User:Pertio00/sandbox

=== Uniform grid ===

=== Uniform grid ===

For simple [[regular grid#related grids|Cartesian grids]], the tracking algorithm is straightforward. Knowing the grid first point in space <math>\mathbf{x_0}=(x_0, y_0, z_0) </math> and the grid spacing <math> \mathbf{\Delta}=(\Delta_x,\Delta_y,\Delta_z) </math> then the coordinate of the center of cell <math>(i,j,k) </math> is uniquely identified as:

For simple [[regular grid#related grids|Cartesian grids]], the tracking algorithm is straightforward, as the problem is decoupled along the three directions and the grid coordinates can be directly computed knowing the cell index. Knowing the grid first point in space <math>\mathbf{x_0}=(x_0, y_0, z_0) </math> and the grid spacing <math> \mathbf{\Delta}=(\Delta_x,\Delta_y,\Delta_z) </math> then the coordinate of the center of cell <math>(i,j,k) </math> is uniquely identified as:

<math> \begin{cases}

<math> \begin{cases}

Where <math>\lfloor\cdot\rceil </math> is the rounding operator<ref name="sadarjoen-walsum-etal-1994"></ref>.

Where <math>\lfloor\cdot\rceil </math> is the rounding operator<ref name="sadarjoen-walsum-etal-1994"></ref>.

=== Rectilinear grid ===

=== Rectilinear grid ===

In [[regular grid#related grids|rectilinear grids]], the coordinates of mesh elements at a given index can't be computed directly and has to be stored explicitly. In rectilinear grids, the coordinates in a given direction only depend on the index in the same directions:

In [[regular grid#related grids|rectilinear grids]], the coordinates of mesh elements at a given index can't be computed directly and has to be stored explicitly. In rectilinear grids, the coordinates in a given direction only depend on the index in the same directions: