# Feel++

## Geometry

### Points

#### Current Point:

 Feel++ Keyword Math Object Description Dimension `P()` \overrightarrow{P} (P_x, P_y, P_z)^T d \times 1 `Px()` P_x x coordinate of \overrightarrow{P} 1 \times 1 `Py()` P_y y coordinate of \overrightarrow{P} (value is 0 in 1D) 1 \times 1 `Pz()` P_z z coordinate of \overrightarrow{P} (value is 0 in 1D and 2D) 1 \times 1

#### Element Barycenter Point:

Feel++ Keyword Math Object Description Dimension

`C()`

\overrightarrow{C}

(C_x, C_y, C_z)^T

d \times 1

`Cx()`

C_x

x coordinate of \overrightarrow{C}

1 \times 1

`Cy()`

C_y

y coordinate of \overrightarrow{C} (value is 0 in 1D)

1 \times 1

`Cz()`

C_z

z coordinate of \overrightarrow{C} (value is 0 in 1D and 2D)

1 \times 1

#### Normal at Current Point:

 Feel++ Keyword Math Object Description Dimension `N()` \overrightarrow{N} (N_x, N_y, N_z)^T d \times 1 `Nx()` N_x x coordinate of \overrightarrow{N} 1 \times 1 `Ny()` N_y y coordinate of \overrightarrow{N} (value is 0 in 1D) 1 \times 1 `Nz()` N_z z coordinate of \overrightarrow{N} (value is 0 in 1D and 2D) 1 \times 1

### Geometric Transformations

#### Jacobian Matrix

You can access to the jacobian matrix, J, of the geometric transformation, using the keyword: `J()` There are some tools to manipulate this jacobian.

 Feel++ Keyword Math Object Description `detJ()` \det(J) Determinant of jacobian matrix `invJT()` (J^{-1})^T Transposed inverse of jacobian matrix