/usr/share/octave/packages/geometry-1.7.0/geom2d/createBasisTransform.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{T} = } createBasisTransfrom (@var{@var{target}})
## @deftypefnx {Function File} {@var{T} = } createBasisTransfrom (@var{@var{source}}, @var{@var{target}})
## Compute matrix for transforming a basis into another basis
##
## With only one input arguemnt, assumes the @var{source} is the standard (Oij) basis, with origin at (0,0),
## first direction vector equal to (1,0) and second direction vector
## equal to (0,1). Otherwise @var{@var{source}} specifies the @var{source} basis.
##
## Both @var{source} and @var{target} represent basis, in the following form:
## [x0 y0 ex1 ey1 ex2 ey2]
## [y0 y0] is the origin of the basis, [ex1 ey1] is the first direction
## vector, and [ex2 ey2] is the second direction vector.
##
## The result @var{T} is a 3-by-3 matrix such that a point expressed with
## coordinates of the first basis will be represented by new coordinates
## @code{P2 = transformPoint(P1, @var{T})} in the @var{target} basis.
##
## Example
## @example
## # standard basis transform
## src = [0 0 1 0 0 1];
## # @var{target} transform, just a rotation by atan(2/3) followed by a scaling
## tgt = [0 0 .75 .5 -.5 .75];
## # compute transform
## trans = createBasisTransform(src, tgt);
## # transform the point (.25,1.25) into the point (1,1)
## p1 = [.25 1.25];
## p2 = transformPoint(p1, trans)
## ans =
## 1 1
## @end example
##
## @seealso{transforms2d}
## @end deftypefn
function transfo = createBasisTransform(source, target)
# init basis transform to identity
t1 = eye(3);
t2 = eye(3);
if nargin==2
# from source to reference basis
t1(1:2, 1) = source(3:4);
t1(1:2, 2) = source(5:6);
t1(1:2, 3) = source(1:2);
else
# if only one input, use first input as target basis, and leave the
# first matrix to identity
target = source;
end
# from reference to target basis
t2(1:2, 1) = target(3:4);
t2(1:2, 2) = target(5:6);
t2(1:2, 3) = target(1:2);
# compute transfo
# same as: transfo = inv(t2)*t1;
transfo = t2\t1;
endfunction
%!demo
%! # standard basis transform
%! src = [0 0 1 0 0 1];
%! # target transform, just a rotation by atan(2/3) followed by a scaling
%! tgt = [0 0 .75 .5 -.5 .75];
%! # compute transform
%! trans = createBasisTransform(src, tgt);
%! # transform the point (.25,1.25) into the point (1,1)
%! p1 = [.25 1.25];
%! p2 = transformPoint(p1, trans)
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