03 May 2022 06:52:18 AM TRIANGLE_TEST C version Test the TRIANGLE library. TRIANGLE_ANGLES_TEST TRIANGLE_ANGLES computes the angles in a triangle. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 Radians Degrees 0.785398 45 1.5708 90 0.785398 45 TRIANGLE_AREA_TEST TRIANGLE_AREA computes the area of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 Triangle area is 0.5 TRIANGLE_CENTROID_TEST TRIANGLE_CENTROID computes the centroid of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0 1 Centroid: 0: 0.333333 1: 0.333333 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 0.866025 Centroid: 0: 0.5 1: 0.288675 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 10 Centroid: 0: 0.5 1: 3.33333 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 10 2 Centroid: 0: 3.66667 1: 0.666667 TRIANGLE_CIRCUMCIRCLE_TEST TRIANGLE_CIRCUMCIRCLE computes the circumcircle of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0 1 Circumcenter 0: 0.5 1: 0.5 Circumradius: 0.707107 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 0.866025 Circumcenter 0: 0.5 1: 0.288675 Circumradius: 0.57735 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 10 Circumcenter 0: 0.5 1: 4.9875 Circumradius: 5.0125 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 10 2 Circumcenter 0: 0.5 1: 23.5 Circumradius: 23.5053 TRIANGLE_CONTAINS_POINT_TEST TRIANGLE_CONTAINS_POINT reports if a point is inside a triangle. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 X Y Inside 0.250 0.250 11 0.750 0.250 11 1.000 1.000 01 11.000 0.500 01 0.000 1.000 11 0.500 -10.000 01 0.600 0.600 01 Repeat the test, but reverse the triangle vertex ordering. Triangle vertices (reversed): Row: 0 1 Col 0: 0 1 1: 0 1 2: 0 1 X Y Inside 0.250 0.250 11 0.750 0.250 11 1.000 1.000 11 11.000 0.500 11 0.000 1.000 11 0.500 -10.000 11 0.600 0.600 11 TRIANGLE_DIAMETER_TEST TRIANGLE_DIAMETER computes the diameter of the SMALLEST circle around the triangle. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 Diameter = 2.56184 Triangle vertices: Row: 0 1 Col 0: 4 2 1: 5 4 2: 6 6 Diameter = 2.11474 Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: 4 2 Diameter = 2.05977 TRIANGLE_EDGE_LENGTH_TEST TRIANGLE_EDGE_LENGTH computes the edge lengths of a triangle. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 EDGE_LENGTHS: 0: 4.24264 1: 4.24264 2: 6 Triangle vertices: Row: 0 1 Col 0: 4 2 1: 5 4 2: 6 6 EDGE_LENGTHS: 0: 2.23607 1: 2.23607 2: 4.47214 Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: 4 2 EDGE_LENGTHS: 0: 4.24264 1: 4.24264 2: 0 TRIANGLE_INCIRCLE_TEST TRIANGLE_INCIRCLE_2D computes the incircle of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 Incenter 0: 0.292893 1: 6 Incircle radius is 0.292893 TRIANGLE_ORIENTATION_TEST TRIANGLE_ORIENTATION determines the orientation of a triangle. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 The points are counterclockwise. Triangle vertices: Row: 0 1 Col 0: 1 5 1: 4 2 2: 1 -1 The points are clockwise. Triangle vertices: Row: 0 1 Col 0: 1 5 1: 2 7 2: 3 9 The points are colinear. Triangle vertices: Row: 0 1 Col 0: 1 5 1: 4 2 2: 1 5 The points are not distinct. TRIANGLE_ORTHOCENTER_TEST TRIANGLE_ORTHOCENTER_2D computes the orthocenter of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0 1 Orthocenter 0: -0 1: 0 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 0.866025 Orthocenter 0: 0.5 1: 0.288675 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 10 Orthocenter 0: 0.5 1: 0.025 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 10 2 Orthocenter 0: 10 1: -45 TRIANGLE_POINT_DIST_TEST TRIANGLE_POINT_DIST computes the distance from a point to a triangle. