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|
/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/** \file
* \ingroup bli
*/
#ifdef WITH_GMP
# include <algorithm>
# include <fstream>
# include <iostream>
# include "BLI_array.hh"
# include "BLI_assert.h"
# include "BLI_delaunay_2d.h"
# include "BLI_hash.hh"
# include "BLI_map.hh"
# include "BLI_math.h"
# include "BLI_math_boolean.hh"
# include "BLI_math_mpq.hh"
# include "BLI_mesh_intersect.hh"
# include "BLI_mpq3.hh"
# include "BLI_set.hh"
# include "BLI_span.hh"
# include "BLI_stack.hh"
# include "BLI_vector.hh"
# include "BLI_vector_set.hh"
# include "PIL_time.h"
# include "BLI_mesh_boolean.hh"
// # define PERFDEBUG
namespace blender::meshintersect {
/**
* Edge as two `const` Vert *'s, in a canonical order (lower vert id first).
* We use the Vert id field for hashing to get algorithms
* that yield predictable results from run-to-run and machine-to-machine.
*/
class Edge {
const Vert *v_[2]{nullptr, nullptr};
public:
Edge() = default;
Edge(const Vert *v0, const Vert *v1)
{
if (v0->id <= v1->id) {
v_[0] = v0;
v_[1] = v1;
}
else {
v_[0] = v1;
v_[1] = v0;
}
}
const Vert *v0() const
{
return v_[0];
}
const Vert *v1() const
{
return v_[1];
}
const Vert *operator[](int i) const
{
return v_[i];
}
bool operator==(Edge other) const
{
return v_[0]->id == other.v_[0]->id && v_[1]->id == other.v_[1]->id;
}
uint64_t hash() const
{
constexpr uint64_t h1 = 33;
uint64_t v0hash = DefaultHash<int>{}(v_[0]->id);
uint64_t v1hash = DefaultHash<int>{}(v_[1]->id);
return v0hash ^ (v1hash * h1);
}
};
static std::ostream &operator<<(std::ostream &os, const Edge &e)
{
if (e.v0() == nullptr) {
BLI_assert(e.v1() == nullptr);
os << "(null,null)";
}
else {
os << "(" << e.v0() << "," << e.v1() << ")";
}
return os;
}
static std::ostream &operator<<(std::ostream &os, const Span<int> &a)
{
for (int i : a.index_range()) {
os << a[i];
if (i != a.size() - 1) {
os << " ";
}
}
return os;
}
static std::ostream &operator<<(std::ostream &os, const Array<int> &iarr)
{
os << Span<int>(iarr);
return os;
}
/** Holds information about topology of an #IMesh that is all triangles. */
class TriMeshTopology : NonCopyable {
/** Triangles that contain a given Edge (either order). */
Map<Edge, Vector<int> *> edge_tri_;
/** Edges incident on each vertex. */
Map<const Vert *, Vector<Edge>> vert_edges_;
public:
TriMeshTopology(const IMesh &tm);
~TriMeshTopology();
/* If e is manifold, return index of the other triangle (not t) that has it.
* Else return NO_INDEX. */
int other_tri_if_manifold(Edge e, int t) const
{
if (edge_tri_.contains(e)) {
auto *p = edge_tri_.lookup(e);
if (p->size() == 2) {
return ((*p)[0] == t) ? (*p)[1] : (*p)[0];
}
}
return NO_INDEX;
}
/* Which triangles share edge e (in either orientation)? */
const Vector<int> *edge_tris(Edge e) const
{
return edge_tri_.lookup_default(e, nullptr);
}
/* Which edges are incident on the given vertex?
* We assume v has some incident edges. */
const Vector<Edge> &vert_edges(const Vert *v) const
{
return vert_edges_.lookup(v);
}
Map<Edge, Vector<int> *>::ItemIterator edge_tri_map_items() const
{
return edge_tri_.items();
}
};
TriMeshTopology::TriMeshTopology(const IMesh &tm)
{
const int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "TRIMESHTOPOLOGY CONSTRUCTION\n";
}
/* If everything were manifold, `F+V-E=2` and `E=3F/2`.
* So an likely overestimate, allowing for non-manifoldness, is `E=2F` and `V=F`. */
const int estimate_num_edges = 2 * tm.face_size();
const int estimate_num_verts = tm.face_size();
edge_tri_.reserve(estimate_num_edges);
vert_edges_.reserve(estimate_num_verts);
for (int t : tm.face_index_range()) {
const Face &tri = *tm.face(t);
BLI_assert(tri.is_tri());
for (int i = 0; i < 3; ++i) {
const Vert *v = tri[i];
const Vert *vnext = tri[(i + 1) % 3];
Edge e(v, vnext);
Vector<Edge> *edges = vert_edges_.lookup_ptr(v);
if (edges == nullptr) {
vert_edges_.add_new(v, Vector<Edge>());
edges = vert_edges_.lookup_ptr(v);
BLI_assert(edges != nullptr);
}
edges->append_non_duplicates(e);
auto createf = [t](Vector<int> **pvec) { *pvec = new Vector<int>{t}; };
auto modifyf = [t](Vector<int> **pvec) { (*pvec)->append_non_duplicates(t); };
this->edge_tri_.add_or_modify(Edge(v, vnext), createf, modifyf);
}
}
/* Debugging. */
if (dbg_level > 0) {
std::cout << "After TriMeshTopology construction\n";
for (auto item : edge_tri_.items()) {
std::cout << "tris for edge " << item.key << ": " << *item.value << "\n";
constexpr bool print_stats = false;
if (print_stats) {
edge_tri_.print_stats();
}
}
for (auto item : vert_edges_.items()) {
std::cout << "edges for vert " << item.key << ":\n";
for (const Edge &e : item.value) {
std::cout << " " << e << "\n";
}
std::cout << "\n";
}
}
}
TriMeshTopology::~TriMeshTopology()
{
for (const Vector<int> *vec : edge_tri_.values()) {
delete vec;
}
}
/** A Patch is a maximal set of triangles that share manifold edges only. */
class Patch {
Vector<int> tri_; /* Indices of triangles in the Patch. */
public:
Patch() = default;
void add_tri(int t)
{
tri_.append(t);
}
int tot_tri() const
{
return tri_.size();
}
int tri(int i) const
{
return tri_[i];
}
IndexRange tri_range() const
{
return IndexRange(tri_.size());
}
Span<int> tris() const
{
return Span<int>(tri_);
}
int cell_above{NO_INDEX};
int cell_below{NO_INDEX};
int component{NO_INDEX};
};
static std::ostream &operator<<(std::ostream &os, const Patch &patch)
{
os << "Patch " << patch.tris();
if (patch.cell_above != NO_INDEX) {
os << " cell_above=" << patch.cell_above;
}
else {
os << " cell_above not set";
}
if (patch.cell_below != NO_INDEX) {
os << " cell_below=" << patch.cell_below;
}
else {
os << " cell_below not set";
}
return os;
}
class PatchesInfo {
/** All of the Patches for a #IMesh. */
Vector<Patch> patch_;
/** Patch index for corresponding triangle. */
Array<int> tri_patch_;
/** Shared edge for incident patches; (-1, -1) if none. */
Map<std::pair<int, int>, Edge> pp_edge_;
public:
explicit PatchesInfo(int ntri)
{
constexpr int max_expected_patch_patch_incidences = 100;
tri_patch_ = Array<int>(ntri, NO_INDEX);
pp_edge_.reserve(max_expected_patch_patch_incidences);
}
int tri_patch(int t) const
{
return tri_patch_[t];
}
int add_patch()
{
int patch_index = patch_.append_and_get_index(Patch());
return patch_index;
}
void grow_patch(int patch_index, int t)
{
tri_patch_[t] = patch_index;
patch_[patch_index].add_tri(t);
}
bool tri_is_assigned(int t) const
{
return tri_patch_[t] != NO_INDEX;
}
const Patch &patch(int patch_index) const
{
return patch_[patch_index];
}
Patch &patch(int patch_index)
{
return patch_[patch_index];
}
int tot_patch() const
{
return patch_.size();
}
IndexRange index_range() const
{
return IndexRange(patch_.size());
}
const Patch *begin() const
{
return patch_.begin();
}
const Patch *end() const
{
return patch_.end();
}
Patch *begin()
{
return patch_.begin();
}
Patch *end()
{
return patch_.end();
}
void add_new_patch_patch_edge(int p1, int p2, Edge e)
{
pp_edge_.add_new(std::pair<int, int>(p1, p2), e);
pp_edge_.add_new(std::pair<int, int>(p2, p1), e);
}
Edge patch_patch_edge(int p1, int p2)
{
return pp_edge_.lookup_default(std::pair<int, int>(p1, p2), Edge());
}
};
static bool apply_bool_op(BoolOpType bool_optype, const Array<int> &winding);
/**
* A Cell is a volume of 3-space, surrounded by patches.
* We will partition all 3-space into Cells.
* One cell, the Ambient cell, contains all other cells.
*/
class Cell {
Vector<int> patches_;
Array<int> winding_;
int merged_to_{NO_INDEX};
bool winding_assigned_{false};
/* in_output_volume_ will be true when this cell should be in the output volume. */
bool in_output_volume_{false};
/* zero_volume_ will be true when this is a zero-volume cell (inside a stack of identical
* triangles). */
bool zero_volume_{false};
public:
Cell() = default;
void add_patch(int p)
{
patches_.append(p);
}
void add_patch_non_duplicates(int p)
{
patches_.append_non_duplicates(p);
}
Span<int> patches() const
{
return Span<int>(patches_);
}
Span<int> winding() const
{
return Span<int>(winding_);
}
void init_winding(int winding_len)
{
winding_ = Array<int>(winding_len);
}
void seed_ambient_winding()
{
winding_.fill(0);
winding_assigned_ = true;
}
void set_winding_and_in_output_volume(const Cell &from_cell,
int shape,
int delta,
BoolOpType bool_optype)
{
std::copy(from_cell.winding().begin(), from_cell.winding().end(), winding_.begin());
if (shape >= 0) {
winding_[shape] += delta;
}
winding_assigned_ = true;
in_output_volume_ = apply_bool_op(bool_optype, winding_);
}
bool in_output_volume() const
{
return in_output_volume_;
}
bool winding_assigned() const
{
return winding_assigned_;
}
bool zero_volume() const
{
return zero_volume_;
}
int merged_to() const
{
return merged_to_;
}
void set_merged_to(int c)
{
merged_to_ = c;
}
/**
* Call this when it is possible that this Cell has zero volume,
* and if it does, set zero_volume_ to true.
*/
void check_for_zero_volume(const PatchesInfo &pinfo, const IMesh &mesh);
};
static std::ostream &operator<<(std::ostream &os, const Cell &cell)
{
os << "Cell patches " << cell.patches();
if (cell.winding().size() > 0) {
os << " winding=" << cell.winding();
os << " in_output_volume=" << cell.in_output_volume();
}
os << " zv=" << cell.zero_volume();
return os;
}
static bool tris_have_same_verts(const IMesh &mesh, int t1, int t2)
{
const Face &tri1 = *mesh.face(t1);
const Face &tri2 = *mesh.face(t2);
BLI_assert(tri1.size() == 3 && tri2.size() == 3);
if (tri1.vert[0] == tri2.vert[0]) {
return ((tri1.vert[1] == tri2.vert[1] && tri1.vert[2] == tri2.vert[2]) ||
(tri1.vert[1] == tri2.vert[2] && tri1.vert[2] == tri2.vert[1]));
}
if (tri1.vert[0] == tri2.vert[1]) {
return ((tri1.vert[1] == tri2.vert[0] && tri1.vert[2] == tri2.vert[2]) ||
(tri1.vert[1] == tri2.vert[2] && tri1.vert[2] == tri2.vert[0]));
}
if (tri1.vert[0] == tri2.vert[2]) {
return ((tri1.vert[1] == tri2.vert[0] && tri1.vert[2] == tri2.vert[1]) ||
(tri1.vert[1] == tri2.vert[1] && tri1.vert[2] == tri2.vert[0]));
}
return false;
}
/**
* A Cell will have zero volume if it is bounded by exactly two patches and those
* patches are geometrically identical triangles (perhaps flipped versions of each other).
* If this Cell has zero volume, set its zero_volume_ member to true.
*/
void Cell::check_for_zero_volume(const PatchesInfo &pinfo, const IMesh &mesh)
{
if (patches_.size() == 2) {
const Patch &p1 = pinfo.patch(patches_[0]);
const Patch &p2 = pinfo.patch(patches_[1]);
if (p1.tot_tri() == 1 && p2.tot_tri() == 1) {
if (tris_have_same_verts(mesh, p1.tri(0), p2.tri(0))) {
zero_volume_ = true;
}
}
}
}
/* Information about all the Cells. */
class CellsInfo {
Vector<Cell> cell_;
public:
CellsInfo() = default;
int add_cell()
{
int index = cell_.append_and_get_index(Cell());
return index;
}
Cell &cell(int c)
{
return cell_[c];
}
const Cell &cell(int c) const
{
return cell_[c];
}
int tot_cell() const
{
return cell_.size();
}
IndexRange index_range() const
{
return cell_.index_range();
}
const Cell *begin() const
{
return cell_.begin();
}
const Cell *end() const
{
return cell_.end();
}
Cell *begin()
{
return cell_.begin();
}
Cell *end()
{
return cell_.end();
}
void init_windings(int winding_len)
{
for (Cell &cell : cell_) {
cell.init_winding(winding_len);
}
}
};
/**
* For Debugging: write a .obj file showing the patch/cell structure or just the cells.
*/
static void write_obj_cell_patch(const IMesh &m,
const CellsInfo &cinfo,
const PatchesInfo &pinfo,
bool cells_only,
const std::string &name)
{
/* Would like to use #BKE_tempdir_base() here, but that brings in dependence on kernel library.
