o object_name [object entities...] o subobject_name [subobject entities...] o [more object entities and subobjects...] oThe o keyword by itself marks the end of an object context. Any number of hierarchical context levels are supported, and there are no rules governing the choice of object names except that they begin with a letter and be made up of printing, non-white ASCII characters. Indentation is not necessary of course, but it does improve readability.

-t dx dy dz translate objects along the given vector -rx degrees rotate objects about the X-axis -ry degrees rotate objects about the Y-axis -rz degrees rotate objects about the Z-axis -s scalefactor scale objects by the given factor -mx mirror objects about the Y-Z plane -my mirror objects about the X-Z plane -mz mirror objects about the X-Y plane -i N repeat the following arguments N times -a N make an array of N geometric instancesTransform arguments have a cumulative effect. That is, a rotation about X of 20 degrees followed by a rotation about X of -50 degrees results in a total rotation of -30 degrees. However, if the two rotations are separated by some translation vector, the cumulative effect is quite different. It is best to think of each argument as acting on the included geometric objects, and each subsequent transformation argument affects the objects relative to their new position/orientation.

For example, rotating an object about its center is most easily done by translating the object back to the origin, applying the desired rotation, and translating it again back to its original position, like so:

# rotate an included object 20 degrees clockwise looking down # an axis parallel to Y and passing through the point (15,0,-35) xf -t -15 0 35 -ry -20 -t 15 0 -35 i object.mgf xfNote that the include entity, i, permits a transformation to be given with it, so the above could have been written more compactly as:

i object.mgf -t -15 0 35 -ry -20 -t 15 0 -35Rotations are given in degrees counter-clockwise about a principal axis. That is, with the thumb of the right hand pointing in the direction of the axis, rotation follows the curl of the fingers.

The transform entity itself is cumulative, but in the reverse order to its arguments. That is, later transformations (i.e. enclosed transformations) are prepended to existing (i.e. enclosing) ones. A transform command with no arguments is used to return to the previous condition. It is necessary that transforms and their end statements ("xf" by itself) be balanced in a file, so that later or enclosing files are not affected.

Transformations apply only to geometric types, e.g. polygons, spheres, etc. Vertices and the components that go into geometry are not directly affected. This is to avoid confusion and the inadvertent multiple application of a given transformation. For example:

xf -t 5 0 0 v v1 = p 0 10 0 n 0 0 1 xf -rx 180 # Transform now in effect is "-rx 180 -t 5 0 0" ring v1 0 2 xf xfThe final ring center is (5,-10,0) -- note that the vertex itself is not affected by the transformation, only the geometry that calls on it. The normal orientation is (0,0,-1) due to the rotation about X, which also reversed the sign of the central Y coordinate.

Multi-dimensional arrays may be specified with a single include entity by giving multiple array commands separated by their corresponding transforms. A final transformation may be given by preceding it with a -i 1 specification. In other words, the scope of an array command continues until the next -i or -a option.

The following MGF description places 60 spheres at a one unit spacing in a 3x4x5 array, then moves the whole thing to an origin of (15,30,45):

v v0 = p 0 0 0 xf -a 3 -t 1 0 0 -a 4 -t 0 1 0 -a 5 -t 0 0 1 -i 1 -t 15 30 45 sph v0 0.1 xfNote the "-i 1" in the specification, which marks the end of the third array arguments before the final translation.