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 P DIST 0.250 0.250 0.250 0.750 0.250 0.000 1.000 1.000 0.707 11.000 0.500 10.012 0.000 1.000 0.000 0.500 -10.000 10.000 0.600 0.600 0.141 TRIANGLE_POINT_NEAR_TEST TRIANGLE_POINT_NEAR computes the nearest point on a triangle to a given point. Triangle vertices: Row: 0 1 Col 0: 0 1 1: 0 0 2: 1 0 P PN 0.250 0.250 0.000 0.250 0.750 0.250 0.750 0.250 1.000 1.000 0.500 0.500 11.000 0.500 1.000 0.000 0.000 1.000 0.000 1.000 0.500 -10.000 0.500 0.000 0.600 0.600 0.500 0.500 TRIANGLE_QUALITY_TEST TRIANGLE_QUALITY computes the quality of a triangle. Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0 1 Quality = 0.828427 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 0.866025 Quality = 1 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 0.5 10 Quality = 0.189775 Triangle vertices: Row: 0 1 Col 0: 0 0 1: 1 0 2: 10 2 Quality = 0.00833469 TRIANGLE_REFERENCE_SAMPLE_TEST TRIANGLE_REFERENCE_SAMPLE samples the reference triangle. Sample points (X,Y) and (XSI1,XSI2,XSI3) coordinates: 0.0204 0.4469 0.5326 0.0204 0.4469 0.3992 0.5116 0.0892 0.3992 0.5116 0.6018 0.0426 0.3556 0.6018 0.0426 0.4517 0.0558 0.4925 0.4517 0.0558 0.0766 0.1327 0.7906 0.0766 0.1327 0.1368 0.1117 0.7516 0.1368 0.1117 0.1554 0.4781 0.3665 0.1554 0.4781 0.8913 0.0016 0.1071 0.8913 0.0016 0.6151 0.3323 0.0526 0.6151 0.3323 0.3033 0.0042 0.6925 0.3033 0.0042 TRIANGLE_SAMPLE_TEST TRIANGLE_SAMPLE samples points from a triangle. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 Sample points (X,Y) and (XSI1,XSI2,XSI3) coordinates: 1.2571 2.0612 0.5326 0.0204 0.4469 -0.2671 3.1976 0.0892 0.3992 0.5116 1.9388 3.8055 0.3556 0.6018 0.0426 2.3100 3.3551 0.4925 0.4517 0.0558 2.9738 2.2299 0.7906 0.0766 0.1327 2.9196 2.4103 0.7516 0.1368 0.1117 0.6653 2.4662 0.3665 0.1554 0.4781 1.3163 4.6738 0.1071 0.8913 0.0016 0.1610 3.8452 0.0526 0.6151 0.3323 3.0650 2.9099 0.6925 0.3033 0.0042 TRIANGLE_XSI_TO_XY_TEST TRIANGLE_XSI_TO_XY converts XSI to XY coordinates. We verify that (X,Y) -> (XSI1,XSI2,XSI3) -> (X,Y) works properly. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 Sample points: 1.0000 3.0000 0.3333 0.3333 0.3333 1.0000 3.0000 3.0000 0.0000 1.1667 -0.6667 0.5000 3.0000 0.0000 1.2571 2.0612 0.5326 0.0204 0.4469 1.2571 2.0612 -0.2671 3.1976 0.0892 0.3992 0.5116 -0.2671 3.1976 1.9388 3.8055 0.3556 0.6018 0.0426 1.9388 3.8055 2.3100 3.3551 0.4925 0.4517 0.0558 2.3100 3.3551 2.9738 2.2299 0.7906 0.0766 0.1327 2.9738 2.2299 2.9196 2.4103 0.7516 0.1368 0.1117 2.9196 2.4103 0.6653 2.4662 0.3665 0.1554 0.4781 0.6653 2.4662 1.3163 4.6738 0.1071 0.8913 0.0016 1.3163 4.6738 TRIANGLE_XY_TO_XSI_TEST TRIANGLE_XY_TO_XSI converts XY to XSI coordinates. We verify that (X,Y) -> (XSI1,XSI2,XSI3) -> (X,Y) works properly. Triangle vertices: Row: 0 1 Col 0: 4 2 1: 1 5 2: -2 2 Sample points: 1.0000 3.0000 0.3333 0.3333 0.3333 1.0000 3.0000 3.0000 0.0000 1.1667 -0.6667 0.5000 3.0000 0.0000 1.2571 2.0612 0.5326 0.0204 0.4469 1.2571 2.0612 -0.2671 3.1976 0.0892 0.3992 0.5116 -0.2671 3.1976 1.9388 3.8055 0.3556 0.6018 0.0426 1.9388 3.8055 2.3100 3.3551 0.4925 0.4517 0.0558 2.3100 3.3551 2.9738 2.2299 0.7906 0.0766 0.1327 2.9738 2.2299 2.9196 2.4103 0.7516 0.1368 0.1117 2.9196 2.4103 0.6653 2.4662 0.3665 0.1554 0.4781 0.6653 2.4662 1.3163 4.6738 0.1071 0.8913 0.0016 1.3163 4.6738 TRIANGLE_TEST Normal end of execution. 03 May 2022 06:52:18 AM