gtkradiant/libs/render.h

/*
Copyright (C) 2001-2006, William Joseph.
All Rights Reserved.

This file is part of GtkRadiant.

GtkRadiant 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.

GtkRadiant 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 GtkRadiant; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
*/

#if !defined(INCLUDED_RENDER_H)
#define INCLUDED_RENDER_H

/// \file
/// \brief High-level constructs for efficient OpenGL rendering.

#include "irender.h"
#include "igl.h"

#include "container/array.h"
#include "math/vector.h" 
#include "math/pi.h"

#include <vector>

typedef unsigned int RenderIndex;
const GLenum RenderIndexTypeID = GL_UNSIGNED_INT;

/// \brief A resizable buffer of indices.
class IndexBuffer
{
  typedef std::vector<RenderIndex> Indices;
  Indices m_data;
public:
  typedef Indices::iterator iterator;
  typedef Indices::const_iterator const_iterator;

  iterator begin()
  {
    return m_data.begin();
  }
  const_iterator begin() const
  {
    return m_data.begin();
  }
  iterator end()
  {
    return m_data.end();
  }
  const_iterator end() const
  {
    return m_data.end();
  }

  bool empty() const
  {
    return m_data.empty();
  }
  std::size_t size() const
  {
    return m_data.size();
  }
  const RenderIndex* data() const
  {
    return &(*m_data.begin());
  }
  RenderIndex& operator[](std::size_t index)
  {
    return m_data[index];
  }
  const RenderIndex& operator[](std::size_t index) const
  {
    return m_data[index];
  }
  void clear()
  {
    m_data.clear();
  }
  void reserve(std::size_t max_indices)
  {
    m_data.reserve(max_indices);
  }
  void insert(RenderIndex index)
  {
    m_data.push_back(index);
  }
  void swap(IndexBuffer& other)
  {
    std::swap(m_data, m_data);
  }
};

namespace std
{
  /// \brief Swaps the values of \p self and \p other.
  /// Overloads std::swap.
  inline void swap(IndexBuffer& self, IndexBuffer& other)
  {
    self.swap(other);
  }
}

/// \brief A resizable buffer of vertices.
/// \param Vertex The vertex data type.
template<typename Vertex>
class VertexBuffer
{
  typedef typename std::vector<Vertex> Vertices;
  Vertices m_data;
public:
  typedef typename Vertices::iterator iterator;
  typedef typename Vertices::const_iterator const_iterator;

  iterator begin()
  {
    return m_data.begin();
  }
  iterator end()
  {
    return m_data.end();
  }
  const_iterator begin() const
  {
    return m_data.begin();
  }
  const_iterator end() const
  {
    return m_data.end();
  }

  bool empty() const
  {
    return m_data.empty();
  }
  RenderIndex size() const
  {
    return RenderIndex(m_data.size());
  }
  const Vertex* data() const
  {
    return &(*m_data.begin());
  }
  Vertex& operator[](std::size_t index)
  {
    return m_data[index];
  }
  const Vertex& operator[](std::size_t index) const
  {
    return m_data[index];
  }

  void clear()
  {
    m_data.clear();
  }
  void reserve(std::size_t max_vertices)
  {
    m_data.reserve(max_vertices);
  }
  void push_back(const Vertex& vertex)
  {
    m_data.push_back(vertex);
  }
};

/// \brief A wrapper around a VertexBuffer which inserts only vertices which have not already been inserted.
/// \param Vertex The vertex data type. Must support operator<, operator== and operator!=.
/// For best performance, quantise vertices before inserting them.
template<typename Vertex>
class UniqueVertexBuffer
{
  typedef VertexBuffer<Vertex> Vertices;
  Vertices& m_data;

  struct bnode
  {
    bnode()
      : m_left(0), m_right(0)
    {
    }
    RenderIndex m_left;
    RenderIndex m_right;
  };

  std::vector<bnode> m_btree;
  RenderIndex m_prev0;
  RenderIndex m_prev1;
  RenderIndex m_prev2;

  const RenderIndex find_or_insert(const Vertex& vertex)
  {
    RenderIndex index = 0;

    while(1)
    {
      if(vertex < m_data[index])
      {
        bnode& node = m_btree[index];
        if(node.m_left != 0)
        {
          index = node.m_left;
          continue;
        }
        else
        {
          node.m_left = RenderIndex(m_btree.size());
          m_btree.push_back(bnode());
          m_data.push_back(vertex);
          return RenderIndex(m_btree.size()-1);
        }
      }
      if(m_data[index] < vertex)
      {
        bnode& node = m_btree[index];
        if(node.m_right != 0)
        {
          index = node.m_right;
          continue;
        }
        else
        {
          node.m_right = RenderIndex(m_btree.size());
          m_btree.push_back(bnode());
          m_data.push_back(vertex);
          return RenderIndex(m_btree.size()-1);
        }
      }

      return index;
    }
  }
public:
  UniqueVertexBuffer(Vertices& data)
    : m_data(data), m_prev0(0), m_prev1(0), m_prev2(0)
  {
  }

