+ add WildMagic algorithm to compute minimum volume oriented box

src/Mod/Mesh/App/CMakeLists.txt

@@ -87,6 +87,10 @@ SOURCE_GROUP("Core" FILES ${Core_SRCS})
 SET(WildMagic4_SRCS
     WildMagic4/Wm4ApprCylinderFit3.cpp
     WildMagic4/Wm4ApprCylinderFit3.h
+    WildMagic4/Wm4ApprGaussPointsFit2.cpp
+    WildMagic4/Wm4ApprGaussPointsFit2.h
+    WildMagic4/Wm4ApprGaussPointsFit3.cpp
+    WildMagic4/Wm4ApprGaussPointsFit3.h
     WildMagic4/Wm4ApprLineFit3.cpp
     WildMagic4/Wm4ApprLineFit3.h
     WildMagic4/Wm4ApprPlaneFit3.cpp
@@ -99,8 +103,22 @@ SET(WildMagic4_SRCS
     WildMagic4/Wm4ApprSphereFit3.h
     WildMagic4/Wm4BandedMatrix.h
     WildMagic4/Wm4BandedMatrix.inl
+    WildMagic4/Wm4Box2.h
+    WildMagic4/Wm4Box2.inl
     WildMagic4/Wm4Box3.h
     WildMagic4/Wm4Box3.inl
+    WildMagic4/Wm4ContBox2.cpp
+    WildMagic4/Wm4ContBox2.h
+    WildMagic4/Wm4ContBox3.cpp
+    WildMagic4/Wm4ContBox3.h
+    WildMagic4/Wm4ConvexHull.cpp
+    WildMagic4/Wm4ConvexHull.h
+    WildMagic4/Wm4ConvexHull1.cpp
+    WildMagic4/Wm4ConvexHull1.h
+    WildMagic4/Wm4ConvexHull2.cpp
+    WildMagic4/Wm4ConvexHull2.h
+    WildMagic4/Wm4ConvexHull3.cpp
+    WildMagic4/Wm4ConvexHull3.h
     WildMagic4/Wm4DelPolygonEdge.cpp
     WildMagic4/Wm4DelPolygonEdge.h
     WildMagic4/Wm4DelPolyhedronFace.cpp
@@ -207,6 +225,9 @@ SET(WildMagic4_SRCS
     WildMagic4/Wm4Polynomial1.inl
     WildMagic4/Wm4QuadricSurface.cpp
     WildMagic4/Wm4QuadricSurface.h
+    WildMagic4/Wm4Quaternion.cpp
+    WildMagic4/Wm4Quaternion.h
+    WildMagic4/Wm4Quaternion.inl
     WildMagic4/Wm4Query.h
     WildMagic4/Wm4Query.inl
     WildMagic4/Wm4Query2.h

src/Mod/Mesh/App/WildMagic4/Wm4ApprGaussPointsFit2.cpp

@@ -0,0 +1,73 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+#include "Wm4FoundationPCH.h"
+#include "Wm4ApprGaussPointsFit2.h"
+#include "Wm4Eigen.h"
+
+namespace Wm4
+{
+//----------------------------------------------------------------------------
+template <class Real>
+Box2<Real> GaussPointsFit2 (int iQuantity, const Vector2<Real>* akPoint)
+{
+    Box2<Real> kBox(Vector2<Real>::ZERO,Vector2<Real>::UNIT_X,
+        Vector2<Real>::UNIT_Y,(Real)1.0,(Real)1.0);
+
+    // compute the mean of the points
+    kBox.Center = akPoint[0];
+    int i;
+    for (i = 1; i < iQuantity; i++)
+    {
+        kBox.Center += akPoint[i];
+    }
+    Real fInvQuantity = ((Real)1.0)/iQuantity;
+    kBox.Center *= fInvQuantity;
+
+    // compute the covariance matrix of the points
+    Real fSumXX = (Real)0.0, fSumXY = (Real)0.0, fSumYY = (Real)0.0;
+    for (i = 0; i < iQuantity; i++)
+    {
+        Vector2<Real> kDiff = akPoint[i] - kBox.Center;
+        fSumXX += kDiff.X()*kDiff.X();
+        fSumXY += kDiff.X()*kDiff.Y();
+        fSumYY += kDiff.Y()*kDiff.Y();
+    }
+
+    fSumXX *= fInvQuantity;
+    fSumXY *= fInvQuantity;
+    fSumYY *= fInvQuantity;
+
+    // setup the eigensolver
+    Eigen<Real> kES(2);
+    kES(0,0) = fSumXX;
+    kES(0,1) = fSumXY;
+    kES(1,0) = fSumXY;
+    kES(1,1) = fSumYY;
+    kES.IncrSortEigenStuff2();
+
+    for (i = 0; i < 2; i++)
+    {
+        kBox.Extent[i] = kES.GetEigenvalue(i);
+        kES.GetEigenvector(i,kBox.Axis[i]);
+    }
+
+    return kBox;
+}
+//----------------------------------------------------------------------------
+
+//----------------------------------------------------------------------------
+// explicit instantiation
+//----------------------------------------------------------------------------
+template WM4_FOUNDATION_ITEM
+Box2<float> GaussPointsFit2<float> (int, const Vector2<float>*);
+
+template WM4_FOUNDATION_ITEM
+Box2<double> GaussPointsFit2<double> (int, const Vector2<double>*);
+//----------------------------------------------------------------------------
+}

