Class xlifepp::Triangle#
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class Triangle : public xlifepp::Polygon#
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definition of a triangular geometry in R^3
Triangle constructors are based on a key-value system. Here are the available keys:
_v1, _v2, _v3: to define the vertices of the triangle, counterclockwise oriented
_nnodes: to define the number of nodes on each edge of the Triangle
_hsteps: to define the local mesh steps on the vertices of the Triangle
_domain_name: to define the domain name
_side_names/_edge_names: to define the side names
_vertex_names: to define the side of side names
_varnames: to define the variable names for print purpose
Public Functions
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Triangle()#
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default constructor
default triangle is (0,0) (1,0) (0,1), parametrization not allocated
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Triangle(const Point &p1, const Point &p2, const Point &p3, const std::vector<number_t> &n = std::vector<number_t>(3, 2), const string_t &domName = string_t(), const std::vector<string_t> &sideNames = std::vector<string_t>(3, ""), const std::vector<string_t> &sideOfSideNames = std::vector<string_t>(3, ""))#
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default constructor with 3 Point
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Triangle(const Point &p1, const Point &p2, const Point &p3, const std::vector<real_t> &h, const string_t &domName = string_t(), const std::vector<string_t> &sideNames = std::vector<string_t>(3, ""), const std::vector<string_t> &sideOfSideNames = std::vector<string_t>(3, ""))#
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default constructor with 3 Point
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inline virtual ~Triangle()#
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destructor
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virtual string_t asString() const#
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format as string
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Vector<real_t> duffyParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#
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duffy parametrization on [0,1]x[0,1]
Duffy parametrization: p=(1-u)*p1+u(1-v)*p2+uv*p3 with 0<= u,v <=1 u=0, 0<=v<=1 -> p1 u=1, 0<=v<=1 -> [p2,p3] v=0, 0<=u<=1 -> [p1,p2] v=1, 0<=u<=1 -> [p1,p3].
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Vector<real_t> funParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#
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barycentric parametrization (1-u-v)*p1+u*p2+v*p3
parametrization (P1) : p = (1-u-v)*p1+u*p2+v*p3 = p1+u*(p2-p1)+v*(p3-p1) with 0<= u+v <=1
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inline virtual Triangle &homothetize(const Parameter &p1, const Parameter &p2)#
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apply a homothety on a Triangle (2 keys)
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inline virtual Triangle &homothetize(const Point &c = Point(0., 0., 0.), real_t factor = 1.)#
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apply a homothety on a Triangle
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Vector<real_t> invDuffyParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#
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inverse of duffy parametrization u,v)=invf(p)
inverse of Duffy parametrization u =( p-p1).o32 / (p2-p1).o32 with o32 any orthogonal vector to p3-p2 uv = (p-p1).o21 / (p3-p2).o21 with o21 any orthogonal vector to p2-p if p=p1 then u=0 and v may be anything
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Vector<real_t> invParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#
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inverse of barycentric parametrization (u,v)=invf(p)
inverse of parametrization (u,v)=invf(p)
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virtual real_t measure() const#
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return the length/area/volume of the geometry
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inline virtual std::vector<number_t> nbElementsForGmshGeneration() const#
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return number of points/arcs/lines/loops/surfaces/extrudable elements of a geometry (only for gmsh generation)
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inline virtual number_t nbSides() const#
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returns the number of sides return number of points/arcs/lines/loops/surfaces/extrudable elementsof a geometry (only for gmsh generation)
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inline virtual Triangle &pointReflect(const Parameter &p1)#
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apply a point reflection on a Triangle (1 key)
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inline virtual Triangle &pointReflect(const Point &c = Point(0., 0., 0.))#
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apply a point reflection on a Triangle
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inline virtual Triangle &reflect2d(const Parameter &p1, const Parameter &p2)#
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apply a reflection2d on a Triangle (2 keys)
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inline virtual Triangle &reflect2d(const Point &c, real_t dx, real_t dy = 0.)#
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apply a reflection2d on a Triangle
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inline virtual Triangle &reflect2d(const Point &c = Point(0., 0.), std::vector<real_t> d = std::vector<real_t>(2, 0.))#
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apply a reflection2d on a Triangle
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inline virtual Triangle &reflect3d(const Parameter &p1, const Parameter &p2)#
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apply a reflection3d on a Triangle (2 keys)
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inline virtual Triangle &reflect3d(const Point &c, real_t nx, real_t ny, real_t nz = 0.)#
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apply a reflection3d on a Triangle
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inline virtual Triangle &reflect3d(const Point &c = Point(0., 0., 0.), std::vector<real_t> n = std::vector<real_t>(3, 0.))#
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apply a reflection3d on a Triangle
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inline virtual Triangle &rotate2d(const Parameter &p1, const Parameter &p2)#
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apply a rotation 2D on a Triangle (2 keys)
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inline virtual Triangle &rotate2d(const Point &c, real_t angle = 0.)#
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apply a rotation 2D on a Triangle
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inline virtual Triangle &rotate3d(const Parameter &p1, const Parameter &p2)#
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apply a rotation 3D on a Triangle (2 keys)
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inline virtual Triangle &rotate3d(const Parameter &p1, const Parameter &p2, const Parameter &p3)#
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apply a rotation 3D on a Triangle (3 keys)
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inline virtual Triangle &rotate3d(const Point &c, real_t dx, real_t dy, real_t angle)#
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apply a rotation on a Triangle
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inline virtual Triangle &rotate3d(const Point &c, real_t dx, real_t dy, real_t dz, real_t angle)#
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apply a rotation on a Triangle
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inline virtual Triangle &rotate3d(const Point &c, std::vector<real_t> d = std::vector<real_t>(3, 0.), real_t angle = 0.)#
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apply a rotation 3D on a Triangle
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inline virtual Triangle &rotate3d(real_t dx, real_t dy, real_t angle)#
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apply a rotation 3D on a Triangle
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inline virtual Triangle &rotate3d(real_t dx, real_t dy, real_t dz, real_t angle)#
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apply a rotation 3D on a Triangle
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virtual std::vector<std::pair<ShapeType, std::vector<const Point*>>> surfs() const#
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return list of surfaces (const)
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virtual Triangle &transform(const Transformation &t)#
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apply a geometrical transformation on a Triangle
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inline virtual Triangle &translate(real_t ux, real_t uy = 0., real_t uz = 0.)#
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apply a translation on a Triangle (3 reals version)