Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / createBasisTransform.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/createBasisTransform.m b/octave_packages/geometry-1.5.0/geom2d/createBasisTransform.m
new file mode 100644 (file)
index 0000000..312da94
--- /dev/null
+++ b/octave_packages/geometry-1.5.0/geom2d/createBasisTransform.m
@@ -0,0 +1,108 @@
+%% Copyright (c) 2011, INRA
+%% 2010-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% Redistribution and use in @var{source} and binary forms, with or without
+%% modification, are permitted provided that the following conditions are met:
+%%
+%% 1. Redistributions of @var{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 notice, 
+%%    this list of conditions and the following disclaimer in the documentation
+%%    and/or other materials provided with the distribution.
+%%
+%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+%% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+%% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+%% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+%% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
+%% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+%% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
+%% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+%% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%% POSSIBILITY OF SUCH DAMAGE.
+%%
+%% The views and conclusions contained in the software and documentation are
+%% those of the authors and should not be interpreted as representing official
+%% policies, either expressed or implied, of copyright holder.
+
+%% -*- 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)
+