src/Mod/Mesh/App/WildMagic4/Wm4ApprGaussPointsFit2.h

@@ -0,0 +1,28 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+#ifndef WM4APPRGAUSSPOINTSFIT2_H
+#define WM4APPRGAUSSPOINTSFIT2_H
+
+#include "Wm4FoundationLIB.h"
+#include "Wm4Box2.h"
+
+namespace Wm4
+{
+
+// Fit points with a Gaussian distribution.  The center is the mean of the
+// points, the axes are the eigenvectors of the covariance matrix, and the
+// extents are the eigenvalues of the covariance matrix and are returned in
+// increasing order.  The quantites are stored in a Box2<Real> just to have a
+// single container.
+template <class Real> WM4_FOUNDATION_ITEM
+Box2<Real> GaussPointsFit2 (int iQuantity, const Vector2<Real>* akPoint);
+
+}
+
+#endif

src/Mod/Mesh/App/WildMagic4/Wm4ApprGaussPointsFit3.cpp

@@ -0,0 +1,86 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+#include "Wm4FoundationPCH.h"
+#include "Wm4ApprGaussPointsFit3.h"
+#include "Wm4Eigen.h"
+
+namespace Wm4
+{
+//----------------------------------------------------------------------------
+template <class Real>
+Box3<Real> GaussPointsFit3 (int iQuantity, const Vector3<Real>* akPoint)
+{
+    Box3<Real> kBox(Vector3<Real>::ZERO,Vector3<Real>::UNIT_X,
+        Vector3<Real>::UNIT_Y,Vector3<Real>::UNIT_Z,(Real)1.0,(Real)1.0,
+        (Real)1.0);
+
+    // compute the mean of the points
+    kBox.Center = akPoint[0];
+    int i;
+    for (i = 1; i < iQuantity; i++)
+    {
+        kBox.Center += akPoint[i];
+    }
+    Real fInvQuantity = ((Real)1.0)/iQuantity;
+    kBox.Center *= fInvQuantity;
+
+    // compute the covariance matrix of the points
+    Real fSumXX = (Real)0.0, fSumXY = (Real)0.0, fSumXZ = (Real)0.0;
+    Real fSumYY = (Real)0.0, fSumYZ = (Real)0.0, fSumZZ = (Real)0.0;
+    for (i = 0; i < iQuantity; i++)
+    {
+        Vector3<Real> kDiff = akPoint[i] - kBox.Center;
+        fSumXX += kDiff.X()*kDiff.X();
+        fSumXY += kDiff.X()*kDiff.Y();
+        fSumXZ += kDiff.X()*kDiff.Z();
+        fSumYY += kDiff.Y()*kDiff.Y();
+        fSumYZ += kDiff.Y()*kDiff.Z();
+        fSumZZ += kDiff.Z()*kDiff.Z();
+    }
+
+    fSumXX *= fInvQuantity;
+    fSumXY *= fInvQuantity;
+    fSumXZ *= fInvQuantity;
+    fSumYY *= fInvQuantity;
+    fSumYZ *= fInvQuantity;
+    fSumZZ *= fInvQuantity;
+
+    // setup the eigensolver
+    Eigen<Real> kES(3);
+    kES(0,0) = fSumXX;
+    kES(0,1) = fSumXY;
+    kES(0,2) = fSumXZ;
+    kES(1,0) = fSumXY;
+    kES(1,1) = fSumYY;
+    kES(1,2) = fSumYZ;
+    kES(2,0) = fSumXZ;
+    kES(2,1) = fSumYZ;
+    kES(2,2) = fSumZZ;
+    kES.IncrSortEigenStuff3();
+
+    for (i = 0; i < 3; i++)
+    {
+        kBox.Extent[i] = kES.GetEigenvalue(i);
+        kES.GetEigenvector(i,kBox.Axis[i]);
+    }
+
+    return kBox;
+}
+//----------------------------------------------------------------------------
+
+//----------------------------------------------------------------------------
+// explicit instantiation
+//----------------------------------------------------------------------------
+template WM4_FOUNDATION_ITEM
+Box3<float> GaussPointsFit3<float> (int, const Vector3<float>*);
+
+template WM4_FOUNDATION_ITEM
+Box3<double> GaussPointsFit3<double> (int, const Vector3<double>*);
+//----------------------------------------------------------------------------
+}

