Curve.cpp

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/* SPDX-FileCopyrightText: 2010-2023 Blender Authors
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */

 
#include <cstdio> /* printf */
 
#include "Curve.h"
#include "CurveAdvancedIterators.h"
#include "CurveIterators.h"
 
#include "BKE_global.hh"
#include "BLI_utildefines.h"
 
namespace Freestyle {
 
/**********************************/
/*                                */
/*                                */
/*             CurvePoint         */
/*                                */
/*                                */
/**********************************/
 
CurvePoint::CurvePoint()
{
  __A = nullptr;
  __B = nullptr;
  _t2d = 0;
}
 
CurvePoint::CurvePoint(SVertex *iA, SVertex *iB, float t)
{
  __A = iA;
  __B = iB;
  _t2d = t;
  if ((iA == nullptr) && (t == 1.0f)) {
    _Point2d = __B->point2d();
    _Point3d = __B->point3d();
  }
  else if ((iB == nullptr) && (t == 0.0f)) {
    _Point2d = __A->point2d();
    _Point3d = __A->point3d();
  }
  else {
    _Point2d = __A->point2d() + _t2d * (__B->point2d() - __A->point2d());
    _Point3d = __A->point3d() + _t2d * (__B->point3d() - __A->point3d());
  }
}
 
CurvePoint::CurvePoint(CurvePoint *iA, CurvePoint *iB, float t3)
{
  __A = nullptr;
  __B = nullptr;
  float t1 = iA->t2d();
  float t2 = iB->t2d();
  if ((iA->A() == iB->A()) && (iA->B() == iB->B()) && (iA->A() != nullptr) &&
      (iA->B() != nullptr) && (iB->A() != nullptr) && (iB->B() != nullptr))
  {
    __A = iA->A();
    __B = iB->B();
    _t2d = t1 + t2 * t3 - t1 * t3;
  }
  else if ((iA->B() == nullptr) && (iB->B() == nullptr)) {
    __A = iA->A();
    __B = iB->A();
    _t2d = t3;
  }
  else if ((iA->t2d() == 0) && (iB->t2d() == 0)) {
    __A = iA->A();
    __B = iB->A();
    _t2d = t3;
  }
  else if (iA->A() == iB->A()) {
  iA_A_eq_iB_A:
    if (iA->t2d() == 0) {
      __A = iB->A();
      __B = iB->B();
      _t2d = t3;
    }
    else if (iB->t2d() == 0) {
      __A = iA->A();
      __B = iA->B();
      _t2d = t3;
    }
  }
  else if (iA->B() == iB->B()) {
  iA_B_eq_iB_B:
    if (iA->t2d() == 1) {
      __A = iB->A();
      __B = iB->B();
      _t2d = t3;
    }
    else if (iB->t2d() == 1) {
      __A = iA->A();
      __B = iA->B();
      _t2d = t3;
    }
  }
  else if (iA->B() == iB->A()) {
  iA_B_eq_iB_A:
    if ((iA->t2d() != 1.0f) && (iB->t2d() == 0.0f)) {
      __A = iA->A();
      __B = iA->B();
      _t2d = t1 + t3 - t1 * t3;
      //_t2d = t3;
    }
    else if ((iA->t2d() == 1.0f) && (iB->t2d() != 0.0f)) {
      __A = iB->A();
      __B = iB->B();
      //_t2d = t3;
      _t2d = t2 * t3;
    }
    else if ((iA->getPoint2D() - iB->getPoint2D()).norm() < 1.0e-6) {
      __A = iB->A();
      __B = iB->B();
      //_t2d = t3;
      _t2d = t2 * t3;
    }
  }
  else if (iA->A() != nullptr && iB->A() != nullptr &&
           (iA->A()->point3d() - iB->A()->point3d()).norm() < 1.0e-6)
  {
    goto iA_A_eq_iB_A;
  }
  else if (iA->B() != nullptr && iB->B() != nullptr &&
           (iA->B()->point3d() - iB->B()->point3d()).norm() < 1.0e-6)
  {
    goto iA_B_eq_iB_B;
  }
  else if (iA->B() != nullptr && iB->A() != nullptr &&
           (iA->B()->point3d() - iB->A()->point3d()).norm() < 1.0e-6)
  {
    goto iA_B_eq_iB_A;
  }
 
