Mercurial > hg > octave-lyh

annotate scripts/general/cart2sph.m @ 9168:742cf6388a8f

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Update section 17.7 (Coordinate Transformations) of arith.txi
author Rik <rdrider0-list@yahoo.com>
date Sat, 02 May 2009 07:20:35 -0700
parents eb63fbe60fab
children a8ce6bdecce5
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
8920
eb63fbe60fab update copyright notices
John W. Eaton <jwe@octave.org>
parents: 8533
diff changeset
1 ## Copyright (C) 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2009 Kai Habel
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
2 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
3 ## This file is part of Octave.
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
4 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
6 ## under the terms of the GNU General Public License as published by
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
8 ## your option) any later version.
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
9 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
13 ## General Public License for more details.
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
14 ##
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
15 ## You should have received a copy of the GNU General Public License
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 6786
diff changeset
17 ## <http://www.gnu.org/licenses/>.
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
18
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
19 ## -*- texinfo -*-
5610
9761b7d24e9e [project @ 2006-02-09 09:12:02 by dbateman]
dbateman
parents: 5307
diff changeset
20 ## @deftypefn {Function File} {[@var{theta}, @var{phi}, @var{r}] =} cart2sph (@var{x}, @var{y}, @var{z})
9168
742cf6388a8f Update section 17.7 (Coordinate Transformations) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
21 ## Transform Cartesian to spherical coordinates.
742cf6388a8f Update section 17.7 (Coordinate Transformations) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
22 ## @var{x}, @var{y} and @var{z} must be the same shape, or scalar.
742cf6388a8f Update section 17.7 (Coordinate Transformations) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 8920
diff changeset
23 ## @var{theta} describes the angle relative to the positive x-axis.
8491
aaff46fef256 [docs] fix hypenation: x - axis => x-axis, etc
Brian Gough <bjg@gnu.org>
parents: 7017
diff changeset
24 ## @var{phi} is the angle relative to the xy-plane.
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
25 ## @var{r} is the distance to the origin (0, 0, 0).
5642
2618a0750ae6 [project @ 2006-03-06 21:26:48 by jwe]
jwe
parents: 5610
diff changeset
26 ## @seealso{pol2cart, cart2pol, sph2cart}
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
27 ## @end deftypefn
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
28
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
29 ## Author: Kai Habel <kai.habel@gmx.de>
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
30 ## Adapted-by: jwe
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
31
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
32 function [theta, phi, r] = cart2sph (x, y, z)
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
33
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
34 if (nargin != 3)
6046
34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe]
jwe
parents: 5642
diff changeset
35 print_usage ();
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
36 endif
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
37
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
38 if ((ismatrix (x) && ismatrix (y) && ismatrix (z))
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
39 && (size_equal (x, y) || isscalar (x) || isscalar (y))
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
40 && (size_equal (x, z) || isscalar (x) || isscalar (z))
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
41 && (size_equal (y, z) || isscalar (y) || isscalar (z)))
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
42
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
43 theta = atan2 (y, x);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
44 phi = atan2 (z, sqrt (x .^ 2 + y .^ 2));
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
45 r = sqrt (x .^ 2 + y .^ 2 + z .^ 2);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
46
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
47 else
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
48 error ("cart2sph: arguments must be matrices of same size, or scalar");
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
49 endif
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
50
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
51 endfunction
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
52
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
53 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
54 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
55 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
56 %! z = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
57 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
58 %! assert (t, [0, pi/4, pi/4], eps);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
59 %! assert (p, [0, 1, 1]*atan(sqrt(0.5)), eps);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
60 %! assert (r, [0, 1, 2]*sqrt(3), eps);
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents:
diff changeset
61
8533
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
62 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
63 %! x = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
64 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
65 %! z = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
66 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
67 %! assert (t, [0, 1, 1] * pi/2, eps);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
68 %! assert (p, [0, 1, 1] * pi/4, eps);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
69 %! assert (r, [0, 1, 2] * sqrt(2), eps);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
70
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
71 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
72 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
73 %! y = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
74 %! z = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
75 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
76 %! assert (t, [0, 0, 0]);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
77 %! assert (p, [0, 1, 1] * pi/4);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
78 %! assert (r, [0, 1, 2] * sqrt(2));
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
79
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
80 %!test
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
81 %! x = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
82 %! y = [0, 1, 2];
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
83 %! z = 0;
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
84 %! [t, p, r] = cart2sph (x, y, z);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
85 %! assert (t, [0, 1, 1] * pi/4);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
86 %! assert (p, [0, 0, 0]);
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
87 %! assert (r, [0, 1, 2] * sqrt(2));
fb1b87ea4af9 Permit scalars when transforming coordinates.
Ben Abbott <bpabbott@mac.com>
parents: 8491
diff changeset
88