  typedef typename Vertices::const_iterator iterator;

  iterator begin() const
  {
    return m_data.begin();
  }
  iterator end() const
  {
    return m_data.end();
  }

  std::size_t size() const
  {
    return m_data.size();
  }
  const Vertex* data() const
  {
    return &(*m_data.begin());
  }
  Vertex& operator[](std::size_t index)
  {
    return m_data[index];
  }
  const Vertex& operator[](std::size_t index) const
  {
    return m_data[index];
  }

  void clear()
  {
    m_prev0 = 0;
    m_prev1 = 0;
    m_prev2 = 0;
    m_data.clear();
    m_btree.clear();
  }
  void reserve(std::size_t max_vertices)
  {
    m_data.reserve(max_vertices);
    m_btree.reserve(max_vertices);
  }
  /// \brief Returns the index of the element equal to \p vertex.
  RenderIndex insert(const Vertex& vertex)
  {
    if(m_data.empty())
    {
      m_data.push_back(vertex);
      m_btree.push_back(bnode());
      return 0;
    }

    if(m_data[m_prev0] == vertex)
      return m_prev0;
    if(m_prev1 != m_prev0 && m_data[m_prev1] == vertex)
      return m_prev1;
    if(m_prev2 != m_prev0 && m_prev2 != m_prev1 && m_data[m_prev2] == vertex)
      return m_prev2;

    m_prev2 = m_prev1;
    m_prev1 = m_prev0;
    m_prev0 = find_or_insert(vertex);

    return m_prev0;
  }
};


/// \brief A 4-byte colour.
struct Colour4b
{
  unsigned char r, g, b, a;

  Colour4b()
  {
  }

  Colour4b(unsigned char _r, unsigned char _g, unsigned char _b, unsigned char _a)
    : r(_r), g(_g), b(_b), a(_a)
  {
  }
};

inline bool operator<(const Colour4b& self, const Colour4b& other)
{
  if(self.r != other.r)
  {
    return self.r < other.r;
  }
  if(self.g != other.g)
  {
    return self.g < other.g;
  }
  if(self.b != other.b)
  {
    return self.b < other.b;
  }
  if(self.a != other.a)
  {
    return self.a < other.a;
  }
  return false;
}

inline bool operator==(const Colour4b& self, const Colour4b& other)
{
  return self.r == other.r && self.g == other.g && self.b == other.b && self.a == other.a;
}

inline bool operator!=(const Colour4b& self, const Colour4b& other)
{
  return !operator==(self, other);
}

/// \brief A 3-float vertex.
struct Vertex3f : public Vector3
{
  Vertex3f()
  {
  }

  Vertex3f(float _x, float _y, float _z)
    : Vector3(_x, _y, _z)
  {
  }
};

inline bool operator<(const Vertex3f& self, const Vertex3f& other)
{
  if(self.x() != other.x())
  {
    return self.x() < other.x();
  }
  if(self.y() != other.y())
  {
    return self.y() < other.y();
  }
  if(self.z() != other.z())
  {
    return self.z() < other.z();
  }
  return false;
}

inline bool operator==(const Vertex3f& self, const Vertex3f& other)
{
  return self.x() == other.x() && self.y() == other.y() && self.z() == other.z();
}

inline bool operator!=(const Vertex3f& self, const Vertex3f& other)
{
  return !operator==(self, other);
}


inline Vertex3f vertex3f_from_array(const float* array)
{
  return Vertex3f(array[0], array[1], array[2]);
}

inline float* vertex3f_to_array(Vertex3f& vertex)
{
  return reinterpret_cast<float*>(&vertex);
}

inline const float* vertex3f_to_array(const Vertex3f& vertex)
{
  return reinterpret_cast<const float*>(&vertex);
}

const Vertex3f vertex3f_identity(0, 0, 0);

inline Vertex3f vertex3f_for_vector3(const Vector3& vector3)
{
  return Vertex3f(vector3.x(), vector3.y(), vector3.z());
}

inline const Vector3& vertex3f_to_vector3(const Vertex3f& vertex)
{
  return vertex;
}

inline Vector3& vertex3f_to_vector3(Vertex3f& vertex)
{
  return vertex;
}


/// \brief A 3-float normal.
struct Normal3f : public Vector3
{
  Normal3f()
  {
  }

