionSorter::section_order(Section const &a, double at, Section const &b, double bt) const {
Point ap = a.curve.get(ps).pointAt(at);
Point bp = b.curve.get(ps).pointAt(bt);
if(are_near(ap[dim], bp[dim], tol)) {
// since the sections are monotonic, if the endpoints are on opposite sides of this
// coincidence, the order is determinable
if(a.tp[dim] < ap[dim] && b.tp[dim] > bp[dim]) return true;
if(a.tp[dim] > ap[dim] && b.tp[dim] < bp[dim]) return false;
//TODO: sampling / higher derivatives when unit tangents match
Point ad = a.curve.get(ps).unitTangentAt(a.f);
Point bd = b.curve.get(ps).unitTangentAt(b.f);
// tangent can point backwards
if(ad[1-dim] < 0) ad = -ad;
if(bd[1-dim] < 0) bd = -bd;
return ad[dim] < bd[dim];
}
return ap[dim] < bp[dim];
}
bool SectionSorter::operator()(Section const &a, Section const &b) const {
if(&a == &b) return false;
Rect ra = a.bbox(), rb = b.bbox();
//TODO: should we use tol in these conditions?
if(ra[dim].max() <= rb[dim].min()) return true;
if(rb[dim].max() <= ra[dim].min()) return false;
//we know that the rects intersect on dim
//by referencing f / t we are assuming that the section was constructed with 1-dim
if(ra[1-dim].intersects(rb[1-dim])) {
if(are_near(a.fp[1-dim], b.fp[1-dim], tol)) {
return section_order(a, a.f > a.t ? a.f - 0.01 : a.f + 0.01,
b, b.f > b.t ? b.f - 0.01 : b.f + 0.01);
} else if(a.fp[1-dim] < b.fp[1-dim]) {
//b inside a
double ta = section_root(a, ps, b.fp[1-dim], Dim2(1-dim));
//TODO: fix bug that necessitates this
if(ta == -1) ta = (a.t + a.f) / 2;
return section_order(a, ta, b, b.f);
} else {
//a inside b
double tb = section_root(b, ps, a.fp[1-dim], Dim2(1-dim));
//TODO: fix bug that necessitates this
if(tb == -1) tb = (b.t + b.f) / 2;
return section_order(a, a.f, b, tb);
}
}
return Point::LexLessRt(dim)(a.fp, b.fp);
}
// splits a section into pieces, as specified by an array of doubles, mutating the section to
// represent the first part, and returning the rest
//TODO: output iterator?
std::vector<boost::shared_ptr<Section> > split_section(boost::shared_ptr<Section> s, PathVector const &ps, std::vector<double> &cuts, Dim2 d) {
std::vector<boost::shared_ptr<Section> > ret;
process_splits(cuts, s->f, s->t);
if(cuts.size() <= 2) return ret;
s->t = cuts[1];
s->tp = s->curve.get(ps)(cuts[1]);
assert(Point::LexLessRt(d)(s->fp, s->tp));
ret.reserve(cuts.size() - 2);
for(int i = cuts.size() - 1; i > 1; i--) ret.push_back(boost::shared_ptr<Section>(new Section(s->curve, cuts[i-1], cuts[i], ps, d)));
return ret;
}
//merges the sorted lists a and b according to comparison z
template<typename X, typename Z>
void merge(X &a, X const &b, Z const &z) {
a.reserve(a.size() + b.size());
unsigned start = a.size();
concatenate(a, b);
std::inplace_merge(a.begin(), a.begin() + start, a.end(), z);
}
//TODO: faster than linear
unsigned find_vertex(std::vector<TopoGraph::Vertex> const &vertices, Point p, double tol) {
for(unsigned i = 0; i < vertices.size(); i++)
if(are_near(vertices[i].avg, p, tol)) return i;
return vertices.size();
}
//takes a vector of T pointers, and returns a vector of T with copies
template<typename T>
std::vector<T> deref_vector(std::vector<boost::shared_ptr<T> > const &xs, unsigned from = 0) {
std::vector<T> ret;
ret.reserve(xs.size() - from);
