1 %% Copyright (c) 2011, INRA
2 %% 2010-2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
5 %% All rights reserved.
6 %% (simplified BSD License)
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35 %% @deftypefn {Function File} {@var{T} = } createBasisTransfrom (@var{@var{target}})
36 %% @deftypefnx {Function File} {@var{T} = } createBasisTransfrom (@var{@var{source}}, @var{@var{target}})
37 %% Compute matrix for transforming a basis into another basis
39 %% With only one input arguemnt, assumes the @var{source} is the standard (Oij) basis, with origin at (0,0),
40 %% first direction vector equal to (1,0) and second direction vector
41 %% equal to (0,1). Otherwise @var{@var{source}} specifies the @var{source} basis.
43 %% Both @var{source} and @var{target} represent basis, in the following form:
44 %% [x0 y0 ex1 ey1 ex2 ey2]
45 %% [y0 y0] is the origin of the basis, [ex1 ey1] is the first direction
46 %% vector, and [ex2 ey2] is the second direction vector.
48 %% The result @var{T} is a 3-by-3 matrix such that a point expressed with
49 %% coordinates of the first basis will be represented by new coordinates
50 %% @code{P2 = transformPoint(P1, @var{T})} in the @var{target} basis.
54 %% % standard basis transform
55 %% src = [0 0 1 0 0 1];
56 %% % @var{target} transform, just a rotation by atan(2/3) followed by a scaling
57 %% tgt = [0 0 .75 .5 -.5 .75];
58 %% % compute transform
59 %% trans = createBasisTransform(src, tgt);
60 %% % transform the point (.25,1.25) into the point (1,1)
62 %% p2 = transformPoint(p1, trans)
67 %% @seealso{transforms2d}
70 function transfo = createBasisTransform(source, target)
72 % init basis transform to identity
77 % from source to reference basis
78 t1(1:2, 1) = source(3:4);
79 t1(1:2, 2) = source(5:6);
80 t1(1:2, 3) = source(1:2);
82 % if only one input, use first input as target basis, and leave the
83 % first matrix to identity
87 % from reference to target basis
88 t2(1:2, 1) = target(3:4);
89 t2(1:2, 2) = target(5:6);
90 t2(1:2, 3) = target(1:2);
93 % same as: transfo = inv(t2)*t1;
99 %! % standard basis transform
100 %! src = [0 0 1 0 0 1];
101 %! % target transform, just a rotation by atan(2/3) followed by a scaling
102 %! tgt = [0 0 .75 .5 -.5 .75];
103 %! % compute transform
104 %! trans = createBasisTransform(src, tgt);
105 %! % transform the point (.25,1.25) into the point (1,1)
107 %! p2 = transformPoint(p1, trans)