Represents a mathematical function.
The FGFunction class is a powerful and versatile resource that allows algebraic functions to be defined in a JSBSim configuration file. It is similar in concept to MathML (Mathematical Markup Language, www.w3.org/Math/), but simpler and more terse. A function definition consists of an operation, a value, a table, or a property (which evaluates to a value). The currently supported operations are:
- sum (takes n args)
- difference (takes n args)
- product (takes n args)
- quotient (takes 2 args)
- pow (takes 2 args)
- sqrt (takes one argument)
- toradians (takes one argument)
- todegrees (takes one argument)
- exp (takes 2 args)
- log2 (takes 1 arg)
- ln (takes 1 arg)
- log10 (takes 1 arg)
- abs (takes 1 arg)
- sin (takes 1 arg)
- cos (takes 1 arg)
- tan (takes 1 arg)
- asin (takes 1 arg)
- acos (takes 1 arg)
- atan (takes 1 arg)
- atan2 (takes 2 args)
- min (takes n args)
- max (takes n args)
- avg (takes n args)
- fraction
- mod
- floor (takes 1 arg)
- ceil (takes 1 arg)
- fmod (takes 2 args)
- lt (less than, takes 2 args)
- le (less equal, takes 2 args)
- gt (greater than, takes 2 args)
- ge (greater than, takes 2 args)
- eq (equal, takes 2 args)
- nq (not equal, takes 2 args)
- and (takes n args)
- or (takes n args)
- not (takes 1 args)
- if-then (takes 2-3 args)
- switch (takes 2 or more args)
- random (Gaussian distribution random number)
- urandom (Uniform random number between -1 and +1)
- pi
- integer
- interpolate 1-dimensional (takes a minimum of five arguments, odd number)
An operation is defined in the configuration file as in the following example:
<sum>
<value> 3.14159 </value>
<property> velocities/qbar </property>
<product>
<value> 0.125 </value>
<property> metrics/wingarea </property>
</product>
</sum>
A full function definition, such as is used in the aerodynamics section of a configuration file includes the function element, and other elements. It should be noted that there can be only one non-optional (non-documentation) element - that is, one operation element - in the top-level function definition. Multiple value and/or property elements cannot be immediate child members of the function element. Almost always, the first operation within the function element will be a product or sum. For example:
<function name="aero/moment/Clr">
<description>Roll moment due to yaw rate</description>
<product>
<property>aero/qbar-area</property>
<property>metrics/bw-ft</property>
<property>aero/bi2vel</property>
<property>velocities/r-aero-rad_sec</property>
<table>
<independentVar>aero/alpha-rad</independentVar>
<tableData>
0.000 0.08
0.094 0.19
</tableData>
</table>
</product>
</function>
The "lowest level" in a function is always a value or a property, which cannot itself contain another element. As shown, operations can contain values, properties, tables, or other operations. In the first above example, the sum element contains all three. What is evaluated is written algebraically as:
3.14159 + qbar + (0.125 * wingarea)
Some operations can take only a single argument. That argument, however, can be an operation (such as sum) which can contain other items. The point to keep in mind is that it evaluates to a single value - which is just what the trigonometric functions require (except atan2, which takes two arguments).
Specific Function Definitions
Note: In the definitions below, a "property" refers to a single property specified within either the <property></property> tag or the shortcut tag, <p></p>. The keyword "value" refers to a single numeric value specified either within the <value></value> tag or the shortcut <v></v> tag. The keyword "table" refers to a single table specified either within the <table></table> tag or the shortcut <t></t> tag. The plural form of any of the three words refers to one or more instances of a property, value, or table.
