EgtGeomKernel 1.5h3 :

- aggiunta IsFlat a tutte le Curve 
- aggiunta ApproxWithArcs a tutte le Curve 
- aggiunto oggetto PolyArc (raccolta ordinata di linee e archi con bulge)
- aggiunto oggetto PointsPCA per stima componenti principali di un insieme di punti
- FromSpheriical e FromPolar di Vector3d sono diventati funzioni e aggiunto FromUprightOrtho
- aggiunte Invert e a Vector3d.

PolyLine.cpp

@@ -14,6 +14,8 @@
 //--------------------------- Include ----------------------------------------
 #include "stdafx.h"
 #include "DistPointLine.h"
+#include "PolygonPlane.h"
+#include "PointsPCA.h"
 #include "\EgtDev\Include\EGkPolyLine.h"
 #include "\EgtDev\Include\EGkPlane3d.h"
 
@@ -379,57 +381,70 @@ PolyLine::GetPrevULine( double* pdIni, Point3d* pptIni, double* pdFin, Point3d*
 
 //----------------------------------------------------------------------------
 bool
-PolyLine::NewellPlane( Plane3d& plPlane, double& dArea) const
+PolyLine::IsFlat( int& nRank, Point3d& ptCen, Vector3d& vtDir, double dToler) const
 {
-  // Compute normal as being proportional to projected areas of polygon onto the yz,
-  // xz, and xy planes. Also compute centroid as representative point on the plane
-   Vector3d vtN ;
-   Point3d ptCen ;
-   int nNumSide = 0 ;
-   Point3d ptIni, ptFin ;
-   for ( bool bFound = GetFirstLine( ptIni, ptFin) ; bFound ; bFound = GetNextLine( ptIni, ptFin)) {
-      vtN.x += ( ptIni.y - ptFin.y) * ( ptIni.z + ptFin.z) ;   // projection on yz
-      vtN.y += ( ptIni.z - ptFin.z) * ( ptIni.x + ptFin.x) ;   // projection on xz
-      vtN.z += ( ptIni.x - ptFin.x) * ( ptIni.y + ptFin.y) ;   // projection on xy
-      ptCen += ptFin ;
-      ++ nNumSide ;
+  // cerco le componenti principali (tramite PCA)
+   Point3d ptP ;
+   PointsPCA ptsPCA ;
+   for ( bool bFound = GetFirstPoint( ptP) ; bFound ; bFound = GetNextPoint( ptP))
+      ptsPCA.AddPoint( ptP) ;
+  // recupero il rango, ovvero la dimensionalità dell'insieme di punti
+   nRank = ptsPCA.GetRank() ;
+  // se dimensione nulla, o non ci sono punti o sono tutti praticamente coincidenti
+   if ( nRank == 0)
+      return ptsPCA.GetCenter( ptCen) ;
+  // se dimensione 1, allora i punti sono distribuiti su una linea
+   if ( nRank == 1) {
+     // assegno il centro e la direzione della linea (il verso è indifferente)
+      ptsPCA.GetCenter( ptCen) ;
+      ptsPCA.GetPrincipalComponent( 0, vtDir) ;
+      return true ;
    }
-  // If open and existent, add segment from last to first points
-   if ( ! IsClosed()  &&  nNumSide > 0) {
-      ptIni = ptFin ;
-      GetFirstPoint( ptFin) ;
-      vtN.x += ( ptIni.y - ptFin.y) * ( ptIni.z + ptFin.z) ;   // projection on yz
-      vtN.y += ( ptIni.z - ptFin.z) * ( ptIni.x + ptFin.x) ;   // projection on xz
-      vtN.z += ( ptIni.x - ptFin.x) * ( ptIni.y + ptFin.y) ;   // projection on xy
-      ptCen += ptFin ;
-      ++ nNumSide ;
+  // altrimenti dimensione 2 o 3, allora è determinato un piano principale, verifico se tutti i punti vi giacciono
+   // Center and normal vector
+   ptsPCA.GetCenter( ptCen) ;
+   Vector3d vtX, vtY ;
+   ptsPCA.GetPrincipalComponent( 0, vtX) ;
+   ptsPCA.GetPrincipalComponent( 1, vtY) ;
+   vtDir = vtX ^ vtY ;
+   if ( ! vtDir.Normalize()) {
+     // riduco la dimensionalità a lineare
+      nRank = 1 ;
+     // assegno il centro e la direzione della linea (il verso è indifferente)
+      ptsPCA.GetCenter( ptCen) ;
+      vtDir = vtX ;
+      return true ;
+   }
+   if ( vtDir.z < 0)
+      vtDir.Invert() ;
+   // Plane calculation
+   Plane3d plPlane ;
+   plPlane.vtN = vtDir ;
+   plPlane.dDist = ( ptCen - ORIG) * plPlane.vtN ;
+   // Test each vertex to see if it is farther from plane than allowed max distance
+   for ( bool bFound = GetFirstPoint( ptP) ; bFound ; bFound = GetNextPoint( ptP)) {
+      double dDist = ( ( ptP - ORIG) * plPlane.vtN) - plPlane.dDist ;
+      if ( fabs( dDist) > dToler)
+         return false ;
    }
-  // At least 3 sides
-   if ( nNumSide < 3)
-      return false ;
-  // Normal must be normalizable (the length of the normal is the double of the area of the polygon)
-   double dLenN = vtN.Len() ;
-   if ( dLenN < EPS_SMALL)
-      return false ;
-   vtN /= dLenN ;
-  // Fill in the plane equation fields
-   plPlane.vtN = vtN ;
-   plPlane.dDist = ( ( ptCen - ORIG) * plPlane.vtN) / nNumSide ; // “centroid / n” is the true centroid point
-  // Set area
-   dArea = 0.5 * dLenN ;
-
    return true ;
 }
 
 //----------------------------------------------------------------------------
 bool
-PolyLine::IsFlat( Plane3d& plPlane, double& dArea, double dToler) const
+PolyLine::IsClosedAndFlat( Plane3d& plPlane, double& dArea, double dToler) const
 {
+  // Test if closed
+   if ( ! IsClosed())
+      return false ;
   // Compute a representative plane for the polygon
-   if ( ! NewellPlane( plPlane, dArea))
+   Point3d ptP ;
+   PolygonPlane PolyPlane ;
+   for ( bool bFound = GetFirstPoint( ptP) ; bFound ; bFound = GetNextPoint( ptP))
+      PolyPlane.AddPoint( ptP) ;
+   if ( ! PolyPlane.GetPlane( plPlane)  ||  ! PolyPlane.GetArea( dArea))
       return false ;
   // Test each vertex to see if it is farther from plane than allowed max distance
-   Point3d ptP ;
    for ( bool bFound = GetFirstPoint( ptP) ; bFound ; bFound = GetNextPoint( ptP)) {
       double dDist = ( ( ptP - ORIG) * plPlane.vtN) - plPlane.dDist ;
       if ( fabs( dDist) > dToler)