  if (!__A || !__B) {
    if (G.debug & G_DEBUG_FREESTYLE) {
      printf(
          "iA A 0x%p p (%f, %f)\n", iA->A(), iA->A()->getPoint2D().x(), iA->A()->getPoint2D().y());
      printf(
          "iA B 0x%p p (%f, %f)\n", iA->B(), iA->B()->getPoint2D().x(), iA->B()->getPoint2D().y());
      printf(
          "iB A 0x%p p (%f, %f)\n", iB->A(), iB->A()->getPoint2D().x(), iB->A()->getPoint2D().y());
      printf(
          "iB B 0x%p p (%f, %f)\n", iB->B(), iB->B()->getPoint2D().x(), iB->B()->getPoint2D().y());
      printf("iA t2d %f p (%f, %f)\n", iA->t2d(), iA->getPoint2D().x(), iA->getPoint2D().y());
      printf("iB t2d %f p (%f, %f)\n", iB->t2d(), iB->getPoint2D().x(), iB->getPoint2D().y());
    }
    cerr << "Fatal error in CurvePoint::CurvePoint(CurvePoint *iA, CurvePoint *iB, float t3)"
         << endl;
  }
  BLI_assert(__A != nullptr && __B != nullptr);
 
#if 0
  _Point2d = __A->point2d() + _t2d * (__B->point2d() - __A->point2d());
  _Point3d = __A->point3d() + _t2d * (__B->point3d() - __A->point3d());
#endif
 
  _Point2d = iA->point2d() + t3 * (iB->point2d() - iA->point2d());
  _Point3d = __A->point3d() + _t2d * (__B->point3d() - __A->point3d());
}
 
CurvePoint::CurvePoint(const CurvePoint &iBrother)
{
  __A = iBrother.__A;
  __B = iBrother.__B;
  _t2d = iBrother._t2d;
  _Point2d = iBrother._Point2d;
  _Point3d = iBrother._Point3d;
}
 
CurvePoint &CurvePoint::operator=(const CurvePoint &iBrother)
{
  __A = iBrother.__A;
  __B = iBrother.__B;
  _t2d = iBrother._t2d;
  _Point2d = iBrother._Point2d;
  _Point3d = iBrother._Point3d;
  return *this;
}
 
FEdge *CurvePoint::fedge()
{
  if (getNature() & Nature::T_VERTEX) {
    return nullptr;
  }
  return __A->fedge();
}
 
FEdge *CurvePoint::getFEdge(Interface0D &inter)
{
  CurvePoint *iVertexB = dynamic_cast<CurvePoint *>(&inter);
  if (!iVertexB) {
    cerr << "Warning: CurvePoint::getFEdge() failed to cast the given 0D element to CurvePoint."
         << endl;
    return nullptr;
  }
  if (((__A == iVertexB->__A) && (__B == iVertexB->__B)) ||
      ((__A == iVertexB->__B) && (__B == iVertexB->__A)))
  {
    return __A->getFEdge(*__B);
  }
  if (__B == nullptr) {
    if (iVertexB->__B == nullptr) {
      return __A->getFEdge(*(iVertexB->__A));
    }
    if (iVertexB->__A == __A) {
      return __A->getFEdge(*(iVertexB->__B));
    }
    if (iVertexB->__B == __A) {
      return __A->getFEdge(*(iVertexB->__A));
    }
  }
  if (iVertexB->__B == nullptr) {
    if (iVertexB->__A == __A) {
      return __B->getFEdge(*(iVertexB->__A));
    }
    if (iVertexB->__A == __B) {
      return __A->getFEdge(*(iVertexB->__A));
    }
  }
  if (__B == iVertexB->__A) {
    if ((_t2d != 1) && (iVertexB->_t2d == 0)) {
      return __A->getFEdge(*__B);
    }
    if ((_t2d == 1) && (iVertexB->_t2d != 0)) {
      return iVertexB->__A->getFEdge(*(iVertexB->__B));
    }
  }
  if (__B == iVertexB->__B) {
    if ((_t2d != 1) && (iVertexB->_t2d == 1)) {
      return __A->getFEdge(*__B);
    }
    if ((_t2d == 1) && (iVertexB->_t2d != 1)) {
      return iVertexB->__A->getFEdge(*(iVertexB->__B));
    }
  }
  if (__A == iVertexB->__A) {
    if ((_t2d == 0) && (iVertexB->_t2d != 0)) {
      return iVertexB->__A->getFEdge(*(iVertexB->__B));
    }
    if ((_t2d != 0) && (iVertexB->_t2d == 0)) {
      return __A->getFEdge(*__B);
    }
  }
  if (__A == iVertexB->__B) {
    if ((_t2d == 0) && (iVertexB->_t2d != 1)) {
      return iVertexB->__A->getFEdge(*(iVertexB->__B));
    }
    if ((_t2d != 0) && (iVertexB->_t2d == 1)) {
      return __A->getFEdge(*__B);
    }
  }
#if 0
  if (G.debug & G_DEBUG_FREESTYLE) {
    printf("__A           0x%p p (%f, %f)\n", __A, __A->getPoint2D().x(), __A->getPoint2D().y());
    printf("__B           0x%p p (%f, %f)\n", __B, __B->getPoint2D().x(), __B->getPoint2D().y());
    printf("iVertexB->A() 0x%p p (%f, %f)\n",
           iVertexB->A(),
           iVertexB->A()->getPoint2D().x(),
           iVertexB->A()->getPoint2D().y());
    printf("iVertexB->B() 0x%p p (%f, %f)\n",
           iVertexB->B(),
           iVertexB->B()->getPoint2D().x(),
           iVertexB->B()->getPoint2D().y());
    printf("_t2d            %f p (%f, %f)\n", _t2d, getPoint2D().x(), getPoint2D().y());
    printf("iVertexB->t2d() %f p (%f, %f)\n",
           iVertexB->t2d(),
           iVertexB->getPoint2D().x(),
           iVertexB->getPoint2D().y());
  }
#endif
  cerr << "Warning: CurvePoint::getFEdge() failed." << endl;
 
