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--- visual3d:documentation:pipeline:expressions:array_and_matrix_functions [2024/07/16 16:58] – removed sgranger
+++ visual3d:documentation:pipeline:expressions:array_and_matrix_functions [2025/05/16 13:01] (current) – Cleaned up page formatting and added links. wikisysop
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+====== Array and Matrix Functions ======
+These array and matrix functions can be used anywhere Visual3D allows [[visual3d:documentation:pipeline:expressions:expressions_overview|expressions]] to be used.
+===== Arrays =====
+Arrays can be thought of as a 1-dimensional ordered list of numerical values.
+==== Vector ====
+**Vector**(a,b, etc) - creates a vector of the number of components specified
+<code>
+! Create a metric signal with 2 components and one frame
+Metric_Explicit
+! /RESULT_METRIC_FOLDER=PROCESSED
+/RESULT_METRIC_NAME=VEC2
+/METRIC_VALUE=2+3
+;
+! Create a vector containing a constant, a two dimensional metric and a 3 dimensional model based signal.
+Evaluate_Expression
+/EXPRESSION=vector (1, METRIC::PROCESSED::VEC2, LINK_MODEL_BASED::ORIGINAL::RKNEE_ANGLE)
+! /SIGNAL_TYPES=
+! /SIGNAL_FOLDER=ORIGINAL
+! /SIGNAL_NAMES=
+! /RESULT_TYPES=DERIVED
+! /RESULT_FOLDERS=PROCESSED
+/RESULT_NAME=TEST
+! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
+;
+</code>
+The resulting signal will have the first three columns (one for the constant, one for the vector of 2 components) buffered to the number of frames of RKNEE_ANGLE by replicating the first frame.
+==== List ====
+**list(a,b,etc)** - creates a list (column vector) of the number of rows specified.
+==== Unit_Vector ====
+**unit_vector (a, b, etc)** - creates a unit vector of the number of components specified.
+===== Rotation Matrices =====
+Rotation matrices are used throughout Visual3D because they can entirely contain the information regarding a segment's [[visual3d:documentation:kinematics_and_kinetics:pose_estimation|pose]].
+==== Rotation Multiply ====
+**Rotation_Multiply**(a,b) - Multiplies two rotation matrices
+Example: Multiply two ROTATION signals
+<code>
+Evaluate_Expression
+/EXPRESSION=ROTATION_MULTIPLY(ROTATION_INVERSE(ROTATION::ORIGINAL::PELVIS_SHIFTED_4x4),CURRENT_SIGNAL)
+/SIGNAL_TYPES=ROTATION
+! /SIGNAL_FOLDER=ORIGINAL
+! /SIGNAL_NAMES=
+/RESULT_TYPES=ROTATION
+! /RESULT_FOLDERS=PROCESSED
+/RESULT_NAME=_MULT
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE
+;
+</code>
+==== Rotation Inverse ====
+**Rotation_Inverse**(a) - Calculates the inverse of a rotation matrix
+Example: Inverse of a 4x4 ROTATION signal or a 3x3 LINK_MODEL_BASED ROTATION
+<code>
+Evaluate_Expression
+/EXPRESSION=ROTATION_INVERSE(ROTATION::ORIGINAL::PELVIS_SHIFTED_4x4)
+/SIGNAL_TYPES=ROTATION
+! /SIGNAL_FOLDER=ORIGINAL
+! /SIGNAL_NAMES=
+/RESULT_TYPES=ROTATION
+! /RESULT_FOLDERS=PROCESSED
+/RESULT_NAME=_INV
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE
+;
+</code>
+**Note**: A good description of the inverse of a ROTATION signals can be found [[http://www.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche0053.html|here]]
+==== Rotation Transpose ====
+**Rotation_Transpose**(a) - Creates the transposition of a rotation matrix.
+Example: Transpose of a 3x3 LINK_MODEL_BASED ROTATION signal
+<code>
+Evaluate_Expression
+/EXPRESSION=ROTATION_TRANSPOSE(ROTATION::ORIGINAL::PELVIS_SHIFTED_4x4)
+/SIGNAL_TYPES=ROTATION
+! /SIGNAL_FOLDER=ORIGINAL
+! /SIGNAL_NAMES=
+/RESULT_TYPES=ROTATION
+! /RESULT_FOLDERS=PROCESSED
+/RESULT_NAME=_T
+/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE
+;
+</code>
+==== Pose_4x4 ====
+**Pose_4x4(a,0,0,0,123)** - Creates a 4x4 rotation signal based on signal "a" with the translation of the origin (0,0,0) and the orientation defined by Euler angles with the Euler sequence 123.
+This function was created in support of the [[id=visual3d:documentation:modeling:segments:segment_overview#shadow_segments|shadow segments]] feature.
+Example: Create a rotation matrix for a shadow segment of the right heel
+<code>
+POSE_4X4(R_HEEL,0,0,0,123)
+</code>
+===== See Also =====
+Go back to see other [[visual3d:documentation:pipeline:expressions:expressions_overview#functions|Expression functions]].