# Mathematical Functions

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Version 45

Odysseus provides a wide range of functions to be used in a Map, Select, or Join operator.

## Trigonometric Functions

### Cos(X)

Returns the trigonometric cosine of an angle

### ACos(X)

Returns the arc cosine of a value

### Cosh(X)

Returns the hyperbolic cosine of a double value

### Sin(X)

Returns the trigonometric sine of an angle

### ASin(X)

Returns the arc sine of a value

### Sinh(X)

Returns the hyperbolic sine of a double value

### Tan(X)

Returns the trigonometric tangent of an angle

### ATan(X)

Returns the arc tangent of a value

### ATan2(Y,X)

Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta)

### Tanh(X)

Returns the hyperbolic tangent of a double value

### Abs(X)

Returns the absolute value of a value

### Sqrt(X)

Returns the square root of a value

### Ceil(X)

Returns the smallest value that is greater than or equal to the argument and is equal to a mathematical integer.

### Floor(X)

Returns the largest value that is less than or equal to the argument and is equal to a mathematical integer.

### Round(X)

Returns the closest number to the argument, with ties rounding up

### Log(X)

Returns the natural logarithm (base e) of a double value

### Exp(X)

Returns Euler's number e raised to the power of a double value

### PI()

Returns the double value that is closer than any other to pi.

### E()

Returns the double value that is closer than any other to e

### ToRadian(X)

Converts an angle measured in degrees to an equivalent angle measured in radians.

### ToDegree(X)

Converts an angle measured in radians to an equivalent angle measured in degrees.

## String Functions

### SubString(String, Begin, End)

Returns a new string that is a substring of the value with given begin and end index

### Length(String)

Returns the length of a string.

### Upper(String)

Returns the string converted to uppercase.

### Lower(String)

Returns the string converted to lowercase.

## Date Functions

### Year(Date)

Extracts the year part of the date

### Month(Date)

Extracts the month part of the date

### Week(Date)

Returns the week number of the date

### Day(Date)

Extracts the day part of the date

### Hour(Date)

Returns the hour of the date

### Minute(Date)

Returns the minute of the date

### Second(Date)

Returns the second of the date

### CurDate()

Return the current system time specific date

### Now()

Returns the difference, measured in milliseconds, between the current time and midnight, January 1, 1970 UTC

### NanoTime()

Returns the current value of the time source, in nanoseconds.

## Datatype Functions

### DoubleToShort(X)

Converts the given double value to a short value

### DoubleToByte(X)

Converts the given double value to a byte value

### DoubleToFloat(X)

Converts the given double value to a float value

### DoubleToLong(X)

Converts the given double value to a long value

### ToShort(X)

Converts the given value to a short value. This function converts any value to a short value, thus it is more time consuming than the DoubleToShort function for double values.

### ToByte(X)

Converts the given value to a byte value. This function converts any value to a byte value, thus it is more time consuming than the DoubleToByte function for double values.

### ToFloat(X)

Converts the given value to a float value. This function converts any value to a float value, thus it is more time consuming than the DoubleToFloat function for double values.

### ToLong(X)

Converts the given value to a long value. This function converts any value to a long value, thus it is more time consuming than the DoubleToLong function for double values.

## Encryption Functions

### MD5(String)

Calculates an MD5 checksum for the string.

### SHA1(String)

Calculates an SHA-1 checksum for the string.

### SHA256(String)

Calculates an SHA-265 checksum for the string.

## Miscellaneous Functions

### UUID()

Returns a Universal Unique Identifier (UUID).

# Optional Functions

The following MEP functions are not part of the Odysseus Core and may be restricted.

## Spatial Functions (Spatial Feature)

### AsCartesianCoordinates(SpatialPolarCoordinate[])

Transform the list of spatial polar coordinates into a list of Cartesian coordinates

### GetCentroid(Geometry)

Returns the centroid of the given geometry

### SpatialBuffer(Geometry, Double)

Creates a buffer of the given size around the given geometry

### SpatialContains(Geometry, Geometry)

Checks whether the first geometry contains the second geometry.

### SpatialConvexHull(Geometry)

Computes the smallest convex spatial p`olygon` that contains all the points in the `geometry`

### ToCartesianCoordinate(SpatialPolarCoordinate)

Transforms the given spatial polar coordinate into a spatial Cartesian coordinate.

### ToPolarCoordinate(SpatialCoordinate)

Transforms the given spatial Cartesian coordinate into a polar coordinate

## Spatial Grid Functions (Spatial Grid Feature)

### MoveViewPoint(Geometry, Coordinate)

The MoveViewPoint has 2 parameter: A geometry and the new origin of the new view point.

### RotateViewPoint(Geometry, Double)

The RotateViewPoint has 2 parameter: A geometry and the rotation angle in radians for the new view point.

### ToGrid(Geometry, Coordinate, Integer, Integer, Double)

The ToGrid function has 5 parameter: A geometry defining the free  and occupied area, the origin of the grid, the width and height of the grid in cells, and the size of a cell.

### RotateGrid(Grid, Double)

The RotateGrid has 2 parameter: A grid and the rotation angle in radians. The result is the rotated grid.

### SpreadOccupancyGrid(Grid, Timestamp, Timestamp, Double)

The SpreadOccupancyGrid function takes 4 parameters: A cartesian grid, the timestamp of the grid, the current timestamp, and the velocity of objects in the environment.

### MergeOccupancyGrid(Grid, PolarCoordinate[], Origin, Double, Double, Integer)

The MergOccupancyGrid function takes 6 parameters: A cartesian grid, the polar coordinates, the origin, the transform angle, the polar radius, and the polar cellsize.

## Probabilistic Functions (Probabilistic Feature)

### MVN(Distribution, Lower Limit, Upper Limit)

Estimates the multivariate normal distribution probability with lower and upper integration limit.

## Project specific Functions

### ClassifyObject(SpatialMultiLineString)

The ClassifyObject functions takes multiple segments as a spatial multi line string and performs a classification of the line strings. The result of the function is a list of classified objects

Most function descriptions on this page are copied from the openjdk documentation.

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