  return nullptr;
}
 
Vec3r CurvePoint::normal() const
{
  if (__B == nullptr) {
    return __A->normal();
  }
  if (__A == nullptr) {
    return __B->normal();
  }
  Vec3r Na = __A->normal();
  if (Exception::getException()) {
    Na = Vec3r(0, 0, 0);
  }
  Vec3r Nb = __B->normal();
  if (Exception::getException()) {
    Nb = Vec3r(0, 0, 0);
  }
  // compute t3d:
  real t3d = SilhouetteGeomEngine::ImageToWorldParameter(__A->getFEdge(*__B), _t2d);
  return ((1 - t3d) * Na + t3d * Nb);
}
 
#if 0
Material CurvePoint::material() const
{
  if (__A == 0) {
    return __B->material();
  }
  return __A->material();
}
 
Id CurvePoint::shape_id() const
{
  if (__A == 0) {
    return __B->shape_id();
  }
  return __A->shape_id();
}
#endif
 
const SShape *CurvePoint::shape() const
{
  if (__A == nullptr) {
    return __B->shape();
  }
  return __A->shape();
}
 
#if 0
float CurvePoint::shape_importance() const
{
  if (__A == 0) {
    return __B->shape_importance();
  }
  return __A->shape_importance();
}
 
const uint CurvePoint::qi() const
{
  if (__A == 0) {
    return __B->qi();
  }
  if (__B == 0) {
    return __A->qi();
  }
  return __A->getFEdge(*__B)->qi();
}
#endif
 
occluder_container::const_iterator CurvePoint::occluders_begin() const
{
  if (__A == nullptr) {
    return __B->occluders_begin();
  }
  if (__B == nullptr) {
    return __A->occluders_begin();
  }
  return __A->getFEdge(*__B)->occluders_begin();
}
 
occluder_container::const_iterator CurvePoint::occluders_end() const
{
  if (__A == nullptr) {
    return __B->occluders_end();
  }
  if (__B == nullptr) {
    return __A->occluders_end();
  }
  return __A->getFEdge(*__B)->occluders_end();
}
 
bool CurvePoint::occluders_empty() const
{
  if (__A == nullptr) {
    return __B->occluders_empty();
  }
  if (__B == nullptr) {
    return __A->occluders_empty();
  }
  return __A->getFEdge(*__B)->occluders_empty();
}
 