* This is just for developer debugging anyway,
* and should never be called in production Blender. */
# ifdef _WIN_32
const char *objdir = BLI_getenv("HOME");
# else
const char *objdir = "/tmp/";
# endif
std::string fname = std::string(objdir) + name + std::string("_cellpatch.obj");
std::ofstream f;
f.open(fname);
if (!f) {
std::cout << "Could not open file " << fname << "\n";
return;
}
/* Copy IMesh so can populate verts. */
IMesh mm = m;
mm.populate_vert();
f << "o cellpatch\n";
for (const Vert *v : mm.vertices()) {
const double3 dv = v->co;
f << "v " << dv[0] << " " << dv[1] << " " << dv[2] << "\n";
}
if (!cells_only) {
for (int p : pinfo.index_range()) {
f << "g patch" << p << "\n";
const Patch &patch = pinfo.patch(p);
for (int t : patch.tris()) {
const Face &tri = *mm.face(t);
f << "f ";
for (const Vert *v : tri) {
f << mm.lookup_vert(v) + 1 << " ";
}
f << "\n";
}
}
}
for (int c : cinfo.index_range()) {
f << "g cell" << c << "\n";
const Cell &cell = cinfo.cell(c);
for (int p : cell.patches()) {
const Patch &patch = pinfo.patch(p);
for (int t : patch.tris()) {
const Face &tri = *mm.face(t);
f << "f ";
for (const Vert *v : tri) {
f << mm.lookup_vert(v) + 1 << " ";
}
f << "\n";
}
}
}
f.close();
}
static void merge_cells(int merge_to, int merge_from, CellsInfo &cinfo, PatchesInfo &pinfo)
{
if (merge_to == merge_from) {
return;
}
Cell &merge_from_cell = cinfo.cell(merge_from);
Cell &merge_to_cell = cinfo.cell(merge_to);
int final_merge_to = merge_to;
while (merge_to_cell.merged_to() != NO_INDEX) {
final_merge_to = merge_to_cell.merged_to();
merge_to_cell = cinfo.cell(final_merge_to);
}
for (Patch &patch : pinfo) {
if (patch.cell_above == merge_from) {
patch.cell_above = final_merge_to;
}
if (patch.cell_below == merge_from) {
patch.cell_below = final_merge_to;
}
}
for (int cell_p : merge_from_cell.patches()) {
merge_to_cell.add_patch_non_duplicates(cell_p);
}
merge_from_cell.set_merged_to(final_merge_to);
}
/**
* Partition the triangles of \a tm into Patches.
*/
static PatchesInfo find_patches(const IMesh &tm, const TriMeshTopology &tmtopo)
{
const int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "\nFIND_PATCHES\n";
}
int ntri = tm.face_size();
PatchesInfo pinfo(ntri);
/* Algorithm: Grow patches across manifold edges as long as there are unassigned triangles. */
Stack<int> cur_patch_grow;
for (int t : tm.face_index_range()) {
if (pinfo.tri_patch(t) == -1) {
cur_patch_grow.push(t);
int cur_patch_index = pinfo.add_patch();
while (!cur_patch_grow.is_empty()) {
int tcand = cur_patch_grow.pop();
if (dbg_level > 1) {
std::cout << "pop tcand = " << tcand << "; assigned = " << pinfo.tri_is_assigned(tcand)
<< "\n";
}
if (pinfo.tri_is_assigned(tcand)) {
continue;
}
if (dbg_level > 1) {
std::cout << "grow patch from seed tcand=" << tcand << "\n";
}
pinfo.grow_patch(cur_patch_index, tcand);
const Face &tri = *tm.face(tcand);
for (int i = 0; i < 3; ++i) {
Edge e(tri[i], tri[(i + 1) % 3]);
int t_other = tmtopo.other_tri_if_manifold(e, tcand);
if (dbg_level > 1) {
std::cout << " edge " << e << " generates t_other=" << t_other << "\n";
}
if (t_other != NO_INDEX) {
if (!pinfo.tri_is_assigned(t_other)) {
if (dbg_level > 1) {
std::cout << " push t_other = " << t_other << "\n";
}
cur_patch_grow.push(t_other);
}
}
else {
/* e is non-manifold. Set any patch-patch incidences we can. */
if (dbg_level > 1) {
std::cout << " e non-manifold case\n";
}
const Vector<int> *etris = tmtopo.edge_tris(e);
if (etris != nullptr) {
for (int i : etris->index_range()) {
int t_other = (*etris)[i];
if (t_other != tcand && pinfo.tri_is_assigned(t_other)) {
int p_other = pinfo.tri_patch(t_other);
if (p_other == cur_patch_index) {
continue;
}
if (pinfo.patch_patch_edge(cur_patch_index, p_other).v0() == nullptr) {
pinfo.add_new_patch_patch_edge(cur_patch_index, p_other, e);
if (dbg_level > 1) {
std::cout << "added patch_patch_edge (" << cur_patch_index << "," << p_other
<< ") = " << e << "\n";
}
}
}
}
}
}
}
}
}
}
if (dbg_level > 0) {
std::cout << "\nafter FIND_PATCHES: found " << pinfo.tot_patch() << " patches\n";
for (int p : pinfo.index_range()) {
std::cout << p << ": " << pinfo.patch(p) << "\n";
}
if (dbg_level > 1) {
std::cout << "\ntriangle map\n";
for (int t : tm.face_index_range()) {
std::cout << t << ": " << tm.face(t) << " patch " << pinfo.tri_patch(t) << "\n";
}
}
std::cout << "\npatch-patch incidences\n";
for (int p1 : pinfo.index_range()) {
for (int p2 : pinfo.index_range()) {
Edge e = pinfo.patch_patch_edge(p1, p2);
if (e.v0() != nullptr) {
std::cout << "p" << p1 << " and p" << p2 << " share edge " << e << "\n";
}
}
}
}
return pinfo;
}
/**
* If e is an edge in tri, return the vertex that isn't part of tri,
* the "flap" vertex, or nullptr if e is not part of tri.
* Also, e may be reversed in tri.
* Set *r_rev to true if it is reversed, else false.
*/
static const Vert *find_flap_vert(const Face &tri, const Edge e, bool *r_rev)
{
*r_rev = false;
const Vert *flapv;
if (tri[0] == e.v0()) {
if (tri[1] == e.v1()) {
*r_rev = false;
flapv = tri[2];
}
else {
if (tri[2] != e.v1()) {
return nullptr;
}
*r_rev = true;
flapv = tri[1];
}
}
else if (tri[1] == e.v0()) {
if (tri[2] == e.v1()) {
*r_rev = false;
flapv = tri[0];
}
else {
if (tri[0] != e.v1()) {
return nullptr;
}
*r_rev = true;
flapv = tri[2];
}
}
else {
if (tri[2] != e.v0()) {
return nullptr;
}
if (tri[0] == e.v1()) {
*r_rev = false;
flapv = tri[1];
}
else {
if (tri[1] != e.v1()) {
return nullptr;
}
*r_rev = true;
flapv = tri[0];
}
}
return flapv;
}
/**
* Triangle \a tri and tri0 share edge e.
* Classify \a tri with respect to tri0 as described in
* sort_tris_around_edge, and return 1, 2, 3, or 4 as \a tri is:
* (1) co-planar with tri0 and on same side of e
* (2) co-planar with tri0 and on opposite side of e
* (3) below plane of tri0
* (4) above plane of tri0
* For "above" and "below", we use the orientation of non-reversed
* orientation of tri0.
* Because of the way the intersect mesh was made, we can assume
* that if a triangle is in class 1 then it is has the same flap vert
* as tri0.
*/
static int sort_tris_class(const Face &tri, const Face &tri0, const Edge e)
{
const int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "classify e = " << e << "\n";
}
mpq3 a0 = tri0[0]->co_exact;
mpq3 a1 = tri0[1]->co_exact;
mpq3 a2 = tri0[2]->co_exact;
bool rev;
bool rev0;
const Vert *flapv0 = find_flap_vert(tri0, e, &rev0);
const Vert *flapv = find_flap_vert(tri, e, &rev);
if (dbg_level > 0) {
std::cout << " t0 = " << tri0[0] << " " << tri0[1] << " " << tri0[2];
std::cout << " rev0 = " << rev0 << " flapv0 = " << flapv0 << "\n";
std::cout << " t = " << tri[0] << " " << tri[1] << " " << tri[2];
std::cout << " rev = " << rev << " flapv = " << flapv << "\n";
}
BLI_assert(flapv != nullptr && flapv0 != nullptr);
const mpq3 flap = flapv->co_exact;
/* orient will be positive if flap is below oriented plane of a0,a1,a2. */
int orient = orient3d(a0, a1, a2, flap);
int ans;
if (orient > 0) {
ans = rev0 ? 4 : 3;
}
else if (orient < 0) {
ans = rev0 ? 3 : 4;
}
else {
ans = flapv == flapv0 ? 1 : 2;
}
if (dbg_level > 0) {
std::cout << " orient = " << orient << " ans = " << ans << "\n";
}
return ans;
}
constexpr int EXTRA_TRI_INDEX = INT_MAX;
/**
* To ensure consistent ordering of co-planar triangles if they happen to be sorted around
* more than one edge, sort the triangle indices in g (in place) by their index -- but also apply
* a sign to the index: positive if the triangle has edge e in the same orientation,
* otherwise negative.
*/
static void sort_by_signed_triangle_index(Vector<int> &g,
const Edge e,
const IMesh &tm,
const Face *extra_tri)
{
Array<int> signed_g(g.size());
for (int i : g.index_range()) {
const Face &tri = g[i] == EXTRA_TRI_INDEX ? *extra_tri : *tm.face(g[i]);
bool rev;
find_flap_vert(tri, e, &rev);
signed_g[i] = rev ? -g[i] : g[i];
}
std::sort(signed_g.begin(), signed_g.end());
for (int i : g.index_range()) {
g[i] = abs(signed_g[i]);
}
}
/**
* Sort the triangles \a tris, which all share edge e, as they appear
* geometrically clockwise when looking down edge e.
* Triangle t0 is the first triangle in the top-level call
* to this recursive routine. The merge step below differs
* for the top level call and all the rest, so this distinguishes those cases.
* Care is taken in the case of duplicate triangles to have
* an ordering that is consistent with that which would happen
* if another edge of the triangle were sorted around.
*
* We sometimes need to do this with an extra triangle that is not part of tm.
* To accommodate this:
* If extra_tri is non-null, then an index of EXTRA_TRI_INDEX should use it for the triangle.
*/
static Array<int> sort_tris_around_edge(const IMesh &tm,
const TriMeshTopology &tmtopo,
const Edge e,
const Span<int> tris,
const int t0,
const Face *extra_tri)
{
/* Divide and conquer, quick-sort-like sort.
* Pick a triangle t0, then partition into groups:
* (1) co-planar with t0 and on same side of e
* (2) co-planar with t0 and on opposite side of e
* (3) below plane of t0
* (4) above plane of t0
* Each group is sorted and then the sorts are merged to give the answer.
* We don't expect the input array to be very large - should typically
* be only 3 or 4 - so OK to make copies of arrays instead of swapping
* around in a single array. */
const int dbg_level = 0;
if (tris.size() == 0) {
return Array<int>();
}
if (dbg_level > 0) {
if (t0 == tris[0]) {
std::cout << "\n";
}
std::cout << "sort_tris_around_edge " << e << "\n";
std::cout << "tris = " << tris << "\n";
std::cout << "t0 = " << t0 << "\n";
}
Vector<int> g1{tris[0]};
Vector<int> g2;
Vector<int> g3;
Vector<int> g4;
std::array<Vector<int> *, 4> groups = {&g1, &g2, &g3, &g4};
const Face &triref = *tm.face(tris[0]);
for (int i : tris.index_range()) {
if (i == 0) {
continue;
}
int t = tris[i];
BLI_assert(t < tm.face_size() || (t == EXTRA_TRI_INDEX && extra_tri != nullptr));
const Face &tri = (t == EXTRA_TRI_INDEX) ? *extra_tri : *tm.face(t);
if (dbg_level > 2) {
std::cout << "classifying tri " << t << " with respect to " << tris[0] << "\n";
}
int group_num = sort_tris_class(tri, triref, e);
if (dbg_level > 2) {
std::cout << " classify result : " << group_num << "\n";
}
groups[group_num - 1]->append(t);
}
if (dbg_level > 1) {
std::cout << "g1 = " << g1 << "\n";
std::cout << "g2 = " << g2 << "\n";
std::cout << "g3 = " << g3 << "\n";
std::cout << "g4 = " << g4 << "\n";
}
if (g1.size() > 1) {
sort_by_signed_triangle_index(g1, e, tm, extra_tri);
if (dbg_level > 1) {
std::cout << "g1 sorted: " << g1 << "\n";
}
}
if (g2.size() > 1) {
sort_by_signed_triangle_index(g2, e, tm, extra_tri);
if (dbg_level > 1) {
std::cout << "g2 sorted: " << g2 << "\n";
}
}
if (g3.size() > 1) {
Array<int> g3sorted = sort_tris_around_edge(tm, tmtopo, e, g3, t0, extra_tri);
std::copy(g3sorted.begin(), g3sorted.end(), g3.begin());
if (dbg_level > 1) {
std::cout << "g3 sorted: " << g3 << "\n";
}
}
if (g4.size() > 1) {
Array<int> g4sorted = sort_tris_around_edge(tm, tmtopo, e, g4, t0, extra_tri);
std::copy(g4sorted.begin(), g4sorted.end(), g4.begin());
if (dbg_level > 1) {
std::cout << "g4 sorted: " << g4 << "\n";
}
}
int group_tot_size = g1.size() + g2.size() + g3.size() + g4.size();
Array<int> ans(group_tot_size);
int *p = ans.begin();
if (tris[0] == t0) {
p = std::copy(g1.begin(), g1.end(), p);
p = std::copy(g4.begin(), g4.end(), p);
p = std::copy(g2.begin(), g2.end(), p);
std::copy(g3.begin(), g3.end(), p);
}
else {
p = std::copy(g3.begin(), g3.end(), p);
p = std::copy(g1.begin(), g1.end(), p);
p = std::copy(g4.begin(), g4.end(), p);
std::copy(g2.begin(), g2.end(), p);
}
if (dbg_level > 0) {
std::cout << "sorted tris = " << ans << "\n";
}
return ans;
}
/**
* Find the Cells around edge e.
* This possibly makes new cells in \a cinfo, and sets up the
* bipartite graph edges between cells and patches.
* Will modify \a pinfo and \a cinfo and the patches and cells they contain.