for(unsigned i = from; i < xs.size(); i++)
ret.push_back(T(*xs[i]));
return ret;
}
//used to create reversed sorting predicates
template<typename C>
struct ReverseAdapter {
typedef typename C::second_argument_type first_argument_type;
typedef typename C::first_argument_type second_argument_type;
typedef typename C::result_type result_type;
const C &comp;
ReverseAdapter(const C &c) : comp(c) {}
result_type operator()(const first_argument_type &a, const second_argument_type &b) const { return comp(b, a); }
};
//used to sort std::vector<Section*>
template<typename C>
struct DerefAdapter {
typedef typename boost::shared_ptr<typename C::first_argument_type> first_argument_type;
typedef typename boost::shared_ptr<typename C::second_argument_type> second_argument_type;
typedef typename C::result_type result_type;
const C &comp;
DerefAdapter(const C &c) : comp(c) {}
result_type operator()(const first_argument_type a, const second_argument_type b) const {
if(!a) return false;
if(!b) return true;
return comp(*a, *b);
}
};
struct EdgeSorter {
typedef TopoGraph::Edge first_argument_type;
typedef TopoGraph::Edge second_argument_type;
typedef bool result_type;
SectionSorter s;
EdgeSorter(const PathVector &rs, Dim2 d, double t) : s(rs, d, t) {}
bool operator()(TopoGraph::Edge const &e1, TopoGraph::Edge const &e2) const { return s(*e1.section, *e2.section); }
};
#ifdef SWEEP_GRAPH_DEBUG
//used for debugging purposes - each element represents a subsequent iteration of the algorithm.
std::vector<std::vector<Section> > monoss;
std::vector<std::vector<Section> > chopss;
std::vector<std::vector<Section> > contexts;
#endif
/*
1) take item off sweep sorted todo
2) find all of the to-values before the beginning of this section
3) sort these lexicographically, process them in order, grouping other sections in the context, and constructing a vertex in one fell swoop.
4) add our section into context, splitting on intersections
3 is novel, we perform it by storing
*/
template<typename A, typename B, typename Z>
struct MergeIterator {
A const &a;
B &b;
Z const &z;
unsigned ai;
bool on_a;
MergeIterator(A const &av, B &bv, Z const &zv) : a(av), b(bv), z(zv), ai(0), on_a(b.empty() || z(a[0], b.back())) {}
MergeIterator &operator++() {
if(!done()) {
on_a = b.empty() ? true : (ai >= a.size() ? false : z(a[ai], b.back()));
if(on_a) {
++ai;
if(ai >= a.size()) on_a = false;
} else {
b.erase(b.end());
if(b.empty()) on_a = true;
}
}
return *this;
}
typename A::value_type operator*() {
assert(!done());
return on_a ? a[ai] : b.back();
}
bool done() { return b.empty() && ai >= a.size() - 1; }
typename A::value_type operator->() { assert(!done()); return on_a ? a[ai] : b.back(); }
};
void modify_windings(std::vector<int> &windings, boost::shared_ptr<Section> sec, Dim2 d) {
unsigned k = sec->curve.path;
if(k >= windings.size() || sec->fp[d] == sec->tp[d]) return;
if(sec->f < sec->t) windings[k]++;
if(sec->f > sec->t) windings[k]--;
}
struct Context {
boost::shared_ptr<Section> section;
int from_vert;
int to_vert;
Context(boost::shared_ptr<Section> sect, int from) : section(sect), from_vert(from), to_vert(-1) {}
};
template<typename C>
struct ContextAdapter {
typedef Context first_argument_type;
typedef typename C::second_argument_type second_argument_type;