int CurvePoint::occluders_size() const
{
  if (__A == nullptr) {
    return __B->occluders_size();
  }
  if (__B == nullptr) {
    return __A->occluders_size();
  }
  return __A->getFEdge(*__B)->occluders_size();
}
 
const SShape *CurvePoint::occluded_shape() const
{
  if (__A == nullptr) {
    return __B->occluded_shape();
  }
  if (__B == nullptr) {
    return __A->occluded_shape();
  }
  return __A->getFEdge(*__B)->occluded_shape();
}
 
const Polygon3r &CurvePoint::occludee() const
{
  if (__A == nullptr) {
    return __B->occludee();
  }
  if (__B == nullptr) {
    return __A->occludee();
  }
  return __A->getFEdge(*__B)->occludee();
}
 
bool CurvePoint::occludee_empty() const
{
  if (__A == nullptr) {
    return __B->occludee_empty();
  }
  if (__B == nullptr) {
    return __A->occludee_empty();
  }
  return __A->getFEdge(*__B)->occludee_empty();
}
 
real CurvePoint::z_discontinuity() const
{
  if (__A == nullptr) {
    return __B->z_discontinuity();
  }
  if (__B == nullptr) {
    return __A->z_discontinuity();
  }
  if (__A->getFEdge(*__B) == nullptr) {
    return 0.0;
  }
 
  return __A->getFEdge(*__B)->z_discontinuity();
}
 
#if 0
float CurvePoint::local_average_depth() const
{
  return local_average_depth_function<CurvePoint>(this);
}
 
float CurvePoint::local_depth_variance() const
{
  return local_depth_variance_function<CurvePoint>(this);
}
 
real CurvePoint::local_average_density(float sigma) const
{
  // return local_average_density<CurvePoint >(this);
  return density_function<CurvePoint>(this);
}
 
Vec3r shaded_color() const;
 
Vec3r CurvePoint::orientation2d() const
{
  if (__A == 0) {
    return __B->orientation2d();
  }
  if (__B == 0) {
    return __A->orientation2d();
  }
  return __B->point2d() - __A->point2d();
}
 
Vec3r CurvePoint::orientation3d() const
{
  if (__A == 0) {
    return __B->orientation3d();
  }
  if (__B == 0) {
    return __A->orientation3d();
  }
  return __B->point3d() - __A->point3d();
}
 
real curvature2d() const
{
  return viewedge()->curvature2d((_VertexA->point2d() + _VertexB->point2d()) / 2.0);
}
 
Vec3r CurvePoint::curvature2d_as_vector() const
{
#  if 0
  Vec3r edgeA = (_FEdges[0])->orientation2d().normalize();
  Vec3r edgeB = (_FEdges[1])->orientation2d().normalize();
  return edgeA + edgeB;
#  endif
  if (__A == 0) {
    return __B->curvature2d_as_vector();
  }
  if (__B == 0) {
    return __A->curvature2d_as_vector();
  }
  return ((1 - _t2d) * __A->curvature2d_as_vector() + _t2d * __B->curvature2d_as_vector());
}
 
real CurvePoint::curvature2d_as_angle() const
{
#  if 0
  Vec3r edgeA = (_FEdges[0])->orientation2d();
  Vec3r edgeB = (_FEdges[1])->orientation2d();
  Vec2d N1(-edgeA.y(), edgeA.x());
  N1.normalize();
  Vec2d N2(-edgeB.y(), edgeB.x());
  N2.normalize();
  return acos((N1 * N2));
#  endif
  if (__A == 0) {
    return __B->curvature2d_as_angle();
  }
  if (__B == 0) {
    return __A->curvature2d_as_angle();
  }
  return ((1 - _t2d) * __A->curvature2d_as_angle() + _t2d * __B->curvature2d_as_angle());
}
 
real CurvePoint::curvatureFredo() const
{
  if (__A == 0) {
    return __B->curvatureFredo();
  }
  if (__B == 0) {
    return __A->curvatureFredo();
  }
  return ((1 - _t2d) * __A->curvatureFredo() + _t2d * __B->curvatureFredo());
}
 
Vec2d CurvePoint::directionFredo() const
{
  if (__A == 0) {
    return __B->directionFredo();
  }
  if (__B == 0) {
    return __A->directionFredo();
  }
  return ((1 - _t2d) * __A->directionFredo() + _t2d * __B->directionFredo());
}
#endif
 
