vec3 localToWorld( vec3 _VERTEX, mat4 _MODEL_MATRIX )
{
  return ( _MODEL_MATRIX * vec4( _VERTEX, 1.0 ) ).xyz;
}

vec3 localToWorldDirection( vec3 _VERTEX, mat4 _MODEL_MATRIX )
{
  mat4 mw = _MODEL_MATRIX;
  mw[ 3 ][ 0 ] = 0.0;
  mw[ 3 ][ 1 ] = 0.0;
  mw[ 3 ][ 2 ] = 0.0;
  mw[ 3 ][ 3 ] = 1.0;

  return ( mw * vec4( _VERTEX, 1.0 ) ).xyz;
}

vec3 worldToLocal( vec3 _VERTEX, mat4 _MODEL_MATRIX )
{
  return ( inverse( _MODEL_MATRIX ) * vec4( _VERTEX, 1.0 ) ).xyz;
}

vec3 extractScale( mat3 _MODEL_NORMAL_MATRIX )
{
  mat3 m = _MODEL_NORMAL_MATRIX;
  
  float x = length( vec3( m[ 0 ][ 0 ], m[ 1 ][ 0 ], m[ 2 ][ 0 ] ) ); 
  float y = length( vec3( m[ 0 ][ 1 ], m[ 1 ][ 1 ], m[ 2 ][ 1 ] ) ); 
  float z = length( vec3( m[ 0 ][ 2 ], m[ 1 ][ 2 ], m[ 2 ][ 2 ] ) ); 

  return vec3( x, y, z );
}

vec2 tilingOffset( vec2 uv, vec4 tilingOffset )
{
  uv *= tilingOffset.xy;
  uv += tilingOffset.zw;

  return uv;
}

vec2 tilingOffsetRepeat( vec2 uv, vec4 tilingOffset )
{
  uv *= tilingOffset.xy;
  uv += tilingOffset.zw;

  return mod( uv, vec2(1,1) );
}

vec3 billboardWorldOffset( vec2 _UV, mat4 _INV_VIEW_MATRIX, mat4 _MODEL_MATRIX  )
{
  vec2 mappedUV = mix( vec2(-1,1), vec2( 1, -1 ), _UV );
  vec4 offset = vec4( mappedUV.x, mappedUV.y, 0, 0 );

  offset = _INV_VIEW_MATRIX * offset;
  mat4 mw = _MODEL_MATRIX;
  mw[ 3 ][ 0 ] = 0.0;
  mw[ 3 ][ 1 ] = 0.0;
  mw[ 3 ][ 2 ] = 0.0;

  vec3 worldOffset = worldToLocal( offset.xyz, mw );
  worldOffset = normalize( worldOffset );

  return worldOffset;
}

vec2 rotate_v2( vec2 uv, float angle )
{
  float s = sin( angle );
  float c = cos( angle );

    
  float x = uv.x;
  float y = uv.y; 
 
  uv.x = c * x - s * y;
  uv.y = s * x + c * y;

  return uv;
}

vec2 rotateAround_v2( vec2 uv, float angle, vec2 pivot )
{
  uv -= pivot;
  uv =  rotate_v2( uv, angle );
  uv += pivot;

  return uv;
}

vec3 cameraWorldPosition( mat4 _INV_VIEW_MATRIX )
{
  return (_INV_VIEW_MATRIX * vec4(vec3(0.0), 1.0)).xyz;
}

vec3 cameraWorldForward( mat4 _INV_VIEW_MATRIX )
{
  vec3 pos = cameraWorldPosition( _INV_VIEW_MATRIX );
  return normalize( (_INV_VIEW_MATRIX * vec4( vec3(0.0,0.0,1.0), 1.0)).xyz - pos );
}