From 4e9510bcaad142ecfb91e74fddf3aa19aea7334e Mon Sep 17 00:00:00 2001
From: Susan Hert <hert@mpi-sb.mpg.de>
Date: Wed, 7 Feb 2001 17:55:18 +0000
Subject: [PATCH] added volume, squared_area function

---
 Packages/H3/changes.txt                  |  1 +
 Packages/H3/include/CGAL/Iso_cuboidH3.h  | 11 +++++--
 Packages/H3/include/CGAL/TetrahedronH3.h | 38 ++++++++++++++++++++----
 Packages/H3/include/CGAL/TriangleH3.h    | 14 +++++++++
 4 files changed, 57 insertions(+), 7 deletions(-)

diff --git a/Packages/H3/changes.txt b/Packages/H3/changes.txt
index 65a47c92020..43bef06b16d 100644
--- a/Packages/H3/changes.txt
+++ b/Packages/H3/changes.txt
@@ -1,5 +1,6 @@
 2.16   (?? ??? 2001)
 - Macro cleanups.
+- squared_area() and volume() functions added
 
 2.15   (22 Jan 2001)
 - CGAL::compare -> CGAL_NTS compare in SphereH3 to fix a warning.
diff --git a/Packages/H3/include/CGAL/Iso_cuboidH3.h b/Packages/H3/include/CGAL/Iso_cuboidH3.h
index c6c9fe604b0..2f3e1e143ed 100644
--- a/Packages/H3/include/CGAL/Iso_cuboidH3.h
+++ b/Packages/H3/include/CGAL/Iso_cuboidH3.h
@@ -56,8 +56,7 @@ public:
   bool      has_on_bounded_side(const PointH3<FT,RT>& p) const;
   bool      has_on_unbounded_side(const PointH3<FT,RT>& p) const;
   bool      is_degenerate() const;
-  Bbox_2
-            bbox() const;
+  Bbox_2    bbox() const;
   FT        xmin() const;
   FT        ymin() const;
   FT        zmin() const;
@@ -65,6 +64,7 @@ public:
   FT        ymax() const;
   FT        zmax() const;
 
+  FT        volume() const;
 
 };
 
@@ -193,6 +193,12 @@ FT
 Iso_cuboidH3<FT,RT>::zmax() const
 { return  FT( max().hz() ) / FT( max().hw() ); }
 
+template < class FT, class RT >
+inline
+FT
+Iso_cuboidH3<FT,RT>::volume() const
+{ return  (xmax() - xmin()) * (ymax() - ymin()) * (zmax() - zmin()); }
+
 template < class FT, class RT >
 CGAL_KERNEL_LARGE_INLINE
 PointH3<FT,RT>
@@ -224,6 +230,7 @@ PointH3<FT,RT>
 Iso_cuboidH3<FT,RT>::operator[](int i) const
 { return vertex(i); }
 
+
 template < class FT, class RT >
 CGAL_KERNEL_MEDIUM_INLINE
 Bounded_side
diff --git a/Packages/H3/include/CGAL/TetrahedronH3.h b/Packages/H3/include/CGAL/TetrahedronH3.h
index cbfe9150ae3..83b1f254c27 100644
--- a/Packages/H3/include/CGAL/TetrahedronH3.h
+++ b/Packages/H3/include/CGAL/TetrahedronH3.h
@@ -70,6 +70,8 @@ public:
   bool           operator==(const TetrahedronH3<FT,RT> &t) const;
   bool           operator!=(const TetrahedronH3<FT,RT> &t) const;
   Bbox_3         bbox() const;
+  FT             volume() const;
+
   TetrahedronH3<FT,RT>
                  transform(const Aff_transformationH3<FT,RT> &t) const;
   Orientation    orientation() const;
@@ -102,7 +104,6 @@ TetrahedronH3<FT,RT>::TetrahedronH3(const PointH3<FT,RT> &p,
 {}
 
 
-
 template < class FT, class RT >
 CGAL_KERNEL_INLINE
 bool
@@ -127,12 +128,12 @@ TetrahedronH3<FT,RT>::operator==(const TetrahedronH3<FT,RT> &t) const
   return V1 == V2;
 }
 
