isCoplanar

ISCOPLANAR Tests input points for coplanarity in 3-space.

 COPL = isCoplanar(PTS)
 Tests the coplanarity of the input points in array PTS. Input array must
 be 4-by-3, each row containing coordinate of one point.

 COPL = isCoplanar(PTS, TOLERANCE)
 Specifies the tolerance value used for checking coplanarity. Default is
 zero.
 
 
 Example: 
   iscoplanar([1 2 -2; -3 1 -14; -1 2 -6; 1 -2 -8], eps)

0001 function copl = isCoplanar(x,y,z,tol)
0002 %ISCOPLANAR Tests input points for coplanarity in 3-space.
0003 %
0004 % COPL = isCoplanar(PTS)
0005 % Tests the coplanarity of the input points in array PTS. Input array must
0006 % be 4-by-3, each row containing coordinate of one point.
0007 %
0008 % COPL = isCoplanar(PTS, TOLERANCE)
0009 % Specifies the tolerance value used for checking coplanarity. Default is
0010 % zero.
0011 %
0012 %
0013 % Example:
0014 %   iscoplanar([1 2 -2; -3 1 -14; -1 2 -6; 1 -2 -8], eps)
0015 
0016 %
0017 % Adapted from a function originally written by Brett Shoelson, Ph.D.
0018 % brett.shoelson@joslin.harvard.edu
0019 % https://fr.mathworks.com/matlabcentral/fileexchange/46-iscoplanar-m
0020 %
0021 
0022 if nargin == 0
0023     error('Requires at least one input argument.'); 
0024     
0025 elseif nargin == 1
0026     if size(x,2) == 3
0027         % Matrix of all x,y,z is input
0028         pts = x;
0029         tol = 0;
0030     else
0031         error('Invalid input.')
0032     end
0033     
0034 elseif nargin == 2
0035     if size(x,2) == 3
0036         % Matrix of all x,y,z is input
0037         pts = x;
0038         tol = y;
0039     else
0040         error('Invalid input.')
0041     end
0042 elseif nargin == 3
0043     % Compile a matrix of all x,y,z
0044     pts = [x y z];
0045     tol = 0;
0046 else
0047     pts = [x y z];
0048 end
0049 
0050 if size(x, 1) < 4
0051     error('Requires at least four points to compute coplanarity');
0052 end
0053 
0054 % replace first point at the origin and compute SVD of the matrix
0055 sv = svd(bsxfun(@minus, pts(2:end,:), pts(1,:)));
0056 copl = sv(3) <= tol * sv(1);
0057 
0058 % % Alterantive version that computes the rank of the matrix
0059 % rnk = rank(bsxfun(@minus, pts(2:end,:), pts(1,:)), tol);
0060 % copl = rnk <= size(pts, 2) - 1;
0061 
0062 % % Old version:
0063 % %Compare all 4-tuples of point combinations; {P1:P4} are coplanar iff
0064 % %det([x1 y1 z1 1;x2 y2 z2 1;x3 y3 z3 1;x4 y4 z4 1])==0
0065 % tmp = nchoosek(1:size(pts,1),4);
0066 % for ii = 1:size(tmp,1)
0067 %     copl = abs(det([pts(tmp(ii, :), :) ones(4,1)])) <= tolerance;
0068 %     if ~copl
0069 %         break
0070 %     end
0071 % end