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blender-archive/source/blender/blenlib/intern/delaunay_2d.cc
2021-02-09 10:42:00 +11:00

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C++

/*
* 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
*/
#include <algorithm>
#include <fstream>
#include <iostream>
#include <sstream>
#include "BLI_array.hh"
#include "BLI_double2.hh"
#include "BLI_linklist.h"
#include "BLI_math_boolean.hh"
#include "BLI_math_mpq.hh"
#include "BLI_mpq2.hh"
#include "BLI_vector.hh"
#include "BLI_delaunay_2d.h"
namespace blender::meshintersect {
/* Throughout this file, template argument T will be an
* arithmetic-like type, like float, double, or mpq_class. */
template<typename T> T math_abs(const T v)
{
return (v < 0) ? -v : v;
}
#ifdef WITH_GMP
template<> mpq_class math_abs<mpq_class>(const mpq_class v)
{
return abs(v);
}
#endif
template<> double math_abs<double>(const double v)
{
return fabs(v);
}
template<typename T> double math_to_double(const T UNUSED(v))
{
BLI_assert(false); /* Need implementation for other type. */
return 0.0;
}
#ifdef WITH_GMP
template<> double math_to_double<mpq_class>(const mpq_class v)
{
return v.get_d();
}
#endif
template<> double math_to_double<double>(const double v)
{
return v;
}
/**
* Define a templated 2D arrangement of vertices, edges, and faces.
* The #SymEdge data structure is the basis for a structure that allows
* easy traversal to neighboring (by topology) geometric elements.
* Each of #CDTVert, #CDTEdge, and #CDTFace have an input_id linked list,
* whose nodes contain integers that keep track of which input verts, edges,
* and faces, respectively, that the element was derived from.
*
* While this could be cleaned up some, it is usable by other routines in Blender
* that need to keep track of a 2D arrangement, with topology.
*/
template<typename Arith_t> struct CDTVert;
template<typename Arith_t> struct CDTEdge;
template<typename Arith_t> struct CDTFace;
template<typename Arith_t> struct SymEdge {
/** Next #SymEdge in face, doing CCW traversal of face. */
SymEdge<Arith_t> *next{nullptr};
/** Next #SymEdge CCW around vert. */
SymEdge<Arith_t> *rot{nullptr};
/** Vert at origin. */
CDTVert<Arith_t> *vert{nullptr};
/** Un-directed edge this is for. */
CDTEdge<Arith_t> *edge{nullptr};
/** Face on left side. */
CDTFace<Arith_t> *face{nullptr};
SymEdge() = default;
};
/**
* Return other #SymEdge for same #CDTEdge as \a se.
*/
template<typename T> inline SymEdge<T> *sym(const SymEdge<T> *se)
{
return se->next->rot;
}
/** Return #SymEdge whose next is \a se. */
template<typename T> inline SymEdge<T> *prev(const SymEdge<T> *se)
{
return se->rot->next->rot;
}
/** A coordinate class with extra information for fast filtered orient tests. */
template<typename T> struct FatCo {
vec2<T> exact;
vec2<double> approx;
vec2<double> abs_approx;
FatCo();
#ifdef WITH_GMP
FatCo(const vec2<mpq_class> &v);
#endif
FatCo(const vec2<double> &v);
};
#ifdef WITH_GMP
template<> struct FatCo<mpq_class> {
vec2<mpq_class> exact;
vec2<double> approx;
vec2<double> abs_approx;
FatCo()
: exact(vec2<mpq_class>(0, 0)), approx(vec2<double>(0, 0)), abs_approx(vec2<double>(0, 0))
{
}
FatCo(const vec2<mpq_class> &v)
{
exact = v;
approx = vec2<double>(v.x.get_d(), v.y.get_d());
abs_approx = vec2<double>(fabs(approx.x), fabs(approx.y));
}
FatCo(const vec2<double> &v)
{
exact = vec2<mpq_class>(v.x, v.y);
approx = v;
abs_approx = vec2<double>(fabs(approx.x), fabs(approx.y));
}
};
#endif
template<> struct FatCo<double> {
vec2<double> exact;
vec2<double> approx;
vec2<double> abs_approx;
FatCo() : exact(vec2<double>(0, 0)), approx(vec2<double>(0, 0)), abs_approx(vec2<double>(0, 0))
{
}
#ifdef WITH_GMP
FatCo(const vec2<mpq_class> &v)
{
exact = vec2<double>(v.x.get_d(), v.y.get_d());
approx = exact;
abs_approx = vec2<double>(fabs(approx.x), fabs(approx.y));
}
#endif
FatCo(const vec2<double> &v)
{
exact = v;
approx = v;
abs_approx = vec2<double>(fabs(approx.x), fabs(approx.y));
}
};
template<typename T> std::ostream &operator<<(std::ostream &stream, const FatCo<T> &co)
{
stream << "(" << co.approx.x << ", " << co.approx.y << ")";
return stream;
}
template<typename T> struct CDTVert {
/** Coordinate. */
FatCo<T> co;
/** Some edge attached to it. */
SymEdge<T> *symedge{nullptr};
/** List of corresponding vertex input ids. */
LinkNode *input_ids{nullptr};
/** Index into array that #CDTArrangement keeps. */
int index{-1};
/** Index of a CDTVert that this has merged to. -1 if no merge. */
int merge_to_index{-1};
/** Used by algorithms operating on CDT structures. */
int visit_index{0};
CDTVert() = default;
explicit CDTVert(const vec2<T> &pt);
};
template<typename Arith_t> struct CDTEdge {
/** List of input edge ids that this is part of. */
LinkNode *input_ids{nullptr};
/** The directed edges for this edge. */
SymEdge<Arith_t> symedges[2]{SymEdge<Arith_t>(), SymEdge<Arith_t>()};
CDTEdge() = default;
};
template<typename Arith_t> struct CDTFace {
/** A symedge in face; only used during output, so only valid then. */
SymEdge<Arith_t> *symedge{nullptr};
/** List of input face ids that this is part of. */
LinkNode *input_ids{nullptr};
/** Used by algorithms operating on CDT structures. */
int visit_index{0};
/** Marks this face no longer used. */
bool deleted{false};
CDTFace() = default;
};
template<typename Arith_t> struct CDTArrangement {
/* The arrangement owns the memory pointed to by the pointers in these vectors.
* They are pointers instead of actual structures because these vectors may be resized and
* other elements refer to the elements by pointer. */
/** The verts. Some may be merged to others (see their merge_to_index). */
Vector<CDTVert<Arith_t> *> verts;
/** The edges. Some may be deleted (SymEdge next and rot pointers are null). */
Vector<CDTEdge<Arith_t> *> edges;
/** The faces. Some may be deleted (see their delete member). */
Vector<CDTFace<Arith_t> *> faces;
/** Which CDTFace is the outer face. */
CDTFace<Arith_t> *outer_face{nullptr};
CDTArrangement() = default;
~CDTArrangement();
/** Hint to how much space to reserve in the Vectors of the arrangement,
* based on these counts of input elements. */
void reserve(int num_verts, int num_edges, int num_faces);
/**
* Add a new vertex to the arrangement, with the given 2D coordinate.
* It will not be connected to anything yet.
*/
CDTVert<Arith_t> *add_vert(const vec2<Arith_t> &pt);
/**
* Add an edge from v1 to v2. The edge will have a left face and a right face,
* specified by \a fleft and \a fright. The edge will not be connected to anything yet.
* If the vertices do not yet have a #SymEdge pointer,
* their pointer is set to the #SymEdge in this new edge.
*/
CDTEdge<Arith_t> *add_edge(CDTVert<Arith_t> *v1,
CDTVert<Arith_t> *v2,
CDTFace<Arith_t> *fleft,
CDTFace<Arith_t> *fright);
/**
* Add a new face. It is disconnected until an add_edge makes it the
* left or right face of an edge.
*/
CDTFace<Arith_t> *add_face();
/** Make a new edge from v to se->vert, splicing it in. */
CDTEdge<Arith_t> *add_vert_to_symedge_edge(CDTVert<Arith_t> *v, SymEdge<Arith_t> *se);
/**
* Assuming s1 and s2 are both #SymEdge's in a face with > 3 sides and one is not the next of the
* other, Add an edge from `s1->v` to `s2->v`, splitting the face in two. The original face will
* be the one that s1 has as left face, and a new face will be added and made s2 and its
* next-cycle's left face.
*/
CDTEdge<Arith_t> *add_diagonal(SymEdge<Arith_t> *s1, SymEdge<Arith_t> *s2);
/**
* Connect the verts of se1 and se2, assuming that currently those two #SymEdge's are on the
* outer boundary (have face == outer_face) of two components that are isolated from each other.
*/
CDTEdge<Arith_t> *connect_separate_parts(SymEdge<Arith_t> *se1, SymEdge<Arith_t> *se2);
/**
* Split se at fraction lambda, and return the new #CDTEdge that is the new second half.
* Copy the edge input_ids into the new one.
*/
CDTEdge<Arith_t> *split_edge(SymEdge<Arith_t> *se, Arith_t lambda);
/**
* Delete an edge. The new combined face on either side of the deleted edge will be the one that
* was e's face. There will now be an unused face, which will be marked deleted, and an unused
* #CDTEdge, marked by setting the next and rot pointers of its #SymEdge's to #nullptr.
*/
void delete_edge(SymEdge<Arith_t> *se);
/**
* If the vertex with index i in the vert array has not been merge, return it.
* Else return the one that it has merged to.
*/
CDTVert<Arith_t> *get_vert_resolve_merge(int i)
{
CDTVert<Arith_t> *v = this->verts[i];
if (v->merge_to_index != -1) {
v = this->verts[v->merge_to_index];
}
return v;
}
};
template<typename T> class CDT_state {
public:
CDTArrangement<T> cdt;
/** How many verts were in input (will be first in vert_array). */
int input_vert_tot;
/** Used for visiting things without having to initialized their visit fields. */
int visit_count;
/**
* Edge ids for face start with this, and each face gets this much index space
* to encode positions within the face.
