05 August 2018 02:27:27 PM GEOMETRY_TEST C version Test the GEOMETRY library. ANGLE_BOX_2D_TEST ANGLE_BOX_2D Compute P4 and P5, normal to line through P1 and P2, and line through P2 and P3, and DIST units from P2. DIST 1.000000 P1: 0.000000 0.000000 P2: 3.000000 0.000000 P3: 4.000000 2.000000 P4: 2.381966 1.000000 P5: 3.618034 -1.000000 DIST 1.000000 P1: 0.000000 0.000000 P2: 3.000000 0.000000 P3: 2.000000 -2.000000 P4: 3.618034 -1.000000 P5: 2.381966 1.000000 DIST 1.000000 P1: 3.000000 0.000000 P2: 3.000000 0.000000 P3: 2.000000 -2.000000 P4: 2.105573 0.447214 P5: 3.894427 -0.447214 ANGLE_CONTAINS_RAY_2D_TEST ANGLE_CONTAINS_RAY_2D sees if a ray lies within an angle. Vertex A 0: 1.000000 1: 0.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: 1.000000 1: 1.000000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 0 6.12323e-17 1 0 -0.5 0.866025 0 -0.866025 0.5 0 -1 1.22465e-16 0 -0.866025 -0.5 0 -0.5 -0.866025 0 -1.83697e-16 -1 0 0.5 -0.866025 0 0.866025 -0.5 0 1 -2.44929e-16 0 Vertex A 0: 1.000000 1: 0.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: 0.000000 1: 1.000000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 1 6.12323e-17 1 1 -0.5 0.866025 0 -0.866025 0.5 0 -1 1.22465e-16 0 -0.866025 -0.5 0 -0.5 -0.866025 0 -1.83697e-16 -1 0 0.5 -0.866025 0 0.866025 -0.5 0 1 -2.44929e-16 0 Vertex A 0: 1.000000 1: -1.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: 0.000000 1: 1.000000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 1 6.12323e-17 1 1 -0.5 0.866025 0 -0.866025 0.5 0 -1 1.22465e-16 0 -0.866025 -0.5 0 -0.5 -0.866025 0 -1.83697e-16 -1 0 0.5 -0.866025 0 0.866025 -0.5 1 1 -2.44929e-16 1 Vertex A 0: 1.000000 1: 0.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: -1.000000 1: 0.000000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 1 6.12323e-17 1 1 -0.5 0.866025 1 -0.866025 0.5 1 -1 1.22465e-16 1 -0.866025 -0.5 0 -0.5 -0.866025 0 -1.83697e-16 -1 0 0.5 -0.866025 0 0.866025 -0.5 0 1 -2.44929e-16 0 Vertex A 0: 1.000000 1: 0.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: 0.000000 1: -1.000000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 1 6.12323e-17 1 1 -0.5 0.866025 1 -0.866025 0.5 1 -1 1.22465e-16 1 -0.866025 -0.5 1 -0.5 -0.866025 1 -1.83697e-16 -1 1 0.5 -0.866025 0 0.866025 -0.5 0 1 -2.44929e-16 0 Vertex A 0: 1.000000 1: 0.000000 Vertex B 0: 0.000000 1: 0.000000 Vertex C 0: 1.000000 1: -0.010000 X Y Inside? 1 0 1 0.866025 0.5 1 0.5 0.866025 1 6.12323e-17 1 1 -0.5 0.866025 1 -0.866025 0.5 1 -1 1.22465e-16 1 -0.866025 -0.5 1 -0.5 -0.866025 1 -1.83697e-16 -1 1 0.5 -0.866025 1 0.866025 -0.5 1 1 -2.44929e-16 0 ANGLE_DEG_2D_TEST ANGLE_DEG_2D computes an angle. X Y Theta ATAN2(y, x), ANGLE_DEG_2D 1.000 0.000 0.000 0.000 0.000 0.866 0.500 30.000 30.000 30.000 0.500 0.866 60.000 60.000 60.000 0.000 1.000 90.000 90.000 90.000 -0.500 0.866 120.000 120.000 120.000 -0.866 0.500 150.000 150.000 150.000 -1.000 0.000 180.000 180.000 180.000 -0.866 -0.500 210.000 -150.000 210.000 -0.500 -0.866 240.000 -120.000 240.000 -0.000 -1.000 270.000 -90.000 270.000 0.500 -0.866 300.000 -60.000 300.000 0.866 -0.500 330.000 -30.000 330.000 1.000 -0.000 360.000 -0.000 360.000 ANGLE_RAD_ND_TEST ANGLE_RAD_ND computes an angle. X Y Theta ATAN2(y, x), ANGLE_RAD_ND 1.000 0.000 0.000 0.000 0.000 0.866 0.500 30.000 30.000 0.524 0.500 0.866 60.000 60.000 1.047 0.000 1.000 90.000 90.000 1.571 -0.500 0.866 120.000 120.000 2.094 -0.866 0.500 150.000 150.000 2.618 -1.000 0.000 180.000 180.000 3.142 -0.866 -0.500 210.000 -150.000 2.618 -0.500 -0.866 240.000 -120.000 2.094 -0.000 -1.000 270.000 -90.000 1.571 0.500 -0.866 300.000 -60.000 1.047 0.866 -0.500 330.000 -30.000 0.524 1.000 -0.000 360.000 -0.000 0.000 BALL01_VOLUME_TEST BALL01_VOLUME returns the volume of the unit ball. Volume = 4.18879 CIRCLE_DIA2IMP_2D_TEST CIRCLE_DIA2IMP_2D converts a diameter to an implicit circle in 2D. P1: 0: -0.080734 1: 6.546487 P2: 0: 4.080734 1: -2.546487 The implicit circle: Radius = 5.000000 Center = ( 2.000000, 2.000000 ) CIRCLE_IMP_POINT_DIST_2D_TEST CIRCLE_IMP_POINT_DIST_2D finds the distance from a point to a circle. The circle: Radius = 5.000000 Center = ( 0.000000, 0.000000 ) X Y D -5.631634 9.126352 9.487128 6.590185 1.233909 4.466885 -1.693858 -8.677625 7.291799 -4.848444 -7.800864 7.704602 -9.123420 2.679314 8.087986 -8.765455 -1.009221 7.269920 -1.973874 5.093470 2.199912 5.945739 -9.963233 10.469853 7.950081 -2.984953 6.863945 -8.109105 -9.727662 11.635506 CIRCLE_LUNE_ANGLE_BY_HEIGHT_2D_TEST CIRCLE_LUNE_ANGLE_BY_HEIGHT_2D computes the angle of a circular lune based on the 'height' of the circular triangle. R H Angle 2.000000 -2.000000 6.283185 2.000000 -1.666667 5.111814 2.000000 -1.333333 4.601048 2.000000 -1.000000 4.188790 2.000000 -0.666667 3.821266 2.000000 -0.333333 3.476489 2.000000 0.000000 3.141593 2.000000 0.333333 2.806696 2.000000 0.666667 2.461919 2.000000 1.000000 2.094395 2.000000 1.333333 1.682137 2.000000 1.666667 1.171371 2.000000 2.000000 0.000000 CIRCLE_LUNE_AREA_BY_ANGLE_2D_TEST CIRCLE_LUNE_AREA_BY_ANGLE_2D computes the area of a circular lune, defined by joining the endpoints of a circular arc. R Theta1 Theta2 Area 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.523599 0.011799 1.000000 0.000000 1.047198 0.090586 1.000000 0.000000 1.570796 0.285398 1.000000 0.000000 2.094395 0.614185 1.000000 0.000000 2.617994 1.058997 1.000000 0.000000 3.141593 1.570796 1.000000 0.000000 3.665191 2.082596 1.000000 0.000000 4.188790 2.527408 1.000000 0.000000 4.712389 2.856194 1.000000 0.000000 5.235988 3.051007 1.000000 0.000000 5.759587 3.129793 1.000000 0.000000 6.283185 3.141593 CIRCLE_LUNE_AREA_BY_HEIGHT_2D_TEST CIRCLE_LUNE_AREA_BY_HEIGHT_2D computes the area of a circular lune, defined by joining the endpoints of a circular arc. R Height Area 2.000000 -2.000000 12.566371 2.000000 -1.666667 12.066198 2.000000 -1.333333 11.189712 2.000000 -1.000000 10.109631 2.000000 -0.666667 8.899612 2.000000 -0.333333 7.610320 2.000000 0.000000 6.283185 2.000000 0.333333 4.956051 2.000000 0.666667 3.666759 2.000000 1.000000 2.456739 2.000000 1.333333 1.376659 2.000000 1.666667 0.500173 2.000000 2.000000 0.000000 CIRCLE_LUNE_HEIGHT_BY_ANGLE_2D_TEST CIRCLE_LUNE_HEIGHT_BY_ANGLE_2D computes the height of the triangle of a circular lune, given the subtended