*/
static void find_cells_from_edge(const IMesh &tm,
const TriMeshTopology &tmtopo,
PatchesInfo &pinfo,
CellsInfo &cinfo,
const Edge e)
{
const int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_CELLS_FROM_EDGE " << e << "\n";
}
const Vector<int> *edge_tris = tmtopo.edge_tris(e);
BLI_assert(edge_tris != nullptr);
Array<int> sorted_tris = sort_tris_around_edge(
tm, tmtopo, e, Span<int>(*edge_tris), (*edge_tris)[0], nullptr);
int n_edge_tris = edge_tris->size();
Array<int> edge_patches(n_edge_tris);
for (int i = 0; i < n_edge_tris; ++i) {
edge_patches[i] = pinfo.tri_patch(sorted_tris[i]);
if (dbg_level > 1) {
std::cout << "edge_patches[" << i << "] = " << edge_patches[i] << "\n";
}
}
for (int i = 0; i < n_edge_tris; ++i) {
int inext = (i + 1) % n_edge_tris;
int r_index = edge_patches[i];
int rnext_index = edge_patches[inext];
Patch &r = pinfo.patch(r_index);
Patch &rnext = pinfo.patch(rnext_index);
bool r_flipped;
bool rnext_flipped;
find_flap_vert(*tm.face(sorted_tris[i]), e, &r_flipped);
find_flap_vert(*tm.face(sorted_tris[inext]), e, &rnext_flipped);
int *r_follow_cell = r_flipped ? &r.cell_below : &r.cell_above;
int *rnext_prev_cell = rnext_flipped ? &rnext.cell_above : &rnext.cell_below;
if (dbg_level > 0) {
std::cout << "process patch pair " << r_index << " " << rnext_index << "\n";
std::cout << " r_flipped = " << r_flipped << " rnext_flipped = " << rnext_flipped << "\n";
std::cout << " r_follow_cell (" << (r_flipped ? "below" : "above")
<< ") = " << *r_follow_cell << "\n";
std::cout << " rnext_prev_cell (" << (rnext_flipped ? "above" : "below")
<< ") = " << *rnext_prev_cell << "\n";
}
if (*r_follow_cell == NO_INDEX && *rnext_prev_cell == NO_INDEX) {
/* Neither is assigned: make a new cell. */
int c = cinfo.add_cell();
*r_follow_cell = c;
*rnext_prev_cell = c;
Cell &cell = cinfo.cell(c);
cell.add_patch(r_index);
cell.add_patch(rnext_index);
cell.check_for_zero_volume(pinfo, tm);
if (dbg_level > 0) {
std::cout << " made new cell " << c << "\n";
std::cout << " p" << r_index << "." << (r_flipped ? "cell_below" : "cell_above") << " = c"
<< c << "\n";
std::cout << " p" << rnext_index << "." << (rnext_flipped ? "cell_above" : "cell_below")
<< " = c" << c << "\n";
}
}
else if (*r_follow_cell != NO_INDEX && *rnext_prev_cell == NO_INDEX) {
int c = *r_follow_cell;
*rnext_prev_cell = c;
Cell &cell = cinfo.cell(c);
cell.add_patch(rnext_index);
cell.check_for_zero_volume(pinfo, tm);
if (dbg_level > 0) {
std::cout << " reuse r_follow: p" << rnext_index << "."
<< (rnext_flipped ? "cell_above" : "cell_below") << " = c" << c << "\n";
}
}
else if (*r_follow_cell == NO_INDEX && *rnext_prev_cell != NO_INDEX) {
int c = *rnext_prev_cell;
*r_follow_cell = c;
Cell &cell = cinfo.cell(c);
cell.add_patch(r_index);
cell.check_for_zero_volume(pinfo, tm);
if (dbg_level > 0) {
std::cout << " reuse rnext prev: rprev_p" << r_index << "."
<< (r_flipped ? "cell_below" : "cell_above") << " = c" << c << "\n";
}
}
else {
if (*r_follow_cell != *rnext_prev_cell) {
if (dbg_level > 0) {
std::cout << " merge cell " << *rnext_prev_cell << " into cell " << *r_follow_cell
<< "\n";
}
merge_cells(*r_follow_cell, *rnext_prev_cell, cinfo, pinfo);
}
}
}
}
/**
* Find the partition of 3-space into Cells.
* This assigns the cell_above and cell_below for each Patch.
*/
static CellsInfo find_cells(const IMesh &tm, const TriMeshTopology &tmtopo, PatchesInfo &pinfo)
{
const int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "\nFIND_CELLS\n";
}
CellsInfo cinfo;
/* For each unique edge shared between patch pairs, process it. */
Set<Edge> processed_edges;
int np = pinfo.tot_patch();
for (int p = 0; p < np; ++p) {
for (int q = p + 1; q < np; ++q) {
Edge e = pinfo.patch_patch_edge(p, q);
if (e.v0() != nullptr) {
if (!processed_edges.contains(e)) {
processed_edges.add_new(e);
find_cells_from_edge(tm, tmtopo, pinfo, cinfo, e);
}
}
}
}
/* Some patches may have no cells at this point. These are either:
* (a) a closed manifold patch only incident on itself (sphere, torus, klein bottle, etc.).
* (b) an open manifold patch only incident on itself (has non-manifold boundaries).
* Make above and below cells for these patches. This will create a disconnected patch-cell
* bipartite graph, which will have to be fixed later. */
for (int p : pinfo.index_range()) {
Patch &patch = pinfo.patch(p);
if (patch.cell_above == NO_INDEX) {
int c = cinfo.add_cell();
patch.cell_above = c;
Cell &cell = cinfo.cell(c);
cell.add_patch(p);
}
if (patch.cell_below == NO_INDEX) {
int c = cinfo.add_cell();
patch.cell_below = c;
Cell &cell = cinfo.cell(c);
cell.add_patch(p);
}
}
if (dbg_level > 0) {
std::cout << "\nFIND_CELLS found " << cinfo.tot_cell() << " cells\nCells\n";
for (int i : cinfo.index_range()) {
std::cout << i << ": " << cinfo.cell(i) << "\n";
}
std::cout << "Patches\n";
for (int i : pinfo.index_range()) {
std::cout << i << ": " << pinfo.patch(i) << "\n";
}
if (dbg_level > 1) {
write_obj_cell_patch(tm, cinfo, pinfo, false, "postfindcells");
}
}
return cinfo;
}
/**
* Find the connected patch components (connects are via intermediate cells), and put
* component numbers in each patch.
* Return a Vector of components - each a Vector of the patch ids in the component.
*/
static Vector<Vector<int>> find_patch_components(const CellsInfo &cinfo, PatchesInfo &pinfo)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_PATCH_COMPONENTS\n";
}
if (pinfo.tot_patch() == 0) {
return Vector<Vector<int>>();
}
int current_component = 0;
Stack<int> stack; /* Patch indices to visit. */
Vector<Vector<int>> ans;
for (int pstart : pinfo.index_range()) {
Patch &patch_pstart = pinfo.patch(pstart);
if (patch_pstart.component != NO_INDEX) {
continue;
}
ans.append(Vector<int>());
ans[current_component].append(pstart);
stack.push(pstart);
patch_pstart.component = current_component;
while (!stack.is_empty()) {
int p = stack.pop();
Patch &patch = pinfo.patch(p);
BLI_assert(patch.component == current_component);
for (int c : {patch.cell_above, patch.cell_below}) {
for (int pn : cinfo.cell(c).patches()) {
Patch &patch_neighbor = pinfo.patch(pn);
if (patch_neighbor.component == NO_INDEX) {
patch_neighbor.component = current_component;
stack.push(pn);
ans[current_component].append(pn);
}
}
}
}
++current_component;
}
if (dbg_level > 0) {
std::cout << "found " << ans.size() << " components\n";
for (int comp : ans.index_range()) {
std::cout << comp << ": " << ans[comp] << "\n";
}
}
return ans;
}
/**
* Do all patches have cell_above and cell_below set?
* Is the bipartite graph connected?
*/
static bool patch_cell_graph_ok(const CellsInfo &cinfo, const PatchesInfo &pinfo)
{
for (int c : cinfo.index_range()) {
const Cell &cell = cinfo.cell(c);
if (cell.merged_to() != NO_INDEX) {
continue;
}
if (cell.patches().size() == 0) {
std::cout << "Patch/Cell graph disconnected at Cell " << c << " with no patches\n";
return false;
}
for (int p : cell.patches()) {
if (p >= pinfo.tot_patch()) {
std::cout << "Patch/Cell graph has bad patch index at Cell " << c << "\n";
return false;
}
}
}
for (int p : pinfo.index_range()) {
const Patch &patch = pinfo.patch(p);
if (patch.cell_above == NO_INDEX || patch.cell_below == NO_INDEX) {
std::cout << "Patch/Cell graph disconnected at Patch " << p
<< " with one or two missing cells\n";
return false;
}
if (patch.cell_above >= cinfo.tot_cell() || patch.cell_below >= cinfo.tot_cell()) {
std::cout << "Patch/Cell graph has bad cell index at Patch " << p << "\n";
return false;
}
}
return true;
}
/**
* Is trimesh tm PWN ("Piece-wise constant Winding Number")?
* See Zhou et al. paper for exact definition, but roughly
* means that the faces connect so as to form closed volumes.
* The actual definition says that if you calculate the
* generalized winding number of every point not exactly on
* the mesh, it will always be an integer.
* Necessary (but not sufficient) conditions that a mesh be PWN:
* No edges with a non-zero sum of incident face directions.
* I think that cases like Klein bottles are likely to satisfy
* this without being PWN. So this routine will be only
* approximately right.
*/
static bool is_pwn(const IMesh &tm, const TriMeshTopology &tmtopo)
{
constexpr int dbg_level = 0;
for (auto item : tmtopo.edge_tri_map_items()) {
const Edge &edge = item.key;
int tot_orient = 0;
/* For each face t attached to edge, add +1 if the edge
* is positively in t, and -1 if negatively in t. */
for (int t : *item.value) {
const Face &face = *tm.face(t);
BLI_assert(face.size() == 3);
for (int i : face.index_range()) {
if (face[i] == edge.v0()) {
if (face[(i + 1) % 3] == edge.v1()) {
++tot_orient;
}
else {
BLI_assert(face[(i + 3 - 1) % 3] == edge.v1());
--tot_orient;
}
}
}
}
if (tot_orient != 0) {
if (dbg_level > 0) {
std::cout << "edge causing non-pwn: " << edge << "\n";
}
return false;
}
}
return true;
}
/**
* Find which of the cells around edge e contains point p.
* Do this by inserting a dummy triangle containing v and sorting the
* triangles around the edge to find out where in the sort order
* the dummy triangle lies, then finding which cell is between
* the two triangles on either side of the dummy.
*/
static int find_cell_for_point_near_edge(mpq3 p,
const Edge &e,
const IMesh &tm,
const TriMeshTopology &tmtopo,
const PatchesInfo &pinfo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_CELL_FOR_POINT_NEAR_EDGE, p=" << p << " e=" << e << "\n";
}
const Vector<int> *etris = tmtopo.edge_tris(e);
const Vert *dummy_vert = arena->add_or_find_vert(p, NO_INDEX);
const Face *dummy_tri = arena->add_face({e.v0(), e.v1(), dummy_vert},
NO_INDEX,
{NO_INDEX, NO_INDEX, NO_INDEX},
{false, false, false});
BLI_assert(etris != nullptr);
Array<int> edge_tris(etris->size() + 1);
std::copy(etris->begin(), etris->end(), edge_tris.begin());
edge_tris[edge_tris.size() - 1] = EXTRA_TRI_INDEX;
Array<int> sorted_tris = sort_tris_around_edge(
tm, tmtopo, e, edge_tris, edge_tris[0], dummy_tri);
if (dbg_level > 0) {
std::cout << "sorted tris = " << sorted_tris << "\n";
}
int *p_sorted_dummy = std::find(sorted_tris.begin(), sorted_tris.end(), EXTRA_TRI_INDEX);
BLI_assert(p_sorted_dummy != sorted_tris.end());
int dummy_index = p_sorted_dummy - sorted_tris.begin();
int prev_tri = (dummy_index == 0) ? sorted_tris[sorted_tris.size() - 1] :
sorted_tris[dummy_index - 1];
int next_tri = (dummy_index == sorted_tris.size() - 1) ? sorted_tris[0] :
sorted_tris[dummy_index + 1];
if (dbg_level > 0) {
std::cout << "prev tri to dummy = " << prev_tri << "; next tri to dummy = " << next_tri
<< "\n";
}
const Patch &prev_patch = pinfo.patch(pinfo.tri_patch(prev_tri));
if (dbg_level > 0) {
std::cout << "prev_patch = " << prev_patch << "\n";
}
bool prev_flipped;
find_flap_vert(*tm.face(prev_tri), e, &prev_flipped);
int c = prev_flipped ? prev_patch.cell_below : prev_patch.cell_above;
if (dbg_level > 0) {
std::cout << "find_cell_for_point_near_edge returns " << c << "\n";
}
return c;
}
/**
* Find the ambient cell -- that is, the cell that is outside
* all other cells.
* If component_patches != nullptr, restrict consideration to patches
* in that vector.
*
* The method is to find an edge known to be on the convex hull
* of the mesh, then insert a dummy triangle that has that edge
* and a point known to be outside the whole mesh. Then sorting
* the triangles around the edge will reveal where the dummy triangle
* fits in that sorting order, and hence, the two adjacent patches
* to the dummy triangle - thus revealing the cell that the point
* known to be outside the whole mesh is in.
*/
static int find_ambient_cell(const IMesh &tm,
const Vector<int> *component_patches,
const TriMeshTopology &tmtopo,
const PatchesInfo &pinfo,
IMeshArena *arena)
{
int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_AMBIENT_CELL\n";
}
/* First find a vertex with the maximum x value. */
/* Prefer not to populate the verts in the #IMesh just for this. */
const Vert *v_extreme;
mpq_class extreme_x;
if (component_patches == nullptr) {
v_extreme = (*tm.face(0))[0];
extreme_x = v_extreme->co_exact.x;
for (const Face *f : tm.faces()) {
for (const Vert *v : *f) {
const mpq_class &x = v->co_exact.x;
if (x > extreme_x) {
v_extreme = v;
extreme_x = x;
}
}
}
}
else {
if (dbg_level > 0) {
std::cout << "restrict to patches " << *component_patches << "\n";
}
int p0 = (*component_patches)[0];
v_extreme = (*tm.face(pinfo.patch(p0).tri(0)))[0];
extreme_x = v_extreme->co_exact.x;
for (int p : *component_patches) {
for (int t : pinfo.patch(p).tris()) {
const Face *f = tm.face(t);
for (const Vert *v : *f) {
const mpq_class &x = v->co_exact.x;
if (x > extreme_x) {
v_extreme = v;
extreme_x = x;
}
}
}
}
}
if (dbg_level > 0) {
std::cout << "v_extreme = " << v_extreme << "\n";
}
/* Find edge attached to v_extreme with max absolute slope
* when projected onto the XY plane. That edge is guaranteed to
* be on the convex hull of the mesh. */
const Vector<Edge> &edges = tmtopo.vert_edges(v_extreme);
const mpq_class extreme_y = v_extreme->co_exact.y;
Edge ehull;
mpq_class max_abs_slope = -1;
for (Edge e : edges) {
const Vert *v_other = (e.v0() == v_extreme) ? e.v1() : e.v0();
const mpq3 &co_other = v_other->co_exact;
mpq_class delta_x = co_other.x - extreme_x;
if (delta_x == 0) {
/* Vertical slope. */
ehull = e;
break;
}
mpq_class abs_slope = abs((co_other.y - extreme_y) / delta_x);
if (abs_slope > max_abs_slope) {
ehull = e;
max_abs_slope = abs_slope;
}
}
if (dbg_level > 0) {
std::cout << "ehull = " << ehull << " slope = " << max_abs_slope << "\n";
}
/* Sort triangles around ehull, including a dummy triangle that include a known point in ambient
* cell. */
mpq3 p_in_ambient = v_extreme->co_exact;
p_in_ambient.x += 1;
int c_ambient = find_cell_for_point_near_edge(p_in_ambient, ehull, tm, tmtopo, pinfo, arena);
if (dbg_level > 0) {
std::cout << "FIND_AMBIENT_CELL returns " << c_ambient << "\n";
}
return c_ambient;
}
/**
* We need an edge on the convex hull of the edges incident on \a closestp
* in order to sort around, including a dummy triangle that has \a testp and
* the sorting edge vertices. So we don't want an edge that is co-linear
* with the line through \a testp and \a closestp.