-
 template < class FT, class RT >
 inline
 bool
 TetrahedronH3<FT,RT>::operator!=(const TetrahedronH3<FT,RT> &t) const
 { return !(*this == t); }
+
 template < class FT, class RT >
 CGAL_KERNEL_INLINE
 PointH3<FT,RT>
@@ -316,6 +317,33 @@ TetrahedronH3<FT,RT>::bbox() const
   vertex(0).bbox() + vertex(1).bbox() + vertex(2).bbox() + vertex(3).bbox();
 }
 
+template < class FT, class RT >
+CGAL_KERNEL_MEDIUM_INLINE
+FT
+TetrahedronH3<FT,RT>::volume() const
+{
+  VectorH3<FT,RT> vec1 = vertex(1) - vertex(0);
+  VectorH3<FT,RT> vec2 = vertex(2) - vertex(0);
+  VectorH3<FT,RT> vec3 = vertex(3) - vertex(0);
+
+  // first compute (vec1.hw * vec2.hw * vec3.hw * det(vec1, vec2, vec3))
+  // then divide by (6 * vec1.hw * vec2.hw * vec3.hw)
+  FT w123 = vec1.hw() * vec2.hw() * vec3.hw();
+  FT hx1 =  vec1.hx();
+  FT hy1 =  vec1.hy();
+  FT hz1 =  vec1.hz();
+  FT hx2 =  vec2.hx();
+  FT hy2 =  vec2.hy();
+  FT hz2 =  vec2.hz();
+  FT hx3 =  vec3.hx();
+  FT hy3 =  vec3.hy();
+  FT hz3 =  vec3.hz();
+
+  return (  (hx1 * (hy2 * hz3 - hy3 * hz2))
+          - (hy1 * (hx2 * hz3 - hx3 * hz2))
+          + (hz1 * (hx2 * hy3 - hx3 * hy2)))/ (FT(6) * w123);
+}
+
 template < class FT, class RT >
 inline
 TetrahedronH3<FT,RT>
@@ -323,9 +351,9 @@ TetrahedronH3<FT,RT>::
 transform(const Aff_transformationH3<FT,RT> &t) const
 {
   return TetrahedronH3<FT,RT>(t.transform(vertex(0)),
-                                   t.transform(vertex(1)),
-                                   t.transform(vertex(2)),
-                                   t.transform(vertex(3)));
+                              t.transform(vertex(1)),
+                              t.transform(vertex(2)),
+                              t.transform(vertex(3)));
 }
 
 
diff --git a/Packages/H3/include/CGAL/TriangleH3.h b/Packages/H3/include/CGAL/TriangleH3.h
index 63e35df0184..28532db61b4 100644
--- a/Packages/H3/include/CGAL/TriangleH3.h
+++ b/Packages/H3/include/CGAL/TriangleH3.h
@@ -56,6 +56,8 @@ public:
   PointH3<FT,RT> vertex(int i) const;
   PointH3<FT,RT> operator[](int i) const;
 
+  FT       squared_area() const;
+
   Bbox_3   bbox() const;
 
 };
@@ -109,12 +111,24 @@ TriangleH3<FT,RT>::vertex(int i) const
   }
   // return PointH3<FT,RT>();
 }
+
 template < class FT, class RT >
 inline
 PointH3<FT,RT>
 TriangleH3<FT,RT>::operator[](int i) const
 { return vertex(i); }
 
+template < class FT, class RT >
+CGAL_KERNEL_MEDIUM_INLINE
+FT
+TriangleH3<FT,RT>::squared_area() const
+{ 
+   VectorH3<FT,RT> v1 = vertex(1) - vertex(0);
+   VectorH3<FT,RT> v2 = vertex(2) - vertex(0);
+   VectorH3<FT,RT> v3 = cross_product(v1, v2);
+   return (v3 * v3)/FT(4); 
+}
+
 template < class FT, class RT >
 CGAL_KERNEL_INLINE
 PlaneH3<FT,RT>