From ab9345670c4412b1ee52a5955344693b9fe5c033 Mon Sep 17 00:00:00 2001
From: vmora <vincent.mora@oslandia.com>
Date: Mon, 31 Mar 2014 16:43:19 +0200
Subject: [PATCH] fixes polygon triangulation

---
 include/SFCGAL/algorithm/plane.h               |  9 +++++++--
 .../ConstraintDelaunayTriangulation.cpp        | 15 +++++----------
 src/SFCGAL/triangulate/triangulatePolygon.cpp  | 18 ++++++++++--------
 3 files changed, 22 insertions(+), 20 deletions(-)

diff --git a/include/SFCGAL/algorithm/plane.h b/include/SFCGAL/algorithm/plane.h
index 90e8beb0..ff71e137 100644
--- a/include/SFCGAL/algorithm/plane.h
+++ b/include/SFCGAL/algorithm/plane.h
@@ -112,8 +112,13 @@ void plane3D(
 template < typename Kernel >
 CGAL::Plane_3< Kernel > plane3D( const Polygon& polygon, bool exact = true )
 {
-    CGAL::Vector_3< Kernel > normal = normal3D< Kernel >( polygon, exact );
-    return CGAL::Plane_3< Kernel >( polygon.exteriorRing().pointN( 0 ).toPoint_3(), normal );
+    CGAL::Vector_3< Kernel > nrml = normal3D< Kernel >( polygon, exact );
+    if ( !exact )
+    {
+        const double nrm = std::sqrt( CGAL::to_double( nrml.squared_length() ) );
+        nrml = CGAL::Vector_3< Kernel >( nrml.x()/nrm, nrml.y()/nrm, nrml.z()/nrm );
+    }
+    return CGAL::Plane_3< Kernel >( polygon.exteriorRing().pointN( 0 ).toPoint_3(), nrml );
 }
 
 
diff --git a/src/SFCGAL/detail/triangulate/ConstraintDelaunayTriangulation.cpp b/src/SFCGAL/detail/triangulate/ConstraintDelaunayTriangulation.cpp
index c0318019..c2ac150b 100644
--- a/src/SFCGAL/detail/triangulate/ConstraintDelaunayTriangulation.cpp
+++ b/src/SFCGAL/detail/triangulate/ConstraintDelaunayTriangulation.cpp
@@ -50,16 +50,11 @@ ConstraintDelaunayTriangulation::Vertex_handle ConstraintDelaunayTriangulation::
                                ) );
     }
 
-    if ( _projectionPlane ) {
-        Vertex_handle vertex = _cdt.insert( _projectionPlane->to_2d( position.toPoint_3() ) );
-        vertex->info().original = position ;
-        return vertex ;
-    }
-    else {
-        Vertex_handle vertex = _cdt.insert( position.toPoint_2() );
-        vertex->info().original = position ;
-        return vertex ;
-    }
+    Vertex_handle vertex = _projectionPlane
+        ? _cdt.insert( _projectionPlane->to_2d( position.toPoint_3() ) )
+        : _cdt.insert( position.toPoint_2() );
+    vertex->info().original = position ;
+    return vertex ;
 }
 
 ///
diff --git a/src/SFCGAL/triangulate/triangulatePolygon.cpp b/src/SFCGAL/triangulate/triangulatePolygon.cpp
index 5ade8ed2..946f100c 100644
--- a/src/SFCGAL/triangulate/triangulatePolygon.cpp
+++ b/src/SFCGAL/triangulate/triangulatePolygon.cpp
@@ -28,6 +28,7 @@
 #include <SFCGAL/detail/triangulate/ConstraintDelaunayTriangulation.h>
 
 #include <SFCGAL/algorithm/plane.h>
+#include <SFCGAL/algorithm/normal.h>
 #include <SFCGAL/algorithm/isValid.h>
 
 #include <iostream>
@@ -162,17 +163,18 @@ void triangulatePolygon3D(
     for ( size_t i = 0; i < polygon.numRings(); i++ ) {
         const LineString& ring  = polygon.ringN( i );
 
-        Vertex_handle v_prev ;
-
-        for ( size_t j = 0; j < ring.numPoints(); j++ ) {
+        /*
+         * note, we do not include the last point, since it's equal to the last and that
+         */
+        if (!ring.numPoints()) continue;
+        Vertex_handle v_prev = cdt.addVertex( ring.pointN( 0 ).coordinate() );
+        Vertex_handle v_0 = v_prev;
+        for ( size_t j = 1; j < ring.numPoints()-1; j++ ) {
             Vertex_handle vh = cdt.addVertex( ring.pointN( j ).coordinate() );
-
-            if ( j != 0 ) {
-                cdt.addConstraint( vh, v_prev );
-            }
-
+            cdt.addConstraint( v_prev, vh );
             v_prev = vh;
         }
+        cdt.addConstraint( v_prev, v_0 );
     }
 
     /*