*/
int face_edge_offset;
/** How close before coords considered equal. */
T epsilon;
explicit CDT_state(int num_input_verts, int num_input_edges, int num_input_faces, T epsilon);
~CDT_state()
{
}
};
template<typename T> CDTArrangement<T>::~CDTArrangement()
{
for (int i : this->verts.index_range()) {
CDTVert<T> *v = this->verts[i];
BLI_linklist_free(v->input_ids, nullptr);
delete v;
this->verts[i] = nullptr;
}
for (int i : this->edges.index_range()) {
CDTEdge<T> *e = this->edges[i];
BLI_linklist_free(e->input_ids, nullptr);
delete e;
this->edges[i] = nullptr;
}
for (int i : this->faces.index_range()) {
CDTFace<T> *f = this->faces[i];
BLI_linklist_free(f->input_ids, nullptr);
delete f;
this->faces[i] = nullptr;
}
}
#define DEBUG_CDT
#ifdef DEBUG_CDT
/* Some functions to aid in debugging. */
template<typename T> std::string vertname(const CDTVert<T> *v)
{
std::stringstream ss;
ss << "[" << v->index << "]";
return ss.str();
}
/* Abbreviated pointer value is easier to read in dumps. */
static std::string trunc_ptr(const void *p)
{
constexpr int TRUNC_PTR_MASK = 0xFFFF;
std::stringstream ss;
ss << std::hex << (POINTER_AS_INT(p) & TRUNC_PTR_MASK);
return ss.str();
}
template<typename T> std::string sename(const SymEdge<T> *se)
{
std::stringstream ss;
ss << "{" << trunc_ptr(se) << "}";
return ss.str();
}
template<typename T> std::ostream &operator<<(std::ostream &os, const SymEdge<T> &se)
{
if (se.next) {
os << vertname(se.vert) << "(" << se.vert->co << "->" << se.next->vert->co << ")"
<< vertname(se.next->vert);
}
else {
os << vertname(se.vert) << "(" << se.vert->co << "->NULL)";
}
return os;
}
template<typename T> std::ostream &operator<<(std::ostream &os, const SymEdge<T> *se)
{
os << *se;
return os;
}
template<typename T> std::string short_se_dump(const SymEdge<T> *se)
{
if (se == nullptr) {
return std::string("NULL");
}
return vertname(se->vert) +
(se->next == nullptr ? std::string("[NULL]") : vertname(se->next->vert));
}
template<typename T> std::ostream &operator<<(std::ostream &os, const CDT_state<T> &cdt_state)
{
os << "\nCDT\n\nVERTS\n";
for (const CDTVert<T> *v : cdt_state.cdt.verts) {
os << vertname(v) << " " << trunc_ptr(v) << ": " << v->co
<< " symedge=" << trunc_ptr(v->symedge);
if (v->merge_to_index == -1) {
os << "\n";
}
else {
os << " merge to " << vertname(cdt_state.cdt.verts[v->merge_to_index]) << "\n";
}
const SymEdge<T> *se = v->symedge;
int cnt = 0;
constexpr int print_count_limit = 25;
if (se) {
os << " edges out:\n";
do {
if (se->next == NULL) {
os << " [NULL] next/rot symedge, se=" << trunc_ptr(se) << "\n";
break;
}
if (se->next->next == NULL) {
os << " [NULL] next-next/rot symedge, se=" << trunc_ptr(se) << "\n";
break;
}
const CDTVert<T> *vother = sym(se)->vert;
os << " " << vertname(vother) << "(e=" << trunc_ptr(se->edge)
<< ", se=" << trunc_ptr(se) << ")\n";
se = se->rot;
cnt++;
} while (se != v->symedge && cnt < print_count_limit);
os << "\n";
}
}
os << "\nEDGES\n";
for (const CDTEdge<T> *e : cdt_state.cdt.edges) {
if (e->symedges[0].next == nullptr) {
continue;
}
os << trunc_ptr(&e) << ":\n";
for (int i = 0; i < 2; ++i) {
const SymEdge<T> *se = &e->symedges[i];
os << " se[" << i << "] @" << trunc_ptr(se) << " next=" << trunc_ptr(se->next)
<< ", rot=" << trunc_ptr(se->rot) << ", vert=" << trunc_ptr(se->vert) << " "
<< vertname(se->vert) << " " << se->vert->co << ", edge=" << trunc_ptr(se->edge)
<< ", face=" << trunc_ptr(se->face) << "\n";
}
}
os << "\nFACES\n";
os << "outer_face=" << trunc_ptr(cdt_state.cdt.outer_face) << "\n";
/* Only after prepare_output do faces have non-null symedges. */
if (cdt_state.cdt.outer_face->symedge != nullptr) {
for (const CDTFace<T> *f : cdt_state.cdt.faces) {
if (!f->deleted) {
os << trunc_ptr(f) << " symedge=" << trunc_ptr(f->symedge) << "\n";
}
}
}
return os;
}
template<typename T> void cdt_draw(const std::string &label, const CDTArrangement<T> &cdt)
{
static bool append = false; /* Will be set to true after first call. */
/* 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 _WIN32
const char *drawfile = "./debug_draw.html";
# else
const char *drawfile = "/tmp/debug_draw.html";
# endif
constexpr int max_draw_width = 1800;
constexpr int max_draw_height = 1600;
constexpr double margin_expand = 0.05;
constexpr int thin_line = 1;
constexpr int thick_line = 4;
constexpr int vert_radius = 3;
constexpr bool draw_vert_labels = true;
constexpr bool draw_edge_labels = false;
if (cdt.verts.size() == 0) {
return;
}
vec2<double> vmin(DBL_MAX, DBL_MAX);
vec2<double> vmax(-DBL_MAX, -DBL_MAX);
for (const CDTVert<T> *v : cdt.verts) {
for (int i = 0; i < 2; ++i) {
double dvi = v->co.approx[i];
if (dvi < vmin[i]) {
vmin[i] = dvi;
}
if (dvi > vmax[i]) {
vmax[i] = dvi;
}
}
}
double draw_margin = ((vmax.x - vmin.x) + (vmax.y - vmin.y)) * margin_expand;
double minx = vmin.x - draw_margin;
double maxx = vmax.x + draw_margin;
double miny = vmin.y - draw_margin;
double maxy = vmax.y + draw_margin;
double width = maxx - minx;
double height = maxy - miny;
double aspect = height / width;
int view_width = max_draw_width;
int view_height = static_cast<int>(view_width * aspect);
if (view_height > max_draw_height) {
view_height = max_draw_height;
view_width = static_cast<int>(view_height / aspect);
}
double scale = view_width / width;
# define SX(x) (((x)-minx) * scale)
# define SY(y) ((maxy - (y)) * scale)
std::ofstream f;
if (append) {
f.open(drawfile, std::ios_base::app);
}
else {
f.open(drawfile);
}
if (!f) {
std::cout << "Could not open file " << drawfile << "\n";
return;
}
f << "<div>" << label << "</div>\n<div>\n"
<< "<svg version=\"1.1\" "
"xmlns=\"http://www.w3.org/2000/svg\" "
"xmlns:xlink=\"http://www.w3.org/1999/xlink\" "
"xml:space=\"preserve\"\n"
<< "width=\"" << view_width << "\" height=\"" << view_height << "\">n";
for (const CDTEdge<T> *e : cdt.edges) {
if (e->symedges[0].next == nullptr) {
continue;
}
const CDTVert<T> *u = e->symedges[0].vert;
const CDTVert<T> *v = e->symedges[1].vert;
const vec2<double> &uco = u->co.approx;
const vec2<double> &vco = v->co.approx;
int strokew = e->input_ids == nullptr ? thin_line : thick_line;
f << R"(<line fill="none" stroke="black" stroke-width=")" << strokew << "\" x1=\""
<< SX(uco[0]) << "\" y1=\"" << SY(uco[1]) << "\" x2=\"" << SX(vco[0]) << "\" y2=\""
<< SY(vco[1]) << "\">\n";
f << " <title>" << vertname(u) << vertname(v) << "</title>\n";
f << "</line>\n";
if (draw_edge_labels) {
f << "<text x=\"" << SX((uco[0] + vco[0]) / 2) << "\" y=\"" << SY((uco[1] + vco[1]) / 2)
<< R"(" font-size="small">)";
f << vertname(u) << vertname(v) << sename(&e->symedges[0]) << sename(&e->symedges[1])
<< "</text>\n";
}
}
int i = 0;
for (const CDTVert<T> *v : cdt.verts) {
f << R"(<circle fill="black" cx=")" << SX(v->co.approx[0]) << "\" cy=\"" << SY(v->co.approx[1])
<< "\" r=\"" << vert_radius << "\">\n";
f << " <title>[" << i << "]" << v->co.approx << "</title>\n";
f << "</circle>\n";
if (draw_vert_labels) {
f << "<text x=\"" << SX(v->co.approx[0]) + vert_radius << "\" y=\""
<< SY(v->co.approx[1]) - vert_radius << R"(" font-size="small">[)" << i << "]</text>\n";
}
++i;
}
append = true;
# undef SX
# undef SY
}
#endif
/**
* A filtered version of orient2d, which will usually be much faster when using exact arithmetic.
* See EXACT GEOMETRIC COMPUTATION USING CASCADING, by Burnikel, Funke, and Seel.
*/
template<typename T>
static int filtered_orient2d(const FatCo<T> &a, const FatCo<T> &b, const FatCo<T> &c);
#ifdef WITH_GMP
template<>
int filtered_orient2d<mpq_class>(const FatCo<mpq_class> &a,
const FatCo<mpq_class> &b,
const FatCo<mpq_class> &c)
{
double det = (a.approx[0] - c.approx[0]) * (b.approx[1] - c.approx[1]) -
(a.approx[1] - c.approx[1]) * (b.approx[0] - c.approx[0]);
double supremum = (a.abs_approx[0] + c.abs_approx[0]) * (b.abs_approx[1] + c.abs_approx[1]) +
(a.abs_approx[1] + c.abs_approx[1]) * (b.abs_approx[0] + c.abs_approx[0]);
constexpr double index_orient2d = 6;
double err_bound = supremum * index_orient2d * DBL_EPSILON;
if (fabs(det) > err_bound) {
return det > 0 ? 1 : -1;
}
return orient2d(a.exact, b.exact, c.exact);
}
#endif
template<>
int filtered_orient2d<double>(const FatCo<double> &a,
const FatCo<double> &b,
const FatCo<double> &c)
{
return orient2d(a.approx, b.approx, c.approx);
}
/**
* A filtered version of incircle.
*/
template<typename T>
static int filtered_incircle(const FatCo<T> &a,
const FatCo<T> &b,
const FatCo<T> &c,
const FatCo<T> &d);
#ifdef WITH_GMP
template<>
int filtered_incircle<mpq_class>(const FatCo<mpq_class> &a,
const FatCo<mpq_class> &b,
const FatCo<mpq_class> &c,
const FatCo<mpq_class> &d)
{
double adx = a.approx[0] - d.approx[0];
double bdx = b.approx[0] - d.approx[0];
double cdx = c.approx[0] - d.approx[0];
double ady = a.approx[1] - d.approx[1];
double bdy = b.approx[1] - d.approx[1];
double cdy = c.approx[1] - d.approx[1];
double bdxcdy = bdx * cdy;
double cdxbdy = cdx * bdy;
double alift = adx * adx + ady * ady;
double cdxady = cdx * ady;
double adxcdy = adx * cdy;
double blift = bdx * bdx + bdy * bdy;
double adxbdy = adx * bdy;
double bdxady = bdx * ady;
double clift = cdx * cdx + cdy * cdy;
double det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) + clift * (adxbdy - bdxady);
double sup_adx = a.abs_approx[0] + d.abs_approx[0]; /* index 2. */
double sup_bdx = b.abs_approx[0] + d.abs_approx[0];
double sup_cdx = c.abs_approx[0] + d.abs_approx[0];
double sup_ady = a.abs_approx[1] + d.abs_approx[1];
double sup_bdy = b.abs_approx[1] + d.abs_approx[1];
double sup_cdy = c.abs_approx[1] + d.abs_approx[1];
double sup_bdxcdy = sup_bdx * sup_cdy; /* index 5. */
double sup_cdxbdy = sup_cdx * sup_bdy;
double sup_alift = sup_adx * sup_adx + sup_ady * sup_ady; /* index 6. */
double sup_cdxady = sup_cdx * sup_ady;
double sup_adxcdy = sup_adx * sup_cdy;
double sup_blift = sup_bdx * sup_bdx + sup_bdy * sup_bdy;
double sup_adxbdy = sup_adx * sup_bdy;
double sup_bdxady = sup_bdx * sup_ady;
double sup_clift = sup_cdx * sup_cdx + sup_cdy * sup_cdy;
double sup_det = sup_alift * (sup_bdxcdy + sup_cdxbdy) + sup_blift * (sup_cdxady + sup_adxcdy) +
sup_clift * (sup_adxbdy + sup_bdxady);
int index = 14;
double err_bound = sup_det * index * DBL_EPSILON;
if (fabs(det) > err_bound) {
return det < 0.0 ? -1 : (det > 0.0 ? 1 : 0);
}
return incircle(a.exact, b.exact, c.exact, d.exact);
}
#endif
template<>
int filtered_incircle<double>(const FatCo<double> &a,
const FatCo<double> &b,
const FatCo<double> &c,
const FatCo<double> &d)
{
return incircle(a.approx, b.approx, c.approx, d.approx);
}
/**
* Return true if `a -- b -- c` are in that order, assuming they are on a straight line according
* to #orient2d and we know the order is either `abc` or `bac`.
* This means `ab . ac` and `bc . ac` must both be non-negative.
* Use filtering to speed this up when using exact arithmetic.