angle. R Angle Height 2.000000 0.000000 2.000000 2.000000 0.523599 1.931852 2.000000 1.047198 1.732051 2.000000 1.570796 1.414214 2.000000 2.094395 1.000000 2.000000 2.617994 0.517638 2.000000 3.141593 0.000000 2.000000 3.665191 -0.517638 2.000000 4.188790 -1.000000 2.000000 4.712389 -1.414214 2.000000 5.235988 -1.732051 2.000000 5.759587 -1.931852 2.000000 6.283185 -2.000000 CIRCLE_SECTOR_AREA_2D_TEST CIRCLE_SECTOR_AREA_2D computes the area of a circular sector, defined by joining the endpoints of a circular arc to the center. R Theta1 Theta2 Area 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.523599 0.261799 1.000000 0.000000 1.047198 0.523599 1.000000 0.000000 1.570796 0.785398 1.000000 0.000000 2.094395 1.047198 1.000000 0.000000 2.617994 1.308997 1.000000 0.000000 3.141593 1.570796 1.000000 0.000000 3.665191 1.832596 1.000000 0.000000 4.188790 2.094395 1.000000 0.000000 4.712389 2.356194 1.000000 0.000000 5.235988 2.617994 1.000000 0.000000 5.759587 2.879793 1.000000 0.000000 6.283185 3.141593 CIRCLE_TRIANGLE_AREA_2D_TEST CIRCLE_TRIANGLE_AREA_2D computes the signed area of a triangle, defined by joining the endpoints of a circular arc and the center. R Theta1 Theta2 Area 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.523599 0.250000 1.000000 0.000000 1.047198 0.433013 1.000000 0.000000 1.570796 0.500000 1.000000 0.000000 2.094395 0.433013 1.000000 0.000000 2.617994 0.250000 1.000000 0.000000 3.141593 0.000000 1.000000 0.000000 3.665191 -0.250000 1.000000 0.000000 4.188790 -0.433013 1.000000 0.000000 4.712389 -0.500000 1.000000 0.000000 5.235988 -0.433013 1.000000 0.000000 5.759587 -0.250000 1.000000 0.000000 6.283185 -0.000000 CIRCLES_INTERSECT_AREA_2D_TEST CIRCLES_INTERSECT_AREA_2D determines the area of the intersection of two circes of radius R1 and R2, with a distance D between the centers. R1 R2 D Area 1.000000 0.500000 1.500000 0.000000 1.000000 0.500000 1.000000 0.350767 1.000000 0.500000 0.500000 0.785398 1.000000 1.000000 1.500000 0.453312 1.000000 1.000000 1.000000 1.228370 1.000000 1.000000 0.000000 3.141593 CIRCLES_INTERSECT_POINTS_2D_TEST CIRCLES_IMP_INT_2D determines the intersections of two circles in 2D. The first circle: Radius = 5.000000 Center = ( 0.000000, 0.000000 ) The second circle: Radius = 0.500000 Center = ( 5.000000, 5.000000 ) The circles do not intersect. The second circle: Radius = 5.000000 Center = ( 7.071068, 7.071068 ) The circles intersect at two points: P 3.535329 3.535739 3.535739 3.535329 The second circle: Radius = 3.000000 Center = ( 4.000000, 0.000000 ) The circles intersect at two points: P 4.000000 3.000000 4.000000 -3.000000 The second circle: Radius = 3.000000 Center = ( 6.000000, 0.000000 ) The circles intersect at two points: P 4.333333 2.494438 4.333333 -2.494438 The second circle: Radius = 5.000000 Center = ( 0.000000, 0.000000 ) The circles coincide (infinite intersection). CUBE01_VOLUME_TEST CUBE01_VOLUME returns the volume of the unit cube. Volume = 1 ELLIPSE_AREA1_TEST C version ELLIPSE_AREA1 computes the area of an ellipse. R = 10 Matrix A in ellipse definition x*A*x=r^2 Col: 1 2 Row 1: 5.000000 1.000000 2: 1.000000 2.000000 Area = 104.72 ELLIPSE_AREA1_TEST Normal end of execution. ELLIPSE_AREA2_TEST C version ELLIPSE_AREA2 computes the area of an ellipse. Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10 Area = 104.72 ELLIPSE_AREA2_TEST Normal end of execution. ELLIPSE_AREA3_TEST C version ELLIPSE_AREA3 computes the area of an ellipse. Ellipse: (x/10)^2 + (y/3.33333)^2 = 1 Area = 104.72 ELLIPSE_AREA3_TEST Normal end of execution. LINE_PAR_POINT_DIST_2D_TEST LINE_PAR_POINT_DIST_2D finds the distance between a parametric line (X0,Y0,F,G) and a point P in 2D. Parametric line: X(t) = 1 + 1 * t Y(t) = 3 + -1 * t The point P: 0: 0.000000 1: 0.000000 Distance = 2.82843 The point P: 0: 5.000000 1: -1.000000 Distance = 0 The point P: 0: 5.000000 1: 3.000000 Distance = 2.82843 LINE_PAR_POINT_NEAR_2D_TEST LINE_PAR_POINT_NEAR_2D finds the point on a parametric line (X0,Y0,F,G) nearest a point P in 2D. Parametric line: X(t) = 1 + 1 * t Y(t) = 3 + -1 * t The point P: 0: 0.000000 1: 0.000000 Nearest point PN: 0: 2.000000 1: 2.000000 Distance = 2.82843 The point P: 0: 5.000000 1: -1.000000 Nearest point PN: 0: 5.000000 1: -1.000000 Distance = 0 The point P: 0: 5.000000 1: 3.000000 Nearest point PN: 0: 3.000000 1: 1.000000 Distance = 2.82843 LINE_PAR_POINT_DIST_3D_TEST LINE_PAR_POINT_DIST_3D finds the distance from a parametric line to a point in 3D. Parametric line: X(t) = 1 + 3 * t Y(t) = 3 + -3 * t Z(t) = 2 + -1 * t The point P: 0: 0.000000 1: 0.000000 2: 2.000000 Distance = 2.84697 The point P: 0: 5.000000 1: -1.000000 2: 1.000000 Distance = 0.324443 The point P: 0: 5.000000 1: 3.000000 2: 3.000000 Distance = 3.26061 LINE_PAR_POINT_NEAR_3D_TEST LINE_PAR_POINT_NEAR_3D finds the nearest point on a parametric line to a point in 3D. Parametric line: X(t) = 1 + 3 * t Y(t) = 3 + -3 * t Z(t) = 2 + -1 * t The point P: 0: 0.000000 1: 0.000000 2: 2.000000 Nearest point PN: 0: 1.947368 1: 2.052632 2: 1.684211 Distance = 2.84697 The point P: 0: 5.000000 1: -1.000000 2: 1.000000 Nearest point PN: 0: 4.947368 1: -0.947368 2: 0.684211 Distance = 0.324443 The point P: 0: 5.000000 1: 3.000000 2: 3.000000 Nearest point PN: 0: 2.736842 1: 1.263158 2: 1.421053 Distance = 3.26061 PARALLELOGRAM_AREA_2D_TEST PARALLELOGRAM_AREA_2D finds the area of a parallelogram in 2D. Vertices: Row: 1 2 Col 1: 2.000000 7.000000 2: 5.000000 7.000000 3: 6.000000 9.000000 4: 3.000000 9.000000 AREA = 6.000000 PARALLELOGRAM_AREA_3D_TEST PARALLELOGRAM_AREA_3D finds the area of a parallelogram in 3D. Vertices: Row: 1 2 3 Col 1: 1.000000 2.000000 3.000000 2: 2.414214 3.414214 3.000000 3: 1.707107 2.707107 4.000000 4: 0.292893 0.292893 4.000000 AREA = 2.000000 PLANE_NORMAL_QR_TO_XYZ_TEST PLANE_NORMAL_QR_TO_XYZ converts QR to XYZ coordinates for a normal plane, with point PP and NORMAL vector, and in-plane basis vectors PQ and PR, Maximum difference was 0.000000 PLANE_NORMAL_XYZ_TO_QR_TEST PLANE_NORMAL_XYZ_TO_QR converts XYZ to QR coordinates for a normal plane, with point PP and NORMAL vector, and in-plane basis vectors PQ and PR, Maximum difference was 0.000000 PLANE_NORMAL_TETRAHEDRON_INTERSECT_TEST PLANE_NORMAL_TETRAHEDRON_INTERSECT determines the