===== FP CORNERS =====

This page provides an overview of the [[visual3d:documentation:c3d_signal_types:c3d_format#c3d_parameter_format|C3D Parameter]] FORCE_PLATFORM:CORNERS. This parameter provides information about the location of a force platform's corners, which allows the measurements recorded by this platform to be integrated with other motion capture data.

The force platform's corners are numbered from 1 to 4 with the coordinates for each corner specified in the [[visual3d:documentation:definitions:laboratory_coordinate_system|Laboratory Coordinate System]] in units consistent with the [[visual3d:documentation:c3d_signal_types:target_data_type|POINT data]]. The order is specified by the quadrant numbers in the force platform coordinate system:
  - (+x,+y)
  - (-x, +y)
  - (-x, -y)
  - ( +x, -y).

Visual3D uses these force platform corners to calculate the transformation matrix from the force platform's coordinate system to the laboratory coordinate system. This transformation matrix is then used to transform the force vector from the force platform coordinate system (in which it was collected) into the laboratory coordinate system where it is used for the analysis.

The Force Platform corners can be modified using the [[Visual3D:Documentation:Pipeline:Force_Commands:Modify_Force_Platform_Parameters|Modify_Force_Platform_Parameters]] selection under the Visual3D File Menu

==== Transforming the Ground Reaction Force into the Laboratory Coordinate System ====

The following pseudo-code describes the algorithm for computing the transformation from the Force Platform Coordinate System (FPCS) to the Laboratory Coordinate System (LCS)

<code>
 x_vector = unit_vector(corner3 - corner2)
 y_vector = unit_vector(corner1 - corner2)
 z_vector = cross_product(x_vector , y_vector)
 y_vector = cross_product(z_vector , x_vector)


Rotation Matrix - FPCS to LCS
 fpcs_to_lcs column1= x_vector
 fpcs_to_lcs column2= y_vector
 fpcs_to_lcs column3= z_vector

location of top center of force platform in LCS
platform_top_center_lcs= average(corner1, corner2, corner3, corner4)

vector from plate origin to top center relative to lab
Rotate_to_Lab(forceplatform_origin)

vector from LCS origin to platform origin
platform_origin_lcs= platform_top_center_lcs- vector from plate origin to top center
</code>

==== Example 1: Use average marker locations to define force platform corners ====

Consider the following markers to be placed on the corners of a force platform.
  * FP1_1
  * FP1_2
  * FP1_3
  * FP1_4

Capture a short trial of these markers and create the following pipeline:

<code>
!First define the marker radius as a pipeline parameter
Set_Pipeline_Parameter
/PARAMETER_NAME=MARKER_RADIUS
/PARAMETER_VALUE=10
;

! Compute the median value of the corners over all frames of the trial.
! the result will be placed in the Global Workspace
Metric_Median
/RESULT_METRIC_NAME=_MED
/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE
/RESULT_METRIC_FOLDER=FPLOC
/SIGNAL_TYPES=TARGET
/SIGNAL_NAMES=FP1_1 + FP1_2 + FP1_3 + FP1_4
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_COMPONENTS=ALL_COMPONENTS
/EVENT_SEQUENCE=
/EXCLUDE_EVENTS=
! /GENERATE_MEAN_AND_STDDEV=TRUE
! /APPEND_TO_EXISTING_VALUES=FALSE
;

! If the force platform parameters have already been defined, we only need to modify the corners.
! Note that the markers are in meters, but the following command requires millimeters
Modify_Force_Platform_Parameters
/FP_USED=1
/FP_CORNER1= 1000*GLOBAL::METRIC::FPLOC::FP1_1_MED_MEAN::X
+1000*GLOBAL::METRIC::FPLOC::FP1_1_MED_MEAN::Y
+1000*(GLOBAL::METRIC::FPLOC::FP1_1_MED_MEAN::Z-&::MARKER_RADIUS)
/FP_CORNER2= 1000*GLOBAL::METRIC::FPLOC::FP1_2_MED_MEAN::X
+1000*GLOBAL::METRIC::FPLOC::FP1_2_MED_MEAN::Y
+1000*(GLOBAL::METRIC::FPLOC::FP1_2_MED_MEAN::Z-&::MARKER_RADIUS)
/FP_CORNER3= 1000*GLOBAL::METRIC::FPLOC::FP1_3_MED_MEAN::X
+1000*GLOBAL::METRIC::FPLOC::FP1_3_MED_MEAN::Y
+1000*(GLOBAL::METRIC::FPLOC::FP1_3_MED_MEAN::Z-&::MARKER_RADIUS)
/FP_CORNER4= 1000*GLOBAL::METRIC::FPLOC::FP1_4_MED_MEAN::X
+1000*GLOBAL::METRIC::FPLOC::FP1_4_MED_MEAN::Y
+1000*(GLOBAL::METRIC::FPLOC::FP1_4_MED_MEAN::Z-&::MARKER_RADIUS)
;
</code>

==== Example 2: Modify force platform corners directly ====

This example is possible in **Visual3D Version 5 or later**.

Consider the following markers to be placed on the corners of a force platform in the standing trial:
  * FP1_1
  * FP1_2
  * FP1_3
  * FP1_4

Given MARKER_RADIUS is a [[visual3d:documentation:modeling:model_metrics|model metric]] containing the radius of the markers, use the following pipeline command:

<code>
! If the force platform parameters have already been defined, we only need to modify the corners.
! Note that the markers are in meters, but the following command requires millimeters
Modify_Force_Platform_Parameters
/FP_USED=1
/FP_CORNER1= 1000*MODEL::TARGET::FP1_1::X
+1000*MODEL::TARGET::FP1_1::Y
+1000*(MODEL::TARGET::FP1_1::Z-&::MARKER_RADIUS)
/FP_CORNER2= MODEL::TARGET::FP1_2::X
+1000*MODEL::TARGET::FP1_2::Y
+1000*(MODEL::TARGET::FP1_2::Z-&::MARKER_RADIUS)
/FP_CORNER3= 1000*MODEL::FP1_3::X
+1000*MODEL::TARGET::FP1_3::Y
+1000*(MODEL::TARGET::FP1_3::Z-&::MARKER_RADIUS)
/FP_CORNER4= 1000*MODEL::FP1_4::X
+1000*MODEL::TARGET::FP1_4::Y
+1000*(MODEL::TARGET::FP1_4::Z-&::MARKER_RADIUS)
;
</code>