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Where – in the context of ND-viewing – a single (N+1)x(N+1) matrix is
expected – as in the INST ntransform field, or the
ND-xform* (see GCL) commands – use an ntransform object.
ntransform are NRows x NCols transformation matrix
where usually NRows = N+1 in the context of
N-dimensional objects and viewing. The homogeneous component of an
ntransform sits at column zero (in contrast to ordinary
transform objects where it is located at column
three). ntransform objects operate on points of any dimension: if
a point is to be transformed by an ntransform object and the
dimension of the point does not match the number of rows of the
ntransform object, then either the point is implicitly padded
with zeros to match NRows or the matrix is implicitly padded with
ones down its diagonal (and zeros everywhere else) such that it will
operate as identity on the excess dimensions of the input point.
Syntax for an ntransform object is
<ntransform> ::=
[ "{" ] (curly brace, generally needed to make
the end of the object unambiguous.)
[ "ntransform" ] (optional keyword; unnecessary if the type
is determined by the context, which it
usually is.)
[ "define" <name> ]
(defines a transform named <name>, setting
its value from the stuff which follows)
NRows NCols
(number of rows and columns of the matrix,
typically N+1 N+1, but any dimensions
are possible)
<NRows x NCols floating-point numbers>
(interpreted as a NRows x NCols
homogeneous transform given row by row, intended
to apply to a row vector multiplied on its LEFT,
so that e.g. Euclidean translations appear in the
top row -- in contrast to the ordinary
transform objects where the translations appear
in the bottom row)
|
"<" <filename> (meaning: read transform from that file)
|
":" <name> (meaning: use variable <name>,
defined elsewhere; if undefined the initial
value is the identity transform)
[ "}" ] (matching curly brace)
The whole should be enclosed in { braces }. Braces are not necessarily essential, so e.g. two integers – NRows NCols – followed by a NRows x NCols array of floats standing alone may but needn't have braces.
Some examples, in contexts where they might be used:
# Example 1: A GCL command to define a6x6transform called # "fred", a mere translation by the vector-3 0 1 1 0. This # transform is meant for a five dimensional space, with an homogeneous # component a index zero. (read ntransform { ntransform define fred 6 6 1 -3 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } )
# Example 2: Set the ND-xform of an object -- a geometry or a camera
# cluster. Given the definition above, this puts the object at (-3 0 1 1
# 0) in the five dimensional space.
(ND-xform-set focus : fred)
# or
(ND-xform-set g1 : fred)