#ifndef FILE_SURFACE #define FILE_SURFACE /**************************************************************************/ /* File: surface.hh */ /* Author: Joachim Schoeberl */ /* Date: 1. Dez. 95 */ /**************************************************************************/ namespace netgen { class TriangleApproximation; /** Basis class for implicit surface geometry. This class is used for generation of surface meshes in NETGEN */ class Surface { protected: /// invert normal vector bool inverse; /// maximal h in surface double maxh; /// name of surface char * name; /// boundary condition nr int bcprop; /// boundary condition label string bcname; public: Surface (); /** @name Tangential plane. The tangential plane is used for surface mesh generation. */ virtual ~Surface(); protected: /** @name Points in the surface defining tangential plane. Tangential plane is taken in p1, the local x-axis is directed to p2. */ //@{ /// Point<3> p1; /// Point<3> p2; //@} /** @name Base-vectos for local coordinate system. */ //@{ /// in plane, directed p1->p2 Vec<3> ex; /// in plane Vec<3> ey; /// outer normal direction Vec<3> ez; //@} public: void SetName (const char * aname); const char * Name () const { return name; } //@{ /** Defines tangential plane in ap1. The local x-coordinate axis points to the direction of ap2 */ virtual void DefineTangentialPlane (const Point<3> & ap1, const Point<3> & ap2); /// Transforms 3d point p3d to local coordinates pplane virtual void ToPlane (const Point<3> & p3d, Point<2> & pplane, double h, int & zone) const; /// Transforms point pplane in local coordinates to 3d point virtual void FromPlane (const Point<2> & pplane, Point<3> & p3d, double h) const; //@} /// Project point p onto surface (closest point) virtual void Project (Point<3> & p) const; /// Project along direction virtual void SkewProject(Point<3> & p, const Vec<3> & direction) const; /// Is current surface identic to surface 2 ? virtual int IsIdentic (const Surface & /* s2 */, int & /* inv */, double /* eps */) const { return 0; } /// virtual int PointOnSurface (const Point<3> & p, double eps = 1e-6) const; /** @name Implicit function. Calculate function value and derivatives. */ //@{ /// Calculate implicit function value in point point virtual double CalcFunctionValue (const Point<3> & point) const = 0; /** Calc gradient of implicit function. gradient should be O(1) at surface */ virtual void CalcGradient (const Point<3> & point, Vec<3> & grad) const = 0; /** Calculate second derivatives of implicit function. */ virtual void CalcHesse (const Point<3> & point, Mat<3> & hesse) const; /** Returns outer normal vector. */ // virtual void GetNormalVector (const Point<3> & p, Vec<3> & n) const; virtual Vec<3> GetNormalVector (const Point<3> & p) const; /** Upper bound for spectral norm of Hesse-matrix */ virtual double HesseNorm () const = 0; /** Upper bound for spectral norm of Hesse-matrix in the rad - environment of point c. */ virtual double HesseNormLoc (const Point<3> & /* c */, double /* rad */) const { return HesseNorm (); } //@} /// virtual double MaxCurvature () const; /// virtual double MaxCurvatureLoc (const Point<3> & /* c */ , double /* rad */) const; /** Returns any point in the surface. Needed to start surface mesh generation e.g. on sphere */ virtual Point<3> GetSurfacePoint () const = 0; /// bool Inverse () const { return inverse; } /// void SetInverse (bool ainverse) { inverse = ainverse; } /// virtual void Print (ostream & str) const = 0; /// virtual void Reduce (const BoxSphere<3> & /* box */) { }; /// virtual void UnReduce () { }; /// set max h in surface void SetMaxH (double amaxh) { maxh = amaxh; } /// double GetMaxH () const { return maxh; } /// int GetBCProperty () const { return bcprop; } /// void SetBCProperty (int abc) { bcprop = abc; } /** Determine local mesh-size. Find \[ h \leq hmax, \] such that \[ h \times \kappa (x) \leq c \qquad \mbox{in} B(x, h), \] where kappa(x) is the curvature in x. */ virtual double LocH (const Point<3> & p, double x, double c, const MeshingParameters & mparam, double hmax) const; /** Gets Approximation by triangles, where qual is about the number of triangles per radius */ virtual void GetTriangleApproximation (TriangleApproximation & /* tas */, const Box<3> & /* boundingbox */, double /* facets */ ) const { }; string GetBCName() const { return bcname; } void SetBCName( string abc ) { bcname = abc; } }; inline ostream & operator<< (ostream & ost, const Surface & surf) { surf.Print(ost); return ost; } typedef enum { IS_OUTSIDE = 0, IS_INSIDE = 1, DOES_INTERSECT = 2} INSOLID_TYPE; class DummySurface : public Surface { virtual double CalcFunctionValue (const Point<3> & /* point */) const { return 0; } virtual void CalcGradient (const Point<3> & /* point */, Vec<3> & grad) const { grad = Vec<3> (0,0,0); } virtual Point<3> GetSurfacePoint () const { return Point<3> (0,0,0); } virtual double HesseNorm () const { return 0; } virtual void Project (Point<3> & /* p */) const { ; } virtual void Print (ostream & ost) const { ost << "dummy surface"; } }; class Primitive { public: Primitive (); virtual ~Primitive(); /* Check, whether box intersects solid defined by surface. return values: 0 .. box outside solid \\ 1 .. box in solid \\ 2 .. can't decide (allowed, iff box is close to solid) */ virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const = 0; virtual INSOLID_TYPE PointInSolid (const Point<3> & p, double eps) const = 0; virtual void GetTangentialSurfaceIndices (const Point<3> & p, Array & surfind, double eps) const; virtual INSOLID_TYPE VecInSolid (const Point<3> & p, const Vec<3> & v, double eps) const = 0; // checks if lim s->0 lim t->0 p + t(v1 + s v2) in solid virtual INSOLID_TYPE VecInSolid2 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2, double eps) const; // checks if p + s v1 + s*s/2 v2 is inside virtual INSOLID_TYPE VecInSolid3 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2, double eps) const; // like VecInSolid2, but second order approximation virtual INSOLID_TYPE VecInSolid4 (const Point<3> & p, const Vec<3> & v, const Vec<3> & v2, const Vec<3> & m, double eps) const; virtual void GetTangentialVecSurfaceIndices (const Point<3> & p, const Vec<3> & v, Array & surfind, double eps) const; virtual void GetTangentialVecSurfaceIndices2 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2, Array & surfind, double eps) const; virtual void CalcSpecialPoints (Array > & /* pts */) const { ; } virtual void AnalyzeSpecialPoint (const Point<3> & /* pt */, Array > & /* specpts */) const { ; } virtual Vec<3> SpecialPointTangentialVector (const Point<3> & /* p */, int /* s1 */, int /* s2 */) const { return Vec<3> (0,0,0); } virtual int GetNSurfaces() const = 0; virtual Surface & GetSurface (int i = 0) = 0; virtual const Surface & GetSurface (int i = 0) const = 0; Array surfaceids; Array surfaceactive; int GetSurfaceId (int i = 0) const; void SetSurfaceId (int i, int id); int SurfaceActive (int i) const { return surfaceactive[i]; } virtual int SurfaceInverted (int /* i */ = 0) const { return 0; } virtual void GetPrimitiveData (const char *& classname, Array & coeffs) const; virtual void SetPrimitiveData (Array & coeffs); static Primitive * CreatePrimitive (const char * classname); virtual void Reduce (const BoxSphere<3> & /* box */) { }; virtual void UnReduce () { }; virtual Primitive * Copy () const; virtual void Transform (Transformation<3> & trans); }; class OneSurfacePrimitive : public Surface, public Primitive { public: OneSurfacePrimitive(); ~OneSurfacePrimitive(); virtual INSOLID_TYPE PointInSolid (const Point<3> & p, double eps) const; virtual INSOLID_TYPE VecInSolid (const Point<3> & p, const Vec<3> & v, double eps) const; virtual INSOLID_TYPE VecInSolid2 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2, double eps) const; virtual INSOLID_TYPE VecInSolid3 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2, double eps) const; virtual INSOLID_TYPE VecInSolid4 (const Point<3> & p, const Vec<3> & v, const Vec<3> & v2, const Vec<3> & m, double eps) const; virtual int GetNSurfaces() const; virtual Surface & GetSurface (int i = 0); virtual const Surface & GetSurface (int i = 0) const; }; /** Projects point to edge. The point hp is projected to the edge descibed by f1 and f2. It is assumed that the edge is non-degenerated, and the (generalized) Newton method converges. */ extern void ProjectToEdge (const Surface * f1, const Surface * f2, Point<3> & hp); } #endif