src/Mod/Mesh/App/WildMagic4/Wm4ApprGaussPointsFit3.h

@@ -0,0 +1,28 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+#ifndef WM4APPRGAUSSPOINTSFIT3_H
+#define WM4APPRGAUSSPOINTSFIT3_H
+
+#include "Wm4FoundationLIB.h"
+#include "Wm4Box3.h"
+
+namespace Wm4
+{
+
+// Fit points with a Gaussian distribution.  The center is the mean of the
+// points, the axes are the eigenvectors of the covariance matrix, and the
+// extents are the eigenvalues of the covariance matrix and are returned in
+// increasing order.  The quantites are stored in a Box3<Real> just to have a
+// single container.
+template <class Real> WM4_FOUNDATION_ITEM
+Box3<Real> GaussPointsFit3 (int iQuantity, const Vector3<Real>* akPoint);
+
+}
+
+#endif

src/Mod/Mesh/App/WildMagic4/Wm4Box2.h

@@ -0,0 +1,48 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+#ifndef WM4BOX2_H
+#define WM4BOX2_H
+
+#include "Wm4FoundationLIB.h"
+#include "Wm4Vector2.h"
+
+namespace Wm4
+{
+
+template <class Real>
+class Box2
+{
+public:
+    // A box has center C, axis directions U[0] and U[1] (both unit-length
+    // vectors), and extents e[0] and e[1] (both nonnegative numbers).  A
+    // point X = C+y[0]*U[0]+y[1]*U[1] is inside or on the box whenever
+    // |y[i]| <= e[i] for all i.
+
+    // construction
+    Box2 ();  // uninitialized
+    Box2 (const Vector2<Real>& rkCenter, const Vector2<Real>* akAxis,
+        const Real* afExtent);
+    Box2 (const Vector2<Real>& rkCenter, const Vector2<Real>& rkAxis0,
+        const Vector2<Real>& rkAxis1, Real fExtent0, Real fExtent1);
+
+    void ComputeVertices (Vector2<Real> akVertex[4]) const;
+
+    Vector2<Real> Center;
+    Vector2<Real> Axis[2];  // must be an orthonormal set of vectors
+    Real Extent[2];         // must be nonnegative
+};
+
+#include "Wm4Box2.inl"
+
+typedef Box2<float> Box2f;
+typedef Box2<double> Box2d;
+
+}
+
+#endif

src/Mod/Mesh/App/WildMagic4/Wm4Box2.inl

@@ -0,0 +1,55 @@
+// Geometric Tools, LLC
+// Copyright (c) 1998-2010
+// Distributed under the Boost Software License, Version 1.0.
+// http://www.boost.org/LICENSE_1_0.txt
+// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
+//
+// File Version: 4.10.0 (2009/11/18)
+
+//----------------------------------------------------------------------------
+template <class Real>
+Box2<Real>::Box2 ()
+{
+    // uninitialized
+}
+//----------------------------------------------------------------------------
+template <class Real>
+Box2<Real>::Box2 (const Vector2<Real>& rkCenter, const Vector2<Real>* akAxis,
+    const Real* afExtent)
+    :
+    Center(rkCenter)
+{
+    for (int i = 0; i < 2; i++)
+    {
+        Axis[i] = akAxis[i];
+        Extent[i] = afExtent[i];
+    }
+}
+//----------------------------------------------------------------------------
+template <class Real>
+Box2<Real>::Box2 (const Vector2<Real>& rkCenter, const Vector2<Real>& rkAxis0,
+    const Vector2<Real>& rkAxis1, Real fExtent0, Real fExtent1)
+    :
+    Center(rkCenter)
+{
+    Axis[0] = rkAxis0;
+    Axis[1] = rkAxis1;
+    Extent[0] = fExtent0;
+    Extent[1] = fExtent1;
+}
+//----------------------------------------------------------------------------
+template <class Real>
+void Box2<Real>::ComputeVertices (Vector2<Real> akVertex[4]) const
+{
+    Vector2<Real> akEAxis[2] =
+    {
+        Axis[0]*Extent[0],
+        Axis[1]*Extent[1]
+    };
+
+    akVertex[0] = Center - akEAxis[0] - akEAxis[1];
+    akVertex[1] = Center + akEAxis[0] - akEAxis[1];
+    akVertex[2] = Center + akEAxis[0] + akEAxis[1];
+    akVertex[3] = Center - akEAxis[0] + akEAxis[1];
+}
+//----------------------------------------------------------------------------