62      static inline double cross_product( 
double x1, 
double y1, 
double x2, 
double y2, 
double x3, 
double y3 )
 
   64        return ( x2 - x1 ) * ( y3 - y1 ) - ( x3 - x1 ) * ( y2 - y1 );
 
 
   67      static void findLineCircleIntersection( 
double cx, 
double cy, 
double radius,
 
   68                                              double x1, 
double y1, 
double x2, 
double y2,
 
   69                                              double &xRes, 
double &yRes );
 
   78      static std::vector< int > convexHullId( std::vector<int> &
id, 
const std::vector< double > &x, 
const std::vector< double > &y );
 
   83      static bool isSegIntersects( 
double x1, 
double y1, 
double x2, 
double y2,  
 
   84                                   double x3, 
double y3, 
double x4, 
double y4 ); 
 
   90      static bool computeLineIntersection( 
double x1, 
double y1, 
double x2, 
double y2,  
 
   91                                           double x3, 
double y3, 
double x4, 
double y4,  
 
   92                                           double *x, 
double *y );
 
   95      static bool reorderPolygon( std::vector< double > &x, std::vector< double> &y );
 
  107      static bool containsCandidate( 
const GEOSPreparedGeometry *geom, 
double x, 
double y, 
double width, 
double height, 
double alpha );