/usr/share/octave/packages/geometry-1.7.0/geom3d/normalizePlane.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 | ## 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:
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{plane2} =} normalizePlane (@var{plane1})
## Normalize parametric representation of a plane
##
## PLANE2 = normalizePlane(PLANE1);
## Transforms the plane PLANE1 in the following format:
## [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], where:
## - (X0, Y0, Z0) is a point belonging to the plane
## - (DX1, DY1, DZ1) is a first direction vector
## - (DX2, DY2, DZ2) is a second direction vector
## into another plane, with the same format, but with:
## - (x0 y0 z0) is the closest point of plane to the origin
## - (DX1 DY1 DZ1) has norm equal to 1
## - (DX2 DY2 DZ2) has norm equal to 1 and is orthogonal to (DX1 DY1 DZ1)
##
## @seealso{planes3d, createPlane}
## @end deftypefn
function plane2 = normalizePlane (plane1)
# compute first direction vector
d1 = normalizeVector (plane1(:,4:6));
# compute second direction vector
n = normalizeVector (planeNormal (plane1));
d2 = -normalizeVector (cross (d1, n));
# compute origin point of the plane
origins = repmat ([0 0 0], [size(plane1, 1) 1]);
p0 = projPointOnPlane (origins, [plane1(:,1:3) d1 d2]);
# create the resulting plane
plane2 = [p0 d1 d2];
endfunction
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