# compose-maps¶

## Synopsis¶

compose-maps <f1> <f2>... <g>


## Description¶

Computes the composition g of the given input maps such that

$g(x) = fn o ... o f2 o f1(x)$

The first input map, f1, must be a piecewise linear map defined at a discrete set of points. Values of the composite output map are computed for these input points only and the resulting map is also a piecewise linear map with identical discretized domain. All other maps, except the last one, fn, must have codomain dimension 2 or 3. Each input map can be either a surface map computed with the map-surface command, a volumetric map computed with the map-volume command, or one of the following analytic maps. Parameters of the analytic maps can be passed in parenthesis after the map name and must be separated by comma. See Examples below.

Mapping Description
SquareToDisk Map 2D points in a square to a disk bounded by the incircle.
DiskToSquare Inverse of SquareToDisk.
StereographicProjection Stereographic projection from the sphere to the plane. Use argument ‘N’ or ‘S’ for a projection from the north pole or south pole, respectively. The default projection is to the plane at ‘z=0’. When the input points are within a disk, all points are mapped to hemisphere opposite of the projection pole.
InverseStereographicProjection Inverse of StereographicProjection.

## Standard options¶

-v, -verbose [n]

Increase/Set verbosity of output messages. (default: 0)

-debug [level]

Increase/Set debug level for output of intermediate results. (default: 0)

-version [major.minor]

Print version and exit or set version to emulate.

-revision

Print revision (or version) number only and exit.

-h, -help

Print help and exit.

## Examples¶

### Example 1¶

Command:

compose-maps surface-to-disk.vtp 'InverseStereographicProjection(pole=N,r=1)' surface-to-southern-hemisphere.vtp


Output/Description:

Composes the given input surface map which maps each point on a surface embedded in 3D
Euclidean space to the unit disk with an inverse stereographic projection from the north pole
to the plane containing the disk. The resulting piecewise linear surface map projects the
points onto the southern hemisphere of the unit sphere. The default radius, 'r', is equal
to the maximum distance of the points from the origin along the x and y axis, respectively.