#include "tcenterlinevectP.h"

//#define _SSDEBUG                                              // Uncomment to

// enable the debug viewer

//#define _UPDATE                                               // Shows borders

// updated to current time

//====================================================

// Forward declarations

struct VectorizationContext;

//====================================================

//**************************************************************

//      Rationale

//**************************************************************

/*

  NOTE: Input is a vector of Contours, representing the borders of a

        polygonal region. First border is the outer one, followed by internal

        counter-borders; each Contour is itself a vector of "ContourNode"s,

        ordered so that the region to be thinned is at the RIGHT of segments

        formed by successive nodes.

        Output is a Graph structure representing the straight skeleton of the

        thinned region. Original contours survive the thinning procedure.

*/

//**************************************************************

//      Straight Skeleton Debugger

//**************************************************************

#ifdef _SSDEBUG

#include <qwidget></qwidget>

#include <qtransform></qtransform>

#include <qeventloop></qeventloop>

#include <qpainter></qpainter>

#include <qmouseevent></qmouseevent>

#include <qwheelevent></qwheelevent>

class SSDebugger final : public QWidget {

public:

  VectorizationContext &m_context;

  QPoint m_pos, m_pressPos;

  double m_scale;

  QTransform m_transform;

  QEventLoop m_loop;

public:

  double m_height;

public:

  SSDebugger(VectorizationContext &context);

  ~SSDebugger() {}

  void loop() { m_loop.exec(); }

  void paintEvent(QPaintEvent *event);

  void keyPressEvent(QKeyEvent *event);

  void mouseMoveEvent(QMouseEvent *event);

  void mousePressEvent(QMouseEvent *event);

  void mouseReleaseEvent(QMouseEvent *event);

  void wheelEvent(QWheelEvent *event);

  inline QPoint winToWorld(int x, int y);

  inline QPoint worldToWin(double x, double y);

  inline QPointF winToWorldF(int x, int y);

  inline bool isOnScreen(ContourNode *node);

  // Node Updates

  TPointD updated(ContourNode *input);

};

#endif  // _SSDEBUG

//**************************************************************

//      Classes

//**************************************************************

class ContourEdge {

public:

  enum { NOT_OPPOSITE = 0x1 };

public:

  TPointD m_direction;

  unsigned short m_attributes;

public:

  ContourEdge() : m_attributes(0) {}

  ContourEdge(TPointD dir) : m_direction(dir), m_attributes(0) {}

  int hasAttribute(int attr) const { return m_attributes & attr; }

  void setAttribute(int attr) { m_attributes |= attr; }

  void clearAttribute(int attr) { m_attributes &= ~attr; }

};

//--------------------------------------------------------------------------

class IndexTable {

public:

  typedef std::list<contournode *=""> IndexColumn;</contournode>

  std::vector<indexcolumn></indexcolumn>

      m_columns;  //!< Contours set by 'column identifier'.

  std::vector<int></int>

      m_identifiers;  //!< Column identifiers by original contour index.

  // NOTE: Contours are stored in 'comb' structure (vector of lists) since

  // contours may both

  // be SPLIT (new entry in a list) and MERGED (two lists merge).

public:

  IndexTable() {}

  IndexColumn *operator[](int i) { return &m_columns[i]; }

  IndexColumn &columnOfId(int id) { return m_columns[m_identifiers[id]]; }

  // Initialization

  void build(ContourFamily &family);

  void clear();

  // Specific handlers

  IndexColumn::iterator find(ContourNode *index);

  void merge(IndexColumn::iterator index1, IndexColumn::iterator index2);

  void remove(IndexColumn::iterator index);

};

//--------------------------------------------------------------------------

class Event {

public:

  /*! \remark  Values are sorted by preference at simultaneous events.    */

  enum Type            //! An event's possible types.

