08-Jan-2022 08:56:46 polygon_grid_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test polygon_grid(). POLYGON_GRID_COUNT_TEST: POLYGON_GRID_COUNT counts NG, the number of points in a grid defined with N+1 points on each side of a polygon of NV vertices. Polygonal vertex count NV = 3 N NG 0 1 1 4 2 10 3 19 4 31 5 46 Polygonal vertex count NV = 4 N NG 0 1 1 5 2 13 3 25 4 41 5 61 Polygonal vertex count NV = 5 N NG 0 1 1 6 2 16 3 31 4 51 5 76 POLYGON_GRID_POINTS_TEST01: POLYGON_GRID_POINTS returns grid points for a polygon of NV vertices, with N+1 points on a side For this test, the polygon is a triangle. Polygon vertices: Col: 1 2 Row 1 : 0 0 2 : 1 0 3 : 0.5 0.866025 N = 5 Number of grid points will be NG = 46 1 0 0 5 0.5000 0.2887 2 1 0 4 0.4000 0.2309 3 1 1 3 0.5000 0.1732 4 1 2 2 0.6000 0.1155 5 1 3 1 0.7000 0.0577 6 1 4 0 0.8000 0.0000 7 2 0 3 0.3000 0.1732 8 2 1 2 0.4000 0.1155 9 2 2 1 0.5000 0.0577 10 2 3 0 0.6000 0.0000 11 3 0 2 0.2000 0.1155 12 3 1 1 0.3000 0.0577 13 3 2 0 0.4000 0.0000 14 4 0 1 0.1000 0.0577 15 4 1 0 0.2000 0.0000 16 5 0 0 0.0000 0.0000 17 1 0 4 0.6000 0.2309 18 1 1 3 0.6000 0.3464 19 1 2 2 0.6000 0.4619 20 1 3 1 0.6000 0.5774 21 1 4 0 0.6000 0.6928 22 2 0 3 0.7000 0.1732 23 2 1 2 0.7000 0.2887 24 2 2 1 0.7000 0.4041 25 2 3 0 0.7000 0.5196 26 3 0 2 0.8000 0.1155 27 3 1 1 0.8000 0.2309 28 3 2 0 0.8000 0.3464 29 4 0 1 0.9000 0.0577 30 4 1 0 0.9000 0.1732 31 5 0 0 1.0000 0.0000 32 1 0 4 0.5000 0.4041 33 1 1 3 0.4000 0.3464 34 1 2 2 0.3000 0.2887 35 1 3 1 0.2000 0.2309 36 1 4 0 0.1000 0.1732 37 2 0 3 0.5000 0.5196 38 2 1 2 0.4000 0.4619 39 2 2 1 0.3000 0.4041 40 2 3 0 0.2000 0.3464 41 3 0 2 0.5000 0.6351 42 3 1 1 0.4000 0.5774 43 3 2 0 0.3000 0.5196 44 4 0 1 0.5000 0.7506 45 4 1 0 0.4000 0.6928 46 5 0 0 0.5000 0.8660 The grid point array: Col: 1 2 Row 1 : 0.5 0.288675 2 : 0.4 0.23094 3 : 0.5 0.173205 4 : 0.6 0.11547 5 : 0.7 0.057735 6 : 0.8 0 7 : 0.3 0.173205 8 : 0.4 0.11547 9 : 0.5 0.057735 10 : 0.6 0 11 : 0.2 0.11547 12 : 0.3 0.057735 13 : 0.4 0 14 : 0.1 0.057735 15 : 0.2 0 16 : 0 0 17 : 0.6 0.23094 18 : 0.6 0.34641 19 : 0.6 0.46188 20 : 0.6 0.57735 21 : 0.6 0.69282 22 : 0.7 0.173205 23 : 0.7 0.288675 24 : 0.7 0.404145 25 : 0.7 0.519615 26 : 0.8 0.11547 27 : 0.8 0.23094 28 : 0.8 0.34641 29 : 0.9 0.057735 30 : 0.9 0.173205 31 : 1 0 32 : 0.5 0.404145 33 : 0.4 0.34641 34 : 0.3 0.288675 