typedef typename C::result_type result_type;
const C &comp;
ContextAdapter(const C &c) : comp(c) {}
result_type operator()(const Context &a, const second_argument_type &b) const { return comp(a.section, b); }
};
#define DINF std::numeric_limits<double>::infinity()
TopoGraph::TopoGraph(PathVector const &ps, Dim2 d, double t) : dim(d), tol(t) {
//s_sort = vertical section order
ContextAdapter<DerefAdapter<SectionSorter> > s_sort = DerefAdapter<SectionSorter>(SectionSorter(ps, (Dim2)(1-d), tol));
//sweep_sort = horizontal sweep order
DerefAdapter<SweepSorter> sweep_sort = DerefAdapter<SweepSorter>(SweepSorter(d));
//heap_sort = reverse horizontal sweep order
ReverseAdapter<DerefAdapter<SweepSorter> > heap_sort = ReverseAdapter<DerefAdapter<SweepSorter> >(sweep_sort);
//edge_sort = sorter for edges
EdgeSorter edge_sort = EdgeSorter(ps, (Dim2)(1-d), tol);
std::vector<boost::shared_ptr<Section> > input_sections = mono_sections(ps, d), chops;
std::sort(input_sections.begin(), input_sections.end(), sweep_sort);
std::vector<Context> context;
vertices.reserve(input_sections.size());
//std::vector<unsigned> to_process;
std::vector<int> windings(ps.size(), 0);
for(MergeIterator<Area, Area, DerefAdapter<SweepSorter> > iter(input_sections, chops, sweep_sort); ; ++iter) {
//represents our position in the sweep, which controls what we finalize
//if we have no more to process, finish the rest by setting our position to infinity
Point lim;
if(iter.done()) lim[X] = lim[Y] = DINF; else lim = iter->fp;
/*
//finalize vertices
for(unsigned i = 0; i < to_process.size(); i++) {
if(vertices[to_process[i]].avg[d] + tol < lim[d])
for(unsigned j = 0; j < context.size(); j++) {
}
} */
//find all sections to remove
for(int i = context.size() - 1; i >= 0; i--) {
boost::shared_ptr<Section> sec = context[i].section;
if(Point::LexLessRt(d)(lim, sec->tp)) {
//sec->tp is less than or equal to lim
if(context[i].to_vert == -1) {
//we need to create a new vertex; add everything that enters it
//Point avg;
//unsigned cnt;
std::vector<Edge> enters;
std::fill(windings.begin(), windings.end(), 0);
for(unsigned j = 0; j < context.size(); j++) {
modify_windings(windings, context[j].section, d);
if(are_near(sec->tp, context[j].section->tp, tol)) {
assert(-1 == context[j].to_vert);
context[j].section->windings = windings;
context[j].to_vert = vertices.size();
enters.push_back(Edge(context[j].section, context[j].from_vert));
//avg += context[j].section->tp;
//cnt++;
}
}
//Vertex &v(avg / (double)cnt);
Vertex v(context[i].section->tp);
v.enters = enters;
vertices.push_back(v);
//to_process.push_back(vertices.size() - 1);
}
context.erase(context.begin() + i);
}
}
if(!iter.done()) {
boost::shared_ptr<Section> s = *iter;
//create a new context, associate a beginning vertex, and insert it in the proper location
unsigned ix = find_vertex(vertices, s->fp, tol);
if(ix == vertices.size()) {
vertices.push_back(Vertex(s->fp));
//to_process.push_back(vertices.size() - 1);
}
unsigned context_ix = std::lower_bound(context.begin(), context.end(), s, s_sort) - context.begin();
context.insert(context.begin() + context_ix, Context(s, ix));
Interval si = Interval(s->fp[1-d], s->tp[1-d]);
// Now we intersect with neighbors - do a sweep!
