08-Oct-2025 22:44:10 triangle_symq_rule_original_test() MATLAB/Octave version 6.4.0 Test triangle_symq_rule_original() triangle_symq_rule_test01(): Map points from one triangle to another. R = reference triangle S = simplex T = user-defined triangle. ref_to_triangle(): r => t simplex_to_triangle(): s => t triangle_to_ref(): t => r triangle_to_simplex(): t => s SP1: 0.1125 0.7163 TP1: 0.6212 2.5990 RP1: -0.0587 0.6634 TP2: 0.6212 2.5990 SP2: 0.1125 0.7163 SP1: 0.2817 0.2275 TP1: 1.6176 1.8094 RP1: -0.2091 -0.1833 TP2: 1.6176 1.8094 SP2: 0.2817 0.2275 SP1: 0.3713 0.1101 TP1: 2.0038 1.8154 RP1: -0.1473 -0.3867 TP2: 2.0038 1.8154 SP2: 0.3713 0.1101 SP1: 0.6671 0.0502 TP1: 2.9511 2.8191 RP1: 0.3844 -0.4904 TP2: 2.9511 2.8191 SP2: 0.6671 0.0502 SP1: 0.7252 0.1542 TP1: 3.0213 3.3633 RP1: 0.6046 -0.3103 TP2: 3.0213 3.3633 SP2: 0.7252 0.1542 Region is user-defined triangle. Triangle: 1.0000 0.0000 4.0000 4.0000 0.0000 3.0000 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 8 NUMNODES = 16 J W X Y 1 0.670913 1.34114 1.19399 2 0.670913 2.80601 3.14715 3 0.670913 0.852847 2.65886 4 0.618096 2.29646 2.08141 5 0.618096 1.91859 3.21505 6 0.618096 0.784952 1.70354 7 0.938051 1.66667 2.33333 8 0.21098 1.10109 0.353831 9 0.21098 3.64617 3.74726 10 0.21098 0.252736 2.89891 11 0.176997 1.78094 1.07764 12 0.176997 2.92236 3.70331 13 0.176997 0.296692 2.21906 14 0.176997 3.17708 2.93915 15 0.176997 1.06085 3.23793 16 0.176997 0.762072 0.822918 Weight sum 6.5 Area 6.5 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 8 Number of nodes = 16 Graphics saved as "user08.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 8 Quadrature rule written to file "user08.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 2.75098e-16 Region is standard equilateral triangle. Triangle: -1.0000 -0.5774 1.0000 -0.5774 0.0000 1.1547 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 8 NUMNODES = 16 J W X Y 1 0.178778 -0.488292 -0.281916 2 0.178778 0.488292 -0.281916 3 0.178778 4.44089e-16 0.563831 4 0.164704 0 -0.436336 5 0.164704 0.377878 0.218168 6 0.164704 -0.377878 0.218168 7 0.249962 0 2.22045e-16 8 0.0562198 -0.848358 -0.4898 9 0.0562198 0.848358 -0.4898 10 0.0562198 6.66134e-16 0.9796 11 0.0471643 -0.46538 -0.56281 12 0.0471643 0.720098 -0.121625 13 0.0471643 -0.254718 0.684436 14 0.0471643 0.46538 -0.56281 15 0.0471643 0.254718 0.684436 16 0.0471643 -0.720098 -0.121625 Weight sum 1.73205 Area 1.73205 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 8 Number of nodes = 16 Graphics saved as "equi08.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 8 Quadrature rule written to file "equi08.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 1.39354e-16 Region is the simplex (0,0),(1,0),(0,1). Triangle: 0.0000 0.0000 1.0000 0.0000 0.0000 1.0000 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 4 NUMNODES = 6 J W X Y 1 0.111691 0.445948 0.108103 2 0.111691 0.445948 0.445948 3 0.111691 0.108103 0.445948 4 0.0549759 0.0915762 0.0915762 5 0.0549759 0.816848 0.0915762 6 0.0549759 0.0915762 0.816848 Weight sum 0.5 Area 0.5 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 4 Number of nodes = 6 Graphics saved as "simp04.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 4 Quadrature rule written to file "simp04.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 4 RMS integration error = 7.87137e-17 triangle_symq_rule_original_test(): Normal end of execution. 08-Oct-2025 22:44:10