* The method is to project onto a plane that contains `testp-closestp`,
* and then choose the edge that, when projected, has the maximum absolute
* slope (regarding the line `testp-closestp` as the x-axis for slope computation).
*/
static Edge find_good_sorting_edge(const Vert *testp,
const Vert *closestp,
const TriMeshTopology &tmtopo)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_GOOD_SORTING_EDGE testp = " << testp << ", closestp = " << closestp << "\n";
}
/* We want to project the edges incident to closestp onto a plane
* whose ordinate direction will be regarded as going from closestp to testp,
* and whose abscissa direction is some perpendicular to that.
* A perpendicular direction can be found by swapping two coordinates
* and negating one, and zeroing out the third, being careful that one
* of the swapped vertices is non-zero. */
const mpq3 &co_closest = closestp->co_exact;
const mpq3 &co_test = testp->co_exact;
BLI_assert(co_test != co_closest);
mpq3 abscissa = co_test - co_closest;
/* Find a non-zero-component axis of abscissa. */
int axis;
for (axis = 0; axis < 3; ++axis) {
if (abscissa[axis] != 0) {
break;
}
}
BLI_assert(axis < 3);
int axis_next = (axis + 1) % 3;
int axis_next_next = (axis_next + 1) % 3;
mpq3 ordinate;
ordinate[axis] = abscissa[axis_next];
ordinate[axis_next] = -abscissa[axis];
ordinate[axis_next_next] = 0;
/* By construction, dot(abscissa, ordinate) == 0, so they are perpendicular. */
mpq3 normal = mpq3::cross(abscissa, ordinate);
if (dbg_level > 0) {
std::cout << "abscissa = " << abscissa << "\n";
std::cout << "ordinate = " << ordinate << "\n";
std::cout << "normal = " << normal << "\n";
}
mpq_class nlen2 = normal.length_squared();
mpq_class max_abs_slope = -1;
Edge esort;
const Vector<Edge> &edges = tmtopo.vert_edges(closestp);
for (Edge e : edges) {
const Vert *v_other = (e.v0() == closestp) ? e.v1() : e.v0();
const mpq3 &co_other = v_other->co_exact;
mpq3 evec = co_other - co_closest;
/* Get projection of evec onto plane of abscissa and ordinate. */
mpq3 proj_evec = evec - (mpq3::dot(evec, normal) / nlen2) * normal;
/* The projection calculations along the abscissa and ordinate should
* be scaled by 1/abscissa and 1/ordinate respectively,
* but we can skip: it won't affect which `evec` has the maximum slope. */
mpq_class evec_a = mpq3::dot(proj_evec, abscissa);
mpq_class evec_o = mpq3::dot(proj_evec, ordinate);
if (dbg_level > 0) {
std::cout << "e = " << e << "\n";
std::cout << "v_other = " << v_other << "\n";
std::cout << "evec = " << evec << ", proj_evec = " << proj_evec << "\n";
std::cout << "evec_a = " << evec_a << ", evec_o = " << evec_o << "\n";
}
if (evec_a == 0) {
/* evec is perpendicular to abscissa. */
esort = e;
if (dbg_level > 0) {
std::cout << "perpendicular esort is " << esort << "\n";
}
break;
}
mpq_class abs_slope = abs(evec_o / evec_a);
if (abs_slope > max_abs_slope) {
esort = e;
max_abs_slope = abs_slope;
if (dbg_level > 0) {
std::cout << "with abs_slope " << abs_slope << " new esort is " << esort << "\n";
}
}
}
return esort;
}
/**
* Find the cell that contains v. Consider the cells adjacent to triangle t.
* The close_edge and close_vert values are what were returned by
* #closest_on_tri_to_point when determining that v was close to t.
* They will indicate whether the point of closest approach to t is to
* an edge of t, a vertex of t, or somewhere inside t.
*
* The algorithm is similar to the one for find_ambient_cell, except that
* instead of an arbitrary point known to be outside the whole mesh, we
* have a particular point (v) and we just want to determine the patches
* that that point is between in sorting-around-an-edge order.
*/
static int find_containing_cell(const Vert *v,
int t,
int close_edge,
int close_vert,
const PatchesInfo &pinfo,
const IMesh &tm,
const TriMeshTopology &tmtopo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_CONTAINING_CELL v=" << v << ", t=" << t << "\n";
}
const Face &tri = *tm.face(t);
Edge etest;
if (close_edge == -1 && close_vert == -1) {
/* Choose any edge if closest point is inside the triangle. */
close_edge = 0;
}
if (close_edge != -1) {
const Vert *v0 = tri[close_edge];
const Vert *v1 = tri[(close_edge + 1) % 3];
const Vector<Edge> &edges = tmtopo.vert_edges(v0);
if (dbg_level > 0) {
std::cout << "look for edge containing " << v0 << " and " << v1 << "\n";
std::cout << " in edges: ";
for (Edge e : edges) {
std::cout << e << " ";
}
std::cout << "\n";
}
for (Edge e : edges) {
if ((e.v0() == v0 && e.v1() == v1) || (e.v0() == v1 && e.v1() == v0)) {
etest = e;
break;
}
}
}
else {
int cv = close_vert;
const Vert *vert_cv = tri[cv];
if (vert_cv == v) {
/* Need to use another one to find sorting edge. */
vert_cv = tri[(cv + 1) % 3];
BLI_assert(vert_cv != v);
}
etest = find_good_sorting_edge(v, vert_cv, tmtopo);
}
BLI_assert(etest.v0() != nullptr);
if (dbg_level > 0) {
std::cout << "etest = " << etest << "\n";
}
int c = find_cell_for_point_near_edge(v->co_exact, etest, tm, tmtopo, pinfo, arena);
if (dbg_level > 0) {
std::cout << "find_containing_cell returns " << c << "\n";
}
return c;
}
/**
* Find the closest point in triangle (a, b, c) to point p.
* Return the distance squared to that point.
* Also, if the closest point in the triangle is on a vertex,
* return 0, 1, or 2 for a, b, c in *r_vert; else -1.
* If the closest point is on an edge, return 0, 1, or 2
* for edges ab, bc, or ca in *r_edge; else -1.
* (Adapted from #closest_on_tri_to_point_v3()).
*/
static mpq_class closest_on_tri_to_point(
const mpq3 &p, const mpq3 &a, const mpq3 &b, const mpq3 &c, int *r_edge, int *r_vert)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "CLOSEST_ON_TRI_TO_POINT p = " << p << "\n";
std::cout << " a = " << a << ", b = " << b << ", c = " << c << "\n";
}
/* Check if p in vertex region outside a. */
mpq3 ab = b - a;
mpq3 ac = c - a;
mpq3 ap = p - a;
mpq_class d1 = mpq3::dot(ab, ap);
mpq_class d2 = mpq3::dot(ac, ap);
if (d1 <= 0 && d2 <= 0) {
/* Barycentric coordinates (1,0,0). */
*r_edge = -1;
*r_vert = 0;
if (dbg_level > 0) {
std::cout << " answer = a\n";
}
return mpq3::distance_squared(p, a);
}
/* Check if p in vertex region outside b. */
mpq3 bp = p - b;
mpq_class d3 = mpq3::dot(ab, bp);
mpq_class d4 = mpq3::dot(ac, bp);
if (d3 >= 0 && d4 <= d3) {
/* Barycentric coordinates (0,1,0). */
*r_edge = -1;
*r_vert = 1;
if (dbg_level > 0) {
std::cout << " answer = b\n";
}
return mpq3::distance_squared(p, b);
}
/* Check if p in region of ab. */
mpq_class vc = d1 * d4 - d3 * d2;
if (vc <= 0 && d1 >= 0 && d3 <= 0) {
mpq_class v = d1 / (d1 - d3);
/* Barycentric coordinates (1-v,v,0). */
mpq3 r = a + v * ab;
*r_vert = -1;
*r_edge = 0;
if (dbg_level > 0) {
std::cout << " answer = on ab at " << r << "\n";
}
return mpq3::distance_squared(p, r);
}
/* Check if p in vertex region outside c. */
mpq3 cp = p - c;
mpq_class d5 = mpq3::dot(ab, cp);
mpq_class d6 = mpq3::dot(ac, cp);
if (d6 >= 0 && d5 <= d6) {
/* Barycentric coordinates (0,0,1). */
*r_edge = -1;
*r_vert = 2;
if (dbg_level > 0) {
std::cout << " answer = c\n";
}
return mpq3::distance_squared(p, c);
}
/* Check if p in edge region of ac. */
mpq_class vb = d5 * d2 - d1 * d6;
if (vb <= 0 && d2 >= 0 && d6 <= 0) {
mpq_class w = d2 / (d2 - d6);
/* Barycentric coordinates (1-w,0,w). */
mpq3 r = a + w * ac;
*r_vert = -1;
*r_edge = 2;
if (dbg_level > 0) {
std::cout << " answer = on ac at " << r << "\n";
}
return mpq3::distance_squared(p, r);
}
/* Check if p in edge region of bc. */
mpq_class va = d3 * d6 - d5 * d4;
if (va <= 0 && (d4 - d3) >= 0 && (d5 - d6) >= 0) {
mpq_class w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
/* Barycentric coordinates (0,1-w,w). */
mpq3 r = c - b;
r = w * r;
r = r + b;
*r_vert = -1;
*r_edge = 1;
if (dbg_level > 0) {
std::cout << " answer = on bc at " << r << "\n";
}
return mpq3::distance_squared(p, r);
}
/* p inside face region. Compute barycentric coordinates (u,v,w). */
mpq_class denom = 1 / (va + vb + vc);
mpq_class v = vb * denom;
mpq_class w = vc * denom;
ac = w * ac;
mpq3 r = a + v * ab;
r = r + ac;
*r_vert = -1;
*r_edge = -1;
if (dbg_level > 0) {
std::cout << " answer = inside at " << r << "\n";
}
return mpq3::distance_squared(p, r);
}
struct ComponentContainer {
int containing_component{NO_INDEX};
int nearest_cell{NO_INDEX};
mpq_class dist_to_cell;
ComponentContainer(int cc, int cell, mpq_class d)
: containing_component(cc), nearest_cell(cell), dist_to_cell(d)
{
}
};
/**
* Find out all the components, not equal to comp, that contain a point
* in comp in a non-ambient cell of those components.
* In other words, find the components that comp is nested inside
* (maybe not directly nested, which is why there can be more than one).
*/
static Vector<ComponentContainer> find_component_containers(int comp,
const Vector<Vector<int>> &components,
const Array<int> &ambient_cell,
const IMesh &tm,
const PatchesInfo &pinfo,
const TriMeshTopology &tmtopo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FIND_COMPONENT_CONTAINERS for comp " << comp << "\n";
}
Vector<ComponentContainer> ans;
int test_p = components[comp][0];
int test_t = pinfo.patch(test_p).tri(0);
const Vert *test_v = tm.face(test_t)[0].vert[0];
if (dbg_level > 0) {
std::cout << "test vertex in comp: " << test_v << "\n";
}
for (int comp_other : components.index_range()) {
if (comp == comp_other) {
continue;
}
if (dbg_level > 0) {
std::cout << "comp_other = " << comp_other << "\n";
}
int nearest_tri = NO_INDEX;
int nearest_tri_close_vert = -1;
int nearest_tri_close_edge = -1;
mpq_class nearest_tri_dist_squared;
for (int p : components[comp_other]) {
const Patch &patch = pinfo.patch(p);
for (int t : patch.tris()) {
const Face &tri = *tm.face(t);
if (dbg_level > 1) {
std::cout << "tri " << t << " = " << &tri << "\n";
}
int close_vert;
int close_edge;
mpq_class d2 = closest_on_tri_to_point(test_v->co_exact,
tri[0]->co_exact,
tri[1]->co_exact,
tri[2]->co_exact,
&close_edge,
&close_vert);
if (dbg_level > 1) {
std::cout << " close_edge=" << close_edge << " close_vert=" << close_vert
<< " dsquared=" << d2.get_d() << "\n";
}
if (nearest_tri == NO_INDEX || d2 < nearest_tri_dist_squared) {
nearest_tri = t;
nearest_tri_close_edge = close_edge;
nearest_tri_close_vert = close_vert;
nearest_tri_dist_squared = d2;
}
}
}
if (dbg_level > 0) {
std::cout << "closest tri to comp=" << comp << " in comp_other=" << comp_other << " is t"
<< nearest_tri << "\n";
const Face *tn = tm.face(nearest_tri);
std::cout << "tri = " << tn << "\n";
std::cout << " (" << tn->vert[0]->co << "," << tn->vert[1]->co << "," << tn->vert[2]->co
<< ")\n";
}
int containing_cell = find_containing_cell(test_v,
nearest_tri,
nearest_tri_close_edge,
nearest_tri_close_vert,
pinfo,
tm,
tmtopo,
arena);
if (dbg_level > 0) {
std::cout << "containing cell = " << containing_cell << "\n";
}
if (containing_cell != ambient_cell[comp_other]) {
ans.append(ComponentContainer(comp_other, containing_cell, nearest_tri_dist_squared));
}
}
return ans;
}
/**
* The cells and patches are supposed to form a bipartite graph.
* The graph may be disconnected (if parts of meshes are nested or side-by-side
* without intersection with other each other).
* Connect the bipartite graph. This involves discovering the connected components
* of the patches, then the nesting structure of those components.