*/
template<typename T> static bool in_line(const FatCo<T> &a, const FatCo<T> &b, const FatCo<T> &c);
#ifdef WITH_GMP
template<>
bool in_line<mpq_class>(const FatCo<mpq_class> &a,
const FatCo<mpq_class> &b,
const FatCo<mpq_class> &c)
{
vec2<double> ab = b.approx - a.approx;
vec2<double> bc = c.approx - b.approx;
vec2<double> ac = c.approx - a.approx;
vec2<double> supremum_ab = b.abs_approx + a.abs_approx;
vec2<double> supremum_bc = c.abs_approx + b.abs_approx;
vec2<double> supremum_ac = c.abs_approx + a.abs_approx;
double dot_ab_ac = ab.x * ac.x + ab.y * ac.y;
double supremum_dot_ab_ac = supremum_ab.x * supremum_ac.x + supremum_ab.y * supremum_ac.y;
constexpr double index = 6;
double err_bound = supremum_dot_ab_ac * index * DBL_EPSILON;
if (dot_ab_ac < -err_bound) {
return false;
}
double dot_bc_ac = bc.x * ac.x + bc.y * ac.y;
double supremum_dot_bc_ac = supremum_bc.x * supremum_ac.x + supremum_bc.y * supremum_ac.y;
err_bound = supremum_dot_bc_ac * index * DBL_EPSILON;
if (dot_bc_ac < -err_bound) {
return false;
}
vec2<mpq_class> exact_ab = b.exact - a.exact;
vec2<mpq_class> exact_ac = c.exact - a.exact;
if (vec2<mpq_class>::dot(exact_ab, exact_ac) < 0) {
return false;
}
vec2<mpq_class> exact_bc = c.exact - b.exact;
return vec2<mpq_class>::dot(exact_bc, exact_ac) >= 0;
}
#endif
template<>
bool in_line<double>(const FatCo<double> &a, const FatCo<double> &b, const FatCo<double> &c)
{
vec2<double> ab = b.approx - a.approx;
vec2<double> ac = c.approx - a.approx;
if (vec2<double>::dot(ab, ac) < 0) {
return false;
}
vec2<double> bc = c.approx - b.approx;
return vec2<double>::dot(bc, ac) >= 0;
}
template<> CDTVert<double>::CDTVert(const vec2<double> &pt)
{
this->co.exact = pt;
this->co.approx = pt;
this->co.abs_approx = pt; /* Not used, so doesn't matter. */
this->input_ids = nullptr;
this->symedge = nullptr;
this->index = -1;
this->merge_to_index = -1;
this->visit_index = 0;
}
#ifdef WITH_GMP
template<> CDTVert<mpq_class>::CDTVert(const vec2<mpq_class> &pt)
{
this->co.exact = pt;
this->co.approx = double2(pt.x.get_d(), pt.y.get_d());
this->co.abs_approx = double2(fabs(this->co.approx.x), fabs(this->co.approx.y));
this->input_ids = nullptr;
this->symedge = nullptr;
this->index = -1;
this->merge_to_index = -1;
this->visit_index = 0;
}
#endif
template<typename T> CDTVert<T> *CDTArrangement<T>::add_vert(const vec2<T> &pt)
{
CDTVert<T> *v = new CDTVert<T>(pt);
int index = this->verts.append_and_get_index(v);
v->index = index;
return v;
}
template<typename T>
CDTEdge<T> *CDTArrangement<T>::add_edge(CDTVert<T> *v1,
CDTVert<T> *v2,
CDTFace<T> *fleft,
CDTFace<T> *fright)
{
CDTEdge<T> *e = new CDTEdge<T>();
this->edges.append(e);
SymEdge<T> *se = &e->symedges[0];
SymEdge<T> *sesym = &e->symedges[1];
se->edge = sesym->edge = e;
se->face = fleft;
sesym->face = fright;
se->vert = v1;
if (v1->symedge == nullptr) {
v1->symedge = se;
}
sesym->vert = v2;
if (v2->symedge == nullptr) {
v2->symedge = sesym;
}
se->next = sesym->next = se->rot = sesym->rot = nullptr;
return e;
}
template<typename T> CDTFace<T> *CDTArrangement<T>::add_face()
{
CDTFace<T> *f = new CDTFace<T>();
this->faces.append(f);
return f;
}
template<typename T> void CDTArrangement<T>::reserve(int num_verts, int num_edges, int num_faces)
{
/* These reserves are just guesses; OK if they aren't exactly right since vectors will resize. */
this->verts.reserve(2 * num_verts);
this->edges.reserve(3 * num_verts + 2 * num_edges + 3 * 2 * num_faces);
this->faces.reserve(2 * num_verts + 2 * num_edges + 2 * num_faces);
}
template<typename T>
CDT_state<T>::CDT_state(int num_input_verts, int num_input_edges, int num_input_faces, T epsilon)
{
this->input_vert_tot = num_input_verts;
this->cdt.reserve(num_input_verts, num_input_edges, num_input_faces);
this->cdt.outer_face = this->cdt.add_face();
this->epsilon = epsilon;
this->visit_count = 0;
}
static bool id_in_list(const LinkNode *id_list, int id)
{
const LinkNode *ln;
for (ln = id_list; ln != nullptr; ln = ln->next) {
if (POINTER_AS_INT(ln->link) == id) {
return true;
}
}
return false;
}
/* Is any id in (range_start, range_start+1, ... , range_end) in id_list? */
static bool id_range_in_list(const LinkNode *id_list, int range_start, int range_end)
{
const LinkNode *ln;
int id;
for (ln = id_list; ln != nullptr; ln = ln->next) {
id = POINTER_AS_INT(ln->link);
if (id >= range_start && id <= range_end) {
return true;
}
}
return false;
}
static void add_to_input_ids(LinkNode **dst, int input_id)
{
if (!id_in_list(*dst, input_id)) {
BLI_linklist_prepend(dst, POINTER_FROM_INT(input_id));
}
}
static void add_list_to_input_ids(LinkNode **dst, const LinkNode *src)
{
const LinkNode *ln;
for (ln = src; ln != nullptr; ln = ln->next) {
add_to_input_ids(dst, POINTER_AS_INT(ln->link));
}
}
template<typename T> inline bool is_border_edge(const CDTEdge<T> *e, const CDT_state<T> *cdt)
{
return e->symedges[0].face == cdt->outer_face || e->symedges[1].face == cdt->outer_face;
}
template<typename T> inline bool is_constrained_edge(const CDTEdge<T> *e)
{
return e->input_ids != nullptr;
}
template<typename T> inline bool is_deleted_edge(const CDTEdge<T> *e)
{
return e->symedges[0].next == nullptr;
}
template<typename T> inline bool is_original_vert(const CDTVert<T> *v, CDT_state<T> *cdt)
{
return (v->index < cdt->input_vert_tot);
}
/* Return the Symedge that goes from v1 to v2, if it exists, else return nullptr. */
template<typename T>
SymEdge<T> *find_symedge_between_verts(const CDTVert<T> *v1, const CDTVert<T> *v2)
{
SymEdge<T> *t = v1->symedge;
SymEdge<T> *tstart = t;
do {
if (t->next->vert == v2) {
return t;
}
} while ((t = t->rot) != tstart);
return nullptr;
}
/**
* Return the SymEdge attached to v that has face f, if it exists, else return nullptr.
*/
template<typename T> SymEdge<T> *find_symedge_with_face(const CDTVert<T> *v, const CDTFace<T> *f)
{
SymEdge<T> *t = v->symedge;
SymEdge<T> *tstart = t;
do {
if (t->face == f) {
return t;
}
} while ((t = t->rot) != tstart);
return nullptr;
}
/**
* Is there already an edge between a and b?
*/
template<typename T> inline bool exists_edge(const CDTVert<T> *v1, const CDTVert<T> *v2)
{
return find_symedge_between_verts(v1, v2) != nullptr;
}
/**
* Is the vertex v incident on face f?
*/
template<typename T> bool vert_touches_face(const CDTVert<T> *v, const CDTFace<T> *f)
{
SymEdge<T> *se = v->symedge;
do {
if (se->face == f) {
return true;
}
} while ((se = se->rot) != v->symedge);
return false;
}
/**
* Assume s1 and s2 are both #SymEdges in a face with > 3 sides,
* and one is not the next of the other.
* Add an edge from `s1->v` to `s2->v`, splitting the face in two.
* The original face will continue to be associated with the sub-face
* that has s1, and a new face will be made for s2's new face.
* Return the new diagonal's #CDTEdge pointer.
*/
template<typename T> CDTEdge<T> *CDTArrangement<T>::add_diagonal(SymEdge<T> *s1, SymEdge<T> *s2)
{
CDTFace<T> *fold = s1->face;
CDTFace<T> *fnew = this->add_face();
SymEdge<T> *s1prev = prev(s1);
SymEdge<T> *s1prevsym = sym(s1prev);
SymEdge<T> *s2prev = prev(s2);
SymEdge<T> *s2prevsym = sym(s2prev);
CDTEdge<T> *ediag = this->add_edge(s1->vert, s2->vert, fnew, fold);
SymEdge<T> *sdiag = &ediag->symedges[0];
SymEdge<T> *sdiagsym = &ediag->symedges[1];
sdiag->next = s2;
sdiagsym->next = s1;
s2prev->next = sdiagsym;
s1prev->next = sdiag;
s1->rot = sdiag;
sdiag->rot = s1prevsym;
s2->rot = sdiagsym;
sdiagsym->rot = s2prevsym;
for (SymEdge<T> *se = s2; se != sdiag; se = se->next) {
se->face = fnew;
}
add_list_to_input_ids(&fnew->input_ids, fold->input_ids);
return ediag;
}
template<typename T>
CDTEdge<T> *CDTArrangement<T>::add_vert_to_symedge_edge(CDTVert<T> *v, SymEdge<T> *se)
{
SymEdge<T> *se_rot = se->rot;
SymEdge<T> *se_rotsym = sym(se_rot);
/* TODO: check: I think last arg in next should be sym(se)->face. */
CDTEdge<T> *e = this->add_edge(v, se->vert, se->face, se->face);
SymEdge<T> *new_se = &e->symedges[0];
SymEdge<T> *new_se_sym = &e->symedges[1];
new_se->next = se;
new_se_sym->next = new_se;
new_se->rot = new_se;
new_se_sym->rot = se_rot;
se->rot = new_se_sym;
se_rotsym->next = new_se_sym;
return e;
}
/**
* Connect the verts of se1 and se2, assuming that currently those two #SymEdge's are on
* the outer boundary (have face == outer_face) of two components that are isolated from
* each other.
*/
template<typename T>
CDTEdge<T> *CDTArrangement<T>::connect_separate_parts(SymEdge<T> *se1, SymEdge<T> *se2)
{
BLI_assert(se1->face == this->outer_face && se2->face == this->outer_face);
SymEdge<T> *se1_rot = se1->rot;
SymEdge<T> *se1_rotsym = sym(se1_rot);
SymEdge<T> *se2_rot = se2->rot;
SymEdge<T> *se2_rotsym = sym(se2_rot);
CDTEdge<T> *e = this->add_edge(se1->vert, se2->vert, this->outer_face, this->outer_face);
SymEdge<T> *new_se = &e->symedges[0];
SymEdge<T> *new_se_sym = &e->symedges[1];
new_se->next = se2;
new_se_sym->next = se1;
new_se->rot = se1_rot;
new_se_sym->rot = se2_rot;
se1->rot = new_se;
se2->rot = new_se_sym;
se1_rotsym->next = new_se;
se2_rotsym->next = new_se_sym;
return e;
}
/**
* Split se at fraction lambda,
* and return the new #CDTEdge that is the new second half.
* Copy the edge input_ids into the new one.
*/
template<typename T> CDTEdge<T> *CDTArrangement<T>::split_edge(SymEdge<T> *se, T lambda)
{
/* Split e at lambda. */
const vec2<T> *a = &se->vert->co.exact;
const vec2<T> *b = &se->next->vert->co.exact;
SymEdge<T> *sesym = sym(se);
SymEdge<T> *sesymprev = prev(sesym);
SymEdge<T> *sesymprevsym = sym(sesymprev);
SymEdge<T> *senext = se->next;
CDTVert<T> *v = this->add_vert(vec2<T>::interpolate(*a, *b, lambda));
CDTEdge<T> *e = this->add_edge(v, se->next->vert, se->face, sesym->face);
sesym->vert = v;
SymEdge<T> *newse = &e->symedges[0];
SymEdge<T> *newsesym = &e->symedges[1];
se->next = newse;
newsesym->next = sesym;
newse->next = senext;
newse->rot = sesym;
sesym->rot = newse;
senext->rot = newsesym;
newsesym->rot = sesymprevsym;
sesymprev->next = newsesym;
if (newsesym->vert->symedge == sesym) {
newsesym->vert->symedge = newsesym;
}
add_list_to_input_ids(&e->input_ids, se->edge->input_ids);
return e;
}
/**
* Delete an edge from the structure. The new combined face on either side of
* the deleted edge will be the one that was e's face.
