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function angle = triangle_angles ( t ) %*****************************************************************************80 % %% triangle_angles() computes the angles of a triangle in 2D. % % Discussion: % % The law of cosines is used: % % C^2 = A^2 + B^2 - 2 * A * B * COS ( GAMMA ) % % where GAMMA is the angle opposite side C. % % 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: % % real ANGLE(3,1), the angles opposite % sides P1-P2, P2-P3 and P3-P1, in radians. % % % Compute the length of each side. % a = norm ( t(1,1:2) - t(2,1:2) ); b = norm ( t(2,1:2) - t(3,1:2) ); c = norm ( t(3,1:2) - t(1,1:2) ); angle = zeros ( 3, 1 ); % % Take care of unlikely special cases. % if ( a == 0.0 && b == 0.0 && c == 0.0 ) angle(1:3,1) = 2.0 * pi / 3.0; return end if ( c == 0.0 || a == 0.0 ) angle(1,1) = pi; else angle(1,1) = acos ( ( c * c + a * a - b * b ) / ( 2.0 * c * a ) ); end if ( a == 0.0 || b == 0.0 ) angle(2,1) = pi; else angle(2,1) = acos ( ( a * a + b * b - c * c ) / ( 2.0 * a * b ) ); end if ( b == 0.0 || c == 0.0 ) angle(3,1) = pi; else angle(3,1) = acos ( ( b * b + c * c - a * a ) / ( 2.0 * b * c ) ); end return end