  Normal3f(float _x, float _y, float _z)
    : Vector3(_x, _y, _z)
  {
  }
};

inline bool operator<(const Normal3f& self, const Normal3f& other)
{
  if(self.x() != other.x())
  {
    return self.x() < other.x();
  }
  if(self.y() != other.y())
  {
    return self.y() < other.y();
  }
  if(self.z() != other.z())
  {
    return self.z() < other.z();
  }
  return false;
}

inline bool operator==(const Normal3f& self, const Normal3f& other)
{
  return self.x() == other.x() && self.y() == other.y() && self.z() == other.z();
}

inline bool operator!=(const Normal3f& self, const Normal3f& other)
{
  return !operator==(self, other);
}


inline Normal3f normal3f_from_array(const float* array)
{
  return Normal3f(array[0], array[1], array[2]);
}

inline float* normal3f_to_array(Normal3f& normal)
{
  return reinterpret_cast<float*>(&normal);
}

inline const float* normal3f_to_array(const Normal3f& normal)
{
  return reinterpret_cast<const float*>(&normal);
}

inline Normal3f normal3f_for_vector3(const Vector3& vector3)
{
  return Normal3f(vector3.x(), vector3.y(), vector3.z());
}

inline const Vector3& normal3f_to_vector3(const Normal3f& normal)
{
  return normal;
}

inline Vector3& normal3f_to_vector3(Normal3f& normal)
{
  return normal;
}


/// \brief A 2-float texture-coordinate set.
struct TexCoord2f : public Vector2
{
  TexCoord2f()
  {
  }

  TexCoord2f(float _s, float _t)
    : Vector2(_s, _t)
  {
  }

  float& s()
  {
    return x();
  }
  const float& s() const
  {
    return x();
  }
  float& t()
  {
    return y();
  }
  const float& t() const
  {
    return y();
  }
};

inline bool operator<(const TexCoord2f& self, const TexCoord2f& other)
{
  if(self.s() != other.s())
  {
    return self.s() < other.s();
  }
  if(self.t() != other.t())
  {
    return self.t() < other.t();
  }
  return false;
}

inline bool operator==(const TexCoord2f& self, const TexCoord2f& other)
{
  return self.s() == other.s() && self.t() == other.t();
}

inline bool operator!=(const TexCoord2f& self, const TexCoord2f& other)
{
  return !operator==(self, other);
}


inline float* texcoord2f_to_array(TexCoord2f& texcoord)
{
  return reinterpret_cast<float*>(&texcoord);
}

inline const float* texcoord2f_to_array(const TexCoord2f& texcoord)
{
  return reinterpret_cast<const float*>(&texcoord);
}

inline const TexCoord2f& texcoord2f_from_array(const float* array)
{
  return *reinterpret_cast<const TexCoord2f*>(array);
}

inline TexCoord2f texcoord2f_for_vector2(const Vector2& vector2)
{
  return TexCoord2f(vector2.x(), vector2.y());
}

inline const Vector2& texcoord2f_to_vector2(const TexCoord2f& vertex)
{
  return vertex;
}

inline Vector2& texcoord2f_to_vector2(TexCoord2f& vertex)
{
  return vertex;
}

/// \brief Returns \p normal rescaled to be unit-length. 
inline Normal3f normal3f_normalised(const Normal3f& normal)
{
  return normal3f_for_vector3(vector3_normalised(normal3f_to_vector3(normal)));
}

enum UnitSphereOctant
{
  UNITSPHEREOCTANT_000 = 0 << 0 | 0 << 1 | 0 << 2,
  UNITSPHEREOCTANT_001 = 0 << 0 | 0 << 1 | 1 << 2,
  UNITSPHEREOCTANT_010 = 0 << 0 | 1 << 1 | 0 << 2,
  UNITSPHEREOCTANT_011 = 0 << 0 | 1 << 1 | 1 << 2,
  UNITSPHEREOCTANT_100 = 1 << 0 | 0 << 1 | 0 << 2,
  UNITSPHEREOCTANT_101 = 1 << 0 | 0 << 1 | 1 << 2,
  UNITSPHEREOCTANT_110 = 1 << 0 | 1 << 1 | 0 << 2,
  UNITSPHEREOCTANT_111 = 1 << 0 | 1 << 1 | 1 << 2,
};

/// \brief Returns the octant for \p normal indicating the sign of the region of unit-sphere space it lies within.
inline UnitSphereOctant normal3f_classify_octant(const Normal3f& normal)
{
  return static_cast<UnitSphereOctant>(
    ((normal.x() > 0) << 0) | ((normal.y() > 0) << 1) | ((normal.z() > 0) << 2)
  );
}

/// \brief Returns \p normal with its components signs made positive based on \p octant.
inline Normal3f normal3f_fold_octant(const Normal3f& normal, UnitSphereOctant octant)
{
  switch(octant)
  {
  case UNITSPHEREOCTANT_000:
    return Normal3f(-normal.x(), -normal.y(), -normal.z());
  case UNITSPHEREOCTANT_001:
    return Normal3f(normal.x(), -normal.y(), -normal.z());
  case UNITSPHEREOCTANT_010:
    return Normal3f(-normal.x(), normal.y(), -normal.z());
  case UNITSPHEREOCTANT_011:
    return Normal3f(normal.x(), normal.y(), -normal.z());
  case UNITSPHEREOCTANT_100:
    return Normal3f(-normal.x(), -normal.y(), normal.z());
  case UNITSPHEREOCTANT_101:
    return Normal3f(normal.x(), -normal.y(), normal.z());
  case UNITSPHEREOCTANT_110:
    return Normal3f(-normal.x(), normal.y(), normal.z());
  case UNITSPHEREOCTANT_111:
    return Normal3f(normal.x(), normal.y(), normal.z());
  }
  return Normal3f();
}

