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--- visual3d:documentation:pipeline:expressions:mathematical_operators [2024/06/19 13:59] – created sgranger
+++ visual3d:documentation:pipeline:expressions:mathematical_operators [2024/11/04 20:30] (current) – wikisysop
@@ Line 1: / Line 1: @@
-===== Contents =====
+====== Mathematical Operators  ======
+The [[visual3d:documentation:pipeline:expressions:expressions_overview|Evaluate_Expression]] command can be used to evaluate arbitrary mathematical expressions. Use the following characters for your mathematical operators.
+**Arithmetic Operators**
+  * [[#Plus|Plus ]]
+  * [[#Minus|Minus]]
+  * [[#Multiply|Multiply]]
+  * [[#Divide|Divide]]
+  * [[#Power|Power]]
-  * [[#Plus|1 Plus]]
+**Boolean Operators**
-  * [[#Minus|2 Minus]]
+  * [[#Logical_Or|Logical OR]]
-  * [[#Multiply|3 Multiply]]
+  * [[#Logical_And|Logical AND]]
-  * [[#Divide|4 Divide]]
+  * [[#Using_the_Adjective_NOT|The Adjective NOT]]
-  * [[#Power|5 Power]]
-  * [[#Logical_Or|6 Logical_Or]]
-  * [[#Logical_And|7 Logical_And]]
-  * [[#Equals|8 Equals]]
-  * [[#Not_Equals|9 Not_Equals]]
-  * [[#Using_the_Adjective_NOT|10 Using the Adjective NOT]]
-  * [[#Less_Than|11 Less_Than]]
-  * [[#Less_Than_Or_Equals|12 Less_Than_Or_Equals]]
-  * [[#Greater_Than|13 Greater_Than]]
-  * [[#Greater_Than_Or_Equals|14 Greater_Than_Or_Equals]]
+**Comparison Operators**
+  * [[#Equals|Equals]]
+  * [[#Not_Equals|Not Equals]]
+  * [[#Less_Than|Less Than]]
+  * [[#Less_Than_Or_Equals|Less Than Or Equals]]
+  * [[#Greater_Than|Greater Than]]
+  * [[#Greater_Than_Or_Equals|Greater Than Or Equals]]
-===== Plus =====
+Note: Visual3D parses the mathematical operators before it parses the signal names. If you have a signal name that contains a mathematical operator (e.g. R-Foot1), Visual3D will probably not be able to parse the equation expression properly.
-NOTE: Pipeline command parameters use + as delimiter
+===== Arithmetic Operators =====
-If the user wants to use an expression containing a + in a command parameter that allows multiple signals, Visual3D will likely interpret this plus sign incorrectly.
+Arithmetic operations can generally be performed using syntax that is similar to that found in a variety of programming and scripting languages.
-The workaround is to use a mathematical function add() to express the addition.
+==== Plus ====
-**add(a,b)** -- adds two expressions.
+Addition is accomplished using the + character. An alternative syntax is **add(a,b)** where a and b are expressions that evaluate to numbers.
-===== Minus =====
-===== Multiply =====
+NOTE: Pipeline command parameters use the + character as a delimiter. If the user wants to use an expression containing a + in a command parameter that allows multiple signals, then Visual3D will likely interpret this plus sign incorrectly. In this case the **add(a,b)** syntax should be used.
-===== Divide =====
+<code>
++ 3 = 5
+add(2,3) = 5
+</code>
-===== Power =====
+==== Minus ====
-===== Logical_Or =====
+Subtraction is accomplished using the - character.
-Logical Or
+<code>
-===== Logical_And =====
+- 2 = 1
+</code>
-Logical And
+==== Multiply ====
-===== Equals =====
-**= or ==** - Boolean Operator //equals//
+Multiplication is accomplished using the * character.
-Example: Comparing a model metric with a string
-Consider a model metric that is defined as a string.
+<code>
-**Set_Model_Metric**
+ * 2 = 6
-! /CALIBRATION_FILE=
+</code>
-/METRIC_NAME=TEST
-/METRIC_VALUE="TTT"
-**;**
-Now compare it to the text string "TTT"
-**Evaluate_Expression**
-/EXPRESSION=MODEL::METRIC::TEST="TTT"
-/RESULT_NAME=SCOTT
-/RESULT_TYPE=METRIC
-! /RESULT_FOLDER=PROCESSED
-**;**
-The text strings should be equal so the resulting signal contains a 1
-===== Not_Equals =====
-**<> or ><** - Boolean Operator "Not Equals"
+==== Divide ====
-===== Using the Adjective NOT =====
-NOT can be used with the logical AND and logical OR
+Division is accomplished using the / character.
