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Re-implement monotone chain triangulation to output a DCEL

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This commit is contained in:
Nikita Lisitsa 2022-09-19 23:35:33 +03:00
parent 92ad22f656
commit 7a57c1c1d8
2 changed files with 202 additions and 137 deletions
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56
examples/triangulation.cpp
View file

@ -64,14 +64,20 @@ struct triangulation_app
{ {
prof::profiler prof("triangulate"); prof::profiler prof("triangulate");
auto dcel = cg::ear_clipping<std::uint16_t>(geom::fast, points_.begin(), points_.end()); // auto dcel = cg::ear_clipping<std::uint16_t>(geom::fast, points_.begin(), points_.end());
auto dcel = cg::monotone_triangulation<std::uint16_t>(geom::fast, points_.begin(), points_.end());
edges_ = cg::edge_mesh(dcel); edges_ = cg::edge_mesh(dcel);
triangles_ = cg::triangle_mesh(dcel); triangles_ = cg::triangle_mesh(dcel);
} }
prof::dump(); prof::dump();
log::info() << (triangles_.size() / 3) << " triangles"; log::info() << edges_.size() << " edges";
log::info() << triangles_.size() << " triangles";
log::info() << "Euler chi: " << (points_.size() - edges_.size() + triangles_.size());
closest_points_.resize(points_.size());
std::iota(closest_points_.begin(), closest_points_.end(), std::uint16_t{0});
} }
void on_left_button_down() override void on_left_button_down() override
@ -125,8 +131,7 @@ struct triangulation_app
}; };
random::generator rng; random::generator rng;
for (auto const & e : edges_)
edge(e[0], e[1], gfx::black);
for (auto const & t : triangles_) for (auto const & t : triangles_)
{ {
gfx::color_rgba c; gfx::color_rgba c;
@ -138,14 +143,52 @@ struct triangulation_app
painter_.triangle(points_[t[0]], points_[t[1]], points_[t[2]], c); painter_.triangle(points_[t[0]], points_[t[1]], points_[t[2]], c);
} }
// for (auto const & e : edges_)
// edge(e[0], e[1], gfx::black);
for (std::size_t i = 0; i < points_.size(); ++i) for (std::size_t i = 0; i < points_.size(); ++i)
{
edge(i, (i + 1) % points_.size(), gfx::black); edge(i, (i + 1) % points_.size(), gfx::black);
}
auto camera_transform = geom::orthographic_camera{view_bbox}.transform(); auto camera_transform = geom::orthographic_camera{view_bbox}.transform();
painter_.render(camera_transform); painter_.render(camera_transform);
if (auto m = mouse(); m)
{
geom::point<float, 2> m_world;
m_world[0] = geom::lerp(view_bbox[0], (*m)[0] * 1.f / width());
m_world[1] = geom::lerp(view_bbox[1], 1.f - (*m)[1] * 1.f / height());
auto compare = [&](auto i, auto j){
return geom::distance(points_[i], m_world) < geom::distance(points_[j], m_world);
};
std::size_t const n_closest = 8;
std::partial_sort(closest_points_.begin(), closest_points_.begin() + n_closest, closest_points_.end(), compare);
float max_distance = camera_size_ / 32.f;
for (std::size_t j = 0; j < n_closest; ++j)
{
auto i = closest_points_[j];
if (geom::distance(points_[i], m_world) > max_distance)
break;
gfx::painter::text_options opts;
opts.c = {0, 0, 0, 255};
opts.x = gfx::painter::x_align::left;
opts.y = gfx::painter::y_align::bottom;
opts.scale = 2.f;
auto p = geom::swizzle<0, 1>(geom::as_point(camera_transform * geom::homogeneous(geom::swizzle<0, 1, -1>(points_[i]))));
p[0] = std::round((p[0] * 0.5f + 0.5f) * width());