/// \brief Reverses the effect of normal3f_fold_octant() on \p normal with \p octant.
/// \p normal must have been obtained with normal3f_fold_octant().
/// \p octant must have been obtained with normal3f_classify_octant().
inline Normal3f normal3f_unfold_octant(const Normal3f& normal, UnitSphereOctant octant)
{
  return normal3f_fold_octant(normal, octant);
}

enum UnitSphereSextant
{
  UNITSPHERESEXTANT_XYZ = 0,
  UNITSPHERESEXTANT_XZY = 1,
  UNITSPHERESEXTANT_YXZ = 2,
  UNITSPHERESEXTANT_YZX = 3,
  UNITSPHERESEXTANT_ZXY = 4,
  UNITSPHERESEXTANT_ZYX = 5,
};

/// \brief Returns the sextant for \p normal indicating how to sort its components so that x > y > z.
/// All components of \p normal must be positive.
/// \p normal must be normalised.
inline UnitSphereSextant normal3f_classify_sextant(const Normal3f& normal)
{
  return
    normal.x() >= normal.y()
    ? normal.x() >= normal.z()
      ? normal.y() >= normal.z()
        ? UNITSPHERESEXTANT_XYZ
        : UNITSPHERESEXTANT_XZY
        : UNITSPHERESEXTANT_ZXY
        : normal.y() >= normal.z()
        ? normal.x() >= normal.z()
        ? UNITSPHERESEXTANT_YXZ
        : UNITSPHERESEXTANT_YZX
        : UNITSPHERESEXTANT_ZYX;
}

/// \brief Returns \p normal with its components sorted so that x > y > z based on \p sextant.
/// All components of \p normal must be positive.
/// \p normal must be normalised.
inline Normal3f normal3f_fold_sextant(const Normal3f& normal, UnitSphereSextant sextant)
{
  switch(sextant)
  {
  case UNITSPHERESEXTANT_XYZ:
    return Normal3f(normal.x(), normal.y(), normal.z());
  case UNITSPHERESEXTANT_XZY:
    return Normal3f(normal.x(), normal.z(), normal.y());
  case UNITSPHERESEXTANT_YXZ:
    return Normal3f(normal.y(), normal.x(), normal.z());
  case UNITSPHERESEXTANT_YZX:
    return Normal3f(normal.y(), normal.z(), normal.x());
  case UNITSPHERESEXTANT_ZXY:
    return Normal3f(normal.z(), normal.x(), normal.y());
  case UNITSPHERESEXTANT_ZYX:
    return Normal3f(normal.z(), normal.y(), normal.x());
  }
  return Normal3f();
}

/// \brief Reverses the effect of normal3f_fold_sextant() on \p normal with \p sextant.
/// \p normal must have been obtained with normal3f_fold_sextant().
/// \p sextant must have been obtained with normal3f_classify_sextant().
inline Normal3f normal3f_unfold_sextant(const Normal3f& normal, UnitSphereSextant sextant)
{
	return normal3f_fold_sextant(normal, sextant);
}

const std::size_t c_quantise_normal = 1 << 6;

/// \brief All the components of \p folded must be positive and sorted so that x > y > z.
inline Normal3f normal3f_folded_quantised(const Normal3f& folded)
{
  // compress
  double scale = static_cast<float>(c_quantise_normal) / (folded.x() + folded.y() + folded.z());
  unsigned int zbits = static_cast<unsigned int>(folded.z() * scale);
  unsigned int ybits = static_cast<unsigned int>(folded.y() * scale);

  // decompress
  return normal3f_normalised(Normal3f(
    static_cast<float>(c_quantise_normal - zbits - ybits),
    static_cast<float>(ybits),
    static_cast<float>(zbits)
  ));
}

/// \brief Returns \p normal quantised by compressing and then decompressing its representation.
inline Normal3f normal3f_quantised_custom(const Normal3f& normal)
{
  UnitSphereOctant octant = normal3f_classify_octant(normal);
  Normal3f folded = normal3f_fold_octant(normal, octant);
  UnitSphereSextant sextant = normal3f_classify_sextant(folded);
  folded = normal3f_fold_sextant(folded, sextant);
  return normal3f_unfold_octant(normal3f_unfold_sextant(normal3f_folded_quantised(folded), sextant), octant);
}



struct spherical_t
{
  double longditude, latitude;

  spherical_t(double _longditude, double _latitude)
    : longditude(_longditude), latitude(_latitude)
  {
  }
};

/*
{
  theta = 2pi * U;
  phi = acos((2 * V) - 1);

