Class xlifepp::Triangle#

class Triangle : public xlifepp::Polygon #

Inheritence diagram for xlifepp::Triangle:

Collaboration diagram for xlifepp::Triangle:

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: to define the side names
_varnames: to define the variable names for print purpose

Public Functions

Triangle()#

default constructor

default triangle is (0,0) (1,0) (0,1), parametrization not allocated

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())#: default constructor with 3 Point

Triangle(const Point &p1, const Point &p2, const Point &p3, const std::vector<real_t> &h, const string_t &domName = string_t())#: default constructor with 3 Point

Triangle(Parameter p1, Parameter p2, Parameter p3)#: constructor with 3 Parameter

Triangle(Parameter p1, Parameter p2, Parameter p3, Parameter p4)#: constructor with 4 Parameter

Triangle(Parameter p1, Parameter p2, Parameter p3, Parameter p4, Parameter p5)#: constructor with 5 Parameter

Triangle(Parameter p1, Parameter p2, Parameter p3, Parameter p4, Parameter p5, Parameter p6)#: constructor with 6 Parameter

inline virtual ~Triangle()#: destructor

virtual string_t asString() const#: format as string

inline virtual Geometry *clone() const#: virtual copy constructor for Geometry

inline virtual Polygon *clonePG() const#: virtual copy constructor for Polygon

inline virtual Surface *cloneS() const#: virtual copy constructor for Surface

Vector<real_t> duffyParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#

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].

Vector<real_t> funParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#

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

inline virtual Triangle &homothetize(const Parameter &p1)#: apply a homothety on a Triangle (1 key)

inline virtual Triangle &homothetize(const Parameter &p1, const Parameter &p2)#: apply a homothety on a Triangle (2 keys)

inline virtual Triangle &homothetize(const Point &c = Point(0., 0., 0.), real_t factor = 1.)#: apply a homothety on a Triangle

inline virtual Triangle &homothetize(real_t factor)#: apply a homothety on a Triangle

Vector<real_t> invDuffyParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#

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

Vector<real_t> invParametrization(const Point &pt, Parameters &pars, DiffOpType d = _id) const#

inverse of barycentric parametrization (u,v)=invf(p)

inverse of parametrization (u,v)=invf(p)

virtual real_t measure() const#: return the length/area/volume of the geometry

inline virtual number_t nbSides() const#: returns the number of sides

inline virtual Triangle &pointReflect(const Parameter &p1)#: apply a point reflection on a Triangle (1 key)

inline virtual Triangle &pointReflect(const Point &c = Point(0., 0., 0.))#: apply a point reflection on a Triangle

inline virtual Triangle &reflect2d(const Parameter &p1)#: apply a reflection2d on a Triangle (1 key)

inline virtual Triangle &reflect2d(const Parameter &p1, const Parameter &p2)#: apply a reflection2d on a Triangle (2 keys)

inline virtual Triangle &reflect2d(const Point &c, real_t dx, real_t dy = 0.)#: apply a reflection2d on a Triangle

inline virtual Triangle &reflect2d(const Point &c = Point(0., 0.), std::vector<real_t> d = std::vector<real_t>(2, 0.))#: apply a reflection2d on a Triangle

inline virtual Triangle &reflect3d(const Parameter &p1)#: apply a reflection3d on a Triangle (1 key)

inline virtual Triangle &reflect3d(const Parameter &p1, const Parameter &p2)#: apply a reflection3d on a Triangle (2 keys)

inline virtual Triangle &reflect3d(const Point &c, real_t nx, real_t ny, real_t nz = 0.)#: apply a reflection3d on a Triangle

inline virtual Triangle &reflect3d(const Point &c = Point(0., 0., 0.), std::vector<real_t> n = std::vector<real_t>(3, 0.))#: apply a reflection3d on a Triangle

inline virtual Triangle &rotate2d(const Parameter &p1)#: apply a rotation 2D on a Triangle (1 key)

inline virtual Triangle &rotate2d(const Parameter &p1, const Parameter &p2)#: apply a rotation 2D on a Triangle (2 keys)

inline virtual Triangle &rotate2d(const Point &c, real_t angle = 0.)#: apply a rotation 2D on a Triangle

inline virtual Triangle &rotate3d(const Parameter &p1)#: apply a rotation 3D on a Triangle (1 key)

inline virtual Triangle &rotate3d(const Parameter &p1, const Parameter &p2)#: apply a rotation 3D on a Triangle (2 keys)

inline virtual Triangle &rotate3d(const Parameter &p1, const Parameter &p2, const Parameter &p3)#: apply a rotation 3D on a Triangle (3 keys)

inline virtual Triangle &rotate3d(const Point &c, real_t dx, real_t dy, real_t angle)#: apply a rotation on a Triangle

inline virtual Triangle &rotate3d(const Point &c, real_t dx, real_t dy, real_t dz, real_t angle)#: apply a rotation on a Triangle

inline virtual Triangle &rotate3d(const Point &c, std::vector<real_t> d = std::vector<real_t>(3, 0.), real_t angle = 0.)#: apply a rotation 3D on a Triangle

inline virtual Triangle &rotate3d(real_t dx, real_t dy, real_t angle)#: apply a rotation 3D on a Triangle

inline virtual Triangle &rotate3d(real_t dx, real_t dy, real_t dz, real_t angle)#: apply a rotation 3D on a Triangle

virtual std::vector<std::pair<ShapeType, std::vector<const Point*>>> surfs() const#: return list of surfaces (const)

virtual Triangle &transform(const Transformation &t)#: apply a geometrical transformation on a Triangle

inline virtual Triangle &translate(const Parameter &p1)#: apply a translation on a Triangle (1 key)

inline virtual Triangle &translate(real_t ux, real_t uy = 0., real_t uz = 0.)#: apply a translation on a Triangle (3 reals version)

inline virtual Triangle &translate(std::vector<real_t> u)#: apply a translation on a Triangle (vector version)

inline virtual Triangle *triangle()#: access to child Triangle object

inline virtual const Triangle *triangle() const#: access to child Triangle object (const)