p[1] = std::round((0.5f - p[1] * 0.5f) * height());
painter_.text(p, util::to_string(i), opts);
}
}
painter_.render(geom::window_camera{width(), height()}.transform());
} }
private: private:
@ -158,6 +201,7 @@ private:
float camera_size_tgt_; float camera_size_tgt_;
std::optional<geom::point<int, 2>> drag_start_; std::optional<geom::point<int, 2>> drag_start_;
std::vector<std::uint16_t> closest_points_;
gfx::painter painter_; gfx::painter painter_;

285
libs/cg/include/psemek/cg/triangulation/monotone.hpp
View file

@ -3,6 +3,7 @@
#include <psemek/geom/point.hpp> #include <psemek/geom/point.hpp>
#include <psemek/geom/orientation.hpp> #include <psemek/geom/orientation.hpp>
#include <psemek/geom/contains.hpp> #include <psemek/geom/contains.hpp>
#include <psemek/cg/dcel.hpp>
#include <vector> #include <vector>
#include <set> #include <set>
@ -10,39 +11,43 @@
namespace psemek::cg namespace psemek::cg
{ {
template <typename IndexType = std::size_t, typename RobustTag, typename Iterator, typename OutputIterator> template <typename IndexType = std::size_t, typename RobustTag, typename Iterator>
OutputIterator monotone_triangulation(RobustTag robust_tag, Iterator begin, Iterator end, OutputIterator out) auto monotone_triangulation(RobustTag robust_tag, Iterator begin, Iterator end)
{ {
IndexType const count = std::distance(begin, end); IndexType const count = std::distance(begin, end);
IndexType const null = IndexType(-1);
auto at = [begin](auto i){ return *(begin + i); }; auto at = [begin](IndexType i){ return *(begin + i); };
// Initialize dcel // Initialize dcel
std::vector<IndexType> start(count, 0); using dcel_type = dcel<util::empty, util::empty, util::empty, IndexType>;
std::vector<IndexType> next(count, 0); using point_handle = typename dcel_type::point_handle;
std::vector<IndexType> prev(count, 0);
std::vector<IndexType> twin(count, 0); dcel_type result;
result.push_face();
result.faces[0].edge = count;
result.points.resize(count);
result.edges.resize(2 * count);
for (IndexType i = 0; i < count; ++i) for (IndexType i = 0; i < count; ++i)
{ {
start[i] = i; result.points[i].edge = i;
next[i] = (i + 1) % count;
prev[i] = (i + count - 1) % count; result.edges[i].face = result.null;
twin[i] = null; result.edges[i].origin = i;
result.edges[i].prev = (i + count - 1) % count;
result.edges[i].next = (i + 1) % count;
result.edges[i].twin = i + count;
result.edges[i + count].face = 0;
result.edges[i + count].origin = (i + 1) % count;
result.edges[i + count].prev = count + (i + 1) % count;
result.edges[i + count].next = count + (i + count - 1) % count;
result.edges[i + count].twin = i;
} }
auto finish = [&](auto i)
{
return start[next[i]];
};
struct vertex_id
{
IndexType index;
};
struct sweepline_compare struct sweepline_compare
{ {
struct is_transparent{}; struct is_transparent{};
@ -71,14 +76,14 @@ namespace psemek::cg
return geom::orientation(RobustTag{}, j0, j1, i0) == geom::sign_t::negative; return geom::orientation(RobustTag{}, j0, j1, i0) == geom::sign_t::negative;
} }
bool operator()(IndexType e, vertex_id const & v) const bool operator()(IndexType e, point_handle v) const
{ {
return geom::orientation(RobustTag{}, at(e), at((e + 1) % count), at(v.index)) == geom::sign_t::positive; return geom::orientation(RobustTag{}, at(e), at((e + 1) % count), at(v.index())) == geom::sign_t::positive;