/**********************************/
/*                                */
/*                                */
/*             Curve              */
/*                                */
/*                                */
/**********************************/
 
/* for functions */
 
Curve::~Curve()
{
  if (!_Vertices.empty()) {
    for (vertex_container::iterator it = _Vertices.begin(), itend = _Vertices.end(); it != itend;
         ++it)
    {
      delete (*it);
    }
    _Vertices.clear();
  }
}
 
/* Iterators access. */
 
Curve::point_iterator Curve::points_begin(float step)
{
  vertex_container::iterator second = _Vertices.begin();
  ++second;
  return point_iterator(
      _Vertices.begin(), second, _Vertices.begin(), _Vertices.end(), _nSegments, step, 0.0f, 0.0f);
  // return point_iterator(_Vertices.begin(), second, _nSegments, step, 0.0f, 0.0f);
}
 
Curve::const_point_iterator Curve::points_begin(float step) const
{
  vertex_container::const_iterator second = _Vertices.begin();
  ++second;
  return const_point_iterator(
      _Vertices.begin(), second, _Vertices.begin(), _Vertices.end(), _nSegments, step, 0.0f, 0.0f);
  // return const_point_iterator(_Vertices.begin(), second, _nSegments, step, 0.0f, 0.0f);
}
 
Curve::point_iterator Curve::points_end(float step)
{
  return point_iterator(_Vertices.end(),
                        _Vertices.end(),
                        _Vertices.begin(),
                        _Vertices.end(),
                        _nSegments,
                        step,
                        1.0f,
                        _Length);
  // return point_iterator(_Vertices.end(), _Vertices.end(), _nSegments, step, 1.0f, _Length);
}
 
Curve::const_point_iterator Curve::points_end(float step) const
{
  return const_point_iterator(_Vertices.end(),
                              _Vertices.end(),
                              _Vertices.begin(),
                              _Vertices.end(),
                              _nSegments,
                              step,
                              1.0f,
                              _Length);
  // return const_point_iterator(_Vertices.end(), _Vertices.end(), _nSegments, step, 1.0f,
  // _Length);
}
 
// Adavnced Iterators access
Curve::point_iterator Curve::vertices_begin()
{
  return points_begin(0);
}
 
Curve::const_point_iterator Curve::vertices_begin() const
{
  return points_begin(0);
}
 
Curve::point_iterator Curve::vertices_end()
{
  return points_end(0);
}
 
Curve::const_point_iterator Curve::vertices_end() const
{
  return points_end(0);
}
 
// specialized iterators access
CurveInternal::CurvePointIterator Curve::curvePointsBegin(float t)
{
  vertex_container::iterator second = _Vertices.begin();
  ++second;
  return CurveInternal::CurvePointIterator(_Vertices.begin(),
                                           second,
                                           _Vertices.begin(),
                                           _Vertices.end(),
                                           0,
                                           _nSegments,
                                           _Length,
                                           t,
                                           0.0f,
                                           0.0f);
}
 
CurveInternal::CurvePointIterator Curve::curvePointsEnd(float t)
{
  vertex_container::iterator last = _Vertices.end();
  --last;
  return CurveInternal::CurvePointIterator(last,
                                           _Vertices.end(),
                                           _Vertices.begin(),
                                           _Vertices.end(),
                                           _nSegments,
                                           _nSegments,
                                           _Length,
                                           t,
                                           0.0f,
                                           _Length);
}
 
CurveInternal::CurvePointIterator Curve::curveVerticesBegin()
{
  return curvePointsBegin(0);
}
 
CurveInternal::CurvePointIterator Curve::curveVerticesEnd()
{
  return curvePointsEnd(0);
}
 
Interface0DIterator Curve::pointsBegin(float t)
{
  vertex_container::iterator second = _Vertices.begin();
  ++second;
  Interface0DIterator ret(new CurveInternal::CurvePointIterator(_Vertices.begin(),
                                                                second,
                                                                _Vertices.begin(),
                                                                _Vertices.end(),
                                                                0,
                                                                _nSegments,
                                                                _Length,
                                                                t,
                                                                0.0f,
                                                                0.0f));
  return ret;
}
 