*/
static void finish_patch_cell_graph(const IMesh &tm,
CellsInfo &cinfo,
PatchesInfo &pinfo,
const TriMeshTopology &tmtopo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "FINISH_PATCH_CELL_GRAPH\n";
}
Vector<Vector<int>> components = find_patch_components(cinfo, pinfo);
if (components.size() <= 1) {
if (dbg_level > 0) {
std::cout << "one component so finish_patch_cell_graph does no work\n";
}
return;
}
if (dbg_level > 0) {
std::cout << "components:\n";
for (int comp : components.index_range()) {
std::cout << comp << ": " << components[comp] << "\n";
}
}
Array<int> ambient_cell(components.size());
for (int comp : components.index_range()) {
ambient_cell[comp] = find_ambient_cell(tm, &components[comp], tmtopo, pinfo, arena);
}
if (dbg_level > 0) {
std::cout << "ambient cells:\n";
for (int comp : ambient_cell.index_range()) {
std::cout << comp << ": " << ambient_cell[comp] << "\n";
}
}
int tot_components = components.size();
Array<Vector<ComponentContainer>> comp_cont(tot_components);
for (int comp : components.index_range()) {
comp_cont[comp] = find_component_containers(
comp, components, ambient_cell, tm, pinfo, tmtopo, arena);
}
if (dbg_level > 0) {
std::cout << "component containers:\n";
for (int comp : comp_cont.index_range()) {
std::cout << comp << ": ";
for (const ComponentContainer &cc : comp_cont[comp]) {
std::cout << "[containing_comp=" << cc.containing_component
<< ", nearest_cell=" << cc.nearest_cell << ", d2=" << cc.dist_to_cell << "] ";
}
std::cout << "\n";
}
}
if (dbg_level > 1) {
write_obj_cell_patch(tm, cinfo, pinfo, false, "beforemerge");
}
/* For nested components, merge their ambient cell with the nearest containing cell. */
Vector<int> outer_components;
for (int comp : comp_cont.index_range()) {
if (comp_cont[comp].size() == 0) {
outer_components.append(comp);
}
else {
ComponentContainer &closest = comp_cont[comp][0];
for (int i = 1; i < comp_cont[comp].size(); ++i) {
if (comp_cont[comp][i].dist_to_cell < closest.dist_to_cell) {
closest = comp_cont[comp][i];
}
}
int comp_ambient = ambient_cell[comp];
int cont_cell = closest.nearest_cell;
if (dbg_level > 0) {
std::cout << "merge comp " << comp << "'s ambient cell=" << comp_ambient << " to cell "
<< cont_cell << "\n";
}
merge_cells(cont_cell, comp_ambient, cinfo, pinfo);
}
}
/* For outer components (not nested in any other component), merge their ambient cells. */
if (outer_components.size() > 1) {
int merged_ambient = ambient_cell[outer_components[0]];
for (int i = 1; i < outer_components.size(); ++i) {
if (dbg_level > 0) {
std::cout << "merge comp " << outer_components[i]
<< "'s ambient cell=" << ambient_cell[outer_components[i]] << " to cell "
<< merged_ambient << "\n";
}
merge_cells(merged_ambient, ambient_cell[outer_components[i]], cinfo, pinfo);
}
}
if (dbg_level > 0) {
std::cout << "after FINISH_PATCH_CELL_GRAPH\nCells\n";
for (int i : cinfo.index_range()) {
if (cinfo.cell(i).merged_to() == NO_INDEX) {
std::cout << i << ": " << cinfo.cell(i) << "\n";
}
}
std::cout << "Patches\n";
for (int i : pinfo.index_range()) {
std::cout << i << ": " << pinfo.patch(i) << "\n";
}
if (dbg_level > 1) {
write_obj_cell_patch(tm, cinfo, pinfo, false, "finished");
}
}
}
/**
* Starting with ambient cell c_ambient, with all zeros for winding numbers,
* propagate winding numbers to all the other cells.
* There will be a vector of \a nshapes winding numbers in each cell, one per
* input shape.
* As one crosses a patch into a new cell, the original shape (mesh part)
* that that patch was part of dictates which winding number changes.
* The shape_fn(triangle_number) function should return the shape that the
* triangle is part of.
* Also, as soon as the winding numbers for a cell are set, use bool_optype
* to decide whether that cell is included or excluded from the boolean output.
* If included, the cell's in_output_volume will be set to true.
*/
static void propagate_windings_and_in_output_volume(PatchesInfo &pinfo,
CellsInfo &cinfo,
int c_ambient,
BoolOpType op,
int nshapes,
std::function<int(int)> shape_fn)
{
int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "PROPAGATE_WINDINGS, ambient cell = " << c_ambient << "\n";
}
Cell &cell_ambient = cinfo.cell(c_ambient);
cell_ambient.seed_ambient_winding();
/* Use a vector as a queue. It can't grow bigger than number of cells. */
Vector<int> queue;
queue.reserve(cinfo.tot_cell());
int queue_head = 0;
queue.append(c_ambient);
while (queue_head < queue.size()) {
int c = queue[queue_head++];
if (dbg_level > 1) {
std::cout << "process cell " << c << "\n";
}
Cell &cell = cinfo.cell(c);
for (int p : cell.patches()) {
Patch &patch = pinfo.patch(p);
bool p_above_c = patch.cell_below == c;
int c_neighbor = p_above_c ? patch.cell_above : patch.cell_below;
if (dbg_level > 1) {
std::cout << " patch " << p << " p_above_c = " << p_above_c << "\n";
std::cout << " c_neighbor = " << c_neighbor << "\n";
}
Cell &cell_neighbor = cinfo.cell(c_neighbor);
if (!cell_neighbor.winding_assigned()) {
int winding_delta = p_above_c ? -1 : 1;
int t = patch.tri(0);
int shape = shape_fn(t);
BLI_assert(shape < nshapes);
UNUSED_VARS_NDEBUG(nshapes);
if (dbg_level > 1) {
std::cout << " representative tri " << t << ": in shape " << shape << "\n";
}
cell_neighbor.set_winding_and_in_output_volume(cell, shape, winding_delta, op);
if (dbg_level > 1) {
std::cout << " now cell_neighbor = " << cell_neighbor << "\n";
}
queue.append(c_neighbor);
BLI_assert(queue.size() <= cinfo.tot_cell());
}
}
}
if (dbg_level > 0) {
std::cout << "\nPROPAGATE_WINDINGS result\n";
for (int i = 0; i < cinfo.tot_cell(); ++i) {
std::cout << i << ": " << cinfo.cell(i) << "\n";
}
}
}
/**
* Given an array of winding numbers, where the ith entry is a cell's winding
* number with respect to input shape (mesh part) i, return true if the
* cell should be included in the output of the boolean operation.
* Intersection: all the winding numbers must be nonzero.
* Union: at least one winding number must be nonzero.
* Difference (first shape minus the rest): first winding number must be nonzero
* and the rest must have at least one zero winding number.
*/
static bool apply_bool_op(BoolOpType bool_optype, const Array<int> &winding)
{
int nw = winding.size();
BLI_assert(nw > 0);
switch (bool_optype) {
case BoolOpType::Intersect: {
for (int i = 0; i < nw; ++i) {
if (winding[i] == 0) {
return false;
}
}
return true;
}
case BoolOpType::Union: {
for (int i = 0; i < nw; ++i) {
if (winding[i] != 0) {
return true;
}
}
return false;
}
case BoolOpType::Difference: {
/* if nw > 2, make it shape 0 minus the union of the rest. */
if (winding[0] == 0) {
return false;
}
if (nw == 1) {
return true;
}
for (int i = 1; i < nw; ++i) {
if (winding[i] >= 1) {
return false;
}
}
return true;
}
default:
return false;
}
}
/**
* Special processing for extract_from_in_output_volume_diffs to handle
* triangles that are part of stacks of geometrically identical
* triangles enclosing zero volume cells.
*/
static void extract_zero_volume_cell_tris(Vector<Face *> &r_tris,
const IMesh &tm_subdivided,
const PatchesInfo &pinfo,
const CellsInfo &cinfo,
IMeshArena *arena)
{
int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "extract_zero_volume_cell_tris\n";
}
/* Find patches that are adjacent to zero-volume cells. */
Array<bool> adj_to_zv(pinfo.tot_patch());
for (int p : pinfo.index_range()) {
const Patch &patch = pinfo.patch(p);
if (cinfo.cell(patch.cell_above).zero_volume() || cinfo.cell(patch.cell_below).zero_volume()) {
adj_to_zv[p] = true;
}
else {
adj_to_zv[p] = false;
}
}
/* Partition the adj_to_zv patches into stacks. */
Vector<Vector<int>> patch_stacks;
Array<bool> allocated_to_stack(pinfo.tot_patch(), false);
for (int p : pinfo.index_range()) {
if (!adj_to_zv[p] || allocated_to_stack[p]) {
continue;
}
int stack_index = patch_stacks.size();
patch_stacks.append(Vector<int>{p});
Vector<int> &stack = patch_stacks[stack_index];
Vector<bool> flipped{false};
allocated_to_stack[p] = true;
/* We arbitrarily choose p's above and below directions as above and below for whole stack.
* Triangles in the stack that don't follow that convention are marked with flipped = true.
* The non-zero-volume cell above the whole stack, following this convention, is
* above_stack_cell. The non-zero-volume cell below the whole stack is #below_stack_cell. */
/* First, walk in the above_cell direction from p. */
int pwalk = p;
const Patch *pwalk_patch = &pinfo.patch(pwalk);
int c = pwalk_patch->cell_above;
const Cell *cell = &cinfo.cell(c);
while (cell->zero_volume()) {
/* In zero-volume cells, the cell should have exactly two patches. */
BLI_assert(cell->patches().size() == 2);
int pother = cell->patches()[0] == pwalk ? cell->patches()[1] : cell->patches()[0];
bool flip = pinfo.patch(pother).cell_above == c;
flipped.append(flip);
stack.append(pother);
allocated_to_stack[pother] = true;
pwalk = pother;
pwalk_patch = &pinfo.patch(pwalk);
c = flip ? pwalk_patch->cell_below : pwalk_patch->cell_above;
cell = &cinfo.cell(c);
}
const Cell *above_stack_cell = cell;
/* Now walk in the below_cell direction from p. */
pwalk = p;
pwalk_patch = &pinfo.patch(pwalk);
c = pwalk_patch->cell_below;
cell = &cinfo.cell(c);
while (cell->zero_volume()) {
BLI_assert(cell->patches().size() == 2);
int pother = cell->patches()[0] == pwalk ? cell->patches()[1] : cell->patches()[0];
bool flip = pinfo.patch(pother).cell_below == c;
flipped.append(flip);
stack.append(pother);
allocated_to_stack[pother] = true;
pwalk = pother;
pwalk_patch = &pinfo.patch(pwalk);
c = flip ? pwalk_patch->cell_above : pwalk_patch->cell_below;
cell = &cinfo.cell(c);
}
const Cell *below_stack_cell = cell;
if (dbg_level > 0) {
std::cout << "process zero-volume patch stack " << stack << "\n";
std::cout << "flipped = ";
for (bool b : flipped) {
std::cout << b << " ";
}
std::cout << "\n";
}
if (above_stack_cell->in_output_volume() ^ below_stack_cell->in_output_volume()) {
bool need_flipped_tri = above_stack_cell->in_output_volume();
if (dbg_level > 0) {
std::cout << "need tri " << (need_flipped_tri ? "flipped" : "") << "\n";
}
int t_to_add = NO_INDEX;
for (int i : stack.index_range()) {
if (flipped[i] == need_flipped_tri) {
t_to_add = pinfo.patch(stack[i]).tri(0);
if (dbg_level > 0) {
std::cout << "using tri " << t_to_add << "\n";
}
r_tris.append(tm_subdivided.face(t_to_add));
break;
}
}
if (t_to_add == NO_INDEX) {
const Face *f = tm_subdivided.face(pinfo.patch(p).tri(0));
const Face &tri = *f;
/* We need flipped version or else we would have found it above. */
std::array<const Vert *, 3> flipped_vs = {tri[0], tri[2], tri[1]};
std::array<int, 3> flipped_e_origs = {
tri.edge_orig[2], tri.edge_orig[1], tri.edge_orig[0]};
std::array<bool, 3> flipped_is_intersect = {
tri.is_intersect[2], tri.is_intersect[1], tri.is_intersect[0]};
Face *flipped_f = arena->add_face(
flipped_vs, f->orig, flipped_e_origs, flipped_is_intersect);
r_tris.append(flipped_f);
}
}
}
}
/**
* Extract the output mesh from tm_subdivided and return it as a new mesh.
* The cells in \a cinfo must have cells-to-be-retained with in_output_volume set.
* We keep only triangles between those in the output volume and those not in.
* We flip the normals of any triangle that has an in_output_volume cell above
* and a not-in_output_volume cell below.
* For all stacks of exact duplicate co-planar triangles, we want to
* include either one version of the triangle or none, depending on
* whether the in_output_volume in_output_volumes on either side of the stack are
* different or the same.
*/
static IMesh extract_from_in_output_volume_diffs(const IMesh &tm_subdivided,
const PatchesInfo &pinfo,
const CellsInfo &cinfo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "\nEXTRACT_FROM_FLAG_DIFFS\n";
}
Vector<Face *> out_tris;
out_tris.reserve(tm_subdivided.face_size());
bool any_zero_volume_cell = false;
for (int t : tm_subdivided.face_index_range()) {
int p = pinfo.tri_patch(t);
const Patch &patch = pinfo.patch(p);
const Cell &cell_above = cinfo.cell(patch.cell_above);
const Cell &cell_below = cinfo.cell(patch.cell_below);
if (dbg_level > 0) {
std::cout << "tri " << t << ": cell_above=" << patch.cell_above
<< " cell_below=" << patch.cell_below << "\n";
std::cout << " in_output_volume_above=" << cell_above.in_output_volume()
<< " in_output_volume_below=" << cell_below.in_output_volume() << "\n";
}
bool adjacent_zero_volume_cell = cell_above.zero_volume() || cell_below.zero_volume();
any_zero_volume_cell |= adjacent_zero_volume_cell;
if (cell_above.in_output_volume() ^ cell_below.in_output_volume() &&
!adjacent_zero_volume_cell) {
bool flip = cell_above.in_output_volume();
if (dbg_level > 0) {
std::cout << "need tri " << t << " flip=" << flip << "\n";
}
Face *f = tm_subdivided.face(t);
if (flip) {
Face &tri = *f;
std::array<const Vert *, 3> flipped_vs = {tri[0], tri[2], tri[1]};
std::array<int, 3> flipped_e_origs = {
tri.edge_orig[2], tri.edge_orig[1], tri.edge_orig[0]};
std::array<bool, 3> flipped_is_intersect = {
tri.is_intersect[2], tri.is_intersect[1], tri.is_intersect[0]};
Face *flipped_f = arena->add_face(
flipped_vs, f->orig, flipped_e_origs, flipped_is_intersect);
out_tris.append(flipped_f);
}
else {
out_tris.append(f);
}
}
}
if (any_zero_volume_cell) {
extract_zero_volume_cell_tris(out_tris, tm_subdivided, pinfo, cinfo, arena);
}
return IMesh(out_tris);
}
static const char *bool_optype_name(BoolOpType op)
{
switch (op) {
case BoolOpType::None:
return "none";
case BoolOpType::Intersect:
return "intersect";
case BoolOpType::Union:
return "union";
case BoolOpType::Difference:
return "difference";
default:
return "<unknown>";
}
}
static mpq3 calc_point_inside_tri(const Face &tri)
{
const Vert *v0 = tri.vert[0];
const Vert *v1 = tri.vert[1];
const Vert *v2 = tri.vert[2];
mpq3 ans = v0->co_exact / 3 + v1->co_exact / 3 + v2->co_exact / 3;
return ans;
}
/**
* Return the Generalized Winding Number of point \a testp with respect to the
* volume implied by the faces for which shape_fn returns the value shape.