- sum, sums the values of all immediate child elements:
<sum>
{properties, values, tables, or other function elements}
</sum>
Example: Mach + 0.01
<sum>
<p> velocities/mach </p>
<v> 0.01 </v>
</sum>
- difference, subtracts the values of all immediate child elements from the value of the first child element:
<difference>
{properties, values, tables, or other function elements}
</difference>
Example: Mach - 0.01
<difference>
<p> velocities/mach </p>
<v> 0.01 </v>
</difference>
- product multiplies together the values of all immediate child elements:
<product>
{properties, values, tables, or other function elements}
</product>
Example: qbar*S*beta*CY_beta
<product>
<property> aero/qbar-psf </property>
<property> metrics/Sw-sqft </property>
<property> aero/beta-rad </property>
<property> aero/coefficient/CY_beta </property>
</product>
- quotient, divides the value of the first immediate child element by the second immediate child element:
<quotient>
{property, value, table, or other function element}
{property, value, table, or other function element}
</quotient>
Example: (2*GM)/R
<quotient>
<product>
<v> 2.0 </v>
<p> guidance/executive/gm </p>
</product>
<p> position/radius-to-vehicle-ft </p>
</quotient>
- pow, raises the value of the first immediate child element to the power of the value of the second immediate child element:
<pow>
{property, value, table, or other function element}
{property, value, table, or other function element}
</pow>
Example: Mach^2
<pow>
<p> velocities/mach </p>
<v> 2.0 </v>
</pow>
- sqrt, takes the square root of the value of the immediate child element:
<sqrt>
{property, value, table, or other function element}
</sqrt>
Example: square root of 25
<sqrt> <v> 25.0 </v> </sqrt>
- toradians, converts a presumed argument in degrees to radians by multiplying the value of the immediate child element by pi/180:
<toradians>
{property, value, table, or other function element}
</toradians>
Example: convert 45 degrees to radians
<toradians> <v> 45 </v> </toradians>
- todegrees, converts a presumed argument in radians to degrees by multiplying the value of the immediate child element by 180/pi:
<todegrees>
{property, value, table, or other function element}
</todegrees>
Example: convert 0.5*pi radians to degrees
<todegrees>
<product> <v> 0.5 </v> <pi/> </product>
</todegrees>
- exp, raises "e" to the power of the immediate child element:
<exp>
{property, value, table, or other function element}
</exp>
Example: raise "e" to the 1.5 power, e^1.5
<exp> <v> 1.5 </v> </exp>
- log2, calculates the log base 2 value of the immediate child element:
<log2>
{property, value, table, or other function element}
</log2>
Example:
<log2> <v> 128 </v> </log2>
- ln, calculates the natural logarithm of the value of the immediate child element:
<ln>
{property, value, table, or other function element}
</ln>
Example: ln(128)
<ln> <v> 200 </v> </ln>
- log10, calculates the base 10 logarithm of the value of the immediate child element
<log10>
{property, value, table, or other function element}
</log10>
Example log(Mach)
<log10> <p> velocities/mach </p> </log10>
- abs calculates the absolute value of the immediate child element
<abs>
{property, value, table, or other function element}
</abs>
Example:
<abs> <p> flight-path/gamma-rad </p> </abs>
- sin, calculates the sine of the value of the immediate child element (the argument is expected to be in radians)
<sin>
{property, value, table, or other function element}
</sin>
Example:
<sin> <toradians> <p> fcs/heading-true-degrees </p> </toradians> </sin>
- cos, calculates the cosine of the value of the immediate child element (the argument is expected to be in radians)
<cos>
{property, value, table, or other function element}
</cos>
Example:
<cos> <toradians> <p> fcs/heading-true-degrees </p> </toradians> </cos>
- tan, calculates the tangent of the value of the immediate child element (the argument is expected to be in radians)
<tan>
{property, value, table, or other function element}
</tan>
Example:
<tan> <toradians> <p> fcs/heading-true-degrees </p> </toradians> </tan>
- asin, calculates the arcsine (inverse sine) of the value of the immediate child element. The value provided should be in the range from -1 to +1. The value returned will be expressed in radians, and will be in the range from -pi/2 to +pi/2.
