Matrix Track To

Functionality

Generates the transformation matrix given a location, a scale and a rotation defined by the given set of Track & Up vectors.

The “Track/Up Axes” and the “Track/Up Mapping” settings allow to set any two of the X, Y, Z axes to be the Track axis and the Up axis and to map them to any of the two input vectors A and B (or to their negatives). The first axis listed in these dropdown lists is the Track axis/vector and the second is the Up axis/vector.

The axis selected to be the Track axis (the first letter in “Track/Up Axes” selection) will be precisely oriented along the Track vector (whichever the Track vector is mapped to, based on the “Track/Up mapping”), while the axis selected to be the Up axis (the second letter the “Track/Up Axes” selection) will be approximately oriented along the Up vector (whichever the Up vector is mapped to, based on the “Track/Up mapping” selection). If the A and B inputs happen to be orthogonal to eachother then the Track and Up axes will be precisely oriented along the selected Track/Up vectors, otherwise the Up axis will only approximately be oriented towards the Up vector, perpendicular to the Track axis, and reside within the AB plane. The third axis (X, Y or Z) is determined via cross product from the other two as to provide an ortho-normal, right handed, XYZ coordinate system.

Inputs

All inputs are vectorized and they will accept single or multiple values.

• Location

• Scale

• A

• B

Parameters

• Track/Up Axes

• Track/Up Mapping

Param	Type	Default	Description
Track/Up Axes	Enum: X Y X Z Y X Y Z Z X Z Y	X Y	Selects which of the X,Y,Z axes are the Track axis and the Up axis.
Track/Up Mapping	Enum: A B A -B -A B -A -B B A B -A -B A -B -A	A B	Maps the Track and Up vectors to one of the A, B inputs or to their negatives.
Location	Vector	(0, 0, 0)	Location component of the output matrix.
Scale	Vector	(1, 1, 1)	Scale component of the output matrix.
A	Vector	(1, 0, 0)	First vector (to be assigned to Track or Up).
B	Vector	(0, 1, 0)	Second vector (to be assigned to Track or Up).

Extra Parameters

A set of extra parameters are available on the property panel. These parameters do not receive external input.

• Normalize Vectors

• Flat Output

Extra Param	Type	Default	Description
Normalize Vectors	Bool	True	Normalize the output X, Y, Z vectors and the rotation component of the matrix. Turn this OFF when normalization is not needed to optimize computation.
Flat Output	Bool	True	While active it will join the first level to output a regular matrix list ([M,M,..]) that can be plugged to any other node. If it is disabled the node will keep the original structure outputting a list of matrix lists ([[M,M,..],[M,M,..],..]).

Outputs

Matrix, X, Y, Z. All outputs will be generated when connected.

The Matrix is the homogeneous 4x4 matrix composed by the given location, rotation and scale :

m = T * R * S. [1]

The X, Y, Z are the orthonormal vectors, oriented along the Track and Up axes. [2]

Notes:

• [1] : The rotation component is ortho-normal only if the “Normalize Vectors” option is ON (in the Property Panel).

• [2] : The axes are ortho-normal only if the “Normalize Vectors” option is ON (in the Property Panel), otherwise the vectors are only orthogonal.

Example of usage