Interface0DIterator Curve::pointsEnd(float t)
{
  vertex_container::iterator last = _Vertices.end();
  --last;
  Interface0DIterator ret(new CurveInternal::CurvePointIterator(last,
                                                                _Vertices.end(),
                                                                _Vertices.begin(),
                                                                _Vertices.end(),
                                                                _nSegments,
                                                                _nSegments,
                                                                _Length,
                                                                t,
                                                                0.0f,
                                                                _Length));
  return ret;
}
 
Interface0DIterator Curve::verticesBegin()
{
  return pointsBegin(0);
}
 
Interface0DIterator Curve::verticesEnd()
{
  return pointsEnd(0);
}
 
#if 0
Vec3r shaded_color(int iCombination = 0) const;
 
Vec3r Curve::orientation2d(point_iterator it) const
{
  return (*it)->orientation2d();
}
 
template<class BaseVertex> Vec3r Curve::orientation2d(int iCombination) const
{
  return edge_orientation2d_function<Curve>(this, iCombination);
}
 
Vec3r Curve::orientation3d(point_iterator it) const
{
  return (*it)->orientation3d();
}
 
Vec3r Curve::orientation3d(int iCombination) const
{
  return edge_orientation3d_function<Curve>(this, iCombination);
}
 
real curvature2d(point_iterator it) const
{
  return (*it)->curvature2d();
}
 
real curvature2d(int iCombination = 0) const;
 
Material Curve::material() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  const Material &mat = (*v)->material();
  for (; v != vend; ++v) {
    if ((*v)->material() != mat) {
      Exception::raiseException();
    }
  }
  return mat;
}
 
int Curve::qi() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  int qi_ = (*v)->qi();
  for (; v != vend; ++v) {
    if ((*v)->qi() != qi_) {
      Exception::raiseException();
    }
  }
  return qi_;
}
 
occluder_container::const_iterator occluders_begin() const
{
  return _FEdgeA->occluders().begin();
}
 
occluder_container::const_iterator occluders_end() const
{
  return _FEdgeA->occluders().end();
}
 
int Curve::occluders_size() const
{
  return qi();
}
 
bool Curve::occluders_empty() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  bool empty = (*v)->occluders_empty();
  for (; v != vend; ++v) {
    if ((*v)->occluders_empty() != empty) {
      Exception::raiseException();
    }
  }
  return empty;
}
 
const Polygon3r &occludee() const
{
  return *(_FEdgeA->aFace());
}
 
const SShape *Curve::occluded_shape() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  const SShape *sshape = (*v)->occluded_shape();
  for (; v != vend; ++v) {
    if ((*v)->occluded_shape() != sshape) {
      Exception::raiseException();
    }
  }
  return sshape;
}
 
const bool Curve::occludee_empty() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  bool empty = (*v)->occludee_empty();
  for (; v != vend; ++v) {
    if ((*v)->occludee_empty() != empty) {
      Exception::raiseException();
    }
  }
  return empty;
}
real Curve::z_discontinuity(int iCombination) const
{
  return z_discontinuity_edge_function<Curve>(this, iCombination);
}
 
int Curve::shape_id() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  Id id = (*v)->shape_id();
  for (; v != vend; ++v) {
    if ((*v)->shape_id() != id) {
      Exception::raiseException();
    }
  }
  return id.first;
}
 
const SShape *Curve::shape() const
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end();
  const SShape *sshape = (*v)->shape();
  for (; v != vend; ++v) {
    if ((*v)->shape() != sshape) {
      Exception::raiseException();
    }
  }
  return sshape;
}
 
occluder_container::const_iterator Curve::occluders_begin() const
{
  const_vertex_iterator v = vertices_begin();
  return (*v)->occluders_begin();
}
 
occluder_container::const_iterator Curve::occluders_end() const
{
  const_vertex_iterator v = vertices_end();
  return (*v)->occluders_end();
}
 