* See "Robust Inside-Outside Segmentation using Generalized Winding Numbers"
* by Jacobson, Kavan, and Sorkine-Hornung.
* This is like a winding number in that if it is positive, the point
* is inside the volume. But it is tolerant of not-completely-watertight
* volumes, still doing a passable job of classifying inside/outside
* as we intuitively understand that to mean.
*
* TOOD: speed up this calculation using the hierarchical algorithm in that paper.
*/
static double generalized_winding_number(const IMesh &tm,
std::function<int(int)> shape_fn,
const double3 &testp,
int shape)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "GENERALIZED_WINDING_NUMBER testp = " << testp << ", shape = " << shape << "\n";
}
double gwn = 0;
for (int t : tm.face_index_range()) {
const Face *f = tm.face(t);
const Face &tri = *f;
if (shape_fn(tri.orig) == shape) {
if (dbg_level > 0) {
std::cout << "accumulate for tri t = " << t << " = " << f << "\n";
}
const Vert *v0 = tri.vert[0];
const Vert *v1 = tri.vert[1];
const Vert *v2 = tri.vert[2];
double3 a = v0->co - testp;
double3 b = v1->co - testp;
double3 c = v2->co - testp;
/* Calculate the solid angle of abc relative to origin.
* See "The Solid Angle of a Plane Triangle" by Oosterom and Strackee
* for the derivation of the formula. */
double alen = a.length();
double blen = b.length();
double clen = c.length();
double3 bxc = double3::cross_high_precision(b, c);
double num = double3::dot(a, bxc);
double denom = alen * blen * clen + double3::dot(a, b) * clen + double3::dot(a, c) * blen +
double3::dot(b, c) * alen;
if (denom == 0.0) {
if (dbg_level > 0) {
std::cout << "denom == 0, skipping this tri\n";
}
continue;
}
double x = atan2(num, denom);
double fgwn = 2.0 * x;
if (dbg_level > 0) {
std::cout << "tri contributes " << fgwn << "\n";
}
gwn += fgwn;
}
}
gwn = gwn / (M_PI * 4.0);
if (dbg_level > 0) {
std::cout << "final gwn = " << gwn << "\n";
}
return gwn;
}
/**
* Return true if point \a testp is inside the volume implied by the
* faces for which the shape_fn returns the value shape.
* If \a high_confidence is true then we want a higher degree
* of "insideness" than if it is false.
*/
static bool point_is_inside_shape(const IMesh &tm,
std::function<int(int)> shape_fn,
const double3 &testp,
int shape,
bool high_confidence)
{
double gwn = generalized_winding_number(tm, shape_fn, testp, shape);
/* Due to floating point error, an outside point should get a value
* of zero for gwn, but may have a very slightly positive value instead.
* It is not important to get this epsilon very small, because practical
* cases of interest will have gwn at least 0.2 if it is not zero. */
if (high_confidence) {
return (gwn > 0.9);
}
return (gwn > 0.01);
}
/**
* Use the Generalized Winding Number method for deciding if a patch of the
* mesh is supposed to be included or excluded in the boolean result,
* and return the mesh that is the boolean result.
*/
static IMesh gwn_boolean(const IMesh &tm,
BoolOpType op,
int nshapes,
std::function<int(int)> shape_fn,
const PatchesInfo &pinfo,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "GWN_BOOLEAN\n";
}
IMesh ans;
Vector<Face *> out_faces;
out_faces.reserve(tm.face_size());
Array<int> winding(nshapes, 0);
for (int p : pinfo.index_range()) {
const Patch &patch = pinfo.patch(p);
/* For test triangle, choose one in the middle of patch list
* as the ones near the beginning may be very near other patches. */
int test_t_index = patch.tri(patch.tot_tri() / 2);
Face &tri_test = *tm.face(test_t_index);
/* Assume all triangles in a patch are in the same shape. */
int shape = shape_fn(tri_test.orig);
if (dbg_level > 0) {
std::cout << "process patch " << p << " = " << patch << "\n";
std::cout << "test tri = " << test_t_index << " = " << &tri_test << "\n";
std::cout << "shape = " << shape << "\n";
}
if (shape == -1) {
continue;
}
mpq3 test_point = calc_point_inside_tri(tri_test);
double3 test_point_db(test_point[0].get_d(), test_point[1].get_d(), test_point[2].get_d());
if (dbg_level > 0) {
std::cout << "test point = " << test_point_db << "\n";
}
for (int other_shape = 0; other_shape < nshapes; ++other_shape) {
if (other_shape == shape) {
continue;
}
/* The point_is_inside_shape function has to approximate if the other
* shape is not PWN. For most operations, even a hint of being inside
* gives good results, but when shape is a cutter in a Difference
* operation, we want to be pretty sure that the point is inside other_shape.
* E.g., T75827.
*/
bool need_high_confidence = (op == BoolOpType::Difference) && (shape != 0);
bool inside = point_is_inside_shape(
tm, shape_fn, test_point_db, other_shape, need_high_confidence);
if (dbg_level > 0) {
std::cout << "test point is " << (inside ? "inside" : "outside") << " other_shape "
<< other_shape << "\n";
}
winding[other_shape] = inside;
}
/* Find out the "in the output volume" flag for each of the cases of winding[shape] == 0
* and winding[shape] == 1. If the flags are different, this patch should be in the output.
* Also, if this is a Difference and the shape isn't the first one, need to flip the normals.
*/
winding[shape] = 0;
bool in_output_volume_0 = apply_bool_op(op, winding);
winding[shape] = 1;
bool in_output_volume_1 = apply_bool_op(op, winding);
bool do_remove = in_output_volume_0 == in_output_volume_1;
bool do_flip = !do_remove && op == BoolOpType::Difference && shape != 0;
if (dbg_level > 0) {
std::cout << "winding = ";
for (int i = 0; i < nshapes; ++i) {
std::cout << winding[i] << " ";
}
std::cout << "\niv0=" << in_output_volume_0 << ", iv1=" << in_output_volume_1 << "\n";
std::cout << "result for patch " << p << ": remove=" << do_remove << ", flip=" << do_flip
<< "\n";
}
if (!do_remove) {
for (int t : patch.tris()) {
Face *f = tm.face(t);
if (!do_flip) {
out_faces.append(f);
}
else {
Face &tri = *f;
/* We need flipped version of f. */
Array<const Vert *> flipped_vs = {tri[0], tri[2], tri[1]};
Array<int> flipped_e_origs = {tri.edge_orig[2], tri.edge_orig[1], tri.edge_orig[0]};
Array<bool> flipped_is_intersect = {
tri.is_intersect[2], tri.is_intersect[1], tri.is_intersect[0]};
Face *flipped_f = arena->add_face(
flipped_vs, f->orig, flipped_e_origs, flipped_is_intersect);
out_faces.append(flipped_f);
}
}
}
}
ans.set_faces(out_faces);
return ans;
}
/**
* Which CDT output edge index is for an edge between output verts
* v1 and v2 (in either order)?
* \return -1 if none.
*/
static int find_cdt_edge(const CDT_result<mpq_class> &cdt_out, int v1, int v2)
{
for (int e : cdt_out.edge.index_range()) {
const std::pair<int, int> &edge = cdt_out.edge[e];
if ((edge.first == v1 && edge.second == v2) || (edge.first == v2 && edge.second == v1)) {
return e;
}
}
return -1;
}
/**
* Tessellate face f into triangles and return an array of `const Face *`
* giving that triangulation.
* Care is taken so that the original edge index associated with
* each edge in the output triangles either matches the original edge
* for the (identical) edge of f, or else is -1. So diagonals added
* for triangulation can later be identified by having #NO_INDEX for original.
*/
static Array<Face *> triangulate_poly(Face *f, IMeshArena *arena)
{
int flen = f->size();
CDT_input<mpq_class> cdt_in;
cdt_in.vert = Array<mpq2>(flen);
cdt_in.face = Array<Vector<int>>(1);
cdt_in.face[0].reserve(flen);
for (int i : f->index_range()) {
cdt_in.face[0].append(i);
}
/* Project poly along dominant axis of normal to get 2d coords. */
if (!f->plane_populated()) {
f->populate_plane(false);
}
const double3 &poly_normal = f->plane->norm;
int axis = double3::dominant_axis(poly_normal);
/* If project down y axis as opposed to x or z, the orientation
* of the polygon will be reversed.
* Yet another reversal happens if the poly normal in the dominant
* direction is opposite that of the positive dominant axis. */
bool rev1 = (axis == 1);
bool rev2 = poly_normal[axis] < 0;
bool rev = rev1 ^ rev2;
for (int i = 0; i < flen; ++i) {
int ii = rev ? flen - i - 1 : i;
mpq2 &p2d = cdt_in.vert[ii];
int k = 0;
for (int j = 0; j < 3; ++j) {
if (j != axis) {
p2d[k++] = (*f)[ii]->co_exact[j];
}
}
}
CDT_result<mpq_class> cdt_out = delaunay_2d_calc(cdt_in, CDT_INSIDE);
int n_tris = cdt_out.face.size();
Array<Face *> ans(n_tris);
for (int t = 0; t < n_tris; ++t) {
int i_v_out[3];
const Vert *v[3];
int eo[3];
for (int i = 0; i < 3; ++i) {
i_v_out[i] = cdt_out.face[t][i];
v[i] = (*f)[cdt_out.vert_orig[i_v_out[i]][0]];
}
for (int i = 0; i < 3; ++i) {
int e_out = find_cdt_edge(cdt_out, i_v_out[i], i_v_out[(i + 1) % 3]);
BLI_assert(e_out != -1);
eo[i] = NO_INDEX;
for (int orig : cdt_out.edge_orig[e_out]) {
if (orig != NO_INDEX) {
eo[i] = orig;
break;
}
}
}
if (rev) {
ans[t] = arena->add_face(
{v[0], v[2], v[1]}, f->orig, {eo[2], eo[1], eo[0]}, {false, false, false});
}
else {
ans[t] = arena->add_face(
{v[0], v[1], v[2]}, f->orig, {eo[0], eo[1], eo[2]}, {false, false, false});
}
}
return ans;
}
/**
* Return an #IMesh that is a triangulation of a mesh with general
* polygonal faces, #IMesh.
* Added diagonals will be distinguishable by having edge original
* indices of #NO_INDEX.
*/
static IMesh triangulate_polymesh(IMesh &imesh, IMeshArena *arena)
{
Vector<Face *> face_tris;
constexpr int estimated_tris_per_face = 3;
face_tris.reserve(estimated_tris_per_face * imesh.face_size());
for (Face *f : imesh.faces()) {
/* Tessellate face f, following plan similar to #BM_face_calc_tesselation. */
int flen = f->size();
if (flen == 3) {
face_tris.append(f);
}
else if (flen == 4) {
const Vert *v0 = (*f)[0];
const Vert *v1 = (*f)[1];
const Vert *v2 = (*f)[2];
const Vert *v3 = (*f)[3];
int eo_01 = f->edge_orig[0];
int eo_12 = f->edge_orig[1];
int eo_23 = f->edge_orig[2];
int eo_30 = f->edge_orig[3];
Face *f0 = arena->add_face({v0, v1, v2}, f->orig, {eo_01, eo_12, -1}, {false, false, false});
Face *f1 = arena->add_face({v0, v2, v3}, f->orig, {-1, eo_23, eo_30}, {false, false, false});
face_tris.append(f0);
face_tris.append(f1);
}
else {
Array<Face *> tris = triangulate_poly(f, arena);
for (Face *tri : tris) {
face_tris.append(tri);
}
}
}
return IMesh(face_tris);
}
/**
* If \a tri1 and \a tri2 have a common edge (in opposite orientation),
* return the indices into \a tri1 and \a tri2 where that common edge starts. Else return (-1,-1).
*/
static std::pair<int, int> find_tris_common_edge(const Face &tri1, const Face &tri2)
{
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
if (tri1[(i + 1) % 3] == tri2[j] && tri1[i] == tri2[(j + 1) % 3]) {
return std::pair<int, int>(i, j);
}
}
}
return std::pair<int, int>(-1, -1);
}
struct MergeEdge {
/** Length (squared) of the edge, used for sorting. */
double len_squared = 0.0;
/* v1 and v2 are the ends of the edge, ordered so that `v1->id < v2->id` */
const Vert *v1 = nullptr;
const Vert *v2 = nullptr;
/* left_face and right_face are indices into #FaceMergeState.face. */
int left_face = -1;
int right_face = -1;
int orig = -1; /* An edge orig index that can be used for this edge. */
/** Is it allowed to dissolve this edge? */
bool dissolvable = false;
/** Is this an intersect edge? */
bool is_intersect = false;
MergeEdge() = default;
MergeEdge(const Vert *va, const Vert *vb)
{
if (va->id < vb->id) {
this->v1 = va;
this->v2 = vb;
}
else {
this->v1 = vb;
this->v2 = va;
}
};
};
struct MergeFace {
/** The current sequence of Verts forming this face. */
Vector<const Vert *> vert;
/** For each position in face, what is index in #FaceMergeState of edge for that position? */
Vector<int> edge;
/** If not -1, merge_to gives a face index in #FaceMergeState that this is merged to. */
int merge_to = -1;
/** A face->orig that can be used for the merged face. */
int orig = -1;
};
struct FaceMergeState {
/**
* The faces being considered for merging. Some will already have been merge (merge_to != -1).
*/
Vector<MergeFace> face;
/**
* The edges that are part of the faces in face[], together with current topological
* information (their left and right faces) and whether or not they are dissolvable.
*/
Vector<MergeEdge> edge;
/**
* `edge_map` maps a pair of `const Vert *` ids (in canonical order: smaller id first)
* to the index in the above edge vector in which to find the corresponding #MergeEdge.
