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--- visual3d:documentation:pipeline:expressions:intersection_functions [2025/01/24 18:20] – wikisysop
+++ visual3d:documentation:pipeline:expressions:intersection_functions [2025/01/27 20:25] (current) – wikisysop
@@ Line 147: / Line 147: @@
   * The resulting bounding box is aligned with the Laboratory Coordinate System. The bounding box signal is a 24 column signal containing the X,Y,Z position of 8 vertices.
-Example: Create a 4 targets representing the vertices of the box, and create a bounding box around these targets that will be tracked across an event sequence.
+Example: Create 4 arbitrary targets, and create a bounding box around these targets that will be tracked across an event sequence.
 <code>
@@ Line 203: / Line 203: @@
 ==== Base_Of_Support ====
-{{ visual3D:documentation:pipeline:expressions:BaseOfSupportDgrm.png?300}}
+{{ visual3D:documentation:pipeline:expressions:BOSDiagram.png?300}}
-**Bounding_Box**(Signal,Vector)
+**Base_Of_Support**(Signal,Plane)
+  * Construct a 2D base of support projected onto a plane from a Bounding Box.
+  * The signal input is the [[https://en.wikipedia.org/wiki/Minimum_bounding_box|bounding box]] of the point set, a 24 column signal containing the X,Y,Z position of 8 vertices.
+  * The [[visual3d:documentation:pipeline:expressions:least_squares_fitting_of_data#best_fit_plane|Plane]] parameter is the plane to project the Box onto.
+  * The resulting base of support is a 2D projection of the signal onto the plane. The base of support is a 12 column signal containing the X,Y,Z position of 4 vertices (C1-C4 in the image to the right).
+Example: Create a bounding box around 4 targets between events START and END, and project that box onto the ground using the Base_Of_Support command.
+<code>
+! Create a bounding box using 4 targets V1,V2,V3,V4 to be tracked between events START and END
+Evaluate_Expression
+/EXPRESSION=BOUNDING_BOX(CURRENT_SIGNAL,1)
+/SIGNAL_TYPES=EVENT_LABEL+EVENT_LABEL+TARGET+TARGET+TARGET+TARGET
+/SIGNAL_FOLDER=ORIGINAL
+/SIGNAL_NAMES=START+END+V1+V2+V3+V4
+! /RESULT_TYPES=DERIVED
+/RESULT_FOLDERS=BOUNDING_BOX
+/RESULT_NAME=BOX
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+! Project the bounding box onto the X-Y plane of the laboratory
+Evaluate_Expression
+/EXPRESSION=BASE_OF_SUPPORT(CURRENT_SIGNAL,VECTOR(0,0,1,0))
+/SIGNAL_TYPES=DERIVED
+/SIGNAL_FOLDER=BOUNDING_BOX
+/SIGNAL_NAMES=BOX
+! /SIGNAL_COMPONENTS=
+! /RESULT_TYPES=DERIVED
+/RESULT_FOLDERS=BASE_OF_SUPPORT
+/RESULT_NAME=BOS
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+! Create targets of the resulting Base of Support signal for visualization
+Create_Targets_For_Base_Of_Support
+/SIGNAL_NAMES=BOS
+/SIGNAL_DESCRIPTION=BOS
+/EXPRESSION=DERIVED::BASE_OF_SUPPORT::BOS
+/NUM_TARGETS=8
+;
+</code>
+Example: Projecting a bounding box onto a sloped plane.
+<code>
+!Creating 4 vectors defining a corners of plane (such as a sloped floor)
+Metric_Explicit
+/RESULT_METRIC_FOLDER=FLOOR
+/RESULT_METRIC_NAME=F1
+/METRIC_VALUE=VECTOR(0,0,0)
+;
+Metric_Explicit
+/RESULT_METRIC_FOLDER=FLOOR
+/RESULT_METRIC_NAME=F2
+/METRIC_VALUE=VECTOR(0.2,0,0)
+;
+Metric_Explicit
+/RESULT_METRIC_FOLDER=FLOOR
+/RESULT_METRIC_NAME=F3
+/METRIC_VALUE=VECTOR(0,0.2,0.03)
+;
+Metric_Explicit
+/RESULT_METRIC_FOLDER=FLOOR
+/RESULT_METRIC_NAME=F4
+/METRIC_VALUE=VECTOR(0.2,0.2,0.03)
+;
+! Creating a best fit plane using the 4 vectors defined previously
+Evaluate_Expression
+/EXPRESSION=BEST_FIT_PLANE(CURRENT_SIGNAL)
+/SIGNAL_TYPES=METRIC
+/SIGNAL_FOLDER=FLOOR
+ /SIGNAL_NAMES=F1+F2+F3+F4
+! /SIGNAL_COMPONENTS=
+ /RESULT_TYPES=METRIC
+/RESULT_FOLDERS=FLOOR
+/RESULT_NAME=PLANE
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+! Projecting a bounding box onto the plane to create a base of support
+Evaluate_Expression
+/EXPRESSION=BASE_OF_SUPPORT(CURRENT_SIGNAL,METRIC::FLOOR::PLANE)
+/SIGNAL_TYPES=DERIVED
+/SIGNAL_FOLDER=BOUNDING_BOX
+/SIGNAL_NAMES=BOX
+! /SIGNAL_COMPONENTS=
+! /RESULT_TYPES=DERIVED
+/RESULT_FOLDERS=BASE_OF_SUPPORT
+/RESULT_NAME=BOS2
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+! Highlighting the base of support with targets
+Create_Targets_For_Base_Of_Support
+/SIGNAL_NAMES=BOS
+/SIGNAL_DESCRIPTION=BOS
+/EXPRESSION=DERIVED::BASE_OF_SUPPORT::BOS2
+/NUM_TARGETS=8
+;
+</code>
+==== Extrapolated_COG ====
+**EXTRAPOLATED_COG**(Signal,Signal,Model Metric)
+  * Computes the extrapolated COG or the [[https://www.sciencedirect.com/science/article/abs/pii/S0021929004001642?via%3Dihub|'extrapolated center of mass position']] using the following equation:
+  * xCoM = CoM + vCoM/sqrt(g/l)
+  * Expression requires three inputs:
+    * The first signal input is considered as the CoM position,
+    * second input is considered the velocity of the CoM,
+    * and the third input is the leg length of the model.
+Example: Deriving the extrapolated CoM
+<code>
+Evaluate_Expression
+/EXPRESSION=EXTRAPOLATED_COG(CURRENT_SIGNAL,MODEL::METRIC::LEG_LENGTH)
+/SIGNAL_TYPES=LINK_MODEL_BASED+LINK_MODEL_BASED
+/SIGNAL_FOLDER=ORIGINAL+ORIGINAL
+/SIGNAL_NAMES=COG+COG_VELOCITY
+! /RESULT_TYPES=DERIVED
+/RESULT_FOLDERS=BASE_OF_SUPPORT
+/RESULT_NAME=XCOG
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+</code>
+==== Margin_Of_Stability ====
-  * Construct a 2D plane projected from a Bounding Box signal.
-  * The signal input is the [[https://en.wikipedia.org/wiki/Minimum_bounding_box|bounding box]] of the point set, a 24 column vector containing the X,Y,Z position of 8 vertices.
-  * The Vector parameter is the direction of projection in the lab coordinate system
-     * 0 = static across event_sequence
-     * 1 = computed frame by frame across event_sequence
-  * The resulting bounding box is aligned with the Laboratory Coordinate System.