====== 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]]

**Boolean Operators** 
  * [[#Logical_Or|Logical OR]]
  * [[#Logical_And|Logical AND]]
  * [[#Using_the_Adjective_NOT|The Adjective NOT]]

**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]]

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.

===== Arithmetic Operators =====

Arithmetic operations can generally be performed using syntax that is similar to that found in a variety of programming and scripting languages.

==== Plus ====

Addition is accomplished using the + character. An alternative syntax is **add(a,b)** where a and b are expressions that evaluate to numbers. 

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.

<code>
2 + 3 = 5
add(2,3) = 5
</code>

==== Minus ====

Subtraction is accomplished using the - character.

<code>
3 - 2 = 1
</code>

==== Multiply ====

Multiplication is accomplished using the * character.

<code>
3 * 2 = 6
</code>

==== Divide ====

Division is accomplished using the / character.

<code>
6 / 3 = 2
</code>

==== Power ====

Exponentiation is accomplished using the ^ character.

<code>
2^3 = 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

<code>
Select_Active_File
/FILE_NAME=WALK
/QUERY=BAD
;
</code>

This command results in *trial1.c3d being active

<code>
Select_Active_File
/FILE_NAME=WALK
/QUERY=NOT(BAD)
;
</code>

This command results in *trial2.c3d and *trial3.c3d being active.

===== 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.

===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.

<code>
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===

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.
{{:heel_toe_clearance.jpg}}

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.

<code>
Evaluate_Expression
/EXPRESSION=LIST(1,2,3,4,5)
! /SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /SIGNAL_COMPONENTS=
/RESULT_TYPES=DERIVED
/RESULT_FOLDERS=PROCESSED
/RESULT_NAME=SIGNAL1
! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
;

Evaluate_Expression
/EXPRESSION=LIST(5,4,3,2,1)
! /SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /SIGNAL_COMPONENTS=
/RESULT_TYPES=DERIVED
/RESULT_FOLDERS=PROCESSED
/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
/EXPRESSION=(DERIVED::PROCESSED::SIGNAL1<=DERIVED::PROCESSED::SIGNAL2)*DERIVED::PROCESSED::SIGNAL1
+(DERIVED::PROCESSED::SIGNAL2<DERIVED::PROCESSED::SIGNAL1)*DERIVED::PROCESSED::SIGNAL2
! /SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /SIGNAL_COMPONENTS=
/RESULT_TYPES=DERIVED
/RESULT_FOLDERS=PROCESSED
/RESULT_NAME=SIGNAL_LOWER
! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE
;
</code>

{{:heel_toe_clearance2.jpg}}

==== Less Than Or Equals ====

This boolean operator uses one of the following syntaxes: <= or =<.

The expression (a <= b) is equivalent logically to ((a < b) | (a == b)).

===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
;
</code>

The output signal will be 1 (indicating TRUE) when RFT1::Z is less than or equal to LFT1::Z and 0 (indicating FALSE) otherwise.

==== Greater Than ====

We can test is one value is less than another using the > character.

===Example===

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
;
</code>

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 =>.

The expression (a >= b) is equivalent logically to ((a > b) | (a == b)).