*/
Map<std::pair<int, int>, int> edge_map;
};
static std::ostream &operator<<(std::ostream &os, const FaceMergeState &fms)
{
os << "faces:\n";
for (int f : fms.face.index_range()) {
const MergeFace &mf = fms.face[f];
std::cout << f << ": orig=" << mf.orig << " verts ";
for (const Vert *v : mf.vert) {
std::cout << v << " ";
}
std::cout << "\n";
std::cout << " edges " << mf.edge << "\n";
std::cout << " merge_to = " << mf.merge_to << "\n";
}
os << "\nedges:\n";
for (int e : fms.edge.index_range()) {
const MergeEdge &me = fms.edge[e];
std::cout << e << ": (" << me.v1 << "," << me.v2 << ") left=" << me.left_face
<< " right=" << me.right_face << " dis=" << me.dissolvable << " orig=" << me.orig
<< " is_int=" << me.is_intersect << "\n";
}
return os;
}
/**
* \a tris all have the same original face.
* Find the 2d edge/triangle topology for these triangles, but only the ones facing in the
* norm direction, and whether each edge is dissolvable or not.
*/
static void init_face_merge_state(FaceMergeState *fms,
const Vector<int> &tris,
const IMesh &tm,
const double3 &norm)
{
constexpr int dbg_level = 0;
/* Reserve enough faces and edges so that neither will have to resize. */
fms->face.reserve(tris.size() + 1);
fms->edge.reserve(3 * tris.size());
fms->edge_map.reserve(3 * tris.size());
if (dbg_level > 0) {
std::cout << "\nINIT_FACE_MERGE_STATE\n";
}
for (int t : tris.index_range()) {
MergeFace mf;
const Face &tri = *tm.face(tris[t]);
if (dbg_level > 0) {
std::cout << "process tri = " << &tri << "\n";
}
BLI_assert(tri.plane_populated());
if (double3::dot(norm, tri.plane->norm) <= 0.0) {
if (dbg_level > 0) {
std::cout << "triangle has wrong orientation, skipping\n";
}
continue;
}
mf.vert.append(tri[0]);
mf.vert.append(tri[1]);
mf.vert.append(tri[2]);
mf.orig = tri.orig;
int f = fms->face.append_and_get_index(mf);
if (dbg_level > 1) {
std::cout << "appended MergeFace for tri at f = " << f << "\n";
}
for (int i = 0; i < 3; ++i) {
int inext = (i + 1) % 3;
MergeEdge new_me(mf.vert[i], mf.vert[inext]);
std::pair<int, int> canon_vs(new_me.v1->id, new_me.v2->id);
int me_index = fms->edge_map.lookup_default(canon_vs, -1);
if (dbg_level > 1) {
std::cout << "new_me = canon_vs = " << new_me.v1 << ", " << new_me.v2 << "\n";
std::cout << "me_index lookup = " << me_index << "\n";
}
if (me_index == -1) {
double3 vec = new_me.v2->co - new_me.v1->co;
new_me.len_squared = vec.length_squared();
new_me.orig = tri.edge_orig[i];
new_me.is_intersect = tri.is_intersect[i];
new_me.dissolvable = (new_me.orig == NO_INDEX && !new_me.is_intersect);
fms->edge.append(new_me);
me_index = fms->edge.size() - 1;
fms->edge_map.add_new(canon_vs, me_index);
if (dbg_level > 1) {
std::cout << "added new me with me_index = " << me_index << "\n";
std::cout << " len_squared = " << new_me.len_squared << " orig = " << new_me.orig
<< ", is_intersect" << new_me.is_intersect
<< ", dissolvable = " << new_me.dissolvable << "\n";
}
}
MergeEdge &me = fms->edge[me_index];
if (dbg_level > 1) {
std::cout << "retrieved me at index " << me_index << ":\n";
std::cout << " v1 = " << me.v1 << " v2 = " << me.v2 << "\n";
std::cout << " dis = " << me.dissolvable << " int = " << me.is_intersect << "\n";
std::cout << " left_face = " << me.left_face << " right_face = " << me.right_face << "\n";
}
if (me.dissolvable && tri.edge_orig[i] != NO_INDEX) {
if (dbg_level > 1) {
std::cout << "reassigning orig to " << tri.edge_orig[i] << ", dissolvable = false\n";
}
me.dissolvable = false;
me.orig = tri.edge_orig[i];
}
if (me.dissolvable && tri.is_intersect[i]) {
if (dbg_level > 1) {
std::cout << "reassigning dissolvable = false, is_intersect = true\n";
}
me.dissolvable = false;
me.is_intersect = true;
}
/* This face is left or right depending on orientation of edge. */
if (me.v1 == mf.vert[i]) {
if (dbg_level > 1) {
std::cout << "me.v1 == mf.vert[i] so set edge[" << me_index << "].left_face = " << f
<< "\n";
}
BLI_assert(me.left_face == -1);
fms->edge[me_index].left_face = f;
}
else {
if (dbg_level > 1) {
std::cout << "me.v1 != mf.vert[i] so set edge[" << me_index << "].right_face = " << f
<< "\n";
}
BLI_assert(me.right_face == -1);
fms->edge[me_index].right_face = f;
}
fms->face[f].edge.append(me_index);
}
}
if (dbg_level > 0) {
std::cout << *fms;
}
}
/**
* To have a valid #BMesh, there are constraints on what edges can be removed.
* We cannot remove an edge if (a) it would create two disconnected boundary parts
* (which will happen if there's another edge sharing the same two faces);
* or (b) it would create a face with a repeated vertex.
*/
static bool dissolve_leaves_valid_bmesh(FaceMergeState *fms,
const MergeEdge &me,
int me_index,
const MergeFace &mf_left,
const MergeFace &mf_right)
{
int a_edge_start = mf_left.edge.first_index_of_try(me_index);
BLI_assert(a_edge_start != -1);
int alen = mf_left.vert.size();
int blen = mf_right.vert.size();
int b_left_face = me.right_face;
bool ok = true;
/* Is there another edge, not me, in A's face, whose right face is B's left? */
for (int a_e_index = (a_edge_start + 1) % alen; ok && a_e_index != a_edge_start;
a_e_index = (a_e_index + 1) % alen) {
const MergeEdge &a_me_cur = fms->edge[mf_left.edge[a_e_index]];
if (a_me_cur.right_face == b_left_face) {
ok = false;
}
}
/* Is there a vert in A, not me.v1 or me.v2, that is also in B?
* One could avoid this O(n^2) algorithm if had a structure
* saying which faces a vertex touches. */
for (int a_v_index = 0; ok && a_v_index < alen; ++a_v_index) {
const Vert *a_v = mf_left.vert[a_v_index];
if (!ELEM(a_v, me.v1, me.v2)) {
for (int b_v_index = 0; b_v_index < blen; ++b_v_index) {
const Vert *b_v = mf_right.vert[b_v_index];
if (a_v == b_v) {
ok = false;
}
}
}
}
return ok;
}
/**
* mf_left and mf_right should share a #MergeEdge me, having index me_index.
* We change mf_left to remove edge me and insert the appropriate edges of
* mf_right in between the start and end vertices of that edge.
* We change the left face of the spliced-in edges to be mf_left's index.
* We mark the merge_to property of mf_right, which is now in essence deleted.
*/
static void splice_faces(
FaceMergeState *fms, MergeEdge &me, int me_index, MergeFace &mf_left, MergeFace &mf_right)
{
int a_edge_start = mf_left.edge.first_index_of_try(me_index);
int b_edge_start = mf_right.edge.first_index_of_try(me_index);
BLI_assert(a_edge_start != -1 && b_edge_start != -1);
int alen = mf_left.vert.size();
int blen = mf_right.vert.size();
Vector<const Vert *> splice_vert;
Vector<int> splice_edge;
splice_vert.reserve(alen + blen - 2);
splice_edge.reserve(alen + blen - 2);
int ai = 0;
while (ai < a_edge_start) {
splice_vert.append(mf_left.vert[ai]);
splice_edge.append(mf_left.edge[ai]);
++ai;
}
int bi = b_edge_start + 1;
while (bi != b_edge_start) {
if (bi >= blen) {
bi = 0;
if (bi == b_edge_start) {
break;
}
}
splice_vert.append(mf_right.vert[bi]);
splice_edge.append(mf_right.edge[bi]);
if (mf_right.vert[bi] == fms->edge[mf_right.edge[bi]].v1) {
fms->edge[mf_right.edge[bi]].left_face = me.left_face;
}
else {
fms->edge[mf_right.edge[bi]].right_face = me.left_face;
}
++bi;
}
ai = a_edge_start + 1;
while (ai < alen) {
splice_vert.append(mf_left.vert[ai]);
splice_edge.append(mf_left.edge[ai]);
++ai;
}
mf_right.merge_to = me.left_face;
mf_left.vert = splice_vert;
mf_left.edge = splice_edge;
me.left_face = -1;
me.right_face = -1;
}
/**
* Given that fms has been properly initialized to contain a set of faces that
* together form a face or part of a face of the original #IMesh, and that
* it has properly recorded with faces are dissolvable, dissolve as many edges as possible.
* We try to dissolve in decreasing order of edge length, so that it is more likely
* that the final output doesn't have awkward looking long edges with extreme angles.
*/
static void do_dissolve(FaceMergeState *fms)
{
const int dbg_level = 0;
if (dbg_level > 1) {
std::cout << "\nDO_DISSOLVE\n";
}
Vector<int> dissolve_edges;
for (int e : fms->edge.index_range()) {
if (fms->edge[e].dissolvable) {
dissolve_edges.append(e);
}
}
if (dissolve_edges.size() == 0) {
return;
}
/* Things look nicer if we dissolve the longer edges first. */
std::sort(
dissolve_edges.begin(), dissolve_edges.end(), [fms](const int &a, const int &b) -> bool {
return (fms->edge[a].len_squared > fms->edge[b].len_squared);
});
if (dbg_level > 0) {
std::cout << "Sorted dissolvable edges: " << dissolve_edges << "\n";
}
for (int me_index : dissolve_edges) {
MergeEdge &me = fms->edge[me_index];
if (me.left_face == -1 || me.right_face == -1) {
continue;
}
MergeFace &mf_left = fms->face[me.left_face];
MergeFace &mf_right = fms->face[me.right_face];
if (!dissolve_leaves_valid_bmesh(fms, me, me_index, mf_left, mf_right)) {
continue;
}
if (dbg_level > 0) {
std::cout << "Removing edge " << me_index << "\n";
}
splice_faces(fms, me, me_index, mf_left, mf_right);
if (dbg_level > 1) {
std::cout << "state after removal:\n";
std::cout << *fms;
}
}
}
/**
* Given that \a tris form a triangulation of a face or part of a face that was in \a imesh_in,
* merge as many of the triangles together as possible, by dissolving the edges between them.
* We can only dissolve triangulation edges that don't overlap real input edges, and we
* can only dissolve them if doing so leaves the remaining faces able to create valid #BMesh.
* We can tell edges that don't overlap real input edges because they will have an
* "original edge" that is different from #NO_INDEX.
* \note it is possible that some of the triangles in \a tris have reversed orientation
* to the rest, so we have to handle the two cases separately.
*/
static Vector<Face *> merge_tris_for_face(Vector<int> tris,
const IMesh &tm,
const IMesh &imesh_in,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "merge_tris_for_face\n";
std::cout << "tris: " << tris << "\n";
}
Vector<Face *> ans;
if (tris.size() <= 1) {
if (tris.size() == 1) {
ans.append(tm.face(tris[0]));
}
return ans;
}
bool done = false;
double3 first_tri_normal = tm.face(tris[0])->plane->norm;
double3 second_tri_normal = tm.face(tris[1])->plane->norm;
if (tris.size() == 2 && double3::dot(first_tri_normal, second_tri_normal) > 0.0) {
/* Is this a case where quad with one diagonal remained unchanged?
* Worth special handling because this case will be very common. */
Face &tri1 = *tm.face(tris[0]);
Face &tri2 = *tm.face(tris[1]);
Face *in_face = imesh_in.face(tri1.orig);
if (in_face->size() == 4) {
std::pair<int, int> estarts = find_tris_common_edge(tri1, tri2);
if (estarts.first != -1 && tri1.edge_orig[estarts.first] == NO_INDEX) {
if (dbg_level > 0) {
std::cout << "try recovering orig quad case\n";
std::cout << "tri1 = " << &tri1 << "\n";
std::cout << "tri1 = " << &tri2 << "\n";
}
int i0 = estarts.first;
int i1 = (i0 + 1) % 3;
int i2 = (i0 + 2) % 3;
int j2 = (estarts.second + 2) % 3;
Face tryface({tri1[i1], tri1[i2], tri1[i0], tri2[j2]}, -1, -1, {}, {});
if (tryface.cyclic_equal(*in_face)) {
if (dbg_level > 0) {
std::cout << "inface = " << in_face << "\n";
std::cout << "quad recovery worked\n";
}
ans.append(in_face);
done = true;
}
}
}
}
if (done) {
return ans;
}
double3 first_tri_normal_rev = -first_tri_normal;
for (const double3 &norm : {first_tri_normal, first_tri_normal_rev}) {
FaceMergeState fms;
init_face_merge_state(&fms, tris, tm, norm);
do_dissolve(&fms);
if (dbg_level > 0) {
std::cout << "faces in merged result:\n";
}
for (const MergeFace &mf : fms.face) {
if (mf.merge_to == -1) {
Array<int> e_orig(mf.edge.size());
Array<bool> is_intersect(mf.edge.size());
for (int i : mf.edge.index_range()) {
e_orig[i] = fms.edge[mf.edge[i]].orig;
is_intersect[i] = fms.edge[mf.edge[i]].is_intersect;
}
Face *facep = arena->add_face(mf.vert, mf.orig, e_orig, is_intersect);
ans.append(facep);
if (dbg_level > 0) {
std::cout << " " << facep << "\n";
}
}
}
}
return ans;
}
/**
* Return an array, paralleling imesh_out.vert, saying which vertices can be dissolved.
* A vertex v can be dissolved if (a) it is not an input vertex; (b) it has valence 2;
* and (c) if v's two neighboring vertices are u and w, then (u,v,w) forms a straight line.
* Return the number of dissolvable vertices in r_count_dissolve.
*/
static Array<bool> find_dissolve_verts(IMesh &imesh_out, int *r_count_dissolve)
{
imesh_out.populate_vert();
/* dissolve[i] will say whether imesh_out.vert(i) can be dissolved. */
Array<bool> dissolve(imesh_out.vert_size());
for (int v_index : imesh_out.vert_index_range()) {
const Vert &vert = *imesh_out.vert(v_index);
dissolve[v_index] = (vert.orig == NO_INDEX);
}
/* neighbors[i] will be a pair giving the up-to-two neighboring vertices
* of the vertex v in position i of imesh_out.vert.
