shapes.h

/*
 * Poly2Tri Copyright (c) 2009-2010, Poly2Tri Contributors
 * http://code.google.com/p/poly2tri/
 *
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without modification,
 * are permitted provided that the following conditions are met:
 *
 * * Redistributions of source code must retain the above copyright notice,
 *   this list of conditions and the following disclaimer.
 * * Redistributions in binary form must reproduce the above copyright notice,
 *   this list of conditions and the following disclaimer in the documentation
 *   and/or other materials provided with the distribution.
 * * Neither the name of Poly2Tri nor the names of its contributors may be
 *   used to endorse or promote products derived from this software without specific
 *   prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

// Include guard
#ifndef SHAPES_H
#define SHAPES_H

#include <vector>
#include <cstddef>
#include <assert.h>
#include <cmath>

namespace p2t {
struct Edge;

struct Point
{
    double x, y;

    /// Default constructor does nothing (for performance).
    Point()
    {
        x   = 0.0;
        y   = 0.0;
    }

    /// The edges this point constitutes an upper ending point
    std::vector<Edge*> edge_list;

    /// Construct using coordinates.
    Point( double x, double y ) : x( x ), y( y ) {}

    /// Set this point to all zeros.
    void set_zero()
    {
        x   = 0.0;
        y   = 0.0;
    }

    /// Set this point to some specified coordinates.
    void set( double x_, double y_ )
    {
        x   = x_;
        y   = y_;
    }

    /// Negate this point.
    Point operator -() const
    {
        Point v;

        v.set( -x, -y );
        return v;
    }

    /// Add a point to this point.
    void operator +=( const Point& v )
    {
        x   += v.x;
        y   += v.y;
    }

    /// Subtract a point from this point.
    void operator -=( const Point& v )
    {
        x   -= v.x;
        y   -= v.y;
    }

    /// Multiply this point by a scalar.
    void operator *=( double a )
    {
        x   *= a;
        y   *= a;
    }

    /// Get the length of this point (the norm).
    double Length() const
    {
        return sqrt( x * x + y * y );
    }

    /// Convert this point into a unit point. Returns the Length.
    double Normalize()
    {
        double len = Length();

        x   /= len;
        y   /= len;
        return len;
    }
};

// Represents a simple polygon's edge
struct Edge
{
    Point* p, * q;

    /// Constructor
    Edge( Point& p1, Point& p2 ) : p( &p1 ), q( &p2 )
    {
        if( p1.y > p2.y )
        {
            q   = &p1;
            p   = &p2;
        }
        else if( p1.y == p2.y )
        {
            if( p1.x > p2.x )
            {
                q   = &p1;
                p   = &p2;
            }
            else if( p1.x == p2.x )
            {
                // Repeat points
                assert( false );
            }
        }

        q->edge_list.push_back( this );
    }
};

// Triangle-based data structures are know to have better performance than quad-edge structures
// See: J. Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator"
// "Triangulations in CGAL"
class Triangle
{
public:

/// Constructor
    Triangle( Point& a, Point& b, Point& c );

/// Flags to determine if an edge is a Constrained edge
    bool    constrained_edge[3];
/// Flags to determine if an edge is a Delauney edge
    bool    delaunay_edge[3];

    Point*      GetPoint( const int& index );
    Point*      PointCW( Point& point );
    Point*      PointCCW( Point& point );
    Point*      OppositePoint( Triangle& t, Point& p );

    Triangle*   GetNeighbor( const int& index );
    void        MarkNeighbor( Point* p1, Point* p2, Triangle* t );
    void        MarkNeighbor( Triangle& t );

    void        MarkConstrainedEdge( const int index );
    void        MarkConstrainedEdge( Edge& edge );
    void        MarkConstrainedEdge( Point* p, Point* q );

    int         Index( const Point* p );
    int         EdgeIndex( const Point* p1, const Point* p2 );

    Triangle*   NeighborCW( Point& point );
    Triangle*   NeighborCCW( Point& point );
    bool        GetConstrainedEdgeCCW( Point& p );
    bool        GetConstrainedEdgeCW( Point& p );
    void        SetConstrainedEdgeCCW( Point& p, bool ce );
    void        SetConstrainedEdgeCW( Point& p, bool ce );
    bool        GetDelunayEdgeCCW( Point& p );
    bool        GetDelunayEdgeCW( Point& p );
    void        SetDelunayEdgeCCW( Point& p, bool e );
    void        SetDelunayEdgeCW( Point& p, bool e );

    bool        Contains( Point* p );
    bool        Contains( const Edge& e );
    bool        Contains( Point* p, Point* q );
    void        Legalize( Point& point );
    void        Legalize( Point& opoint, Point& npoint );

/**
 * Clears all references to all other triangles and points
 */
    void        Clear();
    void        ClearNeighbor( Triangle* triangle );
    void        ClearNeighbors();
    void        ClearDelunayEdges();

    inline bool IsInterior();
    inline void IsInterior( bool b );

    Triangle&   NeighborAcross( Point& opoint );

    void        DebugPrint();

private:

/// Triangle points
    Point*      points_[3];
/// Neighbor list
    Triangle*   neighbors_[3];

/// Has this triangle been marked as an interior triangle?
    bool        interior_;
};

inline bool cmp( const Point* a, const Point* b )
{
    if( a->y < b->y )
    {
        return true;
    }
    else if( a->y == b->y )
    {
        // Make sure q is point with greater x value
        if( a->x < b->x )
        {
            return true;
        }
    }

    return false;
}


/// Add two points_ component-wise.
inline Point operator +( const Point& a, const Point& b )
{
    return Point( a.x + b.x, a.y + b.y );
}


/// Subtract two points_ component-wise.
inline Point operator -( const Point& a, const Point& b )
{
    return Point( a.x - b.x, a.y - b.y );
}


/// Multiply point by scalar
inline Point operator *( double s, const Point& a )
{
    return Point( s * a.x, s * a.y );
}


inline bool operator ==( const Point& a, const Point& b )
{
    return a.x == b.x && a.y == b.y;
}


inline bool operator !=( const Point& a, const Point& b )
{
    return !(a.x == b.x) && !(a.y == b.y);
}


/// Peform the dot product on two vectors.
inline double Dot( const Point& a, const Point& b )
{
    return a.x * b.x + a.y * b.y;
}


/// Perform the cross product on two vectors. In 2D this produces a scalar.
inline double Cross( const Point& a, const Point& b )
{
    return a.x * b.y - a.y * b.x;
}


/// Perform the cross product on a point and a scalar. In 2D this produces
/// a point.
inline Point Cross( const Point& a, double s )
{
    return Point( s * a.y, -s * a.x );
}


/// Perform the cross product on a scalar and a point. In 2D this produces
/// a point.
inline Point Cross( const double s, const Point& a )
{
    return Point( -s * a.y, s * a.x );
}


inline Point* Triangle::GetPoint( const int& index )
{
    return points_[index];
}


inline Triangle* Triangle::GetNeighbor( const int& index )
{
    return neighbors_[index];
}


inline bool Triangle::Contains( Point* p )
{
    return p == points_[0] || p == points_[1] || p == points_[2];
}


inline bool Triangle::Contains( const Edge& e )
{
    return Contains( e.p ) && Contains( e.q );
}


inline bool Triangle::Contains( Point* p, Point* q )
{
    return Contains( p ) && Contains( q );
}


inline bool Triangle::IsInterior()
{
    return interior_;
}


inline void Triangle::IsInterior( bool b )
{
    interior_ = b;
}
}

#endif