} }
bool operator()(vertex_id const & v, IndexType e) const bool operator()(point_handle v, IndexType e) const
{ {
return geom::orientation(RobustTag{}, at(e), at((e + 1) % count), at(v.index)) == geom::sign_t::negative; return geom::orientation(RobustTag{}, at(e), at((e + 1) % count), at(v.index())) == geom::sign_t::negative;
} }
}; };
@ -129,11 +134,11 @@ namespace psemek::cg
auto const vi = at(i); auto const vi = at(i);
auto const vj = at(j); auto const vj = at(j);
auto ni = i; auto ni = result.edge(i);
while (true) while (true)
{ {
auto f = at(finish(ni)); auto f = at(ni.next().origin().index());
auto p = at(start[prev[ni]]); auto p = at(ni.prev().origin().index());
bool contains; bool contains;
if (geom::orientation(robust_tag, f, vi, p) == geom::sign_t::negative) if (geom::orientation(robust_tag, f, vi, p) == geom::sign_t::negative)
contains = geom::orientation(robust_tag, f, vi, vj) == geom::sign_t::negative && geom::orientation(robust_tag, vj, vi, p) == geom::sign_t::negative; contains = geom::orientation(robust_tag, f, vi, vj) == geom::sign_t::negative && geom::orientation(robust_tag, vj, vi, p) == geom::sign_t::negative;
@ -141,15 +146,15 @@ namespace psemek::cg
contains = geom::orientation(robust_tag, f, vi, vj) == geom::sign_t::negative || geom::orientation(robust_tag, vj, vi, p) == geom::sign_t::negative; contains = geom::orientation(robust_tag, f, vi, vj) == geom::sign_t::negative || geom::orientation(robust_tag, vj, vi, p) == geom::sign_t::negative;
if (contains) if (contains)
break; break;
ni = twin[prev[ni]]; ni = ni.prev().twin();
} }
auto pi = prev[ni]; auto pi = ni.prev();
auto nj = j; auto nj = result.edge(j);
while (true) while (true)
{ {
auto f = at(finish(nj)); auto f = at(nj.next().origin().index());
auto p = at(start[prev[nj]]); auto p = at(nj.prev().origin().index());
bool contains; bool contains;
if (geom::orientation(robust_tag, f, vj, p) == geom::sign_t::negative) if (geom::orientation(robust_tag, f, vj, p) == geom::sign_t::negative)
contains = geom::orientation(robust_tag, f, vj, vi) == geom::sign_t::negative && geom::orientation(robust_tag, vi, vj, p) == geom::sign_t::negative; contains = geom::orientation(robust_tag, f, vj, vi) == geom::sign_t::negative && geom::orientation(robust_tag, vi, vj, p) == geom::sign_t::negative;
@ -157,37 +162,22 @@ namespace psemek::cg
contains = geom::orientation(robust_tag, f, vj, vi) == geom::sign_t::negative || geom::orientation(robust_tag, vi, vj, p) == geom::sign_t::negative; contains = geom::orientation(robust_tag, f, vj, vi) == geom::sign_t::negative || geom::orientation(robust_tag, vi, vj, p) == geom::sign_t::negative;
if (contains) if (contains)
break; break;
nj = twin[prev[nj]]; nj = nj.prev().twin();
} }
auto pj = prev[nj]; auto pj = nj.prev();
IndexType eij = start.size(); auto eij = result.push_edge();
IndexType eji = eij + 1; auto eji = result.push_edge();
start.emplace_back(); eij.origin(result.point(i));
start.emplace_back(); eij.next(nj); nj.prev(eij);
next.emplace_back(); eij.prev(pi); pi.next(eij);
next.emplace_back(); eij.twin(eji);
prev.emplace_back();
prev.emplace_back();
twin.emplace_back();
twin.emplace_back();
start[eij] = i; eji.origin(result.point(j));
next[eij] = nj; eji.next(ni); ni.prev(eji);
prev[eij] = pi; eji.prev(pj); pj.next(eji);
twin[eij] = eji; eji.twin(eij);