<asin>
{property, value, table, or other function element}
</asin>
Example:
<asin> <v> 0.5 </v> </asin>
- acos, calculates the arccosine (inverse cosine) of the value of the immediate child element. The value provided should be in the range from -1 to +1. The value returned will be expressed in radians, and will be in the range from 0 to pi.
<acos>
{property, value, table, or other function element}
</acos>
Example:
<acos> <v> 0.5 </v> </acos>
- atan, calculates the inverse tangent of the value of the immediate child element. The value returned will be expressed in radians, and will be in the range from -pi/2 to +pi/2.
<atan>
{property, value, table, or other function element}
</atan>
Example:
<atan> <v> 0.5 </v> </atan>
- atan2 calculates the inverse tangent of the value of the immediate child elements, Y/X (in that order). It even works for X values near zero. The value returned will be expressed in radians, and in the range -pi to +pi.
<atan2>
{property, value, table, or other function element} {property, value, table, or other function element}
</atan2>
Example: inverse tangent of 0.5/0.25, evaluates to: 1.107 radians
<atan2> <v> 0.5 </<v> <v> 0.25 </v> </atan2>
- min returns the smallest value from all the immediate child elements
<min>
{properties, values, tables, or other function elements}
</min>
Example: returns the lesser of velocity and 2500
<min>
<p> velocities/eci-velocity-mag-fps </p>
<v> 2500.0 </v>
</min>
- max returns the largest value from all the immediate child elements
<max>
{properties, values, tables, or other function elements}
</max>
Example: returns the greater of velocity and 15000
<max>
<p> velocities/eci-velocity-mag-fps </p>
<v> 15000.0 </v>
</max>
- avg returns the average value of all the immediate child elements
<avg>
{properties, values, tables, or other function elements}
</avg>
Example: returns the average of the four numbers below, evaluates to 0.50.
<avg>
<v> 0.25 </v>
<v> 0.50 </v>
<v> 0.75 </v>
<v> 0.50 </v>
</avg>
- fraction, returns the fractional part of the value of the immediate child element
<fraction>
{property, value, table, or other function element}
</fraction>
Example: returns the fractional part of pi - or, roughly, 0.1415926...
<fraction> <pi/> </fraction>
- integer, returns the integer portion of the value of the immediate child element
<integer>
{property, value, table, or other function element}
</integer>
- mod returns the remainder from the integer division of the value of the first immediate child element by the second immediate child element, X/Y (X modulo Y). The value returned is the value X-I*Y, for the largest integer I such that if Y is nonzero, the result has the same sign as X and magnitude less than the magnitude of Y. For instance, the expression "5 mod 2" would evaluate to 1 because 5 divided by 2 leaves a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0.
<mod>
{property, value, table, or other function element}
{property, value, table, or other function element}
</mod>
Example: 5 mod 2, evaluates to 1
<mod> <v> 5 </v> <v> 2 </v> </mod>
- floor returns the largest integral value that is not greater than X.
<floor>
{property, value, table, or other function element}
</floor>
- ceil returns the smallest integral value that is not less than X.