* There will be now an unused face, marked by setting its deleted flag,
* and an unused #CDTEdge, marked by setting the next and rot pointers of
* its #SymEdges to #nullptr.
* <pre>
* . v2 .
* / \ / \
* /f|j\ / \
* / | \ / \
* |
* A | B A
* \ e| / \ /
* \ | / \ /
* \h|i/ \ /
* . v1 .
* </pre>
* Also handle variant cases where one or both ends
* are attached only to e.
*/
template<typename T> void CDTArrangement<T>::delete_edge(SymEdge<T> *se)
{
SymEdge<T> *sesym = sym(se);
CDTVert<T> *v1 = se->vert;
CDTVert<T> *v2 = sesym->vert;
CDTFace<T> *aface = se->face;
CDTFace<T> *bface = sesym->face;
SymEdge<T> *f = se->next;
SymEdge<T> *h = prev(se);
SymEdge<T> *i = sesym->next;
SymEdge<T> *j = prev(sesym);
SymEdge<T> *jsym = sym(j);
SymEdge<T> *hsym = sym(h);
bool v1_isolated = (i == se);
bool v2_isolated = (f == sesym);
if (!v1_isolated) {
h->next = i;
i->rot = hsym;
}
if (!v2_isolated) {
j->next = f;
f->rot = jsym;
}
if (!v1_isolated && !v2_isolated && aface != bface) {
for (SymEdge<T> *k = i; k != f; k = k->next) {
k->face = aface;
}
}
/* If e was representative symedge for v1 or v2, fix that. */
if (v1_isolated) {
v1->symedge = nullptr;
}
else if (v1->symedge == se) {
v1->symedge = i;
}
if (v2_isolated) {
v2->symedge = nullptr;
}
else if (v2->symedge == sesym) {
v2->symedge = f;
}
/* Mark SymEdge as deleted by setting all its pointers to NULL. */
se->next = se->rot = nullptr;
sesym->next = sesym->rot = nullptr;
if (!v1_isolated && !v2_isolated && aface != bface) {
bface->deleted = true;
if (this->outer_face == bface) {
this->outer_face = aface;
}
}
}
template<typename T> class SiteInfo {
public:
CDTVert<T> *v;
int orig_index;
};
/**
* Compare function for lexicographic sort: x, then y, then index.
*/
template<typename T> bool site_lexicographic_sort(const SiteInfo<T> &a, const SiteInfo<T> &b)
{
const vec2<T> &co_a = a.v->co.exact;
const vec2<T> &co_b = b.v->co.exact;
if (co_a[0] < co_b[0]) {
return true;
}
if (co_a[0] > co_b[0]) {
return false;
}
if (co_a[1] < co_b[1]) {
return true;
}
if (co_a[1] > co_b[1]) {
return false;
}
return a.orig_index < b.orig_index;
}
/**
* Find series of equal vertices in the sorted sites array
* and use the vertices merge_to_index to indicate that
* all vertices after the first merge to the first.
*/
template<typename T> void find_site_merges(Array<SiteInfo<T>> &sites)
{
int n = sites.size();
for (int i = 0; i < n - 1; ++i) {
int j = i + 1;
while (j < n && sites[j].v->co.exact == sites[i].v->co.exact) {
sites[j].v->merge_to_index = sites[i].orig_index;
++j;
}
if (j - i > 1) {
i = j - 1; /* j-1 because loop head will add another 1. */
}
}
}
template<typename T> inline bool vert_left_of_symedge(CDTVert<T> *v, SymEdge<T> *se)
{
return filtered_orient2d(v->co, se->vert->co, se->next->vert->co) > 0;
}
template<typename T> inline bool vert_right_of_symedge(CDTVert<T> *v, SymEdge<T> *se)
{
return filtered_orient2d(v->co, se->next->vert->co, se->vert->co) > 0;
}
/* Is se above basel? */
template<typename T>
inline bool dc_tri_valid(SymEdge<T> *se, SymEdge<T> *basel, SymEdge<T> *basel_sym)
{
return filtered_orient2d(se->next->vert->co, basel_sym->vert->co, basel->vert->co) > 0;
}
/**
* Delaunay triangulate sites[start} to sites[end-1].
* Assume sites are lexicographically sorted by coordinate.
* Return #SymEdge of CCW convex hull at left-most point in *r_le
* and that of right-most point of cw convex null in *r_re.
*/
template<typename T>
void dc_tri(CDTArrangement<T> *cdt,
Array<SiteInfo<T>> &sites,
int start,
int end,
SymEdge<T> **r_le,
SymEdge<T> **r_re)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "DC_TRI start=" << start << " end=" << end << "\n";
}
int n = end - start;
if (n <= 1) {
*r_le = nullptr;
*r_re = nullptr;
return;
}
/* Base case: if n <= 3, triangulate directly. */
if (n <= 3) {
CDTVert<T> *v1 = sites[start].v;
CDTVert<T> *v2 = sites[start + 1].v;
CDTEdge<T> *ea = cdt->add_edge(v1, v2, cdt->outer_face, cdt->outer_face);
ea->symedges[0].next = &ea->symedges[1];
ea->symedges[1].next = &ea->symedges[0];
ea->symedges[0].rot = &ea->symedges[0];
ea->symedges[1].rot = &ea->symedges[1];
if (n == 2) {
*r_le = &ea->symedges[0];
*r_re = &ea->symedges[1];
return;
}
CDTVert<T> *v3 = sites[start + 2].v;
CDTEdge<T> *eb = cdt->add_vert_to_symedge_edge(v3, &ea->symedges[1]);
int orient = filtered_orient2d(v1->co, v2->co, v3->co);
if (orient > 0) {
cdt->add_diagonal(&eb->symedges[0], &ea->symedges[0]);
*r_le = &ea->symedges[0];
*r_re = &eb->symedges[0];
}
else if (orient < 0) {
cdt->add_diagonal(&ea->symedges[0], &eb->symedges[0]);
*r_le = ea->symedges[0].rot;
*r_re = eb->symedges[0].rot;
}
else {
/* Collinear points. Just return a line. */
*r_le = &ea->symedges[0];
*r_re = &eb->symedges[0];
}
return;
}
/* Recursive case. Do left (L) and right (R) halves separately, then join. */
int n2 = n / 2;
BLI_assert(n2 >= 2 && end - (start + n2) >= 2);
SymEdge<T> *ldo;
SymEdge<T> *ldi;
SymEdge<T> *rdi;
SymEdge<T> *rdo;
dc_tri(cdt, sites, start, start + n2, &ldo, &ldi);
dc_tri(cdt, sites, start + n2, end, &rdi, &rdo);
if (dbg_level > 0) {
std::cout << "\nDC_TRI merge step for start=" << start << ", end=" << end << "\n";
std::cout << "ldo " << ldo << "\n"
<< "ldi " << ldi << "\n"
<< "rdi " << rdi << "\n"
<< "rdo " << rdo << "\n";
if (dbg_level > 1) {
std::string lab = "dc_tri (" + std::to_string(start) + "," + std::to_string(start + n2) +
")(" + std::to_string(start + n2) + "," + std::to_string(end) + ")";
cdt_draw(lab, *cdt);
}
}
/* Find lower common tangent of L and R. */
for (;;) {
if (vert_left_of_symedge(rdi->vert, ldi)) {
ldi = ldi->next;
}
else if (vert_right_of_symedge(ldi->vert, rdi)) {
rdi = sym(rdi)->rot; /* Previous edge to rdi with same right face. */
}
else {
break;
}
}
if (dbg_level > 0) {
std::cout << "common lower tangent in between\n"
<< "rdi " << rdi << "\n"
<< "ldi" << ldi << "\n";
}
CDTEdge<T> *ebasel = cdt->connect_separate_parts(sym(rdi)->next, ldi);
SymEdge<T> *basel = &ebasel->symedges[0];
SymEdge<T> *basel_sym = &ebasel->symedges[1];
if (dbg_level > 1) {
std::cout << "basel " << basel;
cdt_draw("after basel made", *cdt);
}
if (ldi->vert == ldo->vert) {
ldo = basel_sym;
}
if (rdi->vert == rdo->vert) {
rdo = basel;
}
/* Merge loop. */
for (;;) {
/* Locate the first point lcand->next->vert encountered by rising bubble,
* and delete L edges out of basel->next->vert that fail the circle test. */
SymEdge<T> *lcand = basel_sym->rot;
SymEdge<T> *rcand = basel_sym->next;
if (dbg_level > 1) {
std::cout << "\ntop of merge loop\n";
std::cout << "lcand " << lcand << "\n"
<< "rcand " << rcand << "\n"
<< "basel " << basel << "\n";
}
if (dc_tri_valid(lcand, basel, basel_sym)) {
if (dbg_level > 1) {
std::cout << "found valid lcand\n";
std::cout << " lcand" << lcand << "\n";
}
while (filtered_incircle(basel_sym->vert->co,
basel->vert->co,
lcand->next->vert->co,
lcand->rot->next->vert->co) > 0.0) {
if (dbg_level > 1) {
std::cout << "incircle says to remove lcand\n";
std::cout << " lcand" << lcand << "\n";
}
SymEdge<T> *t = lcand->rot;
cdt->delete_edge(sym(lcand));
lcand = t;
}
}
/* Symmetrically, locate first R point to be hit and delete R edges. */
if (dc_tri_valid(rcand, basel, basel_sym)) {
if (dbg_level > 1) {
std::cout << "found valid rcand\n";
std::cout << " rcand" << rcand << "\n";
}
while (filtered_incircle(basel_sym->vert->co,
basel->vert->co,
rcand->next->vert->co,
sym(rcand)->next->next->vert->co) > 0.0) {
if (dbg_level > 0) {
std::cout << "incircle says to remove rcand\n";
std::cout << " rcand" << rcand << "\n";
}
SymEdge<T> *t = sym(rcand)->next;
cdt->delete_edge(rcand);
rcand = t;
}
}
/* If both lcand and rcand are invalid, then basel is the common upper tangent. */
bool valid_lcand = dc_tri_valid(lcand, basel, basel_sym);
bool valid_rcand = dc_tri_valid(rcand, basel, basel_sym);
if (dbg_level > 0) {
std::cout << "after bubbling up, valid_lcand=" << valid_lcand
<< ", valid_rand=" << valid_rcand << "\n";
std::cout << "lcand" << lcand << "\n"
<< "rcand" << rcand << "\n";
}
if (!valid_lcand && !valid_rcand) {
break;
}
/* The next cross edge to be connected is to either `lcand->next->vert` or `rcand->next->vert`;
* if both are valid, choose the appropriate one using the #incircle test. */
if (!valid_lcand || (valid_rcand && filtered_incircle(lcand->next->vert->co,
lcand->vert->co,
rcand->vert->co,
rcand->next->vert->co) > 0)) {
if (dbg_level > 0) {
std::cout << "connecting rcand\n";
std::cout << " se1=basel_sym" << basel_sym << "\n";
std::cout << " se2=rcand->next" << rcand->next << "\n";
}
ebasel = cdt->add_diagonal(rcand->next, basel_sym);
}
else {
if (dbg_level > 0) {
std::cout << "connecting lcand\n";
std::cout << " se1=sym(lcand)" << sym(lcand) << "\n";
std::cout << " se2=basel_sym->next" << basel_sym->next << "\n";
}
ebasel = cdt->add_diagonal(basel_sym->next, sym(lcand));
}
basel = &ebasel->symedges[0];
basel_sym = &ebasel->symedges[1];
BLI_assert(basel_sym->face == cdt->outer_face);
if (dbg_level > 2) {
cdt_draw("after adding new crossedge", *cdt);
}
}
*r_le = ldo;
*r_re = rdo;
BLI_assert(sym(ldo)->face == cdt->outer_face && rdo->face == cdt->outer_face);
}
/* Guibas-Stolfi Divide-and_Conquer algorithm. */
template<typename T> void dc_triangulate(CDTArrangement<T> *cdt, Array<SiteInfo<T>> &sites)
{
/* Compress sites in place to eliminated verts that merge to others. */
int i = 0;
int j = 0;
int nsites = sites.size();
while (j < nsites) {
/* Invariant: `sites[0..i-1]` have non-merged verts from `0..(j-1)` in them. */
sites[i] = sites[j++];
if (sites[i].v->merge_to_index < 0) {
i++;
}
}
int n = i;
if (n == 0) {
return;
}
SymEdge<T> *le;
SymEdge<T> *re;
dc_tri(cdt, sites, 0, n, &le, &re);
}
/**
* Do a Delaunay Triangulation of the points in cdt.verts.