intersection of a plane and tetrahedron. Plane normal vector number 1 0.000000 0.000000 1.000000 Point on plane: 0.000000 0.000000 0.000000 Number of intersection points = 3 0 0.000000 0.000000 0.000000 1 1.000000 0.000000 0.000000 2 0.000000 1.000000 0.000000 Point on plane: 0.000000 0.000000 0.200000 Number of intersection points = 3 0 0.000000 0.000000 0.200000 1 0.800000 0.000000 0.200000 2 0.000000 0.800000 0.200000 Point on plane: 0.000000 0.000000 0.400000 Number of intersection points = 3 0 0.000000 0.000000 0.400000 1 0.600000 0.000000 0.400000 2 0.000000 0.600000 0.400000 Point on plane: 0.000000 0.000000 0.600000 Number of intersection points = 3 0 0.000000 0.000000 0.600000 1 0.400000 0.000000 0.600000 2 0.000000 0.400000 0.600000 Point on plane: 0.000000 0.000000 0.800000 Number of intersection points = 3 0 0.000000 0.000000 0.800000 1 0.200000 0.000000 0.800000 2 0.000000 0.200000 0.800000 Point on plane: 0.000000 0.000000 1.000000 Number of intersection points = 1 0 0.000000 0.000000 1.000000 Point on plane: 0.000000 0.000000 1.200000 Number of intersection points = 0 Plane normal vector number 2 0.707107 0.707107 0.000000 Point on plane: 0.000000 0.000000 0.000000 Number of intersection points = 2 0 0.000000 0.000000 0.000000 1 0.000000 0.000000 1.000000 Point on plane: 0.141421 0.141421 0.000000 Number of intersection points = 4 0 0.282843 0.000000 0.000000 1 0.000000 0.282843 0.000000 2 0.282843 0.000000 0.717157 3 0.000000 0.000000 0.000000 Point on plane: 0.282843 0.282843 0.000000 Number of intersection points = 4 0 0.394394 0.171291 0.434315 1 0.000000 0.565685 0.434315 2 0.565685 0.000000 0.434315 3 0.000000 0.282843 0.717157 Point on plane: 0.424264 0.424264 0.000000 Number of intersection points = 4 0 0.651239 0.197289 0.151472 1 0.000000 0.848528 0.151472 2 0.848528 0.000000 0.151472 3 0.000000 0.565685 0.434315 Point on plane: 0.565685 0.565685 0.000000 Number of intersection points = 0 Point on plane: 0.707107 0.707107 0.000000 Number of intersection points = 0 Point on plane: 0.848528 0.848528 0.000000 Number of intersection points = 0 POLYGON_CONTAINS_POINT_2D_TEST POLYGON_CONTAINS_POINT_2D determines if a point is in a polygon. The polygon vertices: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.000000 0.000000 3: 2.000000 1.000000 4: 1.000000 2.000000 5: 0.000000 2.000000 P Inside 1 1 1 3 4 0 0 2 0 0.5 -0.25 0 POLYGON_CONTAINS_POINT_2D_2_TEST POLYGON_CONTAINS_POINT_2D determines if a point is in a polygon. The polygon vertices: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.000000 0.000000 3: 2.000000 1.000000 4: 1.000000 2.000000 5: 0.000000 2.000000 P Inside 1 1 1 3 4 0 0 2 1 0.5 -0.25 0 POLYGON_CONTAINS_POINT_2D_3_TEST POLYGON_CONTAINS_POINT_2D_3 determines if a point is in a polygon. The polygon vertices: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.000000 0.000000 3: 2.000000 1.000000 4: 1.000000 2.000000 5: 0.000000 2.000000 P Inside 1 1 1 3 4 0 0 2 1 0.5 -0.25 0 QUAD_AREA_2D_TEST QUAD_AREA_2D finds the area of a quadrilateral; The vertices: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.000000 0.000000 3: 1.000000 1.000000 