<ceil>
{property, value, table, or other function element}
</ceil>
- fmod returns the floating-point remainder of X/Y (rounded towards zero)
<fmod>
{property, value, table, or other function element}
{property, value, table, or other function element}
</fmod>
- lt returns a 1 if the value of the first immediate child element is less than the value of the second immediate child element, returns 0 otherwise
<lt>
{property, value, table, or other function element}
{property, value, table, or other function element}
</lt>
Example: returns 1 if thrust is less than 10,000, returns 0 otherwise
<lt>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 10000.0 </v>
</lt>
- le, returns a 1 if the value of the first immediate child element is less than or equal to the value of the second immediate child element, returns 0 otherwise
<le>
{property, value, table, or other function element}
{property, value, table, or other function element}
</le>
Example: returns 1 if thrust is less than or equal to 10,000, returns 0 otherwise
<le>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 10000.0 </v>
</le>
- gt returns a 1 if the value of the first immediate child element is greater than the value of the second immediate child element, returns 0 otherwise
<gt>
{property, value, table, or other function element}
{property, value, table, or other function element}
</gt>
Example: returns 1 if thrust is greater than 10,000, returns 0 otherwise
<gt>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 10000.0 </v>
</gt>
- ge, returns a 1 if the value of the first immediate child element is greater than or equal to the value of the second immediate child element, returns 0 otherwise
<ge>
{property, value, table, or other function element}
{property, value, table, or other function element}
</ge>
Example: returns 1 if thrust is greater than or equal to 10,000, returns 0
otherwise
<ge>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 10000.0 </v>
</ge>
- eq returns a 1 if the value of the first immediate child element is equal to the second immediate child element, returns 0 otherwise
<eq>
{property, value, table, or other function element}
{property, value, table, or other function element}
</eq>
Example: returns 1 if thrust is equal to 10,000, returns 0 otherwise
<eq>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 10000.0 </v>
</eq>
- nq returns a 1 if the value of the first immediate child element is not equal to the value of the second immediate child element, returns 0 otherwise
<nq>
{property, value, table, or other function element}
{property, value, table, or other function element}
</nq>
Example: returns 1 if thrust is not 0, returns 0 otherwise
<nq>
<p> propulsion/engine[2]/thrust-lbs </p>
<v> 0.0 </v>
</nq>
- and returns a 1 if the values of the immediate child elements are all 1, returns 0 otherwise. Values provided are expected to be either 1 or 0 within machine precision.
<and>
{properties, values, tables, or other function elements}
</and>
Example: returns 1 if the specified flags are all 1
<and>
<p> guidance/first-stage-flight-flag </p>
<p> control/engines-running-flag </p>
</and>
- or returns a 1 if the values of any of the immediate child elements 1, returns 0 otherwise. Values provided are expected to be either 1 or 0 within machine precision.
<or>
{properties, values, tables, or other function elements}
</or>
Example: returns 1 if any of the specified flags are 1
<or>
<p> guidance/first-stage-flight-flag </p>
<p> control/engines-running-flag </p>
</or>
- not, returns the inverse of the value of the supplied immediate child element (e.g., returns 1 if supplied a 0)
<not>
{property, value, table, or other function element}
</not>
Example: returns 0 if the value of the supplied flag is 1
<not> <p> guidance/first-stage-flight-flag </p> </not>
- ifthen if the value of the first immediate child element is 1, then the value of the second immediate child element is returned, otherwise the value of the third child element is returned
<ifthen>
{property, value, table, or other function element}
{property, value, table, or other function element}
{property, value, table, or other function element}
</ifthen>
Example: if flight-mode is greater than 2, then a value of 0.00 is
returned, otherwise the value of the property control/pitch-lag is
returned.
<ifthen>
<gt> <p> executive/flight-mode </p> <v> 2 </v> </gt>
<v> 0.00 </v>
<p> control/pitch-lag </p>
</ifthen>
- switch uses the integer value of the first immediate child element as an index to select one of the subsequent immediate child elements to return the value of
<switch>
{property, value, table, or other function element}
{property, value, table, or other function element}
{property, value, table, or other function element}
...
</switch>
Example: if flight-mode is 2, the switch function returns 0.50
<switch>
<p> executive/flight-mode </p>
<v> 0.25 </v>
<v> 0.50 </v>
<v> 0.75 </v>
<v> 1.00 </v>
</switch>
- random Returns a normal distributed random number. The function, without parameters, returns a normal distributed random value with a distribution defined by the parameters mean = 0.0 and standard deviation (stddev) = 1.0 The Mean of the distribution (its expected value, μ). Which coincides with the location of its peak. Standard deviation (σ): The square root of variance, representing the dispersion of values from the distribution mean. This shall be a positive value (σ>0).
