Code covered by the BSD License

# geom3d

### David Legland (view profile)

19 Jun 2009 (Updated )

Library to handle 3D geometric primitives: create, intersect, display, and make basic computations

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

anglePoints3d(varargin)
```function alpha = anglePoints3d(varargin)
%ANGLEPOINTS3D Compute angle between three 3D points
%
%   ALPHA = anglePoints3d(P1, P2)
%   Computes angle (P1, O, P2), in radians, between 0 and PI.
%
%   ALPHA = anglePoints3d(P1, P2, P3)
%   Computes angle (P1, P2, P3), in radians, between 0 and PI.
%
%   ALPHA = anglePoints3d(PTS)
%   PTS is a 3x3 or 2x3 array containing coordinate of points.
%
%   points3d, angles3d
%
%   ---------
%   author : David Legland
%   INRA - TPV URPOI - BIA IMASTE
%   created the 21/02/2005.
%

%   HISTORY
%   20/09/2005: add case of single argument for all points
%   04/01/2007: check typo
%   27/05/2014: adjust known vector sizes n1, n0, n2 once corrected for

p2 = [0 0 0];
if length(varargin) == 1
pts = varargin{1};
if size(pts, 1)==2
p1 = pts(1,:);
p0 = [0 0 0];
p2 = pts(2,:);
else
p1 = pts(1,:);
p0 = pts(2,:);
p2 = pts(3,:);
end

elseif length(varargin) == 2
p1 = varargin{1};
p0 = [0 0 0];
p2 = varargin{2};

elseif length(varargin) == 3
p1 = varargin{1};
p0 = varargin{2};
p2 = varargin{3};
end

% ensure all data have same size
n1 = size(p1, 1);
n2 = size(p2, 1);
n0 = size(p0, 1);

if n1 ~= n0
if n1 == 1
p1 = repmat(p1, [n0 1]);
n1 = n0;
elseif n0==1
p0 = repmat(p0, [n1 1]);
else
error('Arguments P1 and P0 must have the same size');
end
end

if n1 ~= n2
if n1 == 1
p1 = repmat(p1, [n2 1]);
elseif n2 == 1
p2 = repmat(p2, [n1 1]);
else
error('Arguments P1 and P2 must have the same size');
end
end

% normalized vectors
p1 = normalizeVector3d(p1 - p0);
p2 = normalizeVector3d(p2 - p0);

% compute angle
alpha = acos(dot(p1, p2, 2));
```