35 : 0.2 0.23094 36 : 0.1 0.173205 37 : 0.5 0.519615 38 : 0.4 0.46188 39 : 0.3 0.404145 40 : 0.2 0.34641 41 : 0.5 0.635085 42 : 0.4 0.57735 43 : 0.3 0.519615 44 : 0.5 0.750555 45 : 0.4 0.69282 46 : 0.5 0.866025 Plot written to the file "polygon_grid_points_test01.png". Data written to the file "polygon_grid_points_test01.xy". POLYGON_GRID_POINTS_TEST02: POLYGON_GRID_POINTS returns grid points for a polygon of NV vertices, with N+1 points on a side For this test, the polygon is a convex quadrilateral with sides of varying length. Polygon vertices: Col: 1 2 Row 1 : 1 1 2 : 2 0 3 : 4 3 4 : 0 5 N = 7 Number of grid points will be NG = 113 1 0 0 7 1.7500 2.2500 2 1 0 6 1.6429 2.0714 3 1 1 5 1.6786 1.7500 4 1 2 4 1.7143 1.4286 5 1 3 3 1.7500 1.1071 6 1 4 2 1.7857 0.7857 7 1 5 1 1.8214 0.4643 8 1 6 0 1.8571 0.1429 9 2 0 5 1.5357 1.8929 10 2 1 4 1.5714 1.5714 11 2 2 3 1.6071 1.2500 12 2 3 2 1.6429 0.9286 13 2 4 1 1.6786 0.6071 14 2 5 0 1.7143 0.2857 15 3 0 4 1.4286 1.7143 16 3 1 3 1.4643 1.3929 17 3 2 2 1.5000 1.0714 18 3 3 1 1.5357 0.7500 19 3 4 0 1.5714 0.4286 20 4 0 3 1.3214 1.5357 21 4 1 2 1.3571 1.2143 22 4 2 1 1.3929 0.8929 23 4 3 0 1.4286 0.5714 24 5 0 2 1.2143 1.3571 25 5 1 1 1.2500 1.0357 26 5 2 0 1.2857 0.7143 27 6 0 1 1.1071 1.1786 28 6 1 0 1.1429 0.8571 29 7 0 0 1.0000 1.0000 30 1 0 6 1.7857 1.9286 31 1 1 5 2.1071 2.0357 32 1 2 4 2.4286 2.1429 33 1 3 3 2.7500 2.2500 34 1 4 2 3.0714 2.3571 35 1 5 1 3.3929 2.4643 36 1 6 0 3.7143 2.5714 37 2 0 5 1.8214 1.6071 38 2 1 4 2.1429 1.7143 39 2 2 3 2.4643 1.8214 40 2 3 2 2.7857 1.9286 41 2 4 1 3.1071 2.0357 42 2 5 0 3.4286 2.1429 43 3 0 4 1.8571 1.2857 44 3 1 3 2.1786 1.3929 45 3 2 2 2.5000 1.5000 46 3 3 1 2.8214 1.6071 47 3 4 0 3.1429 1.7143 48 4 0 3 1.8929 0.9643 49 4 1 2 2.2143 1.0714 50 4 2 1 2.5357 1.1786 51 4 3 0 2.8571 1.2857 52 5 0 2 1.9286 0.6429 53 5 1 1 2.2500 0.7500 54 5 2 0 2.5714 0.8571 55 6 0 1 1.9643 0.3214 56 6 1 0 2.2857 0.4286 57 7 0 0 2.0000 0.0000 58 1 0 6 2.0714 2.3571 59 1 1 5 1.8214 2.7500 60 1 2 4 1.5714 3.1429 61 1 3 3 1.3214 3.5357 62 1 4 2 1.0714 3.9286 63 1 5 1 0.8214 4.3214 64 1 6 0 0.5714 4.7143 65 2 0 5 2.3929 2.4643 66 2 1 4 2.1429 2.8571 67 2 2 3 1.8929 3.2500 68 2 3 2 1.6429 3.6429 69 2 4 1 1.3929 4.0357 70 2 5 0 1.1429 4.4286 71 3 0 4 2.7143 2.5714 72 3 1 3 2.4643 2.9643 73 3 2 2 2.2143 3.3571 74 3 3 1 1.9643 3.7500 75 3 4 0 1.7143 