00001 // Wild Magic Source Code 00002 // David Eberly 00003 // http://www.geometrictools.com 00004 // Copyright (c) 1998-2007 00005 // 00006 // This library is free software; you can redistribute it and/or modify it 00007 // under the terms of the GNU Lesser General Public License as published by 00008 // the Free Software Foundation; either version 2.1 of the License, or (at 00009 // your option) any later version. The license is available for reading at 00010 // either of the locations: 00011 // http://www.gnu.org/copyleft/lgpl.html 00012 // http://www.geometrictools.com/License/WildMagicLicense.pdf 00013 // The license applies to versions 0 through 4 of Wild Magic. 00014 // 00015 // Version: 4.0.0 (2006/06/28) 00016 00017 #ifndef WM4IMPLICITSURFACE_H 00018 #define WM4IMPLICITSURFACE_H 00019 00020 #include "Wm4FoundationLIB.h" 00021 #include "Wm4Matrix3.h" 00022 #include "Wm4Surface.h" 00023 00024 namespace Wm4 00025 { 00026 00027 template <class Real> 00028 class WM4_FOUNDATION_ITEM ImplicitSurface : public Surface<Real> 00029 { 00030 public: 00031 // Surface is defined by F(x,y,z) = 0. In all member functions it is 00032 // the application's responsibility to ensure that (x,y,z) is a solution 00033 // to F = 0. 00034 00035 // abstract base class 00036 virtual ~ImplicitSurface (); 00037 00038 // the function 00039 virtual Real F (const Vector3<Real>& rkP) const = 0; 00040 00041 // first-order partial derivatives 00042 virtual Real FX (const Vector3<Real>& rkP) const = 0; 00043 virtual Real FY (const Vector3<Real>& rkP) const = 0; 00044 virtual Real FZ (const Vector3<Real>& rkP) const = 0; 00045 00046 // second-order partial derivatives 00047 virtual Real FXX (const Vector3<Real>& rkP) const = 0; 00048 virtual Real FXY (const Vector3<Real>& rkP) const = 0; 00049 virtual Real FXZ (const Vector3<Real>& rkP) const = 0; 00050 virtual Real FYY (const Vector3<Real>& rkP) const = 0; 00051 virtual Real FYZ (const Vector3<Real>& rkP) const = 0; 00052 virtual Real FZZ (const Vector3<Real>& rkP) const = 0; 00053 00054 // verify point is on surface (within the tolerance specified by epsilon) 00055 bool IsOnSurface (const Vector3<Real>& rkP, Real fEpsilon) const; 00056 00057 // first-order derivatives 00058 Vector3<Real> GetGradient (const Vector3<Real>& rkP) const; 00059 00060 // second-order derivatives 00061 Matrix3<Real> GetHessian (const Vector3<Real>& rkP) const; 00062 00063 // Compute a coordinate frame. The set {T0,T1,N} is a right-handed 00064 // orthonormal set. 00065 void GetFrame (const Vector3<Real>& rkP, Vector3<Real>& rkTangent0, 00066 Vector3<Real>& rkTangent1, Vector3<Real>& rkNormal) const; 00067 00068 // Differential geometric quantities. The returned scalars are the 00069 // principal curvatures and the returned vectors are the corresponding 00070 // principal directions. 00071 bool ComputePrincipalCurvatureInfo (const Vector3<Real>& rkP, 00072 Real& rfCurv0, Real& rfCurv1, Vector3<Real>& rkDir0, 00073 Vector3<Real>& rkDir1); 00074 00075 protected: 00076 ImplicitSurface (); 00077 }; 00078 00079 typedef ImplicitSurface<float> ImplicitSurfacef; 00080 typedef ImplicitSurface<double> ImplicitSurfaced; 00081 00082 } 00083 00084 #endif
1.6.1