4: 0.000000 1.000000 QUAD_AREA_2D area is 1.000000 QUAD_AREA2_2D_TEST QUAD_AREA2_2D finds the area of a quadrilateral. The vertices: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.000000 0.000000 3: 1.000000 1.000000 4: 0.000000 1.000000 QUAD_AREA2_2D area is 1.000000 QUAD_AREA_3D_TEST For a quadrilateral in 3D: QUAD_AREA_3D finds the area. The vertices: Row: 1 2 3 Col 1: 2.000000 2.000000 0.000000 2: 0.000000 0.000000 0.000000 3: 1.000000 1.000000 1.000000 4: 3.000000 3.000000 1.000000 QUAD_AREA_3D area is 2.828427 Sum of TRIANGLE_AREA_3D: 2.828427 SPHERE_EXP2IMP_3D_TEST SPHERE_EXP2IMP_3D: explicit sphere => implicit form; Initial form of explicit sphere: P1: 4.000000 2.000000 3.000000 P2: 1.000000 5.000000 3.000000 P3: 1.000000 2.000000 6.000000 P4: -2.000000 2.000000 3.000000 Computed form of implicit sphere: Imputed radius = 3.000000 Imputed center: 0: 1.000000 1: 2.000000 2: 3.000000 Computed form of explicit sphere: P1: 1.000000 2.000000 6.000000 P2: 3.598076 2.000000 1.500000 P3: -0.299038 4.250000 1.500000 P4: -0.299038 -0.250000 1.500000 SPHERE_IMP2EXP_3D_TEST SPHERE_IMP2EXP_3D: implicit sphere => explicit form. Initial form of explicit sphere: P1: 4.000000 2.000000 3.000000 P2: 1.000000 5.000000 3.000000 P3: 1.000000 2.000000 6.000000 P4: -2.000000 2.000000 3.000000 Computed form of implicit sphere: Imputed radius = 3.000000 Imputed center: 0: 1.000000 1: 2.000000 2: 3.000000 Computed form of explicit sphere: P1: 1.000000 2.000000 6.000000 P2: 3.598076 2.000000 1.500000 P3: -0.299038 4.250000 1.500000 P4: -0.299038 -0.250000 1.500000 SPHERE_EXP2IMP_ND_TEST SPHERE_EXP2IMP_ND: explicit sphere => implicit form; Initial form of explicit sphere: Row: 1 2 3 Col 1: 4.000000 2.000000 3.000000 2: 1.000000 5.000000 3.000000 3: 1.000000 2.000000 6.000000 4: -2.000000 2.000000 3.000000 Computed form of implicit sphere: Imputed radius = 3.000000 True radius = 3.000000 Imputed center 0: 1.000000 1: 2.000000 2: 3.000000 True center 0: 1.000000 1: 2.000000 2: 3.000000 TRIANGLE_CIRCUMCENTER_2D_TEST TRIANGLE_CIRCUMCENTER_2D computes the circumcenter of a triangle; Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.000000 6.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D: 0: 10.500000 1: 5.500000 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.500000 5.866025 Circumcenter by TRIANGLE_CIRCUMCENTER_2D: 0: 10.500000 1: 5.288675 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.500000 15.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D: 0: 10.500000 1: 9.987500 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 20.000000 7.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D: 0: 10.500000 1: 28.500000 TRIANGLE_CIRCUMCENTER_2D_2_TEST TRIANGLE_CIRCUMCENTER_2D_2 computes the circumcenter of a triangle; Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.000000 6.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D_2: 0: 10.500000 1: 5.500000 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.500000 5.866025 Circumcenter by TRIANGLE_CIRCUMCENTER_2D_2: 0: 10.500000 1: 5.288675 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 10.500000 15.