4.1429 76 4 0 3 3.0357 2.6786 77 4 1 2 2.7857 3.0714 78 4 2 1 2.5357 3.4643 79 4 3 0 2.2857 3.8571 80 5 0 2 3.3571 2.7857 81 5 1 1 3.1071 3.1786 82 5 2 0 2.8571 3.5714 83 6 0 1 3.6786 2.8929 84 6 1 0 3.4286 3.2857 85 7 0 0 4.0000 3.0000 86 1 0 6 1.5000 2.6429 87 1 1 5 1.3929 2.4643 88 1 2 4 1.2857 2.2857 89 1 3 3 1.1786 2.1071 90 1 4 2 1.0714 1.9286 91 1 5 1 0.9643 1.7500 92 1 6 0 0.8571 1.5714 93 2 0 5 1.2500 3.0357 94 2 1 4 1.1429 2.8571 95 2 2 3 1.0357 2.6786 96 2 3 2 0.9286 2.5000 97 2 4 1 0.8214 2.3214 98 2 5 0 0.7143 2.1429 99 3 0 4 1.0000 3.4286 100 3 1 3 0.8929 3.2500 101 3 2 2 0.7857 3.0714 102 3 3 1 0.6786 2.8929 103 3 4 0 0.5714 2.7143 104 4 0 3 0.7500 3.8214 105 4 1 2 0.6429 3.6429 106 4 2 1 0.5357 3.4643 107 4 3 0 0.4286 3.2857 108 5 0 2 0.5000 4.2143 109 5 1 1 0.3929 4.0357 110 5 2 0 0.2857 3.8571 111 6 0 1 0.2500 4.6071 112 6 1 0 0.1429 4.4286 113 7 0 0 0.0000 5.0000 The grid point array: Col: 1 2 Row 1 : 1.75 2.25 2 : 1.64286 2.07143 3 : 1.67857 1.75 4 : 1.71429 1.42857 5 : 1.75 1.10714 6 : 1.78571 0.785714 7 : 1.82143 0.464286 8 : 1.85714 0.142857 9 : 1.53571 1.89286 10 : 1.57143 1.57143 11 : 1.60714 1.25 12 : 1.64286 0.928571 13 : 1.67857 0.607143 14 : 1.71429 0.285714 15 : 1.42857 1.71429 16 : 1.46429 1.39286 17 : 1.5 1.07143 18 : 1.53571 0.75 19 : 1.57143 0.428571 20 : 1.32143 1.53571 21 : 1.35714 1.21429 22 : 1.39286 0.892857 23 : 1.42857 0.571429 24 : 1.21429 1.35714 25 : 1.25 1.03571 26 : 1.28571 0.714286 27 : 1.10714 1.17857 28 : 1.14286 0.857143 29 : 1 1 30 : 1.78571 1.92857 31 : 2.10714 2.03571 32 : 2.42857 2.14286 33 : 2.75 2.25 34 : 3.07143 2.35714 35 : 3.39286 2.46429 36 : 3.71429 2.57143 37 : 1.82143 1.60714 38 : 2.14286 1.71429 39 : 2.46429 1.82143 40 : 2.78571 1.92857 41 : 3.10714 2.03571 42 : 3.42857 2.14286 43 : 1.85714 1.28571 44 : 2.17857 1.39286 45 : 2.5 1.5 46 : 2.82143 1.60714 47 : 3.14286 1.71429 48 : 1.89286 0.964286 49 : 2.21429 1.07143 50 : 2.53571 1.17857 51 : 2.85714 1.28571 52 : 1.92857 0.642857 53 : 2.25 0.75 54 : 2.57143 0.857143 55 : 1.96429 0.321429 56 : 2.28571 0.428571 57 : 2 0 58 : 2.07143 2.35714 59 : 1.82143 2.75 60 : 1.57143 3.14286 61 : 1.32143 3.53571 62 : 1.07143 3.92857 63 : 0.821429 4.32143 64 : 0.571429 4.71429 65 : 2.39286 2.46429 66 : 2.14286 2.85714 67 : 1.89286 3.25 68 : 1.64286 3.64286 69 : 1.39286 4.03571 70 : 1.14286 4.42857 71 : 2.71429 