* This is only a first step in the Constrained Delaunay triangulation,
* because it doesn't yet deal with the segment constraints.
* The algorithm used is the Divide & Conquer algorithm from the
* Guibas-Stolfi "Primitives for the Manipulation of General Subdivision
* and the Computation of Voronoi Diagrams" paper.
* The data structure here is similar to but not exactly the same as
* the quad-edge structure described in that paper.
* If T is not exact arithmetic, incircle and CCW tests are done using
* Shewchuk's exact primitives, so that this routine is robust.
*
* As a preprocessing step, we want to merge all vertices that the same.
* This is accomplished by lexicographically
* sorting the coordinates first (which is needed anyway for the D&C algorithm).
* The CDTVerts with merge_to_index not equal to -1 are after this regarded
* as having been merged into the vertex with the corresponding index.
*/
template<typename T> void initial_triangulation(CDTArrangement<T> *cdt)
{
int n = cdt->verts.size();
if (n <= 1) {
return;
}
Array<SiteInfo<T>> sites(n);
for (int i = 0; i < n; ++i) {
sites[i].v = cdt->verts[i];
sites[i].orig_index = i;
}
std::sort(sites.begin(), sites.end(), site_lexicographic_sort<T>);
find_site_merges(sites);
dc_triangulate(cdt, sites);
}
/**
* Re-triangulates, assuring constrained delaunay condition,
* the pseudo-polygon that cycles from se.
* "pseudo" because a vertex may be repeated.
* See Anglada paper, "An Improved incremental algorithm
* for constructing restricted Delaunay triangulations".
*/
template<typename T> static void re_delaunay_triangulate(CDTArrangement<T> *cdt, SymEdge<T> *se)
{
if (se->face == cdt->outer_face || sym(se)->face == cdt->outer_face) {
return;
}
/* 'se' is a diagonal just added, and it is base of area to retriangulate (face on its left) */
int count = 1;
for (SymEdge<T> *ss = se->next; ss != se; ss = ss->next) {
count++;
}
if (count <= 3) {
return;
}
/* First and last are the SymEdges whose verts are first and last off of base,
* continuing from 'se'. */
SymEdge<T> *first = se->next->next;
/* We want to make a triangle with 'se' as base and some other c as 3rd vertex. */
CDTVert<T> *a = se->vert;
CDTVert<T> *b = se->next->vert;
CDTVert<T> *c = first->vert;
SymEdge<T> *cse = first;
for (SymEdge<T> *ss = first->next; ss != se; ss = ss->next) {
CDTVert<T> *v = ss->vert;
if (filtered_incircle(a->co, b->co, c->co, v->co) > 0) {
c = v;
cse = ss;
}
}
/* Add diagonals necessary to make `abc` a triangle. */
CDTEdge<T> *ebc = nullptr;
CDTEdge<T> *eca = nullptr;
if (!exists_edge(b, c)) {
ebc = cdt->add_diagonal(se->next, cse);
}
if (!exists_edge(c, a)) {
eca = cdt->add_diagonal(cse, se);
}
/* Now recurse. */
if (ebc) {
re_delaunay_triangulate(cdt, &ebc->symedges[1]);
}
if (eca) {
re_delaunay_triangulate(cdt, &eca->symedges[1]);
}
}
template<typename T> inline int tri_orient(const SymEdge<T> *t)
{
return filtered_orient2d(t->vert->co, t->next->vert->co, t->next->next->vert->co);
}
/**
* The #CrossData class defines either an endpoint or an intermediate point
* in the path we will take to insert an edge constraint.
* Each such point will either be
* (a) a vertex or
* (b) a fraction lambda (0 < lambda < 1) along some #SymEdge.]
*
* In general, lambda=0 indicates case a and lambda != 0 indicates case be.
* The 'in' edge gives the destination attachment point of a diagonal from the previous crossing,
* and the 'out' edge gives the origin attachment point of a diagonal to the next crossing.
* But in some cases, 'in' and 'out' are undefined or not needed, and will be NULL.
*
* For case (a), 'vert' will be the vertex, and lambda will be 0, and 'in' will be the #SymEdge
* from 'vert' that has as face the one that you go through to get to this vertex. If you go
* exactly along an edge then we set 'in' to NULL, since it won't be needed. The first crossing
* will have 'in' = NULL. We set 'out' to the #SymEdge that has the face we go through to get to
* the next crossing, or, if the next crossing is a case (a), then it is the edge that goes to that
* next vertex. 'out' will be NULL for the last one.
*
* For case (b), vert will be NULL at first, and later filled in with the created split vertex,
* and 'in' will be the #SymEdge that we go through, and lambda will be between 0 and 1,
* the fraction from in's vert to in->next's vert to put the split vertex.
* 'out' is not needed in this case, since the attachment point will be the sym of the first
* half of the split edge.
*/
template<typename T> class CrossData {
public:
T lambda = T(0);
CDTVert<T> *vert;
SymEdge<T> *in;
SymEdge<T> *out;
CrossData() : lambda(T(0)), vert(nullptr), in(nullptr), out(nullptr)
{
}
CrossData(T l, CDTVert<T> *v, SymEdge<T> *i, SymEdge<T> *o) : lambda(l), vert(v), in(i), out(o)
{
}
CrossData(const CrossData &other)
: lambda(other.lambda), vert(other.vert), in(other.in), out(other.out)
{
}
CrossData(CrossData &&other) noexcept
: lambda(std::move(other.lambda)),
vert(std::move(other.vert)),
in(std::move(other.in)),
out(std::move(other.out))
{
}
~CrossData() = default;
CrossData &operator=(const CrossData &other)
{
if (this != &other) {
lambda = other.lambda;
vert = other.vert;
in = other.in;
out = other.out;
}
return *this;
}
CrossData &operator=(CrossData &&other) noexcept
{
lambda = std::move(other.lambda);
vert = std::move(other.vert);
in = std::move(other.in);
out = std::move(other.out);
return *this;
}
};
template<typename T>
bool get_next_crossing_from_vert(CDT_state<T> *cdt_state,
CrossData<T> *cd,
CrossData<T> *cd_next,
const CDTVert<T> *v2);
/**
* As part of finding crossings, we found a case where the next crossing goes through vert v.
* If it came from a previous vert in cd, then cd_out is the edge that leads from that to v.
* Else cd_out can be NULL, because it won't be used.
* Set *cd_next to indicate this. We can set 'in' but not 'out'. We can set the 'out' of the
* current cd.
*/
template<typename T>
void fill_crossdata_for_through_vert(CDTVert<T> *v,
SymEdge<T> *cd_out,
CrossData<T> *cd,
CrossData<T> *cd_next)
{
SymEdge<T> *se;
cd_next->lambda = T(0);
cd_next->vert = v;
cd_next->in = nullptr;
cd_next->out = nullptr;
if (cd->lambda == 0) {
cd->out = cd_out;
}
else {
/* One of the edges in the triangle with edge sym(cd->in) contains v. */
se = sym(cd->in);
if (se->vert != v) {
se = se->next;
if (se->vert != v) {
se = se->next;
}
}
BLI_assert(se->vert == v);
cd_next->in = se;
}
}
/**
* As part of finding crossings, we found a case where orient tests say that the next crossing
* is on the #SymEdge t, while intersecting with the ray from \a curco to \a v2.
* Find the intersection point and fill in the #CrossData for that point.
* It may turn out that when doing the intersection, we get an answer that says that
* this case is better handled as through-vertex case instead, so we may do that.
* In the latter case, we want to avoid a situation where the current crossing is on an edge
* and the next will be an endpoint of the same edge. When that happens, we "rewrite history"
* and turn the current crossing into a vert one, and then extend from there.
*
* We cannot fill cd_next's 'out' edge yet, in the case that the next one ends up being a vert
* case. We need to fill in cd's 'out' edge if it was a vert case.
*/
template<typename T>
void fill_crossdata_for_intersect(const FatCo<T> &curco,
const CDTVert<T> *v2,
SymEdge<T> *t,
CrossData<T> *cd,
CrossData<T> *cd_next,
const T epsilon)
{
CDTVert<T> *va = t->vert;
CDTVert<T> *vb = t->next->vert;
CDTVert<T> *vc = t->next->next->vert;
SymEdge<T> *se_vcvb = sym(t->next);
SymEdge<T> *se_vcva = t->next->next;
BLI_assert(se_vcva->vert == vc && se_vcva->next->vert == va);
BLI_assert(se_vcvb->vert == vc && se_vcvb->next->vert == vb);
UNUSED_VARS_NDEBUG(vc);
auto isect = vec2<T>::isect_seg_seg(va->co.exact, vb->co.exact, curco.exact, v2->co.exact);
T &lambda = isect.lambda;
switch (isect.kind) {
case vec2<T>::isect_result::LINE_LINE_CROSS: {
#ifdef WITH_GMP
if (!std::is_same<T, mpq_class>::value) {
#else
if (true) {
#endif
double len_ab = vec2<double>::distance(va->co.approx, vb->co.approx);
if (lambda * len_ab <= epsilon) {
fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
}
else if ((1 - lambda) * len_ab <= epsilon) {
fill_crossdata_for_through_vert(vb, se_vcvb, cd, cd_next);
}
else {
*cd_next = CrossData<T>(lambda, nullptr, t, nullptr);
if (cd->lambda == 0) {
cd->out = se_vcva;
}
}
}
else {
*cd_next = CrossData<T>(lambda, nullptr, t, nullptr);
if (cd->lambda == 0) {
cd->out = se_vcva;
}
}
break;
}
case vec2<T>::isect_result::LINE_LINE_EXACT: {
if (lambda == 0) {
fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
}
else if (lambda == 1) {
fill_crossdata_for_through_vert(vb, se_vcvb, cd, cd_next);
}
else {
*cd_next = CrossData<T>(lambda, nullptr, t, nullptr);
if (cd->lambda == 0) {
cd->out = se_vcva;
}
}
break;
}
case vec2<T>::isect_result::LINE_LINE_NONE: {
#ifdef WITH_GMP
if (std::is_same<T, mpq_class>::value) {
BLI_assert(false);
}
#endif
/* It should be very near one end or other of segment. */
const T middle_lambda = 0.5;
if (lambda <= middle_lambda) {
fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
}
else {
fill_crossdata_for_through_vert(vb, se_vcvb, cd, cd_next);
}
break;
}
case vec2<T>::isect_result::LINE_LINE_COLINEAR: {
if (vec2<double>::distance_squared(va->co.approx, v2->co.approx) <=
vec2<double>::distance_squared(vb->co.approx, v2->co.approx)) {
fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
}
else {
fill_crossdata_for_through_vert(vb, se_vcvb, cd, cd_next);
}
break;
}
}
} // namespace blender::meshintersect
/**
* As part of finding the crossings of a ray to v2, find the next crossing after 'cd', assuming
* 'cd' represents a crossing that goes through a vertex.
*
* We do a rotational scan around cd's vertex, looking for the triangle where the ray from cd->vert
* to v2 goes between the two arms from cd->vert, or where it goes along one of the edges.