-Example: Given a workspace containing 3 trials (*trial1.c3d, *trial2.c3d, and *trial3.c3d)
+<code>
+/ 3 = 2
+</code>
-All trials are assigned a TAG labeled WALK
+==== Power ====
+Exponentiation is accomplished using the ^ character.
+<code>
+^3 = 8
+</code>
+===== Boolean Operators =====
+Boolean operators deal with boolean values, such as TRUE and FALSE. These are represented numerically as 1 (TRUE) and 0 (FALSE).
+==== Logical OR ====
+The Logical OR operator is signified by the | character. It takes two boolean values as input and returns TRUE if either of the input values is TRUE.
+<code>
+FALSE | FALSE = FALSE
+FALSE | TRUE = TRUE
+TRUE | FALSE = TRUE
+TRUE | TRUE = FALSE
+</code>
+==== Logical AND ====
+The Logical AND operator is signified by the & character. It takes two boolean values as input and returns TRUE when both input values are TRUE.
+<code>
+FALSE | FALSE = FALSE
+FALSE | TRUE = FALSE
+TRUE | FALSE = FALSE
+TRUE | TRUE = FALSE
+</code>
+==== The Adjective NOT ====
+The logical adjective NOT can be used with both the logical AND and logical OR operators. It takes one boolean value as input and negates that boolean value.
+<code>
+NOT(FALSE) = TRUE
+NOT(TRUE) = FALSE
+</code>
+===Example===
+Given a workspace containing 3 trials (*trial1.c3d, *trial2.c3d, and *trial3.c3d).
+  * All trials are assigned a TAG labeled WALK
   * trial1.c3d is also assigned a TAG labeled BAD
-[[Visual3D:Documentation:Pipeline:File_Commands:Select_Active_File|Select_Active_File]]
+<code>
+Select_Active_File
 /FILE_NAME=WALK
 /QUERY=BAD
-**;**
+;
+</code>
 This command results in *trial1.c3d being active
-[[Visual3D:Documentation:Pipeline:File_Commands:Select_Active_File|Select_Active_File]]
+<code>
+Select_Active_File
 /FILE_NAME=WALK
 /QUERY=NOT(BAD)
-**;**
+;
+</code>
 This command results in *trial2.c3d and *trial3.c3d being active.
-===== Less_Than =====
+===== Comparison Operators =====
+Comparison operators take two inputs of the same type and return a boolean value.
+==== Equals ====
+Equality is tested using either = or ==. It returns TRUE if the two inputs have the same value and FALSE if they do not.
+===Example===
+Consider a model metric that is defined as a string and compare it to an explicitly defined string.
+<code>
+Set_Model_Metric
+! /CALIBRATION_FILE=
+/METRIC_NAME=TEST
+/METRIC_VALUE="TTT"
+;
+Evaluate_Expression**
+/EXPRESSION=MODEL::METRIC::TEST="TTT"
+/RESULT_NAME=SCOTT
+/RESULT_TYPE=METRIC
+! /RESULT_FOLDER=PROCESSED
+;
+</code>
+The text strings are equal, so the resulting signal contains a 1 (indicating TRUE).
+==== Not Equals ====
+Non-equality is tested using either <> or ><. Its behaviour is opposite that of equality.
+If (a==b) is TRUE then (a<>b) is FALSE. Similarly, if (a==b) is FALSE, then (a<>b) is TRUE.
+==== Less Than ====
+We can test is one value is less than another using the < character.
-**<** Boolean Operator //less than//
+===Example===
-**Example**
+Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator < to identify when the Z component of RFT1 is less than the Z component of LFT1.
-Given two signals
+<code>
-TARGET::ORIGINAL::RFT1
+Evaluate_Expression
-TARGET::ORIGINAL::LFT1
-Use the Boolean operator < to identify when the Z component of RFT1 is less than the Z component of LFT1
-**Evaluate_Expression**
 /EXPRESSION= TARGET::ORIGINAL::RFT1::Z < TARGET::ORIGINAL::LFT1::Z
 /RESULT_NAME=RFT1_GREATER
 /RESULT_TYPE=DERIVED
 /RESULT_FOLDER=PROCESSED
-**;**
+;
+</code>
 The output signal will be 1 when RFT1::Z is less than LFT1::Z and 0 otherwise
-**Example - Foot Clearance**
-Given the following situation. Heel and Toe clearance are defined by two paths.
+===Example - Foot Clearance===
-One might consider Foot clearance to be the lower value of the heel and toe clearance values at each frame.
