> For the complete documentation index, see [llms.txt](https://particle-analytics-1.gitbook.io/iotasuite-user-manual/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://particle-analytics-1.gitbook.io/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg/cg_averaging/cg_averaging_spatial_averaging.md).
# Spatial Averaging
This section allows users to define the options for the the spatial averaging process, including the calculation of spatial gradients and spatial integrals.
*Figure 67 - "Spatial Averaging" section of* [*coarse-graining*](/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg.md) *module.*
## [Function](/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg/cg_averaging/cg_averaging_spatial_averaging.md#function)
Users can select between different weight functions for the spatial averaging:
* `Gaussian`: particles' contibution varies according to the [Gaussian function](https://en.wikipedia.org/wiki/Normal_distribution) of the given `width`.
* `Heaviside`: particles' contibution will be equally-weighted while they lay in the averaging region being averaged over.
## [Width and Cutoff Factor](/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg/cg_averaging/cg_averaging_spatial_averaging.md#width-and-cutoff-factor)
The value of the `width` determines the length scale for the spatial averaging function. For `Gaussian` function, this corresponds to the standard deviation of the funciton. For `Heaviside`, this determines the size of the representative volume.
The `Cutoff Factor` is used in combination with the `Width` to ignore particles whose contribution will be very small. Since the `Gaussian` function only becomes zero at infinity, all particles would contribute to the spatial average, most giving the tiniest of contributions.
> The values of `Width` and `Cutoff Factor` are problem dependent, but for quasi-static problems or low speed flows a `Width` of 2.5 to 3.0 times the average particle radius can be considered a safe value. For high speed flows and high sampling frequencies, this value can be as low as half the average radius. A `Cutoff Factor` of 3.0 can be considered safe. In the case of high speed flows or sampling frequencies, this value can decrease to obtain a better resolution close to the boundaries.
## [Gradients](/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg/cg_averaging/cg_averaging_spatial_averaging.md#gradients)
This features allows the user to activate the calculation of spatial gradients during the spatial averaging process. This creates the extra results in the Coarse-graining dataset that correspond to spatial gradients of the results: Density, Solid fraction, Momentum, and Velocity.
## [Spatial Integral](/iotasuite-user-manual/coarse_graining_intro/cg_setting_cg/cg_averaging/cg_averaging_spatial_averaging.md#spatial-integral)
This feature allows the users to select if spatial intergral will be performed during the calculation of the coarse-graining results:
* `None`: spatial intergral will not be calculated.
* `1D`: the coarse-grianing results are integrated along one of the main axis-directions: \[`X` / `Y` / `Z`].
* `2D`: the coarse-grianing results are integrated over a plane. Users can select among the following planes for the integration: \[`XY` / `YZ` / `XZ`].
* `1D cylindrical`: the coarse-grianing results are integrated along the tangential of cylindrical coordinate system defined by the user:
* `1D Cylindrical Direction`: defines the axial direction of the cylindrical coordinate system.
* `1D Cylindrical Origin`: defines the position of the origin of the cylindrical coordinate system.