  U = theta / 2pi;
  V = (cos(phi) + 1) / 2;
}

longitude = atan(y / x);
latitude = acos(z);
*/
struct uniformspherical_t
{
  double U, V;

  uniformspherical_t(double U_, double V_)
    : U(U_), V(V_)
  {
  }
};


inline spherical_t spherical_from_normal3f(const Normal3f& normal)
{
  return spherical_t(normal.x() == 0 ? c_pi / 2 : normal.x() > 0 ? atan(normal.y() / normal.x()) : atan(normal.y() / normal.x()) + c_pi, acos(normal.z()));
}

inline Normal3f normal3f_from_spherical(const spherical_t& spherical)
{
  return Normal3f(
    static_cast<float>(cos(spherical.longditude) * sin(spherical.latitude)),
    static_cast<float>(sin(spherical.longditude) * sin(spherical.latitude)),
    static_cast<float>(cos(spherical.latitude))
  );
}

inline uniformspherical_t uniformspherical_from_spherical(const spherical_t& spherical)
{
  return uniformspherical_t(spherical.longditude * c_inv_2pi, (cos(spherical.latitude) + 1) * 0.5);
}

inline spherical_t spherical_from_uniformspherical(const uniformspherical_t& uniformspherical)
{
  return spherical_t(c_2pi * uniformspherical.U, acos((2 * uniformspherical.V) - 1));
}

inline uniformspherical_t uniformspherical_from_normal3f(const Normal3f& normal)
{
  return uniformspherical_from_spherical(spherical_from_normal3f(normal));
  //return uniformspherical_t(atan2(normal.y / normal.x) * c_inv_2pi, (normal.z + 1) * 0.5);
}

inline Normal3f normal3f_from_uniformspherical(const uniformspherical_t& uniformspherical)
{
  return normal3f_from_spherical(spherical_from_uniformspherical(uniformspherical));
}

/// \brief Returns a single-precision \p component quantised to \p precision.
inline float float_quantise(float component, float precision)
{
  return float_snapped(component, precision);
}

/// \brief Returns a double-precision \p component quantised to \p precision.
inline double double_quantise(double component, double precision)
{
  return float_snapped(component, precision);
}

inline spherical_t spherical_quantised(const spherical_t& spherical, float snap)
{
  return spherical_t(double_quantise(spherical.longditude, snap), double_quantise(spherical.latitude, snap));
}

inline uniformspherical_t uniformspherical_quantised(const uniformspherical_t& uniformspherical, float snap)
{
  return uniformspherical_t(double_quantise(uniformspherical.U, snap), double_quantise(uniformspherical.V, snap));
}

/// \brief Returns a \p vertex quantised to \p precision.
inline Vertex3f vertex3f_quantised(const Vertex3f& vertex, float precision)
{
  return Vertex3f(float_quantise(vertex.x(), precision), float_quantise(vertex.y(), precision), float_quantise(vertex.z(), precision));
}

/// \brief Returns a \p normal quantised to a fixed precision.
inline Normal3f normal3f_quantised(const Normal3f& normal)
{
	return normal3f_quantised_custom(normal);
  //return normal3f_from_spherical(spherical_quantised(spherical_from_normal3f(normal), snap));
  //return normal3f_from_uniformspherical(uniformspherical_quantised(uniformspherical_from_normal3f(normal), snap));
  //  float_quantise(normal.x, snap), float_quantise(normal.y, snap), float_quantise(normal.y, snap));
}

/// \brief Returns a \p texcoord quantised to \p precision.
inline TexCoord2f texcoord2f_quantised(const TexCoord2f& texcoord, float precision)
{
  return TexCoord2f(float_quantise(texcoord.s(), precision), float_quantise(texcoord.t(), precision));
}

/// \brief Standard vertex type for lines and points.
struct PointVertex
{
  Colour4b colour;
  Vertex3f vertex;

  PointVertex()
  {
  }
  PointVertex(Vertex3f _vertex)
    : colour(Colour4b(255, 255, 255, 255)), vertex(_vertex)
  {
  }
  PointVertex(Vertex3f _vertex, Colour4b _colour)
    : colour(_colour), vertex(_vertex)
  {
  }
};

inline bool operator<(const PointVertex& self, const PointVertex& other)
{
  if(self.vertex != other.vertex)
  {
    return self.vertex < other.vertex;
  }
  if(self.colour != other.colour)
  {
    return self.colour < other.colour;
  }
  return false;
}

inline bool operator==(const PointVertex& self, const PointVertex& other)
{
  return self.colour == other.colour && self.vertex == other.vertex;
}

inline bool operator!=(const PointVertex& self, const PointVertex& other)
{
  return !operator==(self, other);
}

/// \brief Standard vertex type for lit/textured meshes.
struct ArbitraryMeshVertex
{
  TexCoord2f texcoord;
  Normal3f normal;
  Vertex3f vertex;
  Normal3f tangent;
  Normal3f bitangent;