2.57143 72 : 2.46429 2.96429 73 : 2.21429 3.35714 74 : 1.96429 3.75 75 : 1.71429 4.14286 76 : 3.03571 2.67857 77 : 2.78571 3.07143 78 : 2.53571 3.46429 79 : 2.28571 3.85714 80 : 3.35714 2.78571 81 : 3.10714 3.17857 82 : 2.85714 3.57143 83 : 3.67857 2.89286 84 : 3.42857 3.28571 85 : 4 3 86 : 1.5 2.64286 87 : 1.39286 2.46429 88 : 1.28571 2.28571 89 : 1.17857 2.10714 90 : 1.07143 1.92857 91 : 0.964286 1.75 92 : 0.857143 1.57143 93 : 1.25 3.03571 94 : 1.14286 2.85714 95 : 1.03571 2.67857 96 : 0.928571 2.5 97 : 0.821429 2.32143 98 : 0.714286 2.14286 99 : 1 3.42857 100 : 0.892857 3.25 101 : 0.785714 3.07143 102 : 0.678571 2.89286 103 : 0.571429 2.71429 104 : 0.75 3.82143 105 : 0.642857 3.64286 106 : 0.535714 3.46429 107 : 0.428571 3.28571 108 : 0.5 4.21429 109 : 0.392857 4.03571 110 : 0.285714 3.85714 111 : 0.25 4.60714 112 : 0.142857 4.42857 113 : 0 5 Plot written to the file "polygon_grid_points_test02.png". Data written to the file "polygon_grid_points_test02.xy". POLYGON_GRID_POINTS_TEST03: POLYGON_GRID_POINTS returns grid points for a polygon of NV vertices, with N+1 points on a side For this test, the polygon is nonconvex and six sided. Two degenerate triangles are created, and some grid points are generated several times. Polygon vertices: Col: 1 2 Row 1 : 0 0 2 : 2 0 3 : 2 1 4 : 1 1 5 : 1 2 6 : 0 2 N = 5 Number of grid points will be NG = 91 1 0 0 5 1.0000 1.0000 2 1 0 4 0.8000 0.8000 3 1 1 3 1.0000 0.6000 4 1 2 2 1.2000 0.4000 5 1 3 1 1.4000 0.2000 6 1 4 0 1.6000 0.0000 7 2 0 3 0.6000 0.6000 8 2 1 2 0.8000 0.4000 9 2 2 1 1.0000 0.2000 10 2 3 0 1.2000 0.0000 11 3 0 2 0.4000 0.4000 12 3 1 1 0.6000 0.2000 13 3 2 0 0.8000 0.0000 14 4 0 1 0.2000 0.2000 15 4 1 0 0.4000 0.0000 16 5 0 0 0.0000 0.0000 17 1 0 4 1.2000 0.8000 18 1 1 3 1.4000 0.8000 19 1 2 2 1.6000 0.8000 20 1 3 1 1.8000 0.8000 21 1 4 0 2.0000 0.8000 22 2 0 3 1.4000 0.6000 23 2 1 2 1.6000 0.6000 24 2 2 1 1.8000 0.6000 25 2 3 0 2.0000 0.6000 26 3 0 2 1.6000 0.4000 27 3 1 1 1.8000 0.4000 28 3 2 0 2.0000 0.4000 29 4 0 1 1.8000 0.2000 30 4 1 0 2.0000 0.2000 31 5 0 0 2.0000 0.0000 32 1 0 4 1.2000 1.0000 33 1 1 3 1.2000 1.0000 34 1 2 2 1.2000 1.0000 35 1 3 1 1.2000 1.0000 36 1 4 0 1.2000 1.0000 37 2 0 3 1.4000 1.0000 38 2 1 2 1.4000 1.0000 39 2 2 1 1.4000 1.0000 40 2 3 0 1.4000 1.0000 41 3 0 2 1.6000 1.0000 42 3 1 1 1.6000 1.0000 43 3 2 0 1.6000 1.0000 44 4 