Vector Functions

All vector functions work with sequences of length 2 or 3 that typically define the XY or XYZ components (commonly referred to as the IJK components) of a vector. With the exception of the angle and cross product functions, vector functions can take vectors of any length. For those functions that take 2 input vectors, both vectors should have the same length. Vector functions that return a vector do so by returning a sequence with the same length as that of the shortest input vector.

Vectors can be constructed using the $FSEQ function or the { } sequence operators. For example, the following are equivalent:

V1=$FSEQ(0,0,1)
V1={0,0,1}

It is important to note that vectors are sequences and not arrays. Vector functions do not work with arrays.

$FVADD(v1,v2)

Vector addition Returns: Sequence

This function adds two arbitrarily long vector sequences v1 and v2, then returns the result as a vector sequence.

$FVANG(v1,v2)

Angle (degrees) between two vectors Returns: Numeric or $NULL

This function returns the angle in degrees between two vector sequences v1 and v2. The input vectors v1 and v2 must be sequences of length 2 or 3 only (a diagnostic is output and a value of $NULL is returned if the input vectors have less than 2 or more than 3 elements). They should also have a non-zero length to return a meaningful result.

For 3D vectors (i.e., vectors with 3 elements), the return angle ranges from 0 through 180.

For 2D vectors, a signed angle is returned in the range –180<angle<=180. Positive angles are measured in a counterclockwise direction from vector v1.

$FVCROSS(v1,v2)

Vector cross product Returns: Sequence or $NULL

This function computes the cross product of two vector sequences v1 and v2, then returns the result as a vector sequence. The input vectors v1 and v2 must be sequences of length 2 or 3 only (a diagnostic is output and a value of $NULL is returned if the input vectors have less than 2 or more than 3 elements). They should also have a non-zero length to return a meaningful result. The length of the returned vector equals the sine of the angle between the vectors.

$FVDOT(v1,v2)

Vector dot product Returns: Numeric

This function computes the dot product of two arbitrarily long vector sequences v1 and v2, then returns the result as number (i.e., the cosine of the angle between the vectors). The input vectors v1 and v2 should have a non-zero length to return a meaningful result.

$FVLEN(v)

Vector length Returns: Numeric

This function returns the length of an arbitrarily long vector sequence v.

$FVMULT(v,n)

Vector multiplication Returns: Sequence

This function multiplies an arbitrarily long vector sequence v by the number n, then returns the result as a vector sequence.

$FVNORM(v)

Vector normalization Returns: Sequence

This function normalizes the arbitrarily long vector sequence v, then returns the result as a vector sequence. If the input vector v has a length of zero, then a zero length vector will be returned.

$FVROTN(v1,v2,n)

Normalized vector rotation Returns: Sequence

This function computes a vector at a normalized angular distance between two vectors v1 and v2. When n=0, vector v1 is returned; and when |n|=1, vector v2 is returned. For other values of n, the cross product of v1 and v2 defines the plane of rotation and n defines the normalized rotation distance calculated as the “desired rotation angle divided by the angle between vectors”.

The results are undefined if v1 and v2 are opposite each other.

$FVROTV(angle,v1,v2[,toler])

Rotation of a vector about an axis Returns: Sequence

This function returns a vector resulting from the angle degrees CCLW rotation of vector v1 about an axis defined by vector v2. The CCLW rotation direction is defined by the orientation of the v2 vector, which must have a non-zero length.

When v1 and v2 are parallel the returned vector is equal to v1. The toler parameter defines the tolerance utilized to test if the v1 and v2 vectors are parallel. The default tolerance is 0.0001 degrees.

The input vectors do not have to be normalized. The length of the returned vector is the same as the length of v1.

$FVSUB(v1,v2)

Vector subtraction Returns: Sequence

This function subtracts one arbitrarily long vector sequence from another (i.e., v1–v2) and returns the result as a vector sequence.