C 代码 执行与圆段关联的计算，包括 高度、角度、面积、质心、采样和正交.rar

03 March 2022 06:54:35 PM CIRCLE_SEGMENT_TEST C version Test the CIRCLE_SEGMENT library. TEST01 CIRCLE_SEGMENT_AREA_FROM_HEIGHT computes the area of a circle segment. R H Area 1.000000 1.000000 1.570796 1.000000 0.500000 0.614185 1.000000 0.250000 0.226656 1.000000 0.125000 0.081753 1.000000 0.062500 0.029185 1.000000 0.031250 0.010368 1.000000 0.015625 0.003674 1.000000 0.007812 0.001301 1.000000 0.003906 0.000460 1.000000 0.001953 0.000163 1.000000 0.000977 0.000058 CIRCLE_SEGMENT_TEST05 For circle segment with a given radius R, CIRCLE_SEGMENT_AREA_FROM_HEIGHT computes the area A, given the height. CIRCLE_SEGMENT_HEIGHT_FROM_AREA computes height H, given the area. Check that these functions are inverses of each other using random values of R, A, and H. R H => A => H2 1.092091 2.088773 3.689558 2.088773 4.147546 4.659316 31.255434 4.659316 2.076535 0.274596 0.383139 0.274596 1.287889 0.283224 0.311686 0.283224 0.219145 0.277861 0.100860 0.277861 R A => H => A2 0.308636 0.134527 0.284147 0.134527 2.006531 9.545549 2.833249 9.545548 3.986435 0.091781 0.084254 0.091781 4.487520 22.190306 3.425477 22.190306 0.472724 0.009560 0.038196 0.009560 CIRCLE_SEGMENT_TEST06 CIRCLE_SEGMENT_SAMPLE_FROM_HEIGHT samples a circle segment. Plot 100 points from several segments. Created boundary file "sample01_boundary.txt". Created data file "sample01_data.txt". Created command file "sample01_commands.txt". Created boundary file "sample02_boundary.txt". Created data file "sample02_data.txt". Created command file "sample02_commands.txt". Created boundary file "sample03_boundary.txt". Created data file "sample03_data.txt". Created command file "sample03_commands.txt". Created boundary file "sample04_boundary.txt". Created data file "sample04_data.txt". Created command file "sample04_commands.txt". TEST07 For circle segment with a given radius R, CIRCLE_SEGMENT_ANGLE_FROM_HEIGHT computes the angle THETA, given the height. CIRCLE_SEGMENT_HEIGHT_FROM_ANGLE computes height H, given the angle. Check that these functions are inverses of each other using random values of R, T, and H. R H => T => H2 1.092091 2.088773 5.440962 2.088773 4.147546 4.659316 3.389005 4.659316 2.076535 0.274596 1.040228 0.274596 1.287889 0.283224 1.351985 0.283224 0.219145 0.277861 3.684083 0.277861 R T => H => T2 0.308636 2.824537 0.259913 2.824537 2.006531 4.741753 3.446041 4.741753 3.986435 0.011551 0.000066 0.011551 4.487520 2.203842 2.459685 2.203842 0.472724 0.085557 0.000432 0.085557 TEST08 CIRCLE_SEGMENT_CONTAINS_POINT reports whether a circle segment contains a point. Pick a circle segment at random. Compute 1000 sample points in the surrounding box. Compare the area of the segment to the percentage of points contained in the circle segment. N Omega1 Omega2 Area Estimate 1000 1.37236 6.00872 2.81673 2.812 1000 0.776884 6.92149 3.14137 3.176 1000 2.78572 3.60979 0.0450766 0.036 1000 1.42744 1.71406 0.00195431 0 1000 5.36344 11.0425 3.12355 3.18 CIRCLE_SEGMENT_TEST09 CIRCLE_SEGMENT_AREA_FROM_CHORD and CIRCLE_SEGMENT_CENTROID_FROM_CHORD evaluate the area and centroid of a circle segment, given R, C and P1:P2. CIRCLE_SEGMENT_AREA_FROM_SAMPLE and CIRCLE_SEGMENT_CENTROID_FROM_SAMPLE give us Monte Carlo estimates. GQCIRCSEGM can estimate these values by quadrature. Start easy, with R = 1, C = (0,0), and Theta centered. Area CentroidX CentroidY 0.0391457 0.954429 3.7087e-16 0.0391457 0.954429 -0 0.0367566 0.954632 0.000339091 TEST11: CIRCLE_SEGMENT_ROTATION_FROM_CHORD is given the endpoints of a chord, and is asked to determine the angle of the central radius vector. We make a table of all pairs of angles that are multiples of pi/12, determine the corresponding chord endpoints, and compute the rotation angle, also printed as a multiple of pi/12. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 0 6.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1 6.5 7.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 2 7.0 7.5 8.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 3 7.5 8.0 8.5 9.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 4 8.0 8.5 9.0 9.5 10.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 5 8.5 9.0 9.5 10.0 10.5 11.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 6 9.0 9.5 10.0 10.5 11.0 11.5 0.0 6.5 7.0 7.5 8.0 8.5 9.0 7 9.5 10.0 10.5 11.0 11.5 0.0 0.5 1.0 7.5 8.0 8.5 9.0 9.5 8 10.0 10.5 11.0 11.5 0.0 0.5 1.0 1.5 2.0 8.5 9.0 9.5 10.0 9 10.5 11.0 11.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 9.5 10.0 10.5 10 11.0 11.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 10.5 11.0 11 11.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 11.5 12 6.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 TEST13 GAUSS computes the points and weights for a Gauss quadrature rule, given the ALPHA and BETA recursion coefficients. LEGENDRE RULE Point Weight -0.973907 0.0666713 -0.865063 0.149451 -0.67941 0.219086 -0.433395 0.269267 -0.148874 0.295524 0.148874 0.295524 0.433395 0.269267 0.67941 0.219086 0.865063 0.149451 0.973907 0.0666713 HERMITE RULE Point Weight -3.43616 7.64043e-06 -2.53273 0.00134365 -1.75668 0.0338744 -1.03661 0.240139 -0.342901 0.610863 0.342901 0.610863 1.03661 0.240139 1.75668 0.0338744 2.53273 0.00134365 3.43616 7.64043e-06 LAGUERRE RULE Point Weight 0.137793 0.308441 0.729455 0.40112 1.80834 0.218068 3.40143 0.0620875 5.5525 0.00950152 8.33015 0.000753008 11.8438 2.82592e-05 16.2793 4.24931e-07 21.9966 1.83956e-09 29.9207 9.91183e-13 TEST14 R_JACOBI computes recursion coefficients ALPHA and BETA Gauss quadrature rule, given the ALPHA and BETA recursion coefficients. Legendre weight A = 0, B = 0 Alpha Beta 0 2 0 0.333333 0 0.266667 0 0.257143 0 0.253968 0 0.252525 0 0.251748 0 0.251282 0 0.25098 0 0.250774 Chebyshev Type 1 weight A = -0.5, B = -0.5 Alpha