  ArbitraryMeshVertex() : tangent(0, 0, 0), bitangent(0, 0, 0)
  {
  }
  ArbitraryMeshVertex(Vertex3f _vertex, Normal3f _normal, TexCoord2f _texcoord)
    : texcoord(_texcoord), normal(_normal), vertex(_vertex), tangent(0, 0, 0), bitangent(0, 0, 0)
  {
  }
};

inline bool operator<(const ArbitraryMeshVertex& self, const ArbitraryMeshVertex& other)
{
  if(self.texcoord != other.texcoord)
  {
    return self.texcoord < other.texcoord;
  }
  if(self.normal != other.normal)
  {
    return self.normal < other.normal;
  }
  if(self.vertex != other.vertex)
  {
    return self.vertex < other.vertex;
  }
  return false;
}

inline bool operator==(const ArbitraryMeshVertex& self, const ArbitraryMeshVertex& other)
{
  return self.texcoord == other.texcoord && self.normal == other.normal && self.vertex == other.vertex;
}

inline bool operator!=(const ArbitraryMeshVertex& self, const ArbitraryMeshVertex& other)
{
  return !operator==(self, other);
}

const float c_quantise_vertex = 1.f / static_cast<float>(1 << 3);

/// \brief Returns \p v with vertex quantised to a fixed precision.
inline PointVertex pointvertex_quantised(const PointVertex& v)
{
  return PointVertex(vertex3f_quantised(v.vertex, c_quantise_vertex), v.colour);
}

const float c_quantise_texcoord = 1.f / static_cast<float>(1 << 8);

/// \brief Returns \p v with vertex, normal and texcoord quantised to a fixed precision.
inline ArbitraryMeshVertex arbitrarymeshvertex_quantised(const ArbitraryMeshVertex& v)
{
  return ArbitraryMeshVertex(vertex3f_quantised(v.vertex, c_quantise_vertex), normal3f_quantised(v.normal), texcoord2f_quantised(v.texcoord, c_quantise_texcoord));
}


/// \brief Sets up the OpenGL colour and vertex arrays for \p array.
inline void pointvertex_gl_array(const PointVertex* array)
{
  glColorPointer(4, GL_UNSIGNED_BYTE, sizeof(PointVertex), &array->colour);
  glVertexPointer(3, GL_FLOAT, sizeof(PointVertex), &array->vertex);
}

class RenderablePointArray : public OpenGLRenderable
{
  const Array<PointVertex>& m_array;
  const GLenum m_mode;
public:
  RenderablePointArray(const Array<PointVertex>& array, GLenum mode)
    : m_array(array), m_mode(mode)
  {
  }
  void render(RenderStateFlags state) const
  {
#define NV_DRIVER_BUG 1
#if NV_DRIVER_BUG
    glColorPointer(4, GL_UNSIGNED_BYTE, 0, 0);
    glVertexPointer(3, GL_FLOAT, 0, 0);
    glDrawArrays(GL_TRIANGLE_FAN, 0, 0);
#endif
    pointvertex_gl_array(m_array.data());
    glDrawArrays(m_mode, 0, GLsizei(m_array.size()));
  }
};

class RenderablePointVector : public OpenGLRenderable
{
  std::vector<PointVertex> m_vector;
  const GLenum m_mode;
public:
  RenderablePointVector(GLenum mode)
    : m_mode(mode)
  {
  }

  void render(RenderStateFlags state) const
  {
    pointvertex_gl_array(&m_vector.front());
    glDrawArrays(m_mode, 0, GLsizei(m_vector.size()));
  }

  std::size_t size() const
  {
    return m_vector.size();
  }
  bool empty() const
  {
    return m_vector.empty();
  }
  void clear()
  {
    m_vector.clear();
  }
  void reserve(std::size_t size)
  {
    m_vector.reserve(size);
  }
  void push_back(const PointVertex& point)
  {
    m_vector.push_back(point);
  }
};


class RenderableVertexBuffer : public OpenGLRenderable
{
  const GLenum m_mode;
  const VertexBuffer<PointVertex>& m_vertices;
public:
  RenderableVertexBuffer(GLenum mode, const VertexBuffer<PointVertex>& vertices)
    : m_mode(mode), m_vertices(vertices)
  {
  }

  void render(RenderStateFlags state) const
  {
    pointvertex_gl_array(m_vertices.data());
    glDrawArrays(m_mode, 0, m_vertices.size());
  }
};

class RenderableIndexBuffer : public OpenGLRenderable
{
  const GLenum m_mode;
  const IndexBuffer& m_indices;
  const VertexBuffer<PointVertex>& m_vertices;
public:
  RenderableIndexBuffer(GLenum mode, const IndexBuffer& indices, const VertexBuffer<PointVertex>& vertices)
    : m_mode(mode), m_indices(indices), m_vertices(vertices)
  {
  }