<random/>
<random seed="1234"/>
<random seed="time_now"/>
<random seed="time_now" mean="0.0" stddev="1.0"/>
- urandom Returns a uniformly distributed random number. The function, without parameters, returns a random value between the minimum value -1.0 and the maximum value of 1.0 The two maximum and minimum values can be modified using the lower and upper parameters.
<urandom/>
<random seed="1234"/>
<random seed="time_now"/>
<random seed="time_now" lower="-1.0" upper="1.0"/>
- pi Takes no argument and returns the value of Pi
- interpolate1d returns the result from a 1-dimensional interpolation of the supplied values, with the value of the first immediate child element representing the lookup value into the table, and the following pairs of values representing the independent and dependent values. The first provided child element is expected to be a property. The interpolation does not extrapolate, but holds the highest value if the provided lookup value goes outside of the provided range.
<interpolate1d>
{property, value, table, or other function element}
{property, value, table, or other function element} {property, value, table, or other function element}
...
</interpolate1d>
Example: If mach is 0.4, the interpolation will return 0.375. If mach is
1.5, the interpolation will return 0.60.
<interpolate1d>
<p> velocities/mach </p>
<v> 0.00 </v> <v> 0.25 </v>
<v> 0.80 </v> <v> 0.50 </v>
<v> 0.90 </v> <v> 0.60 </v>
</interpolate1d>
- Author
- Jon Berndt
Definition at line 754 of file FGFunction.h.
|
| enum class | OddEven { Either
, Odd
, Even
} |
| |
| enum | { eL = 1
, eM
, eN
} |
| | Moments L, M, N.
|
| |
| enum | { eP = 1
, eQ
, eR
} |
| | Rates P, Q, R.
|
| |
| enum | { eU = 1
, eV
, eW
} |
| | Velocities U, V, W.
|
| |
| enum | { eX = 1
, eY
, eZ
} |
| | Positions X, Y, Z.
|
| |
| enum | { ePhi = 1
, eTht
, ePsi
} |
| | Euler angles Phi, Theta, Psi.
|
| |
| enum | { eDrag = 1
, eSide
, eLift
} |
| | Stability axis forces, Drag, Side force, Lift.
|
| |
| enum | { eRoll = 1
, ePitch
, eYaw
} |
| | Local frame orientation Roll, Pitch, Yaw.
|
| |
| enum | { eNorth = 1
, eEast
, eDown
} |
| | Local frame position North, East, Down.
|
| |
| enum | { eLat = 1
, eLong
, eRad
} |
| | Locations Radius, Latitude, Longitude.
|
| |
| enum | {
inNone = 0
, inDegrees
, inRadians
, inMeters
,
inFeet
} |
| | Conversion specifiers.
|
| |
|
| static const std::string & | GetVersion (void) |
| | Returns the version number of JSBSim. More...
|
| |
| static constexpr double | KelvinToFahrenheit (double kelvin) |
| | Converts from degrees Kelvin to degrees Fahrenheit. More...
|
| |
| static constexpr double | CelsiusToRankine (double celsius) |
| | Converts from degrees Celsius to degrees Rankine. More...
|
| |
| static constexpr double | RankineToCelsius (double rankine) |
| | Converts from degrees Rankine to degrees Celsius. More...
|
| |
| static constexpr double | KelvinToRankine (double kelvin) |
| | Converts from degrees Kelvin to degrees Rankine. More...
|
| |
| static constexpr double | RankineToKelvin (double rankine) |
| | Converts from degrees Rankine to degrees Kelvin. More...
|
| |
| static constexpr double | FahrenheitToCelsius (double fahrenheit) |
| | Converts from degrees Fahrenheit to degrees Celsius. More...
|
| |
| static constexpr double | CelsiusToFahrenheit (double celsius) |
| | Converts from degrees Celsius to degrees Fahrenheit. More...
|
| |
| static constexpr double | CelsiusToKelvin (double celsius) |
| | Converts from degrees Celsius to degrees Kelvin. More...