* If we encounter a third, then v will not be dissolvable. */
Array<std::pair<const Vert *, const Vert *>> neighbors(
imesh_out.vert_size(), std::pair<const Vert *, const Vert *>(nullptr, nullptr));
for (int f : imesh_out.face_index_range()) {
const Face &face = *imesh_out.face(f);
for (int i : face.index_range()) {
const Vert *v = face[i];
int v_index = imesh_out.lookup_vert(v);
BLI_assert(v_index != NO_INDEX);
if (dissolve[v_index]) {
const Vert *n1 = face[face.next_pos(i)];
const Vert *n2 = face[face.prev_pos(i)];
const Vert *f_n1 = neighbors[v_index].first;
const Vert *f_n2 = neighbors[v_index].second;
if (f_n1 != nullptr) {
/* Already has a neighbor in another face; can't dissolve unless they are the same. */
if (!((n1 == f_n2 && n2 == f_n1) || (n1 == f_n1 && n2 == f_n2))) {
/* Different neighbors, so can't dissolve. */
dissolve[v_index] = false;
}
}
else {
/* These are the first-seen neighbors. */
neighbors[v_index] = std::pair<const Vert *, const Vert *>(n1, n2);
}
}
}
}
int count = 0;
for (int v_out : imesh_out.vert_index_range()) {
if (dissolve[v_out]) {
dissolve[v_out] = false; /* Will set back to true if final condition is satisfied. */
const std::pair<const Vert *, const Vert *> &nbrs = neighbors[v_out];
if (nbrs.first != nullptr) {
BLI_assert(nbrs.second != nullptr);
dissolve[v_out] = true;
++count;
}
}
}
if (r_count_dissolve != nullptr) {
*r_count_dissolve = count;
}
return dissolve;
}
/**
* The dissolve array parallels the `imesh.vert` array. Wherever it is true,
* remove the corresponding vertex from the vertices in the faces of
* `imesh.faces` to account for the close-up of the gaps in `imesh.vert`.
*/
static void dissolve_verts(IMesh *imesh, const Array<bool> dissolve, IMeshArena *arena)
{
constexpr int inline_face_size = 100;
Vector<bool, inline_face_size> face_pos_erase;
bool any_faces_erased = false;
for (int f : imesh->face_index_range()) {
const Face &face = *imesh->face(f);
face_pos_erase.clear();
int num_erase = 0;
for (const Vert *v : face) {
int v_index = imesh->lookup_vert(v);
BLI_assert(v_index != NO_INDEX);
if (dissolve[v_index]) {
face_pos_erase.append(true);
++num_erase;
}
else {
face_pos_erase.append(false);
}
}
if (num_erase > 0) {
any_faces_erased |= imesh->erase_face_positions(f, face_pos_erase, arena);
}
}
imesh->set_dirty_verts();
if (any_faces_erased) {
imesh->remove_null_faces();
}
}
/**
* The main boolean function operates on a triangle #IMesh and produces a
* Triangle #IMesh as output.
* This function converts back into a general polygonal mesh by removing
* any possible triangulation edges (which can be identified because they
* will have an original edge that is NO_INDEX.
* Not all triangulation edges can be removed: if they ended up non-trivially overlapping a real
* input edge, then we need to keep it. Also, some are necessary to make the output satisfy
* the "valid #BMesh" property: we can't produce output faces that have repeated vertices in them,
* or have several disconnected boundaries (e.g., faces with holes).
*/
static IMesh polymesh_from_trimesh_with_dissolve(const IMesh &tm_out,
const IMesh &imesh_in,
IMeshArena *arena)
{
const int dbg_level = 0;
if (dbg_level > 1) {
std::cout << "\nPOLYMESH_FROM_TRIMESH_WITH_DISSOLVE\n";
}
/* For now: need plane normals for all triangles. */
for (Face *tri : tm_out.faces()) {
tri->populate_plane(false);
}
/* Gather all output triangles that are part of each input face.
* face_output_tris[f] will be indices of triangles in tm_out
* that have f as their original face. */
int tot_in_face = imesh_in.face_size();
Array<Vector<int>> face_output_tris(tot_in_face);
for (int t : tm_out.face_index_range()) {
const Face &tri = *tm_out.face(t);
int in_face = tri.orig;
face_output_tris[in_face].append(t);
}
if (dbg_level > 1) {
std::cout << "face_output_tris:\n";
for (int f : face_output_tris.index_range()) {
std::cout << f << ": " << face_output_tris[f] << "\n";
}
}
/* Merge triangles that we can from face_output_tri to make faces for output.
* face_output_face[f] will be new original const Face *'s that
* make up whatever part of the boolean output remains of input face f. */
Array<Vector<Face *>> face_output_face(tot_in_face);
int tot_out_face = 0;
for (int in_f : imesh_in.face_index_range()) {
if (dbg_level > 1) {
std::cout << "merge tris for face " << in_f << "\n";
}
int num_out_tris_for_face = face_output_tris.size();
if (num_out_tris_for_face == 0) {
continue;
}
face_output_face[in_f] = merge_tris_for_face(face_output_tris[in_f], tm_out, imesh_in, arena);
tot_out_face += face_output_face[in_f].size();
}
Array<Face *> face(tot_out_face);
int out_f_index = 0;
for (int in_f : imesh_in.face_index_range()) {
const Vector<Face *> &f_faces = face_output_face[in_f];
if (f_faces.size() > 0) {
std::copy(f_faces.begin(), f_faces.end(), &face[out_f_index]);
out_f_index += f_faces.size();
}
}
IMesh imesh_out(face);
/* Dissolve vertices that were (a) not original; and (b) now have valence 2 and
* are between two other vertices that are exactly in line with them.
* These were created because of triangulation edges that have been dissolved. */
int count_dissolve;
Array<bool> v_dissolve = find_dissolve_verts(imesh_out, &count_dissolve);
if (count_dissolve > 0) {
dissolve_verts(&imesh_out, v_dissolve, arena);
}
if (dbg_level > 1) {
write_obj_mesh(imesh_out, "boolean_post_dissolve");
}
return imesh_out;
}
/**
* This function does a boolean operation on a TriMesh with nshapes inputs.
* All the shapes are combined in tm_in.
* The shape_fn function should take a triangle index in tm_in and return
* a number in the range 0 to `nshapes-1`, to say which shape that triangle is in.
*/
IMesh boolean_trimesh(IMesh &tm_in,
BoolOpType op,
int nshapes,
std::function<int(int)> shape_fn,
bool use_self,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "BOOLEAN of " << nshapes << " operand" << (nshapes == 1 ? "" : "s")
<< " op=" << bool_optype_name(op) << "\n";
if (dbg_level > 1) {
tm_in.populate_vert();
std::cout << "boolean_trimesh input:\n" << tm_in;
write_obj_mesh(tm_in, "boolean_in");
}
}
if (tm_in.face_size() == 0) {
return IMesh(tm_in);
}
# ifdef PERFDEBUG
double start_time = PIL_check_seconds_timer();
std::cout << " boolean_trimesh, timing begins\n";
# endif
IMesh tm_si = trimesh_nary_intersect(tm_in, nshapes, shape_fn, use_self, arena);
if (dbg_level > 1) {
write_obj_mesh(tm_si, "boolean_tm_si");
std::cout << "\nboolean_tm_input after intersection:\n" << tm_si;
}
# ifdef PERFDEBUG
double intersect_time = PIL_check_seconds_timer();
std::cout << " intersected, time = " << intersect_time - start_time << "\n";
# endif
/* It is possible for tm_si to be empty if all the input triangles are bogus/degenerate. */
if (tm_si.face_size() == 0 || op == BoolOpType::None) {
return tm_si;
}
auto si_shape_fn = [shape_fn, tm_si](int t) { return shape_fn(tm_si.face(t)->orig); };
TriMeshTopology tm_si_topo(tm_si);
# ifdef PERFDEBUG
double topo_time = PIL_check_seconds_timer();
std::cout << " topology built, time = " << topo_time - intersect_time << "\n";
# endif
PatchesInfo pinfo = find_patches(tm_si, tm_si_topo);
# ifdef PERFDEBUG
double patch_time = PIL_check_seconds_timer();
std::cout << " patches found, time = " << patch_time - topo_time << "\n";
# endif
IMesh tm_out;
if (!is_pwn(tm_si, tm_si_topo)) {
# ifdef PERFDEBUG
double pwn_check_time = PIL_check_seconds_timer();
std::cout << " pwn checked (not pwn), time = " << pwn_check_time - patch_time << "\n";
# endif
if (dbg_level > 0) {
std::cout << "Input is not PWN, using gwn method\n";
}
tm_out = gwn_boolean(tm_si, op, nshapes, shape_fn, pinfo, arena);
# ifdef PERFDEBUG
double gwn_time = PIL_check_seconds_timer();
std::cout << " gwn, time = " << gwn_time - pwn_check_time << "\n";
# endif
}
else {
# ifdef PERFDEBUG
double pwn_time = PIL_check_seconds_timer();
std::cout << " pwn checked (ok), time = " << pwn_time - patch_time << "\n";
# endif
CellsInfo cinfo = find_cells(tm_si, tm_si_topo, pinfo);
if (dbg_level > 0) {
std::cout << "Input is PWN\n";
}
# ifdef PERFDEBUG
double cell_time = PIL_check_seconds_timer();
std::cout << " cells found, time = " << cell_time - pwn_time << "\n";
# endif
finish_patch_cell_graph(tm_si, cinfo, pinfo, tm_si_topo, arena);
# ifdef PERFDEBUG
double finish_pc_time = PIL_check_seconds_timer();
std::cout << " finished patch-cell graph, time = " << finish_pc_time - cell_time << "\n";
# endif
bool pc_ok = patch_cell_graph_ok(cinfo, pinfo);
if (!pc_ok) {
/* TODO: if bad input can lead to this, diagnose the problem. */
std::cout << "Something funny about input or a bug in boolean\n";
return IMesh(tm_in);
}
cinfo.init_windings(nshapes);
int c_ambient = find_ambient_cell(tm_si, nullptr, tm_si_topo, pinfo, arena);
# ifdef PERFDEBUG
double amb_time = PIL_check_seconds_timer();
std::cout << " ambient cell found, time = " << amb_time - finish_pc_time << "\n";
# endif
if (c_ambient == NO_INDEX) {
/* TODO: find a way to propagate this error to user properly. */
std::cout << "Could not find an ambient cell; input not valid?\n";
return IMesh(tm_si);
}
propagate_windings_and_in_output_volume(pinfo, cinfo, c_ambient, op, nshapes, si_shape_fn);
# ifdef PERFDEBUG
double propagate_time = PIL_check_seconds_timer();
std::cout << " windings propagated, time = " << propagate_time - amb_time << "\n";
# endif
tm_out = extract_from_in_output_volume_diffs(tm_si, pinfo, cinfo, arena);
# ifdef PERFDEBUG
double extract_time = PIL_check_seconds_timer();
std::cout << " extracted, time = " << extract_time - propagate_time << "\n";
# endif
if (dbg_level > 0) {
/* Check if output is PWN. */
TriMeshTopology tm_out_topo(tm_out);
if (!is_pwn(tm_out, tm_out_topo)) {
std::cout << "OUTPUT IS NOT PWN!\n";
}
}
}
if (dbg_level > 1) {
write_obj_mesh(tm_out, "boolean_tm_output");
std::cout << "boolean tm output:\n" << tm_out;
}
# ifdef PERFDEBUG
double end_time = PIL_check_seconds_timer();
std::cout << " boolean_trimesh done, total time = " << end_time - start_time << "\n";
# endif
return tm_out;
}
static void dump_test_spec(IMesh &imesh)
{
std::cout << "test spec = " << imesh.vert_size() << " " << imesh.face_size() << "\n";
for (const Vert *v : imesh.vertices()) {
std::cout << v->co_exact[0] << " " << v->co_exact[1] << " " << v->co_exact[2] << " # "
<< v->co[0] << " " << v->co[1] << " " << v->co[2] << "\n";
}
for (const Face *f : imesh.faces()) {
for (const Vert *fv : *f) {
std::cout << imesh.lookup_vert(fv) << " ";
}
std::cout << "\n";
}
}
/**
* Do the boolean operation op on the polygon mesh imesh_in.
* See the header file for a complete description.
*/
IMesh boolean_mesh(IMesh &imesh,
BoolOpType op,
int nshapes,
std::function<int(int)> shape_fn,
bool use_self,
IMesh *imesh_triangulated,
IMeshArena *arena)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "\nBOOLEAN_MESH\n"
<< nshapes << " operand" << (nshapes == 1 ? "" : "s")
<< " op=" << bool_optype_name(op) << "\n";
if (dbg_level > 1) {
write_obj_mesh(imesh, "boolean_mesh_in");
std::cout << imesh;
if (dbg_level > 2) {
dump_test_spec(imesh);
}
}
}
IMesh *tm_in = imesh_triangulated;
IMesh our_triangulation;
# ifdef PERFDEBUG
double start_time = PIL_check_seconds_timer();
std::cout << "boolean_mesh, timing begins\n";
# endif
if (tm_in == nullptr) {
our_triangulation = triangulate_polymesh(imesh, arena);
tm_in = &our_triangulation;
}
# ifdef PERFDEBUG
double tri_time = PIL_check_seconds_timer();
std::cout << "triangulated, time = " << tri_time - start_time << "\n";
# endif
if (dbg_level > 1) {
write_obj_mesh(*tm_in, "boolean_tm_in");
}
IMesh tm_out = boolean_trimesh(*tm_in, op, nshapes, shape_fn, use_self, arena);
# ifdef PERFDEBUG
double bool_tri_time = PIL_check_seconds_timer();
std::cout << "boolean_trimesh done, time = " << bool_tri_time - tri_time << "\n";
# endif
if (dbg_level > 1) {
std::cout << "bool_trimesh_output:\n" << tm_out;
write_obj_mesh(tm_out, "bool_trimesh_output");
}
IMesh ans = polymesh_from_trimesh_with_dissolve(tm_out, imesh, arena);
# ifdef PERFDEBUG
double dissolve_time = PIL_check_seconds_timer();
std::cout << "polymesh from dissolving, time = " << dissolve_time - bool_tri_time << "\n";
# endif
if (dbg_level > 0) {
std::cout << "boolean_mesh output:\n" << ans;
if (dbg_level > 2) {
ans.populate_vert();
dump_test_spec(ans);
}
}
# ifdef PERFDEBUG
double end_time = PIL_check_seconds_timer();
std::cout << "boolean_mesh done, total time = " << end_time - start_time << "\n";
# endif
return ans;
}
} // namespace blender::meshintersect
#endif // WITH_GMP
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