  void render(RenderStateFlags state) const
  {
#if 1
    pointvertex_gl_array(m_vertices.data());
    glDrawElements(m_mode, GLsizei(m_indices.size()), RenderIndexTypeID, m_indices.data());
#else
    glBegin(m_mode);
    if(state & RENDER_COLOURARRAY != 0)
    {
      for(std::size_t i = 0; i < m_indices.size(); ++i)
      {
        glColor4ubv(&m_vertices[m_indices[i]].colour.r);
        glVertex3fv(&m_vertices[m_indices[i]].vertex.x);
      }
    }
    else
    {
      for(std::size_t i = 0; i < m_indices.size(); ++i)
      {
        glVertex3fv(&m_vertices[m_indices[i]].vertex.x);
      }
    }
    glEnd();
#endif
  }
};


class RemapXYZ
{
public:
  static void set(Vertex3f& vertex, float x, float y, float z)
  {
    vertex.x() = x;
    vertex.y() = y;
    vertex.z() = z;
  }
};

class RemapYZX
{
public:
  static void set(Vertex3f& vertex, float x, float y, float z)
  {
    vertex.x() = z;
    vertex.y() = x;
    vertex.z() = y;
  }
};

class RemapZXY
{
public:
  static void set(Vertex3f& vertex, float x, float y, float z)
  {
    vertex.x() = y;
    vertex.y() = z;
    vertex.z() = x;
  }
};

template<typename remap_policy>
inline void draw_circle(const std::size_t segments, const float radius, PointVertex* vertices, remap_policy remap)
{
  const double increment = c_pi / double(segments << 2);

  std::size_t count = 0;
  float x = radius;
  float y = 0;
  while(count < segments)
  {
    PointVertex* i = vertices + count;
    PointVertex* j = vertices + ((segments << 1) - (count + 1));

    PointVertex* k = i + (segments << 1);
    PointVertex* l = j + (segments << 1);

    PointVertex* m = i + (segments << 2);
    PointVertex* n = j + (segments << 2);
    PointVertex* o = k + (segments << 2);
    PointVertex* p = l + (segments << 2);

    remap_policy::set(i->vertex, x,-y, 0);
    remap_policy::set(k->vertex,-y,-x, 0);
    remap_policy::set(m->vertex,-x, y, 0);
    remap_policy::set(o->vertex, y, x, 0);

    ++count;

    {
      const double theta = increment * count;
      x = static_cast<float>(radius * cos(theta));
      y = static_cast<float>(radius * sin(theta));
    }

    remap_policy::set(j->vertex, y,-x, 0);
    remap_policy::set(l->vertex,-x,-y, 0);
    remap_policy::set(n->vertex,-y, x, 0);
    remap_policy::set(p->vertex, x, y, 0);
  }
}

#if 0
class PointVertexArrayIterator
{
  PointVertex* m_point;
public:
  PointVertexArrayIterator(PointVertex* point)
    : m_point(point)
  {
  }
  PointVertexArrayIterator& operator++()
  {
    ++m_point;
    return *this;
  }
  PointVertexArrayIterator operator++(int)
  {
    PointVertexArrayIterator tmp(*this);
    ++m_point;
    return tmp;
  }
  Vertex3f& operator*()
  {
    return m_point.vertex;
  }
  Vertex3f* operator->()
  {
    return &(operator*());
  }
}

template<typename remap_policy, typename iterator_type
inline void draw_circle(const std::size_t segments, const float radius, iterator_type start, remap_policy remap)
{
  const float increment = c_pi / (double)(segments << 2);

  std::size_t count = 0;
  iterator_type pxpy(start);
  iterator_type pypx(pxpy + (segments << 1));
  iterator_type pynx(pxpy + (segments << 1));
  iterator_type nxpy(pypx + (segments << 1));
  iterator_type nxny(pypx + (segments << 1));
  iterator_type nynx(nxpy + (segments << 1));
  iterator_type nypx(nxpy + (segments << 1));
  iterator_type pxny(start);
  while(count < segments)
  {
    const float theta = increment * count;
    const float x = radius * cos(theta);
    const float y = radius * sin(theta);

    remap_policy::set((*pxpy), x, y, 0);
    remap_policy::set((*pxny), x,-y, 0);
    remap_policy::set((*nxpy),-x, y, 0);
    remap_policy::set((*nxny),-x,-y, 0);

    remap_policy::set((*pypx), y, x, 0);
    remap_policy::set((*pynx), y,-x, 0);
    remap_policy::set((*nypx),-y, x, 0);
    remap_policy::set((*nynx),-y,-x, 0);
  }
}

template<typename remap_policy, typename iterator_type
inline void draw_semicircle(const std::size_t segments, const float radius, iterator_type start, remap_policy remap)
{
  const float increment = c_pi / (double)(segments << 2);

  std::size_t count = 0;
  iterator_type pxpy(start);
  iterator_type pypx(pxpy + (segments << 1));
  iterator_type pynx(pxpy + (segments << 1));
  iterator_type nxpy(pypx + (segments << 1));
  iterator_type nxny(pypx + (segments << 1));
  iterator_type nynx(nxpy + (segments << 1));
  iterator_type nypx(nxpy + (segments << 1));
  iterator_type pxny(start);
  while(count < segments)
  {
    const float theta = increment * count;
    const float x = radius * cos(theta);
    const float y = radius * sin(theta);

    remap_policy::set((*pxpy), x, y, 0);
    remap_policy::set((*pxny), x,-y, 0);
    remap_policy::set((*nxpy),-x, y, 0);
    remap_policy::set((*nxny),-x,-y, 0);

