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=====Metric Compute Volume of a Convex Hull Across Frames=====
====Overview====
The metric command **Compute Volume of a Convex Hull Across Frames** can be used to find the area or volume of the convex hull for a dataset across several frames. A convex hull is defined as the smallest convex set containing all of the points in a Euclidian space. It can be visualized in 2 dimensions as a string or rubber band around the perimeter of a set, or in 3 dimensions as shrink wrap enclosing the entire range of data points.  

{{:convex_hull.jpg|}}

The volume or area of the convex hull of a set can be used to describe the amount of variance in a set or to describe the geometry of the distribution of points. 

====Pipeline Command====
The pipeline command for **Compute Volume of a Convex Hull Across Frames** can be found in the **Metric** folder in the Pipeline Workshop and is as so:

<code>
Metric_Compute_Volume_of_a_Convex_Hull_Across_Frames
/SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /RESULT_FOLDER=PROCESSED
/RESULT_NAME=
! /NUMBER_OF_DIMENSIONS=
! /COMPONENT_SEQUENCE=
! /REQUIRE_ALL_SIGNALS=TRUE
! /START_FRAME=
! /END_FRAME=
! /EVENT_SEQUENCE=
! /EXCLUDE_EVENTS=
;
</code>

====Command Parameters====
The following table shows the command parameters seen above and their descriptions:

|**SIGNAL_TYPES**|**Specify the signal type**|
|**SIGNAL_FOLDER**|**Specify the origin folder**|
|**SIGNAL_NAMES**|**Specify the Signal to be used**|
|**RESULT_FOLDER**|**The name of the result signal folder**|
|**RESULT_NAME**|**The name of the result signal**|
|**NUMBER_OF_DIMENSIONS**|**Number of dimensions the hull will be computed for (2 or 3)**|
|**COMPONENT_SEQUENCE**|**Specify the Signal components to be used (e.g. X + Y + Z or 0 + 1 + 2 etc)**|
|**REQUIRE_ALL_SIGNALS**|**True or False: require all signals to exist**|
|**/START_FRAME=**      |**The frame at which to start recording data.** |
|**END_FRAME=**         |**The frame at which to stop recording data.**|
|**EVENT_SEQUENCE**|**A list of events (separated by "+" signs). For example, LHS+RTO**|
|**EXCLUDE_EVENTS**|**If this event occurs before the first and last event, do not computed a metric**|

====Dialog====
The command can be edited in a text editor or in a dialog form. To edit in the dialog pop up form either click on the **Edit** button in the pipeline workshop or double-click on the pipeline command. The dialog is shown below:

{{:convex_dlg.png|}}

The dialog box allows you to assign values to the command parameters outlined above

====Example: 2D convex hull====
Here the **Metric Compute Volume of a Convex Hull Across Frames** command is used to compute the convex hull for right and left foot GRF data during a balance trial. By computing a 2 dimensional (X and Y) hull for the GRF at each foot we can make comparisons between sides while balancing and identify potential asymmetry. 

The command is as so:

<code>
Metric_Compute_Volume_of_a_Convex_Hull_Across_Frames
/SIGNAL_TYPES=FORCE
/SIGNAL_FOLDER=ORIGINAL
/SIGNAL_NAMES=FP3
/RESULT_FOLDER=PROCESSED
/RESULT_NAME=GRF_right_hull
/NUMBER_OF_DIMENSIONS=2
/COMPONENT_SEQUENCE=X+Y
/REQUIRE_ALL_SIGNALS=TRUE
! /START_FRAME=
! /END_FRAME=
/EVENT_SEQUENCE=Start+End
! /EXCLUDE_EVENTS=
;

Metric_Compute_Volume_of_a_Convex_Hull_Across_Frames
/SIGNAL_TYPES=FORCE
/SIGNAL_FOLDER=ORIGINAL
/SIGNAL_NAMES=FP4
/RESULT_FOLDER=PROCESSED
/RESULT_NAME=GRF_left_hull
/NUMBER_OF_DIMENSIONS=2
/COMPONENT_SEQUENCE=X+Y
/REQUIRE_ALL_SIGNALS=TRUE
! /START_FRAME=
! /END_FRAME=
/EVENT_SEQUENCE=Start+End
! /EXCLUDE_EVENTS=
;
</code>

The resulting metrics show the area of the 2 dimensional hull created for each side, a larger area points to more variation in force during the trial.

Results:

{{:hull_left.png|}}{{:hull_right.png|}}

====Example: 3D convex hull====
In this example **Metric Compute Volume of a Convex Hull Across Frames** is used to find the volume occupied by an individual's thorax segment between events as defined in the workspace. 

The pipeline command is as follows:

<code>
Metric_Compute_Volume_of_a_Convex_Hull_Across_Frames
/SIGNAL_TYPES=TARGET
! /SIGNAL_FOLDER=ORIGINAL
/SIGNAL_NAMES=CLAV+STRN+CV7+T10+RSHO+LSHO
! /RESULT_FOLDER=PROCESSED
/RESULT_NAME=Upper_Thorax_Volume
/NUMBER_OF_DIMENSIONS=3
/COMPONENT_SEQUENCE=ALL
! /REQUIRE_ALL_SIGNALS=TRUE
! /START_FRAME=
! /END_FRAME=
/EVENT_SEQUENCE=EVENT1+EVENT2
! /EXCLUDE_EVENTS=
;
</code>

Here a 3 dimensional hull is used as the resulting metric will represent a 3 dimensional structure in space. The resulting metric value represents the approximate volume of the space that the upper thorax segment travels through between the events listed:

{{:thorax_volume.png|}}
====Additional Resources:====
[[https://www.cis.upenn.edu/~jean/gbooks/new281-282.pdf|Delaunay Triangulation]]\\
[[https://www.geeksforgeeks.org/dsa/convex-hull-algorithm/|Convex Hull Algorithm]]