  { special,           //!< A vertex event that is also an edge event (V case).

    edge,              //!< An edge shrinks to 0 length.

    vertex,            //!< Two contour nodes clash.

    split_regenerate,  //!< Placeholder type for split events that must be

                       //! regenerated.

    split,             //!< An edge is split by a clashing contour node.

    failure };

public:

  double m_height;

  double m_displacement;

  ContourNode *m_generator;

  ContourNode *m_coGenerator;

  Type m_type;

  unsigned int m_algoritmicTime;

  VectorizationContext *m_context;

public:

  // In-builder event constructor

  Event(ContourNode *generator, VectorizationContext *context);

  // Event calculators

  inline void calculateEdgeEvent();

  inline void calculateSplitEvent();

  // Auxiliary event calculators

  inline double splitDisplacementWith(ContourNode *plane);

  inline bool tryRayEdgeCollisionWith(ContourNode *edge);

  // Event handlers

  inline bool process();

  inline void processEdgeEvent();

  inline void processMaxEvent();

  inline void processSplitEvent();

  inline void processVertexEvent();

  inline void processSpecialEvent();

private:

  inline bool testRayEdgeCollision(ContourNode *opposite, double &displacement,

                                   double &height, double &side1,

                                   double &side2);

};

//--------------------------------------------------------------------------

struct EventGreater {

  bool operator()(const Event &event1, const Event &event2) const {

    return event1.m_height > event2.m_height ||

           (event1.m_height == event2.m_height &&

            event1.m_type > event2.m_type);

  }

};

class Timeline final

    : public std::priority_queue<event, std::vector<event="">, EventGreater> {</event,>

public:

  Timeline() {}

  // NOTE: Timeline construction contains the most complex part of

  // vectorization;

  // progress bar partial notification happens there, so thisVectorizer's signal

  // emission methods must be passed and used.

  void build(ContourFamily &polygons, VectorizationContext &context,

             VectorizerCore *thisVectorizer);

};

//==========================================================================

//--------------------------------------

//    Preliminary methods/functions

//--------------------------------------

// IndexTable methods

void IndexTable::build(ContourFamily &family) {

  unsigned int i;

  m_columns.resize(family.size());

  m_identifiers.resize(family.size());

  // NOTE: At the beginning, m_identifiers= 1, .. , m_columns.size() - 1;

  for (i = 0; i < m_columns.size(); ++i) {

    m_identifiers[i] = i;

    m_columns[i].push_back(&family[i][0]);

    // Each node referenced in the Table is signed as 'head' of the cirular

    // list.

    family[i][0].setAttribute(ContourNode::HEAD);

  }

}

//--------------------------------------------------------------------------

// Explanation: during the skeletonization process, ContourNodes and calculated

// Events are unaware of global index-changes generated by other events, so

// the position of index stored in one Event has to be retrieved in the

// IndexTable before event processing begins.

// NOTE: Can this be done in a more efficient way?...

inline IndexTable::IndexColumn::iterator IndexTable::find(ContourNode *sought) {

  int indexId = m_identifiers[sought->m_ancestorContour];

  IndexColumn::iterator res;

  // Search for the HEAD attribute in index's Contour

  for (; !sought->hasAttribute(ContourNode::HEAD); sought = sought->m_next)

    ;

  // Finally, find index through our column

  for (res = m_columns[indexId].begin(); (*res) != sought; ++res)

    ;

  return res;

}

//--------------------------------------------------------------------------

// Handles active contour merging due to split/vertex events

void IndexTable::merge(IndexColumn::iterator index1,

                       IndexColumn::iterator index2) {

  IndexColumn::iterator current;

  int identifier1 = m_identifiers[(*index1)->m_ancestorContour],

      identifier2 = m_identifiers[(*index2)->m_ancestorContour];

  remove(index2);  // We maintain only one index of the merged contour

  // Now, append columns

  if (!m_columns[identifier2].empty()) {

    append<indextable::indexcolumn, indextable::indexcolumn::reverse_iterator="">(</indextable::indexcolumn,>

        m_columns[identifier1], m_columns[identifier2]);

    m_columns[identifier2].clear();

  }

  // Then, update stored identifiers

  for (unsigned int k = 0; k < m_columns.size(); ++k) {

    if (m_identifiers[k] == identifier2) m_identifiers[k] = identifier1;

  }

}

//--------------------------------------------------------------------------

// Removes given index in Table

inline void IndexTable::remove(IndexColumn::iterator index) {

  m_columns[m_identifiers[(*index)->m_ancestorContour]].erase(index);

}

//--------------------------------------------------------------------------

inline void IndexTable::clear() { m_columns.clear(), m_identifiers.clear(); }

//==========================================================================

//                    Straight Skeleton Algorithm

//==========================================================================

//------------------------------

//      Global Variables

//------------------------------

struct VectorizationContext {

  VectorizerCoreGlobals *m_globals;

  // Globals

  unsigned int m_totalNodes;      // Number of original contour nodes

  unsigned int m_contoursCount;   // Number of contours in input region

  IndexTable m_activeTable;       // Index table of active contours

  SkeletonGraph *m_output;        // Output skeleton of input region

  double m_currentHeight;         // Height of our 'roof-flooding' process

  Timeline m_timeline;            // Ordered queue of all possible events

  unsigned int m_algoritmicTime;  // Number of events precessed up to now

  // Containers

  std::vector<contouredge> m_edgesHeap;</contouredge>

  std::vector<contournode> m_nodesHeap;  // of *non-original* nodes only</contournode>

  unsigned int m_nodesHeapCount;         // number of nodes used in nodesHeap

  //'Linear Axis-added' *pseudo-original* nodes and edges

  std::vector<contournode> m_linearNodesHeap;</contournode>

  std::vector<contouredge> m_linearEdgesHeap;</contouredge>

  unsigned int m_linearNodesHeapCount;

public:

  VectorizationContext(VectorizerCoreGlobals *globals) : m_globals(globals) {}

  ContourNode *getNode() { return &m_nodesHeap[m_nodesHeapCount++]; }

  ContourNode *getLinearNode() {

    return &m_linearNodesHeap[m_linearNodesHeapCount];

  }

  ContourEdge *getLinearEdge() {

    return &m_linearEdgesHeap[m_linearNodesHeapCount++];

  }

  inline void addLinearNodeBefore(ContourNode *node);

  inline void repairDegenerations(

      const std::vector<contournode *=""> °enerates);</contournode>

  inline void prepareGlobals();

  inline void prepareContours(ContourFamily &family);

  inline void newSkeletonLink(unsigned int cur, ContourNode *node);

};

//--------------------------------------------------------------------------

// WARNING: To be launched only *after* prepareContours - node countings happen

// there

inline void VectorizationContext::prepareGlobals() {

  // NOTE: Let n be the total number of nodes in the family, k the number of

  // split events

  //      effectively happening in the process, m the number of original

  //      contours of the family.

  //      Now:

  //        * Each split event eliminates its generating reflex node and

  //        introduces

  //          two convex nodes

  //        * Each edge event eliminates its couple of generating nodes and

  //          introduces one new convex node

  //        * Each max event eliminates 3 generating nodes without introducing

  //        new ones

  // So, split events introduce 2k non-original nodes, and (k-m+2) is the number

  // of max events

  // necessarily happening, since (m-1) are the *merging* split events.

  // On the n+k-3(k-m+2) nodes remaining for pure edge events, as many

  // non-original nodes are inserted.

  //=> This yields 2k + n-2k+3m-6= n+3m-6 non-original nodes. Contemporaneous

  // events such as

  // vertex and special events can only decrease the number of non-original

  // nodes requested.

  // Initialize non-original nodes container

  m_nodesHeap.resize(m_totalNodes + 3 * m_contoursCount - 6);

  m_nodesHeapCount = 0;

  // Reset time/height variables

  m_currentHeight  = 0;

  m_algoritmicTime = 0;

  // Clean IndexTable

  m_activeTable.clear();

}

//--------------------------------------------------------------------------

inline void VectorizationContext::newSkeletonLink(unsigned int cur,

                                                  ContourNode *node) {

  if (node->hasAttribute(ContourNode::SK_NODE_DROPPED)) {

    SkeletonArc arcCopy(node);

    m_output->newLink(node->m_outputNode, cur, arcCopy);

    arcCopy.turn();

    m_output->newLink(cur, node->m_outputNode, arcCopy);

  }

}

//==========================================================================

//===================================

//    Thinning Functions/Methods

//===================================

//--------------------------------------------------------------------------

//----------------------------------------

//      Repair Polygon Degenerations

//----------------------------------------

// EXPLANATION: After "Polygonizer", there may be simpleness degenerations

// about polygons which are dangerous to deal in the thinning process.

// Typically, these correspond to cases in which node->m_direction.z ~ 0

//(too fast), and are concave.