    //remap_policy::set((*pypx), y, x, 0);
    //remap_policy::set((*pynx), y,-x, 0);
    //remap_policy::set((*nypx),-y, x, 0);
    //remap_policy::set((*nynx),-y,-x, 0);
  }
}


#endif

inline void draw_quad(const float radius, PointVertex* quad)
{
  (*quad++).vertex = Vertex3f(-radius, radius, 0);
  (*quad++).vertex = Vertex3f(radius, radius, 0);
  (*quad++).vertex = Vertex3f(radius, -radius, 0);
  (*quad++).vertex = Vertex3f(-radius, -radius, 0);
}

inline void draw_cube(const float radius, PointVertex* cube)
{
  (*cube++).vertex = Vertex3f(-radius, -radius, -radius);
  (*cube++).vertex = Vertex3f(radius, -radius, -radius);
  (*cube++).vertex = Vertex3f(-radius, radius, -radius);
  (*cube++).vertex = Vertex3f(radius, radius, -radius);
  (*cube++).vertex = Vertex3f(-radius, -radius, radius);
  (*cube++).vertex = Vertex3f(radius, -radius, radius);
  (*cube++).vertex = Vertex3f(-radius, radius, radius);
  (*cube++).vertex = Vertex3f(radius, radius, radius);
}


/// \brief Calculates the tangent vectors for a triangle \p a, \p b, \p c and stores the tangent in \p s and the bitangent in \p t.
inline void ArbitraryMeshTriangle_calcTangents(const ArbitraryMeshVertex& a, const ArbitraryMeshVertex& b, const ArbitraryMeshVertex& c, Vector3& s, Vector3& t)
{
  s = Vector3(0, 0, 0);
  t = Vector3(0, 0, 0);
  {
    Vector3 cross(
      vector3_cross(
        vector3_subtracted(
          Vector3(b.vertex.x(), b.texcoord.s(), b.texcoord.t()),
          Vector3(a.vertex.x(), a.texcoord.s(), a.texcoord.t())
        ),
        vector3_subtracted(
          Vector3(c.vertex.x(), c.texcoord.s(), c.texcoord.t()),
          Vector3(a.vertex.x(), a.texcoord.s(), a.texcoord.t())
        )
      )
    );

    if(fabs(cross.x()) > 0.000001f)
    {
      s.x() = -cross.y() / cross.x();
    }

    if(fabs(cross.x()) > 0.000001f)
    {
      t.x() = -cross.z() / cross.x();
    }
  }

  {
    Vector3 cross(
      vector3_cross(
        vector3_subtracted(
          Vector3(b.vertex.y(), b.texcoord.s(), b.texcoord.t()),
          Vector3(a.vertex.y(), a.texcoord.s(), a.texcoord.t())
        ),
        vector3_subtracted(
          Vector3(c.vertex.y(), c.texcoord.s(), c.texcoord.t()),
          Vector3(a.vertex.y(), a.texcoord.s(), a.texcoord.t())
        )
      )
    );

    if(fabs(cross.x()) > 0.000001f)
    {
      s.y() = -cross.y() / cross.x();
    }

    if(fabs(cross.x()) > 0.000001f)
    {
      t.y() = -cross.z() / cross.x();
    }
  }

  {
    Vector3 cross(
      vector3_cross(
        vector3_subtracted(
          Vector3(b.vertex.z(), b.texcoord.s(), b.texcoord.t()),
          Vector3(a.vertex.z(), a.texcoord.s(), a.texcoord.t())
        ),
        vector3_subtracted(
          Vector3(c.vertex.z(), c.texcoord.s(), c.texcoord.t()),
          Vector3(a.vertex.z(), a.texcoord.s(), a.texcoord.t())
        )
      )
    );

    if(fabs(cross.x()) > 0.000001f)
    {
      s.z() = -cross.y() / cross.x();
    }

    if(fabs(cross.x()) > 0.000001f)
    {
      t.z() = -cross.z() / cross.x();
    }
  }
}

inline void ArbitraryMeshTriangle_sumTangents(ArbitraryMeshVertex& a, ArbitraryMeshVertex& b, ArbitraryMeshVertex& c)
{
  Vector3 s, t;

  ArbitraryMeshTriangle_calcTangents(a, b, c, s, t);

  reinterpret_cast<Vector3&>(a.tangent) += s;
  reinterpret_cast<Vector3&>(b.tangent) += s;
  reinterpret_cast<Vector3&>(c.tangent) += s;

  reinterpret_cast<Vector3&>(a.bitangent) += t;
  reinterpret_cast<Vector3&>(b.bitangent) += t;
  reinterpret_cast<Vector3&>(c.bitangent) += t;
}


#endif