*/
template<typename T>
bool get_next_crossing_from_vert(CDT_state<T> *cdt_state,
CrossData<T> *cd,
CrossData<T> *cd_next,
const CDTVert<T> *v2)
{
SymEdge<T> *tstart = cd->vert->symedge;
SymEdge<T> *t = tstart;
CDTVert<T> *vcur = cd->vert;
bool ok = false;
do {
/* The ray from `vcur` to v2 has to go either between two successive
* edges around `vcur` or exactly along them. This time through the
* loop, check to see if the ray goes along `vcur-va`
* or between `vcur-va` and `vcur-vb`, where va is the end of t
* and vb is the next vertex (on the next rot edge around vcur, but
* should also be the next vert of triangle starting with `vcur-va`. */
if (t->face != cdt_state->cdt.outer_face && tri_orient(t) < 0) {
BLI_assert(false); /* Shouldn't happen. */
}
CDTVert<T> *va = t->next->vert;
CDTVert<T> *vb = t->next->next->vert;
int orient1 = filtered_orient2d(t->vert->co, va->co, v2->co);
if (orient1 == 0 && in_line<T>(vcur->co, va->co, v2->co)) {
fill_crossdata_for_through_vert(va, t, cd, cd_next);
ok = true;
break;
}
if (t->face != cdt_state->cdt.outer_face) {
int orient2 = filtered_orient2d(vcur->co, vb->co, v2->co);
/* Don't handle orient2 == 0 case here: next rotation will get it. */
if (orient1 > 0 && orient2 < 0) {
/* Segment intersection. */
t = t->next;
fill_crossdata_for_intersect(vcur->co, v2, t, cd, cd_next, cdt_state->epsilon);
ok = true;
break;
}
}
} while ((t = t->rot) != tstart);
return ok;
}
/**
* As part of finding the crossings of a ray to `v2`, find the next crossing after 'cd', assuming
* 'cd' represents a crossing that goes through a an edge, not at either end of that edge.
*
* We have the triangle `vb-va-vc`, where `va` and vb are the split edge and `vc` is the third
* vertex on that new side of the edge (should be closer to `v2`).
* The next crossing should be through `vc` or intersecting `vb-vc` or `va-vc`.
*/
template<typename T>
void get_next_crossing_from_edge(CrossData<T> *cd,
CrossData<T> *cd_next,
const CDTVert<T> *v2,
const T epsilon)
{
CDTVert<T> *va = cd->in->vert;
CDTVert<T> *vb = cd->in->next->vert;
vec2<T> curco = vec2<T>::interpolate(va->co.exact, vb->co.exact, cd->lambda);
FatCo<T> fat_curco(curco);
SymEdge<T> *se_ac = sym(cd->in)->next;
CDTVert<T> *vc = se_ac->next->vert;
int orient = filtered_orient2d(fat_curco, v2->co, vc->co);
if (orient < 0) {
fill_crossdata_for_intersect<T>(fat_curco, v2, se_ac->next, cd, cd_next, epsilon);
}
else if (orient > 0.0) {
fill_crossdata_for_intersect(fat_curco, v2, se_ac, cd, cd_next, epsilon);
}
else {
*cd_next = CrossData<T>{0.0, vc, se_ac->next, nullptr};
}
}
constexpr int inline_crossings_size = 128;
template<typename T>
void dump_crossings(const Vector<CrossData<T>, inline_crossings_size> &crossings)
{
std::cout << "CROSSINGS\n";
for (int i = 0; i < crossings.size(); ++i) {
std::cout << i << ": ";
const CrossData<T> &cd = crossings[i];
if (cd.lambda == 0) {
std::cout << "v" << cd.vert->index;
}
else {
std::cout << "lambda=" << cd.lambda;
}
if (cd.in != nullptr) {
std::cout << " in=" << short_se_dump(cd.in);
std::cout << " out=" << short_se_dump(cd.out);
}
std::cout << "\n";
}
}
/**
* Add a constrained edge between v1 and v2 to cdt structure.
* This may result in a number of #CDTEdges created, due to intersections
* and partial overlaps with existing cdt vertices and edges.
* Each created #CDTEdge will have input_id added to its input_ids list.
*
* If \a r_edges is not NULL, the #CDTEdges generated or found that go from
* v1 to v2 are put into that linked list, in order.
*
* Assumes that #blender_constrained_delaunay_get_output has not been called yet.
*/
template<typename T>
void add_edge_constraint(
CDT_state<T> *cdt_state, CDTVert<T> *v1, CDTVert<T> *v2, int input_id, LinkNode **r_edges)
{
constexpr int dbg_level = 0;
if (dbg_level > 0) {
std::cout << "\nADD EDGE CONSTRAINT\n" << vertname(v1) << " " << vertname(v2) << "\n";
}
LinkNodePair edge_list = {nullptr, nullptr};
if (r_edges) {
*r_edges = nullptr;
}
/*
* Handle two special cases first:
* 1) The two end vertices are the same (can happen because of merging).
* 2) There is already an edge between v1 and v2.
*/
if (v1 == v2) {
return;
}
SymEdge<T> *t = find_symedge_between_verts(v1, v2);
if (t != nullptr) {
/* Segment already there. */
add_to_input_ids(&t->edge->input_ids, input_id);
if (r_edges != nullptr) {
BLI_linklist_append(&edge_list, t->edge);
*r_edges = edge_list.list;
}
return;
}
/*
* Fill crossings array with CrossData points for intersection path from v1 to v2.
*
* At every point, the crossings array has the path so far, except that
* the .out field of the last element of it may not be known yet -- if that
* last element is a vertex, then we won't know the output edge until we
* find the next crossing.
*
* To protect against infinite loops, we keep track of which vertices
* we have visited by setting their visit_index to a new visit epoch.
*
* We check a special case first: where the segment is already there in
* one hop. Saves a bunch of orient2d tests in that common case.
*/
int visit = ++cdt_state->visit_count;
Vector<CrossData<T>, inline_crossings_size> crossings;
crossings.append(CrossData<T>(T(0), v1, nullptr, nullptr));
int n;
while (!((n = crossings.size()) > 0 && crossings[n - 1].vert == v2)) {
crossings.append(CrossData<T>());
CrossData<T> *cd = &crossings[n - 1];
CrossData<T> *cd_next = &crossings[n];
bool ok;
if (crossings[n - 1].lambda == 0) {
ok = get_next_crossing_from_vert(cdt_state, cd, cd_next, v2);
}
else {
get_next_crossing_from_edge<T>(cd, cd_next, v2, cdt_state->epsilon);
ok = true;
}
constexpr int unreasonably_large_crossings = 100000;
if (!ok || crossings.size() == unreasonably_large_crossings) {
/* Shouldn't happen but if does, just bail out. */
BLI_assert(false);
return;
}
if (crossings[n].lambda == 0) {
if (crossings[n].vert->visit_index == visit) {
/* Shouldn't happen but if it does, just bail out. */
BLI_assert(false);
return;
}
crossings[n].vert->visit_index = visit;
}
}
if (dbg_level > 0) {
dump_crossings(crossings);
}
/*
* Post-process crossings.
* Some crossings may have an intersection crossing followed
* by a vertex crossing that is on the same edge that was just
* intersected. We prefer to go directly from the previous
* crossing directly to the vertex. This may chain backwards.
*
* This loop marks certain crossings as "deleted", by setting
* their lambdas to -1.0.
*/
int ncrossings = crossings.size();
for (int i = 2; i < ncrossings; ++i) {
CrossData<T> *cd = &crossings[i];
if (cd->lambda == 0.0) {
CDTVert<T> *v = cd->vert;
int j;
CrossData<T> *cd_prev;
for (j = i - 1; j > 0; --j) {
cd_prev = &crossings[j];
if ((cd_prev->lambda == 0.0 && cd_prev->vert != v) ||
(cd_prev->lambda != 0.0 && cd_prev->in->vert != v && cd_prev->in->next->vert != v)) {
break;
}
cd_prev->lambda = -1.0; /* Mark cd_prev as 'deleted'. */
}
if (j < i - 1) {
/* Some crossings were deleted. Fix the in and out edges across gap. */
cd_prev = &crossings[j];
SymEdge<T> *se;
if (cd_prev->lambda == 0.0) {
se = find_symedge_between_verts(cd_prev->vert, v);
if (se == nullptr) {
return;
}
cd_prev->out = se;
cd->in = nullptr;
}
else {
se = find_symedge_with_face(v, sym(cd_prev->in)->face);
if (se == nullptr) {
return;
}
cd->in = se;
}
}
}
}
/*
* Insert all intersection points on constrained edges.
*/
for (int i = 0; i < ncrossings; ++i) {
CrossData<T> *cd = &crossings[i];
if (cd->lambda != 0.0 && cd->lambda != -1.0 && is_constrained_edge(cd->in->edge)) {
CDTEdge<T> *edge = cdt_state->cdt.split_edge(cd->in, cd->lambda);
cd->vert = edge->symedges[0].vert;
}
}
/*
* Remove any crossed, non-intersected edges.
*/
for (int i = 0; i < ncrossings; ++i) {
CrossData<T> *cd = &crossings[i];
if (cd->lambda != 0.0 && cd->lambda != -1.0 && !is_constrained_edge(cd->in->edge)) {
cdt_state->cdt.delete_edge(cd->in);
}
}
/*
* Insert segments for v1->v2.
*/
SymEdge<T> *tstart = crossings[0].out;
for (int i = 1; i < ncrossings; i++) {
CrossData<T> *cd = &crossings[i];
if (cd->lambda == -1.0) {
continue; /* This crossing was deleted. */
}
t = nullptr;
SymEdge<T> *tnext = t;
CDTEdge<T> *edge;
if (cd->lambda != 0.0) {
if (is_constrained_edge(cd->in->edge)) {
t = cd->vert->symedge;
tnext = sym(t)->next;
}
}
else if (cd->lambda == 0.0) {
t = cd->in;
tnext = cd->out;
if (t == nullptr) {
/* Previous non-deleted crossing must also have been a vert, and segment should exist. */
int j;
CrossData<T> *cd_prev;
for (j = i - 1; j >= 0; j--) {
cd_prev = &crossings[j];
if (cd_prev->lambda != -1.0) {
break;
}
}
BLI_assert(cd_prev->lambda == 0.0);
BLI_assert(cd_prev->out->next->vert == cd->vert);
edge = cd_prev->out->edge;
add_to_input_ids(&edge->input_ids, input_id);
if (r_edges != nullptr) {
BLI_linklist_append(&edge_list, edge);
}
}
}
if (t != nullptr) {
if (tstart->next->vert == t->vert) {
edge = tstart->edge;
}
else {
edge = cdt_state->cdt.add_diagonal(tstart, t);
}
add_to_input_ids(&edge->input_ids, input_id);
if (r_edges != nullptr) {
BLI_linklist_append(&edge_list, edge);
}
/* Now retriangulate upper and lower gaps. */
re_delaunay_triangulate(&cdt_state->cdt, &edge->symedges[0]);
re_delaunay_triangulate(&cdt_state->cdt, &edge->symedges[1]);
}
if (i < ncrossings - 1) {
if (tnext != nullptr) {
tstart = tnext;
}
}
}
if (r_edges) {
*r_edges = edge_list.list;
}
}
/**
* Incrementally add edge input edge as a constraint. This may cause the graph structure
* to change, in cases where the constraints intersect existing edges.
* The code will ensure that #CDTEdge's created will have ids that tie them back
* to the original edge constraint index.
*/
template<typename T> void add_edge_constraints(CDT_state<T> *cdt_state, const CDT_input<T> &input)
{
int ne = input.edge.size();
int nv = input.vert.size();
for (int i = 0; i < ne; i++) {
int iv1 = input.edge[i].first;
int iv2 = input.edge[i].second;
if (iv1 < 0 || iv1 >= nv || iv2 < 0 || iv2 >= nv) {
/* Ignore invalid indices in edges. */
continue;
}
CDTVert<T> *v1 = cdt_state->cdt.get_vert_resolve_merge(iv1);
CDTVert<T> *v2 = cdt_state->cdt.get_vert_resolve_merge(iv2);
add_edge_constraint(cdt_state, v1, v2, i, nullptr);
}
cdt_state->face_edge_offset = ne;
}
/**
* Add face_id to the input_ids lists of all #CDTFace's on the interior of the input face with that
* id. face_symedge is on edge of the boundary of the input face, with assumption that interior is
* on the left of that #SymEdge.