std::vector<double> this_splits;
for(unsigned i = 0; i < context.size(); i++) {
if(context[i].section == context[context_ix].section) continue;
boost::shared_ptr<Section> sec = context[i].section;
if(!si.intersects(Interval(sec->fp[1-d], sec->tp[1-d]))) continue;
std::vector<double> other_splits;
Crossings xs = mono_intersect(s->curve.get(ps), Interval(s->f, s->t),
sec->curve.get(ps), Interval(sec->f, sec->t));
if(xs.empty()) continue;
for(unsigned j = 0; j < xs.size(); j++) {
this_splits.push_back(xs[j].ta);
other_splits.push_back(xs[j].tb);
}
merge(chops, split_section(sec, ps, other_splits, d), heap_sort);
}
if(!this_splits.empty())
merge(chops, split_section(context[context_ix].section, ps, this_splits, d), heap_sort);
std::sort(chops.begin(), chops.end(), heap_sort);
if(context[context_ix].section->tp[d] - context[context_ix].section->fp[d] <= tol) {
if(!are_near(context[context_ix].section->tp, context[context_ix].section->fp, tol)) {
ix = find_vertex(vertices, context[context_ix].section->tp, tol);
if(ix != vertices.size()) {
boost::shared_ptr<Section> sec = context[context_ix].section;
Edge e(sec, context[context_ix].from_vert);
std::vector<Edge>::iterator it = std::lower_bound(vertices[ix].enters.begin(), vertices[ix].enters.end(), e, edge_sort);
if(vertices[ix].enters.empty()) {
std::fill(windings.begin(), windings.end(), 0);
for(unsigned j = 0; j <= context_ix; j++) modify_windings(windings, context[j].section, d);
} else if(it == vertices[ix].enters.end()) {
windings = (it-1)->section->windings;
modify_windings(windings, (it-1)->section, d);
} else {
windings = it->section->windings;
}
sec->windings = windings;
modify_windings(windings, sec, d);
for(std::vector<Edge>::iterator it2 = it; it2 != vertices[ix].enters.end(); ++it2) {
it2->section->windings = windings;
modify_windings(windings, it2->section, d);
}
vertices[ix].enters.insert(it, e);
context.erase(context.begin() + context_ix);
}
} else context.erase(context.begin() + context_ix);
}
}
#ifdef SWEEP_GRAPH_DEBUG
std::vector<Section> rem;
for(unsigned i = iter.ai + 1; i < iter.a.size(); i++) rem.push_back(*iter.a[i]);
monoss.push_back(rem);
chopss.push_back(deref_vector(iter.b));
rem.clear();
for(unsigned i = 0; i < context.size(); i++) rem.push_back(*context[i].section);
contexts.push_back(rem);
#endif
if(iter.done() && context.empty()) return;
}
}
void trim_whiskers(TopoGraph &g) {
std::vector<unsigned> affected;
for(unsigned i = 0; i < g.size(); i++)
if(g[i].degree() == 1) affected.push_back(i);
while(!affected.empty()) {
unsigned j = 0;
for(unsigned i = 0; i < affected.size(); i++)
if(g[affected[i]].degree() == 1)
affected[j++] = g.remove_edge(affected[i], 0).other;
affected.resize(j);
}
}
void add_edge_at(TopoGraph &g, unsigned ix, boost::shared_ptr<Section> s, TopoGraph::Edge jx, bool before = true) {
TopoGraph::Vertex &v = g[ix];
for(unsigned i = 0; i < v.enters.size(); i++) {
if(v.enters[i].section == s) {
v.enters.insert(v.enters.begin() + (before ? i : i + 1), jx);
return;
}
}
for(unsigned i = 0; i < v.exits.size(); i++) {
if(v.exits[i].section == s) {
v.exits.insert(v.exits.begin() + (before ? i : i + 1), jx);
return;
}
}
//TODO: fix the fall through to here
//assert(false);
}