// We then deal with them *before* the process begins, by splitting one

// such node in two slower ones (known as 'Linear Axis' method).

inline void VectorizationContext::addLinearNodeBefore(ContourNode *node) {

  ContourNode *newNode = getLinearNode();

  ContourEdge *newEdge = getLinearEdge();

  newNode->m_position = node->m_position;

  // Build new edge

  if (node->m_direction.z < 0.1)

    newEdge->m_direction = rotate270(node->m_edge->m_direction);

  else

    newEdge->m_direction = normalize(node->m_edge->m_direction +

                                     node->m_prev->m_edge->m_direction);

  newNode->m_edge = newEdge;

  // Link newNode

  newNode->m_prev      = node->m_prev;

  newNode->m_next      = node;

  node->m_prev->m_next = newNode;

  node->m_prev         = newNode;

  // Build remaining infos

  node->buildNodeInfos();  // Rebuild

  newNode->buildNodeInfos();

  newNode->m_updateTime      = 0;

  newNode->m_ancestor        = node->m_ancestor;

  newNode->m_ancestorContour = node->m_ancestorContour;

  // Set node and newNode's edges not to be recognized as possible

  // opposites by the other (could happen in *future* instants)

  //                *DO NOT REMOVE!*

  node->m_notOpposites.push_back(newNode->m_edge);

  node->m_notOpposites.push_back(newNode->m_prev->m_edge);

  newNode->m_notOpposites.push_back(node->m_edge);

  // Further sign newly added node

  newNode->setAttribute(ContourNode::LINEAR_ADDED);

}

//--------------------------------------------------------------------------

inline void VectorizationContext::repairDegenerations(

    const std::vector<contournode *=""> °enerates) {</contournode>

  unsigned int i;

  m_linearNodesHeap.resize(degenerates.size());

  m_linearEdgesHeap.resize(degenerates.size());

  m_linearNodesHeapCount = 0;

  for (i = 0; i < degenerates.size(); ++i) {

    if (!degenerates[i]->hasAttribute(ContourNode::AMBIGUOUS_LEFT)) {

      addLinearNodeBefore(degenerates[i]);

      m_totalNodes++;

    }

  }

}

//--------------------------------------------------------------------------

//--------------------------------

//    Node Infos Construction

//--------------------------------

inline void VectorizationContext::prepareContours(ContourFamily &family) {

  std::vector<contournode *=""> degenerateNodes;</contournode>

  // Build circular links

  unsigned int i, j, k;

  unsigned int current;

  m_contoursCount = family.size();

  m_totalNodes    = 0;

  for (i = 0; i < family.size(); ++i) {

    for (j = 0, k = family[i].size() - 1; j < family[i].size(); k = j, ++j) {

      family[i][k].m_next = &family[i][j];

      family[i][j].m_prev = &family[i][k];

    }

    m_totalNodes += family[i].size();

  }

  // Build node edges

  m_edgesHeap.resize(m_totalNodes);

  current = 0;

  for (i = 0; i < family.size(); ++i) {

    for (j = 0, k = family[i].size() - 1; j < family[i].size(); k = j, ++j) {

      m_edgesHeap[current].m_direction = normalize(

          planeProjection(family[i][j].m_position - family[i][k].m_position));

      family[i][k].m_edge = &m_edgesHeap[current];

      current++;

    }

  }

  bool maxThicknessNotZero = m_globals->currConfig->m_maxThickness > 0.0;

  // Now build remaining infos

  for (i = 0; i < family.size(); ++i) {

    for (j = 0; j < family[i].size(); ++j) {

      family[i][j].buildNodeInfos();

      family[i][j].m_updateTime = 0;

      family[i][j].m_ancestor        = j;

      family[i][j].m_ancestorContour = i;

      // Check the following degeneration

      if (family[i][j].m_concave && family[i][j].m_direction.z < 0.3) {

        // Push this node among degenerate ones

        degenerateNodes.push_back(&family[i][j]);

      }

      // Insert output node in sharp angles

      if (!family[i][j].m_concave && family[i][j].m_direction.z < 0.6 &&

          maxThicknessNotZero) {

        family[i][j].setAttribute(ContourNode::SK_NODE_DROPPED);

        family[i][j].m_outputNode = m_output->newNode(family[i][j].m_position);