|
| |
| static constexpr double | KelvinToCelsius (double kelvin) |
| | Converts from degrees Kelvin to degrees Celsius. More...
|
| |
| static constexpr double | FeetToMeters (double measure) |
| | Converts from feet to meters. More...
|
| |
| static bool | EqualToRoundoff (double a, double b) |
| | Finite precision comparison. More...
|
| |
| static bool | EqualToRoundoff (float a, float b) |
| | Finite precision comparison. More...
|
| |
| static bool | EqualToRoundoff (float a, double b) |
| | Finite precision comparison. More...
|
| |
| static bool | EqualToRoundoff (double a, float b) |
| | Finite precision comparison. More...
|
| |
|
static constexpr double | Constrain (double min, double value, double max) |
| | Constrain a value between a minimum and a maximum value.
|
| |
|
static constexpr double | sign (double num) |
| |
|
static char | highint [5] = {27, '[', '1', 'm', '\0' } |
| | highlights text
|
| |
|
static char | halfint [5] = {27, '[', '2', 'm', '\0' } |
| | low intensity text
|
| |
|
static char | normint [6] = {27, '[', '2', '2', 'm', '\0' } |
| | normal intensity text
|
| |
|
static char | reset [5] = {27, '[', '0', 'm', '\0' } |
| | resets text properties
|
| |
|
static char | underon [5] = {27, '[', '4', 'm', '\0' } |
| | underlines text
|
| |
|
static char | underoff [6] = {27, '[', '2', '4', 'm', '\0' } |
| | underline off
|
| |
|
static char | fgblue [6] = {27, '[', '3', '4', 'm', '\0' } |
| | blue text
|
| |
|
static char | fgcyan [6] = {27, '[', '3', '6', 'm', '\0' } |
| | cyan text
|
| |
|
static char | fgred [6] = {27, '[', '3', '1', 'm', '\0' } |
| | red text
|
| |
|
static char | fggreen [6] = {27, '[', '3', '2', 'm', '\0' } |
| | green text
|
| |
|
static char | fgdef [6] = {27, '[', '3', '9', 'm', '\0' } |
| | default text
|
| |
|
static short | debug_lvl = 1 |
| |
|
static std::string | CreateIndexedPropertyName (const std::string &Property, int index) |
| |
|
static constexpr double | radtodeg = 180. / M_PI |
| |
|
static constexpr double | degtorad = M_PI / 180. |
| |
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static constexpr double | hptoftlbssec = 550.0 |
| |
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static constexpr double | psftoinhg = 0.014138 |
| |
|
static constexpr double | psftopa = 47.88 |
| |
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static constexpr double | fttom = 0.3048 |
| |
|
static constexpr double | ktstofps = 1852./(3600*fttom) |
| |
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static constexpr double | fpstokts = 1.0 / ktstofps |
| |
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static constexpr double | inchtoft = 1.0/12.0 |
| |
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static constexpr double | m3toft3 = 1.0/(fttom*fttom*fttom) |
| |
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static constexpr double | in3tom3 = inchtoft*inchtoft*inchtoft/m3toft3 |
| |
|
static constexpr double | inhgtopa = 3386.38 |
| |
| static constexpr double | slugtolb = 32.174049 |
| | Note that definition of lbtoslug by the inverse of slugtolb and not to a different constant you can also get from some tables will make lbtoslug*slugtolb == 1 up to the magnitude of roundoff. More...
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| |
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static constexpr double | lbtoslug = 1.0/slugtolb |
| |
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static constexpr double | kgtolb = 2.20462 |
| |
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static constexpr double | kgtoslug = 0.06852168 |
| |
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static const std::string | needed_cfg_version = "2.0" |
| |
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static const std::string | JSBSim_version = JSBSIM_VERSION " " __DATE__ " " __TIME__ |
| |
Inheritance diagram for FGFunction:
1.9.1 