start[eji] = j;
next[eji] = ni;
prev[eji] = pj;
twin[eji] = eij;
next[pi] = eij;
prev[nj] = eij;
next[pj] = eji;
prev[ni] = eji;
}; };
// Partition into monotone parts // Partition into monotone parts
@ -208,7 +198,7 @@ namespace psemek::cg
break; break;
case event_type::split: case event_type::split:
{ {
auto l = *std::prev(sweepline.upper_bound(vertex_id{e})); auto l = *std::prev(sweepline.upper_bound(result.point(e)));
connect(e, helper[l]); connect(e, helper[l]);
helper[l] = e; helper[l] = e;
} }
@ -220,7 +210,7 @@ namespace psemek::cg
connect(e, h); connect(e, h);
sweepline.erase(p); sweepline.erase(p);
{ {
auto l = *std::prev(sweepline.upper_bound(vertex_id{e})); auto l = *std::prev(sweepline.upper_bound(result.point(e)));
if (auto h = helper[l]; classify(h) == event_type::merge) if (auto h = helper[l]; classify(h) == event_type::merge)
connect(e, h); connect(e, h);
helper[l] = e; helper[l] = e;
@ -237,7 +227,7 @@ namespace psemek::cg
} }
else else
{ {
auto l = *std::prev(sweepline.upper_bound(vertex_id{e})); auto l = *std::prev(sweepline.upper_bound(result.point(e)));
if (auto h = helper[l]; classify(h) == event_type::merge) if (auto h = helper[l]; classify(h) == event_type::merge)
connect(e, h); connect(e, h);
helper[l] = e; helper[l] = e;
@ -246,125 +236,156 @@ namespace psemek::cg
} }
} }
// Triangulate monotone parts fill_missing_faces(result);
std::vector<bool> used(start.size(), false);
std::vector<IndexType> stack;
for (IndexType e = 0; e < start.size(); ++e)
{
if (used[e]) continue;
auto le = e; IndexType face_count = result.faces.size();
used[e] = true;
// Mark the whole part as used and find leftmost point // Triangulate monotone parts
for (auto ee = next[e]; ee != e; ee = next[ee]) std::vector<IndexType> stack;
for (IndexType f = 1; f < face_count; ++f)
{ {
used[ee] = true; auto e = result.face(f).edge();
if (at(start[ee]) < at(start[le]))
// Find leftmost point
auto le = e;
for (auto ee = e.next(); ee != e; ee = ee.next())
{
if (at(ee.origin().index()) < at(le.origin().index()))
le = ee; le = ee;
} }
bool stack_left = true; bool stack_left = true;
auto re = prev[le]; auto re = le.prev();
stack.push_back(start[le]); stack.push_back(le.index());
le = next[le]; le = le.next();
auto emit_triangle = [&](auto e0_id, auto e1_id)
{
auto e0 = result.edge(e0_id);
auto e1 = result.edge(e1_id);
auto p = e0.prev();
auto n = e1.next();
auto face_out = e0.face();
auto face_in = result.push_face();
auto e_in = result.push_edge();
auto e_out = result.push_edge();
face_in.edge(e_in);
face_out.edge(e_out);
e_in.origin(n.origin());
e_out.origin(e0.origin());
e_in.twin(e_out);
e_out.twin(e_in);
e0.face(face_in);
e1.face(face_in);
e_in.face(face_in);
e_out.face(face_out);
e0.prev(e_in); e_in.next(e0);
e1.next(e_in); e_in.prev(e1);
p.next(e_out); e_out.prev(p);
n.prev(e_out); e_out.next(n);
return e_out.index();
};
while (true) while (true)
{ {
bool last = (le == re); auto ve = le;
IndexType v;
bool left; bool left;
if (at(start[le]) < at(start[re])) if (at(le.origin().index()) < at(re.origin().index()))
{ {
v = start[le]; ve = le;
le = next[le]; le = le.next();
left = true; left = true;
} }
else else
{ {
v = start[re]; ve = re;
re = prev[re]; re = re.prev();
left = false; left = false;
} }
auto orientation = [&](auto e0, auto e1, auto e2)
{