      }

      // Push on nodes having AMBIGUOUS_RIGHT attribute

      if (family[i][j].hasAttribute(ContourNode::AMBIGUOUS_RIGHT))

        family[i][j].m_position += 0.02 * family[i][j].m_direction;

    }

  }

  // Finally, ensure polygon degenerations found are solved

  if (maxThicknessNotZero) repairDegenerations(degenerateNodes);

}

//--------------------------------------------------------------------------

// WARNING: m_edge field of *this* and *previous* node must already be defined.

inline void ContourNode::buildNodeInfos(bool forceConvex) {

  TPointD direction;

  double parameter;

  // Calculate node convexity

  if (forceConvex)

    m_concave = 0;

  else if (cross(m_edge->m_direction, m_prev->m_edge->m_direction) < 0) {

    m_concave = 1;

  } else

    m_concave = 0;

  // Build node direction

  direction = m_edge->m_direction - m_prev->m_edge->m_direction;

  parameter = norm(direction);

  if (parameter > 0.01) {

    direction                = direction * (1 / parameter);

    if (m_concave) direction = -direction;

  } else

    direction = rotate270(m_edge->m_direction);

  m_direction.x = direction.x;

  m_direction.y = direction.y;

  // Calculate node speed

  m_direction.z = cross(planeProjection(m_direction), m_edge->m_direction);

  if (m_direction.z < 0) m_direction.z = 0;

  // Calculate angular momentum

  m_AngularMomentum = cross(m_position, m_direction);

  if (m_concave) {

    m_AuxiliaryMomentum1 = m_AuxiliaryMomentum2 = m_AngularMomentum;

  } else {

    m_AuxiliaryMomentum1 =

        cross(m_position,

              T3DPointD(m_edge->m_direction.y, -m_edge->m_direction.x, 1));

    m_AuxiliaryMomentum2 =

        cross(m_position, T3DPointD(m_prev->m_edge->m_direction.y,

                                    -m_prev->m_edge->m_direction.x, 1));

  }

}

//--------------------------------------------------------------------------

//---------------------------------

//      Timeline Construction

//---------------------------------

// NOTE: In the following, we achieve these results:

//        * Build the timeline - events priority queue

//        * Process those split events which *necessarily* happen

// Pre-processing of split events is useful in order to lower execution times.

// Each node is first associated to a random integer; then a referencing

// vector is ordered according to those integers - events are calculated

// following this order. Split events are therefore calculated sparsely

// along the polygons, allowing a significant time reduction effect.

class RandomizedNode {

public:

  ContourNode *m_node;

  int m_number;

  RandomizedNode() {}

  RandomizedNode(ContourNode *node) : m_node(node), m_number(rand()) {}

  inline ContourNode *operator->(void) { return m_node; }

};

class RandomizedNodeLess {

public:

  RandomizedNodeLess() {}

  inline bool operator()(RandomizedNode a, RandomizedNode b) {

    return (a.m_number < b.m_number);

  }

};

//--------------------------------------------------------------------------

void Timeline::build(ContourFamily &polygons, VectorizationContext &context,

                     VectorizerCore *thisVectorizer) {

  unsigned int i, j, current;

  std::vector<randomizednode> nodesToBeTreated(context.m_totalNodes);</randomizednode>

  T3DPointD momentum, ray;

  // Build casual ordered node-array

  for (i = 0, current = 0; i < polygons.size(); ++i)

    for (j                        = 0; j < polygons[i].size(); ++j)

      nodesToBeTreated[current++] = RandomizedNode(&polygons[i][j]);

  // Same for linear-added nodes

  for (i                        = 0; i < context.m_linearNodesHeapCount; ++i)

    nodesToBeTreated[current++] = RandomizedNode(&context.m_linearNodesHeap[i]);

  double maxThickness = context.m_globals->currConfig->m_maxThickness;

  // Compute events generated by nodes

  // NOTE: are edge events to be computed BEFORE split ones?

  for (i = 0; i < nodesToBeTreated.size(); ++i) {

    // Break calculation at user cancel press

    if (thisVectorizer->isCanceled()) break;

    Event currentEvent(nodesToBeTreated[i].m_node, &context);

