Class xlifepp::Ball#

class Ball : public xlifepp::Ellipsoid #

definition of an spherical geometry in R^3 (volume)

Ball constructors are based on a key-value system. Here are the available keys:

_center: to define the center of the Ball
_v1, _v2, _v6: to define apogees of the Ball
_radius: to define radius of the Ball
_type: indicator to fit curved boundaries (default) or not which gives flat (or plane) boundaries
_nboctants: to define an ellipsoidal sector from octants.
_nnodes: to define the number of nodes on the edges of the Ball
_hsteps: to define the local mesh steps on build points of the Ball
_domain_name: to define the domain name
_side_names/_face_name: to define the side names
_edge_name: to define the side of side names
_vertex_name: to define the side of side of side names
_varnames: to define the variable names for print purpose

Public Functions

Ball()#

default constructor

default is ball of center (0,0,0) and radius 1

Ball(const Ball &b)#: copy constructor

Ball(Parameter p1, Parameter p2)#: key-value constructor

virtual string_t asString() const#

format as string: “Ball (center=(.,.,.), radius = R)”

Format Ball as string: “Ball (center = (.,.,.), radius = R)”.

inline virtual Ball *ball()#: access to child Ball object

inline virtual const Ball *ball() const#: access to child Ball object (const)

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

Vector<real_t> funBoundaryParametrization(const Point &pt, Parameters &pars, DiffOpType dif) const#: parametrization of ball boundary (spherical coordinates) u,v in [0,1]x[0,1]x[0,1], t=pi*(2u-1), l=pi*(v-0.5) x = R*cos(t)*cos(l), y = R*sin(t)*cos(l), z = R*sin(l)

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

parametrization stuff

parametrization of ball (spherical coordinates) u,v,w in [0,1]x[0,1]x[0,1], t=pi*(2u-1), l=pi*(v-0.5), r=w*R x = r*cos(t)*cos(l), y = r*sin(t)*cos(l), z = r*sin(l)

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

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

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

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

Vector<real_t> invBoundaryParametrization(const Point &pt, Parameters &pars, DiffOpType dif) const#: inverse of parametrization (u,v)=invbf(pt)

Vector<real_t> invParametrization(const Point &pt, Parameters &pars, DiffOpType dif) const#: inverse of parametrization (u,v)=invf(pt)

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

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

inline real_t radius() const#: returns radius

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

inline virtual Ball &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 Ball

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

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

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

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

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

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