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D_2: 0: 10.500000 1: 9.987500 Triangle vertices: Row: 1 2 Col 1: 10.000000 5.000000 2: 11.000000 5.000000 3: 20.000000 7.000000 Circumcenter by TRIANGLE_CIRCUMCENTER_2D_2: 0: 10.500000 1: 28.500000 TRIANGLE_CIRCUMCENTER_TEST For a triangle in M dimensions, the circumenter can be computed by: TRIANGLE_CIRCUMCENTER; M2 = 2 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 6.901910 1: 12.913314 Distances from circumcenter to vertices: 0.533001 0.533001 0.533001 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 7.120177 1: 12.863463 Distances from circumcenter to vertices: 0.653938 0.653938 0.653938 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 13.837365 1: 11.329290 Distances from circumcenter to vertices: 7.339086 7.339086 7.339086 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 48.737251 1: 3.358325 Distances from circumcenter to vertices: 43.124048 43.124048 43.124048 M2 = 3 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 5.129152 1: 12.718640 2: 9.079022 Distances from circumcenter to vertices: 0.599947 0.599947 0.599947 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 5.117689 1: 12.716698 2: 9.084280 Distances from circumcenter to vertices: 0.600303 0.600303 0.600303 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 9.168227 1: 13.403043 2: 7.226464 Distances from circumcenter to vertices: 4.525605 4.525605 4.525605 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 76.298618 1: 24.777977 2: -23.563495 Distances from circumcenter to vertices: 79.213443 79.213443 79.213443 M2 = 4 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 3.843413 1: 10.880094 2: 10.148894 3: 7.129777 Distances from circumcenter to vertices: 1.037277 1.037277 1.037277 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 4.080267 1: 10.925792 2: 10.301810 3: 7.196854 Distances from circumcenter to vertices: 0.758041 0.758041 0.758041 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 7.250969 1: 9.694480 2: 10.960800 3: 7.087093 Distances from circumcenter to vertices: 3.158838 3.158838 3.158838 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 114.310906 1: -31.881223 2: 33.211845 3: 3.380955 Distances from circumcenter to vertices: 120.135036 120.135036 120.135036 M2 = 5 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 2.961642 1: 11.849925 2: 10.012935 3: 6.131911 4: 7.594984 Distances from circumcenter to vertices: 1.304893 1.304893 1.304893 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 3.018347 1: 12.062091 2: 10.068589 3: 6.134945 4: 8.277846 Distances from circumcenter to vertices: 0.701475 0.701475 0.701475 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 3.024685 1: 11.822808 2: 8.911660 3: 5.095279 4: 12.542414 Distances from circumcenter to vertices: 4.452400 4.452400 4.452400 Circumcenter by TRIANGLE_CIRCUMCENTER: 0: 3.158069 1: 6.787267 2: -15.435129 3: -16.783780 4: 102.287325 Distances from circumcenter to vertices: 100.062354 100.062354 100.062354 WEDGE01_VOLUME_TEST WEDGE01_VOLUME returns the volume of the unit wedge. Volume = 1 GEOMETRY_TEST Normal end of execution. 05 August 2018 02:27:27 PM