    // Notify event calculation

    if (!nodesToBeTreated[i].m_node->hasAttribute(ContourNode::LINEAR_ADDED))

      thisVectorizer->emitPartialDone();

    if (currentEvent.m_type != Event::failure &&

        currentEvent.m_height < maxThickness)

#ifdef _PREPROCESS

      if (currentEvent.m_type == Event::split) {

        if (currentEvent.m_coGenerator->m_concave) {

          ray =

              T3DPointD(currentEvent.m_coGenerator->m_edge->m_direction.y,

                        -currentEvent.m_coGenerator->m_edge->m_direction.x, 1);

          momentum = cross(currentEvent.m_coGenerator->m_position, ray);

          if (currentEvent.m_generator->m_direction * momentum +

                  ray * currentEvent.m_generator->m_AngularMomentum <

              0) {

            timeline.push(currentEvent);

            continue;

          }

        }

        if (currentEvent.m_coGenerator->m_next->m_concave) {

          ray =

              T3DPointD(currentEvent.m_coGenerator->m_edge->m_direction.y,

                        -currentEvent.m_coGenerator->m_edge->m_direction.x, 1);

          momentum = cross(currentEvent.m_coGenerator->m_next->m_position, ray);

          if (currentEvent.m_generator->m_direction * momentum +

                  ray * currentEvent.m_generator->m_AngularMomentum >

              0) {

            timeline.push(currentEvent);

            continue;

          }

        }

        if (cross(currentEvent.m_generator->m_edge->m_direction,

                  currentEvent.m_coGenerator->m_edge->m_direction) > 0.02 &&

            cross(currentEvent.m_coGenerator->m_edge->m_direction,

                  currentEvent.m_generator->m_prev->m_edge->m_direction) >

                0.02)  // 0.02 in comparison with 'parameter' in buildNodeInfos

        {

          // Pre-processing succeeded

          currentEvent.process();

          continue;

        }

      }

#endif

    push(currentEvent);

  }

}

//--------------------------------------------------------------------------

//------------------------------

//      Event Calculation

//------------------------------

// Calculates event generated by input node

Event::Event(ContourNode *generator, VectorizationContext *context)

    : m_height(infinity)

    , m_displacement(infinity)

    , m_generator(generator)

    , m_type(failure)

    , m_algoritmicTime(context->m_algoritmicTime)

    , m_context(context) {

  if (generator->m_concave)

    calculateSplitEvent();

  else

    calculateEdgeEvent();

}

//--------------------------------------------------------------------------

// The edge event *generated by a node* is defined as the earliest edge event

// generated by its adjacent edges. Remember that 'edge events' correspond to

// those in which one edge gets 0 length.

inline void Event::calculateEdgeEvent() {

  struct locals {

    static inline void buildDisplacements(ContourNode *edgeFirst, double &d1,

                                          double &d2) {

      ContourNode *edgeSecond = edgeFirst->m_next;

      // If bisectors are almost opposite, avoid: there must be another bisector

      // colliding with m_generator *before* coGenerator - allowing a positive

      // result here may interfere with it.

      if ((edgeFirst->m_concave && edgeSecond->m_concave) ||

          edgeFirst->m_direction * edgeSecond->m_direction < -0.9) {

        d1 = d2 = -1.0;

        return;

      }

      double det = edgeFirst->m_direction.y * edgeSecond->m_direction.x -

                   edgeFirst->m_direction.x * edgeSecond->m_direction.y;

      double cx = edgeSecond->m_position.x - edgeFirst->m_position.x,

             cy = edgeSecond->m_position.y - edgeFirst->m_position.y;

      d1 = (edgeSecond->m_direction.x * cy - edgeSecond->m_direction.y * cx) /

           det;

      d2 =

          (edgeFirst->m_direction.x * cy - edgeFirst->m_direction.y * cx) / det;

    }

    static inline double height(ContourNode *node, double displacement) {

      return node->m_position.z + displacement * node->m_direction.z;

    }

  };  // locals

  double minHeight, minDisplacement;

  bool positiveEdgeDispl;

  m_type = edge;

  // Calculate the two possible displacement parameters

  double firstDisplacement, prevDisplacement, nextDisplacement,

      lastDisplacement;

  // right == prev

  locals::buildDisplacements(m_generator, nextDisplacement, lastDisplacement);

  locals::buildDisplacements(m_generator->m_prev, firstDisplacement,

                             prevDisplacement);

  // Take the smallest positive between them and assign the co-generator

  // NOTE: In a missed vertex event, the threshold value is to compare with the

  // possible pushes at the end of processSplit

  // However, admitting slightly negative displacements should be ok: due to the

  // weak linear axis imposed for concave

  // vertices, it is impossible to have little negative displacements apart from

  // the above mentioned pushed case.

