/usr/share/octave/packages/geometry-1.7.0/geom3d/vectorAngle3d.m is in octave-geometry 1.7.0-1build1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | ## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## 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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##
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{theta} =} vectorAngle3d (@var{v1}, @var{v2})
## Angle between two 3D vectors
##
## THETA = vectorAngle3d(V1, V2)
## Computes the angle between the 2 3D vectors V1 and V2. The result THETA
## is given in radians, between 0 and PI.
##
##
## Example
## # angle between 2 orthogonal vectors
## vectorAngle3d([1 0 0], [0 1 0])
## ans =
## 1.5708
##
## # angle between 2 parallel vectors
## v0 = [3 4 5];
## vectorAngle3d(3*v0, 5*v0)
## ans =
## 0
##
## @seealso{vectors3d, vectorNorm}
## @end deftypefn
function theta = vectorAngle3d(v1, v2)
# compute angle using arc-tangent to get better precision for angles near
# zero, see the discussion in:
# http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925#381952
# equivalent to:
# v1 = normalizeVector(v1);
# v2 = normalizeVector(v2);
# theta = acos(dot(v1, v2, 2));
theta = atan2(vectorNorm(cross (v1, v2)), sum(v1.*v2,2));
endfunction
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