TRIANGLEAREA3D Area of a 3D triangle.
AREA = triangleArea3d(P1, P2, P3)
Computes area of the 3D triangle whose vertices are given by P1, P2 and
P3. Each vertex is either a 1-by-3 row vector, or an array with 3
columns, each column representing coordinate of a vertex.
The result AREA has as many rows as the number of rows of the largest
input array.
Compared to polygonArea3d, this function is assumed to be faster, as it
does not requires iteration over vertices. Moreover, it can be used to
computes the area of several triangles simultaneously.
AREA = triangleArea3d(PTS)
Concatenates vertex coordinates in a 3-by-3 array. Each row of the
array contains coordinates of one vertex.
Example
triangleArea3d([10 10 10], [30 10 10], [10 40 10])
ans =
300
See also
polygons3d, polygonArea3d
------
Author: David Legland
e-mail: david.legland@grignon.inra.fr
Created: 2011-08-23, using Matlab 7.9.0.529 (R2009b)
Copyright 2011 INRA - Cepia Software Platform.0001 function area = triangleArea3d(pt1, pt2, pt3) 0002 %TRIANGLEAREA3D Area of a 3D triangle. 0003 % 0004 % AREA = triangleArea3d(P1, P2, P3) 0005 % Computes area of the 3D triangle whose vertices are given by P1, P2 and 0006 % P3. Each vertex is either a 1-by-3 row vector, or an array with 3 0007 % columns, each column representing coordinate of a vertex. 0008 % The result AREA has as many rows as the number of rows of the largest 0009 % input array. 0010 % Compared to polygonArea3d, this function is assumed to be faster, as it 0011 % does not requires iteration over vertices. Moreover, it can be used to 0012 % computes the area of several triangles simultaneously. 0013 % 0014 % AREA = triangleArea3d(PTS) 0015 % Concatenates vertex coordinates in a 3-by-3 array. Each row of the 0016 % array contains coordinates of one vertex. 0017 % 0018 % 0019 % Example 0020 % triangleArea3d([10 10 10], [30 10 10], [10 40 10]) 0021 % ans = 0022 % 300 0023 % 0024 % See also 0025 % polygons3d, polygonArea3d 0026 % 0027 % ------ 0028 % Author: David Legland 0029 % e-mail: david.legland@grignon.inra.fr 0030 % Created: 2011-08-23, using Matlab 7.9.0.529 (R2009b) 0031 % Copyright 2011 INRA - Cepia Software Platform. 0032 0033 % if data is given as one array, split vertices 0034 if nargin == 1 0035 pt2 = pt1(2,:); 0036 pt3 = pt1(3,:); 0037 pt1 = pt1(1,:); 0038 end 0039 0040 % compute individual vectors 0041 v12 = bsxfun(@minus, pt2, pt1); 0042 v13 = bsxfun(@minus, pt3, pt1); 0043 0044 % compute area from cross product 0045 area = vectorNorm3d(cross(v12, v13, 2)) / 2;