  //   ..currently almost true..

  static const double minusTol = -0.03;

  bool prevDispPositive = (prevDisplacement > minusTol);

  bool nextDispPositive = (nextDisplacement > minusTol);

  if (nextDispPositive) {

    if (!prevDispPositive || nextDisplacement < prevDisplacement) {

      m_coGenerator     = m_generator;

      minDisplacement   = nextDisplacement;

      minHeight         = locals::height(m_coGenerator, nextDisplacement);

      positiveEdgeDispl = (nextDispPositive && lastDisplacement > minusTol);

    } else {

      m_coGenerator   = m_generator->m_prev;

      minDisplacement = prevDisplacement;

      minHeight       = locals::height(

          m_coGenerator,

          firstDisplacement);  // Height is built on the edge's first

      positiveEdgeDispl =

          (prevDispPositive &&

           firstDisplacement >

               minusTol);  // endpoint to have the same values on adjacent

    }                      // generators. It's important for SPECIAL events.

  } else if (prevDispPositive) {

    m_coGenerator   = m_generator->m_prev;

    minDisplacement = prevDisplacement;

    minHeight = locals::height(m_coGenerator, firstDisplacement);  // Same here

    positiveEdgeDispl = (prevDispPositive && firstDisplacement > minusTol);

  } else {

    m_type = failure;

    return;

  }

  // NOTA: Le const di tolleranza sono da confrontare tra:

  // a) i push alla fine di processSplit per evitare rogne coi vertex multipli

  // b) Le condizioni di esclusione su side1 e side2 in trySplit che evitano a)

  // c) Le condizioni di riconoscimento di vertex e special events - perche' se

  // mancano...

  // Special cases: (forse da raffinare le condizioni - comunque ora sono

  // efficaci)

  if (nextDispPositive && !m_generator->m_concave) {

    if (m_generator->m_prev->m_concave && m_generator->m_next->m_concave &&

        fabs(nextDisplacement - prevDisplacement) <

            0.1)  // condizione debole per escludere subito i casi evidentemente

                  // innocenti

    {

      // Check 'V' (special) event - can generate a new concave vertex

      ContourNode *prevRay = m_generator->m_prev,

                  *nextRay = m_generator->m_next;

      double side = prevRay->m_direction * nextRay->m_AngularMomentum +

                    nextRay->m_direction * prevRay->m_AngularMomentum;

      // NOTE: fabs(side) / || prevRay->dir x nextRay->dir ||  is the distance

      // between the two rays.

      if (fabs(side) <

          0.03 * norm(cross(prevRay->m_direction, nextRay->m_direction)))

        m_type = special, m_coGenerator = m_generator;

    } else if (fabs(nextDisplacement - prevDisplacement) < 0.01) {

      // Then choose to make the event with a concave vertex (to resemble the

      // 'LL' case)

      m_coGenerator =

          m_generator->m_next->m_concave ? m_generator : m_generator->m_prev;

    }

  }

  // Now, if calculated height is coherent, this Event is valid.

  if (positiveEdgeDispl  // Edges shrinking to a point after a FORWARD

      ||

      minHeight > m_context->m_currentHeight -

                      0.01)  // displacement are processable - this dominates

    m_height = minHeight,

    m_displacement =

        minDisplacement;  // height considerations which may be affected by

  else                    // numerical errors

    m_type = failure;

}

//--------------------------------------------------------------------------

inline void Event::calculateSplitEvent() {

  unsigned int i;

  bool forceFirst;

  ContourNode *opposite, *first, *last;

  std::list<contournode *="">::iterator currentContour;</contournode>

  // Sign *edges* not to be taken as possible opposites

  for (i = 0; i < m_generator->m_notOpposites.size(); ++i)