*
* The algorithm is: starting from the #CDTFace for face_symedge, add the face_id and then
* process all adjacent faces where the adjacency isn't across an edge that was a constraint added
* for the boundary of the input face.
* fedge_start..fedge_end is the inclusive range of edge input ids that are for the given face.
*
* Note: if the input face is not CCW oriented, we'll be labeling the outside, not the inside.
* Note 2: if the boundary has self-crossings, this method will arbitrarily pick one of the
* contiguous set of faces enclosed by parts of the boundary, leaving the other such un-tagged.
* This may be a feature instead of a bug if the first contiguous section is most of the face and
* the others are tiny self-crossing triangles at some parts of the boundary.
* On the other hand, if decide we want to handle these in full generality, then will need a more
* complicated algorithm (using "inside" tests and a parity rule) to decide on the interior.
*/
template<typename T>
void add_face_ids(
CDT_state<T> *cdt_state, SymEdge<T> *face_symedge, int face_id, int fedge_start, int fedge_end)
{
/* Can't loop forever since eventually would visit every face. */
cdt_state->visit_count++;
int visit = cdt_state->visit_count;
Vector<SymEdge<T> *> stack;
stack.append(face_symedge);
while (!stack.is_empty()) {
SymEdge<T> *se = stack.pop_last();
CDTFace<T> *face = se->face;
if (face->visit_index == visit) {
continue;
}
face->visit_index = visit;
add_to_input_ids(&face->input_ids, face_id);
SymEdge<T> *se_start = se;
for (se = se->next; se != se_start; se = se->next) {
if (!id_range_in_list(se->edge->input_ids, fedge_start, fedge_end)) {
SymEdge<T> *se_sym = sym(se);
CDTFace<T> *face_other = se_sym->face;
if (face_other->visit_index != visit) {
stack.append(se_sym);
}
}
}
}
}
/* Return a power of 10 that is greater than or equal to x. */
static int power_of_10_greater_equal_to(int x)
{
if (x <= 0) {
return 1;
}
int ans = 1;
BLI_assert(x < INT_MAX / 10);
while (ans < x) {
ans *= 10;
}
return ans;
}
/**
Incrementally each edge of each input face as an edge constraint.
* The code will ensure that the #CDTEdge's created will have ids that tie them
* back to the original face edge (using a numbering system for those edges
* that starts with cdt->face_edge_offset, and continues with the edges in
* order around each face in turn. And then the next face starts at
* cdt->face_edge_offset beyond the start for the previous face.
*/
template<typename T> void add_face_constraints(CDT_state<T> *cdt_state, const CDT_input<T> &input)
{
int nv = input.vert.size();
int nf = input.face.size();
int fstart = 0;
SymEdge<T> *face_symedge0 = nullptr;
CDTArrangement<T> *cdt = &cdt_state->cdt;
int maxflen = 0;
for (int f = 0; f < nf; f++) {
maxflen = max_ii(maxflen, input.face[f].size());
}
/* For convenience in debugging, make face_edge_offset be a power of 10. */
cdt_state->face_edge_offset = power_of_10_greater_equal_to(
max_ii(maxflen, cdt_state->face_edge_offset));
/* The original_edge encoding scheme doesn't work if the following is false.
* If we really have that many faces and that large a max face length that when multiplied
* together the are >= INT_MAX, then the Delaunay calculation will take unreasonably long anyway.
*/
BLI_assert(INT_MAX / cdt_state->face_edge_offset > nf);
for (int f = 0; f < nf; f++) {
int flen = input.face[f].size();
if (flen <= 2) {
/* Ignore faces with fewer than 3 vertices. */
fstart += flen;
continue;
}
int fedge_start = (f + 1) * cdt_state->face_edge_offset;
for (int i = 0; i < flen; i++) {
int face_edge_id = fedge_start + i;
int iv1 = input.face[f][i];
int iv2 = input.face[f][(i + 1) % flen];
if (iv1 < 0 || iv1 >= nv || iv2 < 0 || iv2 >= nv) {
/* Ignore face edges with invalid vertices. */
continue;
}
CDTVert<T> *v1 = cdt->get_vert_resolve_merge(iv1);
CDTVert<T> *v2 = cdt->get_vert_resolve_merge(iv2);
LinkNode *edge_list;
add_edge_constraint(cdt_state, v1, v2, face_edge_id, &edge_list);
/* Set a new face_symedge0 each time since earlier ones may not
* survive later symedge splits. Really, just want the one when
* i == flen -1, but this code guards against that one somehow
* being null.
*/
if (edge_list != nullptr) {
CDTEdge<T> *face_edge = static_cast<CDTEdge<T> *>(edge_list->link);
face_symedge0 = &face_edge->symedges[0];
if (face_symedge0->vert != v1) {
face_symedge0 = &face_edge->symedges[1];
BLI_assert(face_symedge0->vert == v1);
}
}
BLI_linklist_free(edge_list, nullptr);
}
int fedge_end = fedge_start + flen - 1;
if (face_symedge0 != nullptr) {
add_face_ids(cdt_state, face_symedge0, f, fedge_start, fedge_end);
}
fstart += flen;
}
}
/* Delete_edge but try not to mess up outer face.
* Also faces have symedges now, so make sure not
* to mess those up either. */
template<typename T> void dissolve_symedge(CDT_state<T> *cdt_state, SymEdge<T> *se)
{
CDTArrangement<T> *cdt = &cdt_state->cdt;
SymEdge<T> *symse = sym(se);
if (symse->face == cdt->outer_face) {
se = sym(se);
symse = sym(se);
}
if (ELEM(cdt->outer_face->symedge, se, symse)) {
/* Advancing by 2 to get past possible 'sym(se)'. */
if (se->next->next == se) {
cdt->outer_face->symedge = nullptr;
}
else {
cdt->outer_face->symedge = se->next->next;
}
}
else {
if (se->face->symedge == se) {
se->face->symedge = se->next;
}
if (symse->face->symedge == symse) {
symse->face->symedge = symse->next;
}
}
cdt->delete_edge(se);
}
/**
* Remove all non-constraint edges.
*/
template<typename T> void remove_non_constraint_edges(CDT_state<T> *cdt_state)
{
for (CDTEdge<T> *e : cdt_state->cdt.edges) {
SymEdge<T> *se = &e->symedges[0];
if (!is_deleted_edge(e) && !is_constrained_edge(e)) {
dissolve_symedge(cdt_state, se);
}
}
}
/*
* Remove the non-constraint edges, but leave enough of them so that all of the
* faces that would be #BMesh faces (that is, the faces that have some input representative)
* are valid: they can't have holes, they can't have repeated vertices, and they can't have
* repeated edges.
*
* Not essential, but to make the result look more aesthetically nice,
* remove the edges in order of decreasing length, so that it is more likely that the
* final remaining support edges are short, and therefore likely to make a fairly
* direct path from an outer face to an inner hole face.
*/
/**
* For sorting edges by decreasing length (squared).
*/
template<typename T> struct EdgeToSort {
double len_squared = 0.0;
CDTEdge<T> *e{nullptr};
EdgeToSort() = default;
EdgeToSort(const EdgeToSort &other) : len_squared(other.len_squared), e(other.e)
{
}
EdgeToSort(EdgeToSort &&other) noexcept : len_squared(std::move(other.len_squared)), e(other.e)
{
}
~EdgeToSort() = default;
EdgeToSort &operator=(const EdgeToSort &other)
{
if (this != &other) {
len_squared = other.len_squared;
e = other.e;
}
return *this;
}
EdgeToSort &operator=(EdgeToSort &&other)
{
len_squared = std::move(other.len_squared);
e = other.e;
return *this;
}
};
template<typename T> void remove_non_constraint_edges_leave_valid_bmesh(CDT_state<T> *cdt_state)
{
CDTArrangement<T> *cdt = &cdt_state->cdt;
size_t nedges = cdt->edges.size();
if (nedges == 0) {
return;
}
Vector<EdgeToSort<T>> dissolvable_edges;
dissolvable_edges.reserve(cdt->edges.size());
int i = 0;
for (CDTEdge<T> *e : cdt->edges) {
if (!is_deleted_edge(e) && !is_constrained_edge(e)) {
dissolvable_edges.append(EdgeToSort<T>());
dissolvable_edges[i].e = e;
const vec2<double> &co1 = e->symedges[0].vert->co.approx;
const vec2<double> &co2 = e->symedges[1].vert->co.approx;
dissolvable_edges[i].len_squared = vec2<double>::distance_squared(co1, co2);
i++;
}
}
std::sort(dissolvable_edges.begin(),
dissolvable_edges.end(),
[](const EdgeToSort<T> &a, const EdgeToSort<T> &b) -> bool {
return (a.len_squared < b.len_squared);
});
for (EdgeToSort<T> &ets : dissolvable_edges) {
CDTEdge<T> *e = ets.e;
SymEdge<T> *se = &e->symedges[0];
bool dissolve = true;
CDTFace<T> *fleft = se->face;
CDTFace<T> *fright = sym(se)->face;
if (fleft != cdt->outer_face && fright != cdt->outer_face &&
(fleft->input_ids != nullptr || fright->input_ids != nullptr)) {
/* Is there another #SymEdge with same left and right faces?
* Or is there a vertex not part of e touching the same left and right faces? */
for (SymEdge<T> *se2 = se->next; dissolve && se2 != se; se2 = se2->next) {
if (sym(se2)->face == fright ||
(se2->vert != se->next->vert && vert_touches_face(se2->vert, fright))) {
dissolve = false;
}
}
}
if (dissolve) {
dissolve_symedge(cdt_state, se);
}
}
}
template<typename T> void remove_outer_edges_until_constraints(CDT_state<T> *cdt_state)
{
// LinkNode *fstack = NULL;
// SymEdge *se, *se_start;
// CDTFace *f, *fsym;
int visit = ++cdt_state->visit_count;
cdt_state->cdt.outer_face->visit_index = visit;
/* Walk around outer face, adding faces on other side of dissolvable edges to stack. */
Vector<CDTFace<T> *> fstack;
SymEdge<T> *se_start = cdt_state->cdt.outer_face->symedge;
SymEdge<T> *se = se_start;
do {
if (!is_constrained_edge(se->edge)) {
CDTFace<T> *fsym = sym(se)->face;
if (fsym->visit_index != visit) {
fstack.append(fsym);
}
}
} while ((se = se->next) != se_start);
while (!fstack.is_empty()) {
LinkNode *to_dissolve = nullptr;
bool dissolvable;
CDTFace<T> *f = fstack.pop_last();
if (f->visit_index == visit) {
continue;
}
BLI_assert(f != cdt_state->cdt.outer_face);
f->visit_index = visit;
se_start = se = f->symedge;
do {
dissolvable = !is_constrained_edge(se->edge);
if (dissolvable) {
CDTFace<T> *fsym = sym(se)->face;
if (fsym->visit_index != visit) {
fstack.append(fsym);
}
else {
BLI_linklist_prepend(&to_dissolve, se);
}
}
se = se->next;
} while (se != se_start);
while (to_dissolve != nullptr) {
se = static_cast<SymEdge<T> *>(BLI_linklist_pop(&to_dissolve));
if (se->next != nullptr) {
dissolve_symedge(cdt_state, se);
}
}
}
}
/**
* Remove edges and merge faces to get desired output, as per options.
* \note the cdt cannot be further changed after this.
