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function value = triangle_orientation ( t ) %*****************************************************************************80 % %% triangle_orientation() determines the orientation of a triangle in 2D. % % Discussion: % % Three distinct non-colinear points in the plane define a circle. % If the points are visited in the order P1, P2, and then % P3, this motion defines a clockwise or counterclockwise % rotation along the circle. % % Licensing: % % This code is distributed under the MIT license. % % Modified: % % 29 July 2023 % % Author: % % John Burkardt % % Input: % % real T(3,2), the triangle vertices. % % Output: % % integer VALUE, reports if the three points lie % clockwise on the circle that passes through them. The possible % return values are: % 0, the points are distinct, noncolinear, and lie counterclockwise % on their circle. % 1, the points are distinct, noncolinear, and lie clockwise % on their circle. % 2, the points are distinct and colinear. % 3, at least two of the points are identical. % if ( all ( t(1,1:2) == t(2,1:2) ) || ... all ( t(2,1:2) == t(3,1:2) ) || ... all ( t(3,1:2) == t(1,1:2) ) ) value = 3; return end det = ( t(1,1) - t(3,1) ) * ( t(2,2) - t(3,2) ) ... - ( t(2,1) - t(3,1) ) * ( t(1,2) - t(3,2) ); if ( det == 0.0 ) value = 2; elseif ( det < 0.0 ) value = 1; elseif ( 0.0 < det ) value = 0; end return end