auto point = [&](auto e){ return at(result.edge(e).origin().index()); };
return geom::orientation(robust_tag, point(e0), point(e1), point(e2));
};
if (left && stack_left) if (left && stack_left)
{ {
while (stack.size() >= 2 && geom::orientation(robust_tag, at(v), at(stack.back()), at(stack[stack.size() - 2])) == geom::sign_t::negative) while (stack.size() >= 2 && orientation(ve.index(), stack.back(), stack[stack.size() - 2]) == geom::sign_t::negative)
{ {
*out++ = v; auto new_edge = emit_triangle(stack[stack.size() - 2], stack.back());
*out++ = stack[stack.size() - 2];
*out++ = stack.back();
stack.pop_back(); stack.pop_back();
stack.pop_back();
stack.push_back(new_edge);
} }
stack.push_back(v); stack.push_back(ve.index());
} }
else if (!left && !stack_left) else if (!left && !stack_left)
{ {
while (stack.size() >= 2 && geom::orientation(robust_tag, at(v), at(stack.back()), at(stack[stack.size() - 2])) == geom::sign_t::positive) auto e = ve.index();
while (stack.size() >= 2 && orientation(ve.index(), stack.back(), stack[stack.size() - 2]) == geom::sign_t::positive)
{ {
*out++ = v; e = emit_triangle(e, stack.back());
*out++ = stack.back();
*out++ = stack[stack.size() - 2];
stack.pop_back(); stack.pop_back();
} }
stack.push_back(v); stack.push_back(e);
} }
else if (left && !stack_left) else if (left && !stack_left)
{ {
auto last = stack.back(); auto e = stack.front();
while (stack.size() >= 2) for (auto it = std::next(stack.begin()); it != stack.end(); ++it)
{ e = emit_triangle(*it, e);
*out++ = v; stack.clear();
*out++ = stack.back(); stack.push_back(e);
*out++ = stack[stack.size() - 2]; stack.push_back(ve.index());
stack.pop_back();
}
stack.pop_back();
stack.push_back(last);
stack.push_back(v);
} }
else if (!left && stack_left) else if (!left && stack_left)
{ {
auto e = ve.index();
auto last = stack.back(); auto last = stack.back();
while (stack.size() >= 2) for (auto it = stack.begin(); it != std::prev(stack.end()); ++it)
{ e = emit_triangle(e, *it);
*out++ = v; stack.clear();
*out++ = stack[stack.size() - 2];
*out++ = stack.back();
stack.pop_back();
}
stack.pop_back();
stack.push_back(last); stack.push_back(last);
stack.push_back(v); stack.push_back(e);
} }
stack_left = left; stack_left = left;
if (last) if (le == re)
break; break;
} }
auto de = le.index();
if (stack_left)
{
for (IndexType i = 0; i + 2 < stack.size(); ++i)
de = emit_triangle(de, stack[i]);
}
else
{
for (IndexType i = stack.size() - 1; i > 1; --i)
de = emit_triangle(de, stack[i]);
}
stack.clear(); stack.clear();
} }
return out;
}
template <typename IndexType = std::size_t, typename Iterator, typename OutputIterator>
auto monotone_triangulation(Iterator begin, Iterator end, OutputIterator out)
{
return monotone_triangulation<IndexType>(geom::default_robust_tag, begin, end, out);
}
template <typename IndexType, typename RobustTag, typename Iterator>
std::vector<IndexType> monotone_triangulation(RobustTag robust_tag, Iterator begin, Iterator end)
{
std::vector<IndexType> result;
monotone_triangulation<IndexType>(robust_tag, begin, end, std::back_inserter(result));
return result; return result;
} }
template <typename IndexType, typename Iterator> template <typename IndexType, typename Iterator>
auto monotone_triangulation(Iterator begin, Iterator end) auto monotone_triangulation(Iterator begin, Iterator end)
{ {