*/
template<typename T>
void prepare_cdt_for_output(CDT_state<T> *cdt_state, const CDT_output_type output_type)
{
CDTArrangement<T> *cdt = &cdt_state->cdt;
if (cdt->edges.is_empty()) {
return;
}
/* Make sure all non-deleted faces have a symedge. */
for (CDTEdge<T> *e : cdt->edges) {
if (!is_deleted_edge(e)) {
if (e->symedges[0].face->symedge == nullptr) {
e->symedges[0].face->symedge = &e->symedges[0];
}
if (e->symedges[1].face->symedge == nullptr) {
e->symedges[1].face->symedge = &e->symedges[1];
}
}
}
if (output_type == CDT_CONSTRAINTS) {
remove_non_constraint_edges(cdt_state);
}
else if (output_type == CDT_CONSTRAINTS_VALID_BMESH) {
remove_non_constraint_edges_leave_valid_bmesh(cdt_state);
}
else if (output_type == CDT_INSIDE) {
remove_outer_edges_until_constraints(cdt_state);
}
}
template<typename T>
CDT_result<T> get_cdt_output(CDT_state<T> *cdt_state,
const CDT_input<T> UNUSED(input),
CDT_output_type output_type)
{
prepare_cdt_for_output(cdt_state, output_type);
CDT_result<T> result;
CDTArrangement<T> *cdt = &cdt_state->cdt;
result.face_edge_offset = cdt_state->face_edge_offset;
/* All verts without a merge_to_index will be output.
* vert_to_output_map[i] will hold the output vertex index
* corresponding to the vert in position i in cdt->verts.
* This first loop sets vert_to_output_map for un-merged verts. */
int verts_size = cdt->verts.size();
Array<int> vert_to_output_map(verts_size);
int nv = 0;
for (int i = 0; i < verts_size; ++i) {
CDTVert<T> *v = cdt->verts[i];
if (v->merge_to_index == -1) {
vert_to_output_map[i] = nv;
++nv;
}
}
if (nv <= 0) {
return result;
}
/* Now we can set vert_to_output_map for merged verts,
* and also add the input indices of merged verts to the input_ids
* list of the merge target if they were an original input id. */
if (nv < verts_size) {
for (int i = 0; i < verts_size; ++i) {
CDTVert<T> *v = cdt->verts[i];
if (v->merge_to_index != -1) {
if (i < cdt_state->input_vert_tot) {
add_to_input_ids(&cdt->verts[v->merge_to_index]->input_ids, i);
}
vert_to_output_map[i] = vert_to_output_map[v->merge_to_index];
}
}
}
result.vert = Array<vec2<T>>(nv);
result.vert_orig = Array<Vector<int>>(nv);
int i_out = 0;
for (int i = 0; i < verts_size; ++i) {
CDTVert<T> *v = cdt->verts[i];
if (v->merge_to_index == -1) {
result.vert[i_out] = v->co.exact;
if (i < cdt_state->input_vert_tot) {
result.vert_orig[i_out].append(i);
}
for (LinkNode *ln = v->input_ids; ln; ln = ln->next) {
result.vert_orig[i_out].append(POINTER_AS_INT(ln->link));
}
++i_out;
}
}
/* All non-deleted edges will be output. */
int ne = std::count_if(cdt->edges.begin(), cdt->edges.end(), [](const CDTEdge<T> *e) -> bool {
return !is_deleted_edge(e);
});
result.edge = Array<std::pair<int, int>>(ne);
result.edge_orig = Array<Vector<int>>(ne);
int e_out = 0;
for (const CDTEdge<T> *e : cdt->edges) {
if (!is_deleted_edge(e)) {
int vo1 = vert_to_output_map[e->symedges[0].vert->index];
int vo2 = vert_to_output_map[e->symedges[1].vert->index];
result.edge[e_out] = std::pair<int, int>(vo1, vo2);
for (LinkNode *ln = e->input_ids; ln; ln = ln->next) {
result.edge_orig[e_out].append(POINTER_AS_INT(ln->link));
}
++e_out;
}
}
/* All non-deleted, non-outer faces will be output. */
int nf = std::count_if(cdt->faces.begin(), cdt->faces.end(), [=](const CDTFace<T> *f) -> bool {
return !f->deleted && f != cdt->outer_face;
});
result.face = Array<Vector<int>>(nf);
result.face_orig = Array<Vector<int>>(nf);
int f_out = 0;
for (const CDTFace<T> *f : cdt->faces) {
if (!f->deleted && f != cdt->outer_face) {
SymEdge<T> *se = f->symedge;
BLI_assert(se != nullptr);
SymEdge<T> *se_start = se;
do {
result.face[f_out].append(vert_to_output_map[se->vert->index]);
se = se->next;
} while (se != se_start);
for (LinkNode *ln = f->input_ids; ln; ln = ln->next) {
result.face_orig[f_out].append(POINTER_AS_INT(ln->link));
}
++f_out;
}
}
return result;
}
/**
* Add all the input verts into cdt. This will deduplicate,
* setting vertices merge_to_index to show merges.
*/
template<typename T> void add_input_verts(CDT_state<T> *cdt_state, const CDT_input<T> &input)
{
for (int i = 0; i < cdt_state->input_vert_tot; ++i) {
cdt_state->cdt.add_vert(input.vert[i]);
}
}
template<typename T>
CDT_result<T> delaunay_calc(const CDT_input<T> &input, CDT_output_type output_type)
{
int nv = input.vert.size();
int ne = input.edge.size();
int nf = input.face.size();
CDT_state<T> cdt_state(nv, ne, nf, input.epsilon);
add_input_verts(&cdt_state, input);
initial_triangulation(&cdt_state.cdt);
add_edge_constraints(&cdt_state, input);
add_face_constraints(&cdt_state, input);
return get_cdt_output(&cdt_state, input, output_type);
}
blender::meshintersect::CDT_result<double> delaunay_2d_calc(const CDT_input<double> &input,
CDT_output_type output_type)
{
return delaunay_calc(input, output_type);
}
#ifdef WITH_GMP
blender::meshintersect::CDT_result<mpq_class> delaunay_2d_calc(const CDT_input<mpq_class> &input,
CDT_output_type output_type)
{
return delaunay_calc(input, output_type);
}
#endif
} /* namespace blender::meshintersect */
/* C interface. */
/**
This function uses the double version of #CDT::delaunay_calc.
* Almost all of the work here is to convert between C++ #Arrays<Vector<int>>
* and a C version that linearizes all the elements and uses a "start"
* and "len" array to say where the individual vectors start and how
* long they are.
*/
extern "C" ::CDT_result *BLI_delaunay_2d_cdt_calc(const ::CDT_input *input,
const CDT_output_type output_type)
{
blender::meshintersect::CDT_input<double> in;
in.vert = blender::Array<blender::meshintersect::vec2<double>>(input->verts_len);
in.edge = blender::Array<std::pair<int, int>>(input->edges_len);
in.face = blender::Array<blender::Vector<int>>(input->faces_len);
for (int v = 0; v < input->verts_len; ++v) {
double x = static_cast<double>(input->vert_coords[v][0]);
double y = static_cast<double>(input->vert_coords[v][1]);
in.vert[v] = blender::meshintersect::vec2<double>(x, y);
}
for (int e = 0; e < input->edges_len; ++e) {
in.edge[e] = std::pair<int, int>(input->edges[e][0], input->edges[e][1]);
}
for (int f = 0; f < input->faces_len; ++f) {
in.face[f] = blender::Vector<int>(input->faces_len_table[f]);
int fstart = input->faces_start_table[f];
for (int j = 0; j < input->faces_len_table[f]; ++j) {
in.face[f][j] = input->faces[fstart + j];
}
}
in.epsilon = static_cast<double>(input->epsilon);
blender::meshintersect::CDT_result<double> res = blender::meshintersect::delaunay_2d_calc(
in, output_type);
::CDT_result *output = static_cast<::CDT_result *>(MEM_mallocN(sizeof(*output), __func__));
int nv = output->verts_len = res.vert.size();
int ne = output->edges_len = res.edge.size();
int nf = output->faces_len = res.face.size();
int tot_v_orig = 0;
int tot_e_orig = 0;
int tot_f_orig = 0;
int tot_f_lens = 0;
for (int v = 0; v < nv; ++v) {
tot_v_orig += res.vert_orig[v].size();
}
for (int e = 0; e < ne; ++e) {
tot_e_orig += res.edge_orig[e].size();
}
for (int f = 0; f < nf; ++f) {
tot_f_orig += res.face_orig[f].size();
tot_f_lens += res.face[f].size();
}
output->vert_coords = static_cast<decltype(output->vert_coords)>(
MEM_malloc_arrayN(nv, sizeof(output->vert_coords[0]), __func__));
output->verts_orig = static_cast<int *>(MEM_malloc_arrayN(tot_v_orig, sizeof(int), __func__));
output->verts_orig_start_table = static_cast<int *>(
MEM_malloc_arrayN(nv, sizeof(int), __func__));
output->verts_orig_len_table = static_cast<int *>(MEM_malloc_arrayN(nv, sizeof(int), __func__));
output->edges = static_cast<decltype(output->edges)>(
MEM_malloc_arrayN(ne, sizeof(output->edges[0]), __func__));
output->edges_orig = static_cast<int *>(MEM_malloc_arrayN(tot_e_orig, sizeof(int), __func__));
output->edges_orig_start_table = static_cast<int *>(
MEM_malloc_arrayN(ne, sizeof(int), __func__));
output->edges_orig_len_table = static_cast<int *>(MEM_malloc_arrayN(ne, sizeof(int), __func__));
output->faces = static_cast<int *>(MEM_malloc_arrayN(tot_f_lens, sizeof(int), __func__));
output->faces_start_table = static_cast<int *>(MEM_malloc_arrayN(nf, sizeof(int), __func__));
output->faces_len_table = static_cast<int *>(MEM_malloc_arrayN(nf, sizeof(int), __func__));
output->faces_orig = static_cast<int *>(MEM_malloc_arrayN(tot_f_orig, sizeof(int), __func__));
output->faces_orig_start_table = static_cast<int *>(
MEM_malloc_arrayN(nf, sizeof(int), __func__));
output->faces_orig_len_table = static_cast<int *>(MEM_malloc_arrayN(nf, sizeof(int), __func__));
int v_orig_index = 0;
for (int v = 0; v < nv; ++v) {
output->vert_coords[v][0] = static_cast<float>(res.vert[v][0]);
output->vert_coords[v][1] = static_cast<float>(res.vert[v][1]);
int this_start = v_orig_index;
output->verts_orig_start_table[v] = this_start;
for (int j : res.vert_orig[v].index_range()) {
output->verts_orig[v_orig_index++] = res.vert_orig[v][j];
}
output->verts_orig_len_table[v] = v_orig_index - this_start;
}
int e_orig_index = 0;
for (int e = 0; e < ne; ++e) {
output->edges[e][0] = res.edge[e].first;
output->edges[e][1] = res.edge[e].second;
int this_start = e_orig_index;
output->edges_orig_start_table[e] = this_start;
for (int j : res.edge_orig[e].index_range()) {
output->edges_orig[e_orig_index++] = res.edge_orig[e][j];
}
output->edges_orig_len_table[e] = e_orig_index - this_start;
}
int f_orig_index = 0;
int f_index = 0;
for (int f = 0; f < nf; ++f) {
output->faces_start_table[f] = f_index;
int flen = res.face[f].size();
output->faces_len_table[f] = flen;
for (int j = 0; j < flen; ++j) {
output->faces[f_index++] = res.face[f][j];
}
int this_start = f_orig_index;
output->faces_orig_start_table[f] = this_start;
for (int k : res.face_orig[f].index_range()) {
output->faces_orig[f_orig_index++] = res.face_orig[f][k];
}
output->faces_orig_len_table[f] = f_orig_index - this_start;
}
return output;
}
extern "C" void BLI_delaunay_2d_cdt_free(::CDT_result *result)
{
MEM_freeN(result->vert_coords);
MEM_freeN(result->edges);
MEM_freeN(result->faces);
MEM_freeN(result->faces_start_table);
MEM_freeN(result->faces_len_table);
MEM_freeN(result->verts_orig);
MEM_freeN(result->verts_orig_start_table);
MEM_freeN(result->verts_orig_len_table);
MEM_freeN(result->edges_orig);
MEM_freeN(result->edges_orig_start_table);
MEM_freeN(result->edges_orig_len_table);
MEM_freeN(result->faces_orig);
MEM_freeN(result->faces_orig_start_table);
MEM_freeN(result->faces_orig_len_table);
MEM_freeN(result);
}