Vec3r Curve::curvature2d_as_vector(int iCombination) const
{
  return curvature2d_as_vector_edge_function<Curve>(this, iCombination);
}
 
real Curve::curvature2d_as_angle(int iCombination) const
{
  return curvature2d_as_angle_edge_function<Curve>(this, iCombination);
}
 
float Curve::shape_importance(int iCombination) const
{
  return shape_importance_edge_function<Curve>(this, iCombination);
}
 
float Curve::local_average_depth(int iCombination) const
{
  return local_average_depth_edge_function<Curve>(this, iCombination);
}
 
float Curve::local_depth_variance(int iCombination) const
{
  return local_depth_variance_edge_function<Curve>(this, iCombination);
#  if 0
  local_depth_variance_functor<Point> functor;
  float result;
  Evaluate<float, local_depth_variance_functor<Point>>(&functor, iCombination, result);
  return result;
#  endif
}
 
real Curve::local_average_density(float sigma, int iCombination) const
{
  return density_edge_function<Curve>(this, iCombination);
#  if 0
  density_functor<Point> functor;
  real result;
  Evaluate<real, density_functor<Point>>(&functor, iCombination, result);
  return result;
#  endif
}
 
/* UNUSED */
// #define EPS_CURVA_DIR 0.01
 
void Curve::computeCurvatureAndOrientation()
{
  const_vertex_iterator v = vertices_begin(), vend = vertices_end(), v2, prevV, v0;
  Vec2d p0, p1, p2;
  Vec3r p;
 
  p = (*v)->point2d();
  p0 = Vec2d(p[0], p[1]);
  prevV = v;
  ++v;
  p = (*v)->point2d();
  p1 = Vec2d(p[0], p[1]);
  Vec2d prevDir(p1 - p0);
 
  for (; v ! = vend; ++v) {
    v2 = v;
    ++v2;
    if (v2 == vend) {
      break;
    }
    Vec3r p2 = (*v2)->point2d();
 
    Vec2d BA = p0 - p1;
    Vec2d BC = p2 - p1;
    real lba = BA.norm(), lbc = BC.norm();
    BA.normalizeSafe();
    BC.normalizeSafe();
    Vec2d normalCurvature = BA + BC;
    Vec2d dir = Vec2d(BC - BA);
    Vec2d normal = Vec2d(-dir[1], dir[0]);
 
    normal.normalizeSafe();
    real curvature = normalCurvature * normal;
    if (lba + lbc > MY_EPSILON) {
      curvature /= (0.5 * lba + lbc);
    }
    if (dir.norm() < MY_EPSILON) {
      dir = 0.1 * prevDir;
    }
    (*v)->setCurvatureFredo(curvature);
    (*v)->setDirectionFredo(dir);
 
    prevV = v;
    p0 = p1;
    p1 = p2;
    prevDir = dir;
    prevDir.normalize();
  }
  (*v)->setCurvatureFredo((*prevV)->curvatureFredo());
  (*v)->setDirectionFredo((*v)->point2d() - (*prevV)->point2d());
  v0 = vertices_begin();
  v2 = v0;
  ++v2;
  (*v0)->setCurvatureFredo((*v2)->curvatureFredo());
  (*v0)->setDirectionFredo((*v2)->point2d() - (*v0)->point2d());
 
  // closed curve case one day...
 
  //
  return;
 
  // numerical degeneracy verification... we'll see later
  const_vertex_iterator vLastReliable = vertices_begin();
 
  v = vertices_begin();
  p = (*v)->point2d();
  p0 = Vec2d(p[0], p[1]);
  prevV = v;
  ++v;
  p = (*v)->point2d();
  p1 = Vec2d(p[0], p[1]);
  bool isReliable = false;
  if ((p1 - p0).norm > EPS_CURVA) {
    vLastReliable = v;
    isReliable = true;
  }
 
  for (; v != vend; ++v) {
    v2 = v;
    ++v2;
    if (v2 == vend) {
      break;
    }
    Vec3r p2 = (*v2)->point2d();
 
    Vec2d BA = p0 - p1;
    Vec2d BC = p2 - p1;
    real lba = BA.norm(), lbc = BC.norm();
 
    if ((lba + lbc) < EPS_CURVA) {
      isReliable = false;
      cerr << "/";
    }
    else {
      if (!isReliable) {  // previous points were not reliable
        const_vertex_iterator vfix = vLastReliable;
        ++vfix;
        for (; vfix != v; ++vfix) {
          (*vfix)->setCurvatureFredo((*v)->curvatureFredo());
          (*vfix)->setDirectionFredo((*v)->directionFredo());
        }
      }
      isReliable = true;
      vLastReliable = v;
    }
    prevV = v;
    p0 = p1;
    p1 = p2;
  }
}
#endif
 
} /* namespace Freestyle */