0 1 1.8000 1.0000 45 4 1 0 1.8000 1.0000 46 5 0 0 2.0000 1.0000 47 1 0 4 1.0000 1.0000 48 1 1 3 1.0000 1.2000 49 1 2 2 1.0000 1.4000 50 1 3 1 1.0000 1.6000 51 1 4 0 1.0000 1.8000 52 2 0 3 1.0000 1.0000 53 2 1 2 1.0000 1.2000 54 2 2 1 1.0000 1.4000 55 2 3 0 1.0000 1.6000 56 3 0 2 1.0000 1.0000 57 3 1 1 1.0000 1.2000 58 3 2 0 1.0000 1.4000 59 4 0 1 1.0000 1.0000 60 4 1 0 1.0000 1.2000 61 5 0 0 1.0000 1.0000 62 1 0 4 1.0000 1.2000 63 1 1 3 0.8000 1.4000 64 1 2 2 0.6000 1.6000 65 1 3 1 0.4000 1.8000 66 1 4 0 0.2000 2.0000 67 2 0 3 1.0000 1.4000 68 2 1 2 0.8000 1.6000 69 2 2 1 0.6000 1.8000 70 2 3 0 0.4000 2.0000 71 3 0 2 1.0000 1.6000 72 3 1 1 0.8000 1.8000 73 3 2 0 0.6000 2.0000 74 4 0 1 1.0000 1.8000 75 4 1 0 0.8000 2.0000 76 5 0 0 1.0000 2.0000 77 1 0 4 0.8000 1.2000 78 1 1 3 0.6000 1.0000 79 1 2 2 0.4000 0.8000 80 1 3 1 0.2000 0.6000 81 1 4 0 0.0000 0.4000 82 2 0 3 0.6000 1.4000 83 2 1 2 0.4000 1.2000 84 2 2 1 0.2000 1.0000 85 2 3 0 0.0000 0.8000 86 3 0 2 0.4000 1.6000 87 3 1 1 0.2000 1.4000 88 3 2 0 0.0000 1.2000 89 4 0 1 0.2000 1.8000 90 4 1 0 0.0000 1.6000 91 5 0 0 0.0000 2.0000 The grid point array: Col: 1 2 Row 1 : 1 1 2 : 0.8 0.8 3 : 1 0.6 4 : 1.2 0.4 5 : 1.4 0.2 6 : 1.6 0 7 : 0.6 0.6 8 : 0.8 0.4 9 : 1 0.2 10 : 1.2 0 11 : 0.4 0.4 12 : 0.6 0.2 13 : 0.8 0 14 : 0.2 0.2 15 : 0.4 0 16 : 0 0 17 : 1.2 0.8 18 : 1.4 0.8 19 : 1.6 0.8 20 : 1.8 0.8 21 : 2 0.8 22 : 1.4 0.6 23 : 1.6 0.6 24 : 1.8 0.6 25 : 2 0.6 26 : 1.6 0.4 27 : 1.8 0.4 28 : 2 0.4 29 : 1.8 0.2 30 : 2 0.2 31 : 2 0 32 : 1.2 1 33 : 1.2 1 34 : 1.2 1 35 : 1.2 1 36 : 1.2 1 37 : 1.4 1 38 : 1.4 1 39 : 1.4 1 40 : 1.4 1 41 : 1.6 1 42 : 1.6 1 43 : 1.6 1 44 : 1.8 1 45 : 1.8 1 46 : 2 1 47 : 1 1 48 : 1 1.2 49 : 1 1.4 50 : 1 1.6 51 : 1 1.8 52 : 1 1 53 : 1 1.2 54 : 1 1.4 55 : 1 1.6 56 : 1 1 57 : 1 1.2 58 : 1 1.4 59 : 1 1 60 : 1 1.2 61 : 1 1 62 : 1 1.2 63 : 0.8 1.4 64 : 0.6 1.6 65 : 0.4 1.8 66 : 0.2 2 67 : 1 1.4 68 : 0.8 1.6 69 : 0.6 1.8 70 : 0.4 2 71 : 1 1.6 72 : 0.8 1.8 73 : 0.6 2 74 : 1 1.8 75 : 0.8 2 76 : 1 2 77 : 0.8 1.2 78 : 0.6 1 79 : 0.4 0.8 80 : 0.2 0.6 81 : 0 0.4 82 : 0.6 1.4 83 : 0.4 1.2 84 : 0.2 1 85 : 0 0.8 86 : 0.4 1.6 87 : 0.2 1.4 88 : 0 1.2 89 : 0.2 1.8 90 : 0 1.6 91 : 0 2 Plot written to the file "polygon_grid_points_test03.png". Data written to the file "polygon_grid_points_test03.xy". polygon_grid_test(): Normal end of execution. 08-Jan-2022 08:56:51