void double_whiskers(TopoGraph &g) {
for(unsigned i = 0; i < g.size(); i++) {
if(g[i].degree() == 1) {
unsigned j = i;
TopoGraph::Edge e = g[i][0];
while(true) {
TopoGraph::Edge next_edge = g[j][1 - g[j].find_section(e.section)];
boost::shared_ptr<Section> new_section = boost::shared_ptr<Section>(new Section(*e.section));
add_edge_at(g, j, e.section, TopoGraph::Edge(new_section, e.other), false);
add_edge_at(g, e.other, e.section, TopoGraph::Edge(new_section, j), true);
if(g[e.other].degree() == 3) {
j = e.other;
e = next_edge;
} else break;
}
}
}
}
/*
void remove_degenerate(TopoGraph &g) {
for(unsigned i = 0; i < g.size(); i++) {
for(int j = g[i].degree(); j >= 0; j--) {
if(g[i][j].other == i)
}
}
}*/
/*
void remove_vestigial(TopoGraph &g) {
for(unsigned i = 0; i < g.size(); i++) {
if(g[i].enters.size() == 1 && g[i].exits.size() == 1) {
TopoGraph::Edge &e1 = g[i][0], &e2 = g[i][1];
if(e1.section == e2.section) {
//vestigial vert
Section *new_section = new Section(e1.section->curve,
e1.section->f, e2.section->t,
e1.section->fp, e2.section->tp);
e1.other
Vertex *v1 = e1.other, *v2 = e2.other;
v1->lookup_section(e1.section) = Edge(new_section, v2);
v2->lookup_section(e2.section) = Edge(new_section, v1);
g.erase(g.begin() + i);
}
}
}
}*/
//planar area finding
//linear on number of edges
Areas traverse_areas(TopoGraph const &g) {
Areas ret;
//stores which edges we've visited
std::vector<std::vector<bool> > visited;
for(unsigned i = 0; i < g.size(); i++) visited.push_back(std::vector<bool>(g[i].degree(), false));
for(unsigned vix = 0; vix < g.size(); vix++) {
while(true) {
//find an unvisited edge to start on
unsigned e_ix = std::find(visited[vix].begin(), visited[vix].end(), false) - visited[vix].begin();
if(e_ix == g[vix].degree()) break;
unsigned start = e_ix;
unsigned cur = vix;
Area area;
//std::vector<std::vector<bool> > before(visited);
while(cur < g.size() && !visited[cur][e_ix]) {
visited[cur][e_ix] = true;
TopoGraph::Edge e = g[cur][e_ix];
area.push_back(e.section);
//go to clockwise edge
cur = e.other;
unsigned deg = g[cur].degree();
e_ix = g[cur].find_section(e.section);
if(deg == 1 || e_ix == deg) {
visited[cur][e_ix] = true;
break;
}
e_ix = (e_ix + 1) % deg;
if(cur == vix && start == e_ix) break;
}
//if(vix == cur && start == e_ix) {
ret.push_back(area);
//} else visited = before;
}
}
return ret;
}
void remove_area_whiskers(Areas &areas) {
for(int i = areas.size() - 1; i >= 0; i--)
if(areas[i].size() == 2 && *areas[i][0] == *areas[i][1])
areas.erase(areas.begin() + i);
}
Path area_to_path(PathVector const &ps, Area const &area) {
Path ret;
ret.setStitching(true);
if(area.size() == 0) return ret;
Point prev = area[0]->fp;
for(unsigned i = 0; i < area.size(); i++) {
bool forward = are_near(area[i]->fp, prev, 0.01);
Curve *curv = area[i]->curve.get(ps).portion(
forward ? area[i]->f : area[i]->t,
forward ? area[i]->t : area[i]->f);
ret.append(*curv);
delete curv;
prev = forward ? area[i]->tp : area[i]->fp;
}
ret.setStitching(false);
return ret;
}
PathVector areas_to_paths(PathVector const &ps, Areas const &areas) {
PathVector ret;
//ret.reserve(areas.size());
for(unsigned i = 0; i < areas.size(); ++i)
ret.push_back(area_to_path(ps, areas[i]));
return ret;
}
} // end namespace Geom