-{{heel_toe_clearance.jpg}}
+Heel and toe clearance are defined by two paths. It is possible to model "foot clearance" as the lower value of the heel and toe clearance values at each frame.
-Here is a simplified test of this
+{{:heel_toe_clearance.jpg}}
-Make the Global Workspace Active.
-Create 2 signals as follows
+Here is a simplified test of this. First, make the Global Workspace Active. Then, create 2 toy signals and calculate a third signal containing the lower value of the two toy signals.
-**Evaluate_Expression**
+<code>
+Evaluate_Expression
 /EXPRESSION=LIST(1,2,3,4,5)
 ! /SIGNAL_TYPES=
@@ Line 121: / Line 203: @@
 /RESULT_NAME=SIGNAL1
 ! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-**;**
+;
-**Evaluate_Expression**
+Evaluate_Expression
 /EXPRESSION=LIST(5,4,3,2,1)
 ! /SIGNAL_TYPES=
@@ Line 132: / Line 215: @@
 /RESULT_NAME=SIGNAL2
 ! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-**;**
+;
-!create a new signal that is the lower value of the two signals
-**Evaluate_Expression**
+!create a new signal that is the lower value of the two signals
+Evaluate_Expression
 /EXPRESSION=(DERIVED::PROCESSED::SIGNAL1<=DERIVED::PROCESSED::SIGNAL2)*DERIVED::PROCESSED::SIGNAL1
 +(DERIVED::PROCESSED::SIGNAL2<DERIVED::PROCESSED::SIGNAL1)*DERIVED::PROCESSED::SIGNAL2
@@ Line 146: / Line 229: @@
 /RESULT_NAME=SIGNAL_LOWER
 ! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
-**;**
+;
-{{heel_toe_clearance2.jpg}}
+</code>
-===== Less_Than_Or_Equals =====
-! style="text-align:left;" |      **<=** or **=<** Boolean Operator //less than or equal to//
+{{:heel_toe_clearance2.jpg}}
-Example:
+==== Less Than Or Equals ====
-Given two signals
+This boolean operator uses one of the following syntaxes: <= or =<.
-TARGET::ORIGINAL::RFT1
-TARGET::ORIGINAL::LFT1
+The expression (a <= b) is equivalent logically to ((a < b) | (a == b)).
-Use the Boolean operator <= or the boolean operative =< to identify when the Z component of RFT1 is less than or equal to the Z component of LFT1
-**Evaluate_Expression**
+===Example===
+Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator <= or the boolean operative =< to identify when the Z component of RFT1 is less than or equal to the Z component of LFT1.
+<code>
+Evaluate_Expression
 /EXPRESSION= TARGET::ORIGINAL::RFT1::Z <= TARGET::ORIGINAL::LFT1::Z
 /RESULT_NAME=RFT1_GREATER
 /RESULT_TYPE=DERIVED
 /RESULT_FOLDER=PROCESSED
-**;**
+;
-The output signal will be 1 when RFT1::Z is less than or equal toLFT1::Z and 0 otherwise
+</code>
-===== Greater_Than =====
-**>** Boolean Operator //greater than//
+The output signal will be 1 (indicating TRUE) when RFT1::Z is less than or equal to LFT1::Z and 0 (indicating FALSE) otherwise.
-Example:
+==== Greater Than ====
-Given two signals
+We can test is one value is less than another using the > character.
-TARGET::ORIGINAL::RFT1
-TARGET::ORIGINAL::LFT1
+===Example===
-Use the Boolean operator > to identify when the Y component of RFT1 is greater than the Y component of LFT1
-**Evaluate_Expression**
+Given two signals TARGET::ORIGINAL::RFT1 and TARGET::ORIGINAL::LFT1, use the Boolean operator > to identify when the Y component of RFT1 is greater than the Y component of LFT1.
+<code>
+Evaluate_Expression
 /EXPRESSION= TARGET::ORIGINAL::RFT1::Y > TARGET::ORIGINAL::LFT1::Y
 /RESULT_NAME=RFT1_GREATER
 /RESULT_TYPE=DERIVED
 /RESULT_FOLDER=PROCESSED
-**;**
+;
-The output signal will be 1 when RFT1::Y is greater than LFT1::Y and 0 otherwise
+</code>
-===== Greater_Than_Or_Equals =====
+The output signal will be 1 (indicating TRUE) when RFT1::Y is greater than LFT1::Y and 0 (indicating FALSE) otherwise.
+==== Greater Than Or Equals ====
+This boolean operator uses one of the following syntaxes: >= or =>.
-**>=** Boolean Operator //greater than or equals//
+The expression (a >= b) is equivalent logically to ((a > b) | (a == b)).