# Nimue platform

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modellingcomponents:functions

# Functions

## General

### +

A binlary operator which calculates the sum of two variables. The following combinations of argument types are allowed:

argument 1 argument 2 result
integer integer integer
double double double
integer double double
double integer double
integer complex complex
double complex complex
complex complex complex
complex integer complex
complex double complex
3d vector 3d vector 3d vector
3d matrix 3d matrix 3d matrix

Example

`A + B`

### -

This unary operator changes the sign of the given argument. For matrix argument the matrix inverse is determined.

Types:

Argument Result
integer integer
double double
complex complex
3d vector 3d vector
3d matrix 3d matrix

`  -A`

### abs()

This named function calculates the absolute value of the variable give as argument.

Types:

Argument Result
integer integer
double double
complex complex

#### Examples

``` abs(A)
abs(-3)```

## Trigometric

### acos()

This named function determines the acrcos tangens of the given argument.

Argument Result
integer double
double double
complex double

#### Examples

` acos(a)`

### asin()

This named function determines the arcos sinus of the given argument.

Types:

Argument Result
integer double
double double
complex double

#### Examples

` asin(A)`

### atan()

This named function determines the arcos tangens of the given argument.

Types:

Argument Result
integer double
double double
complex double

#### Examples

` atan(A)`

### asinh()

This named function determines the arcos sinus hyperbolicus of the given argument.

Types:

Argument Result
integer double
double double
complex double

#### Examples

` asinh(A)`

### acosh()

This named function determines the acrcos tangens hyperbolicos of the given argument.

Types:

Argument Result
integer double
double double
complex complex

#### Examples

` acosh(a)`

### asin'

This named function determines the first derivative of the arcos sinus of the given argument: 1d/(sqrt(1d-x*x))

Types:

Argument result
integer double
double double
complex double

asin'(A)

### asin''

This named function determines the second derivative of the arcos sinus of the given argument: x/pow(1-x*x, 1.5).

Types:

Argument result
integer double
double double
complex double

asin''(A)

## 3d

### dot()

Determination of the dot product of two given 3d vectors.

Types:

Argument 1 Argument 2 Result
3d vector 3d vector

#### Examples

` dot(A,B)`

### length()

Determination of the length of a given 3d vector.

Types:

Argument Result
3d vector double

#### Examples

` length(A)`

### lengthSqr()

Determination of the length square of a given 3d vector.

Types:

Argument Result
3d vector double

#### Examples

` length(A)`

### dist()

Distance between two points.

Types:

Argument 1 Argument 2 Result
3d vector 3d vector double

#### Examples

` dist(A,B)`

### vec()

This named function bundles the three double arguments to a 3d vector result value.

Types:

Argument 1 Argument 2 Argument 3 Result
double double double 3d vector

#### Examples

` vec(x,y,z)`

### angle2()

This named function with three arguments calculates the angle between arrows defined by the first two arguments. The third argument is used to define the sign of the resulting angle. It is interpreted as an arrow which defines the rotation direction to rotate the arrow from the first argument to the arrow of the second argument. If this results in angles more than 180 degrees a negativ angle is given instead.

Types:

Argument 1 Argument 2 Argument 3 Result
3d vector 3d vector 3d vector double

#### Examples

` angle2(A,B,t)`

### circc()

Determination of a circles mid point where all three given arguments are laying on.

Argument 1 Argument 2 Argument 3 Result
3d vector 3d vector 3d vector 3d vector

#### Examples

`  circc(A,B,C)`

### angle()

This named function with two arguments calculates the so called atan2(x, y) if the arguments are of the type double. 3d vector arguments are interpreted as arrows and the angle between the two arrows are calculated.

Types:

Argument 1 Argument 2 Result
double double double
3d vector 3d vector double

#### Examples

` angle(A,B)`

### align()

If the vectors of both arguments are directed in the same half-space this named function results in a double value of -1, else +1.

Types:

Argument 1 Argument 2 Result
3d vector 3d vector double (-1 or +1)

## Special

### pocl()

Point of contact straight line: The first two arguments define a straight line. The first is a point on this line and the second defines the direction of the line. A perpendicular is dropped from the point defined by the third point to this line and the result value is the point of contact in the straight line.

Types:

Argument 1 Argument 2 Argument 3 Result
3d vector 3d vector 3d vector 3d vector

#### Examples

` pocl(A,B,C)`
modellingcomponents/functions.txt · Zuletzt geändert: 2017/12/16 11:48 von oliver

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