Remove the naca experimental port to C
Generating some clang static analyzer errors - just removing as the simplest step. Probably not too hard to fix, but we never got this to the point where we were able to generate geometry and the Vehicle Sketch Pad software (OpenVSP, http://openvsp.org/) originally developed by NASA has the ability to generate STEP files. Unless someone wants to pick this up (in which case the VCS has it) the better investment of effort is to firm up our step-g importer's ability to bring in OpenVSP exports.
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Clifford Yapp committed
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@@ -35,8 +35,6 @@ BRLCAD_ADDEXEC(tea_nmg tea_nmg.c "libwdb;libnmg" NO_INSTALL)
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BRLCAD_ADDEXEC(tube tube.c "libwdb;libnmg;${M_LIBRARY}" NO_INSTALL)
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BRLCAD_ADDEXEC(wdb_example wdb_example.c libwdb NO_INSTALL) # NOTE: has manual page
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add_subdirectory(naca)
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# MORE THAN DEVELOPMENT TESTING
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#
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# these have reached a level of maturity where they could provide some
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@@ -1,24 +0,0 @@
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set(naca_srcs
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splprocs.c
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epspsi.c
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nacax.c
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naca456.c
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)
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set(NACA_INCLUDES
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${CMAKE_CURRENT_SOURCE_DIR}
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${OPENNURBS_INCLUDE_DIRS}
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)
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BRLCAD_INCLUDE_DIRS(NACA_INCLUDES)
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BRLCAD_ADDEXEC(naca456 "${naca_srcs}" "libwdb;libbu;${OPENNURBS_LIBRARIES}" NO_INSTALL)
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CMAKEFILES(naca.h)
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CMAKEFILES(CMakeLists.txt)
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# Local Variables:
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# tab-width: 8
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# mode: cmake
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# indent-tabs-mode: t
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# End:
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# ex: shiftwidth=2 tabstop=8
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@@ -1,515 +0,0 @@
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/* E P S P S I . C
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* BRL-CAD
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*
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* Published in 2020 by the United States Government.
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* This work is in the public domain.
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*
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*/
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/** @file epspsi.c
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*
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* BRL-CAD's translation of the calculation of coordinates for NACA airfoils is
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* based on the public domain program naca456 written by Ralph Carmichael of
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* Public Domain Aeronautical Software (PDAS):
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*
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* http://www.pdas.com/naca456.html
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*
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* naca456 is in turn based off of earlier work by several authors at NASA,
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* documented in reports NASA TM X-3284, NASA TM X-3069 and NASA TM 4741. The
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* program naca456 is documented in the paper:
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*
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* Carmichael, Ralph L.: Algorithm for Calculating Coordinates of Cambered NACA
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* Airfoils At Specified Chord Locations. AIAA Paper 2001-5235, November 2001.
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*
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* Disclaimer, per the PDAS distribution:
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*
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* Although many of the works contained herein were developed by national
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* laboratories or their contractors, neither the U.S. Government nor Public
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* Domain Aeronautical Software make any warranty as to the accuracy or
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* appropriateness of the procedure to any particular application.
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*
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* The programs and descriptions have been collected and reproduced with great
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* care and attention to accuracy, but no guarantee or warranty is implied. All
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* programs are offered AS IS and Public Domain Aeronautical Software does not
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* give any express or implied warranty of any kind and any implied warranties are
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* disclaimed. Public Domain Aeronautical Software will not be liable for any
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* direct, indirect, special, incidental, or consequential damages arising out of
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* any use of this software. In no case should the results of any computational
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* scheme be used as a substitute for sound engineering practice and judgment.
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*
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*/
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#include "naca.h"
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const fastf_t EPS1[] = {
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0.00000, 0.00164, 0.00327, 0.00487, 0.00641, 0.00790, 0.00928, 0.01057,
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0.01174, 0.01278, 0.01367, 0.01439, 0.01497, 0.01542, 0.01576, 0.01601,
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0.01619, 0.01632, 0.01642, 0.01651, 0.01661, 0.01673, 0.01688, 0.01705,
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0.01725, 0.01747, 0.01771, 0.01797, 0.01824, 0.01853, 0.01884, 0.01916,
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0.01949, 0.01984, 0.02020, 0.02058, 0.02097, 0.02137, 0.02179, 0.02223,
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0.02268, 0.02315, 0.02363, 0.02413, 0.02464, 0.02517, 0.02571, 0.02626,
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0.02683, 0.02741, 0.02801, 0.02862, 0.02924, 0.02988, 0.03052, 0.03118,
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0.03185, 0.03253, 0.03323, 0.03393, 0.03465, 0.03538, 0.03611, 0.03686,
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0.03762, 0.03839, 0.03917, 0.03995, 0.04075, 0.04156, 0.04237, 0.04319,
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0.04402, 0.04486, 0.04571, 0.04657, 0.04743, 0.04831, 0.04919, 0.05008,
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0.05098, 0.05189, 0.05280, 0.05372, 0.05464, 0.05556, 0.05648, 0.05740,
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0.05831, 0.05921, 0.06011, 0.06099, 0.06187, 0.06273, 0.06357, 0.06440,
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0.06522, 0.06602, 0.06681, 0.06757, 0.06832, 0.06905, 0.06976, 0.07044,
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0.07111, 0.07176, 0.07238, 0.07298, 0.07356, 0.07411, 0.07464, 0.07514,
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0.07562, 0.07607, 0.07650, 0.07690, 0.07727, 0.07761, 0.07793, 0.07822,
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0.07848, 0.07871, 0.07891, 0.07908, 0.07922, 0.07933, 0.07941, 0.07945,
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0.07946, 0.07944, 0.07938, 0.07929, 0.07916, 0.07900, 0.07880, 0.07856,
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0.07829, 0.07799, 0.07764, 0.07726, 0.07685, 0.07640, 0.07591, 0.07539,
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0.07483, 0.07423, 0.07359, 0.07293, 0.07222, 0.07148, 0.07070, 0.06989,
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0.06904, 0.06815, 0.06723, 0.06628, 0.06529, 0.06427, 0.06322, 0.06214,
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0.06103, 0.05989, 0.05871, 0.05751, 0.05628, 0.05502, 0.05374, 0.05243,
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0.05109, 0.04973, 0.04834, 0.04693, 0.04549, 0.04404, 0.04256, 0.04106,
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0.03955, 0.03802, 0.03647, 0.03491, 0.03333, 0.03174, 0.03014, 0.02853,
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0.02690, 0.02527, 0.02363, 0.02198, 0.02032, 0.01865, 0.01698, 0.01530,
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0.01361, 0.01192, 0.01023, 0.00853, 0.00683, 0.00512, 0.00342, 0.00171,
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0.00000
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};
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const fastf_t EPS2[] = {
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0.00000, 0.00233, 0.00465, 0.00693, 0.00915, 0.01130, 0.01337, 0.01532,
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0.01715, 0.01884, 0.02035, 0.02169, 0.02288, 0.02391, 0.02481, 0.02557,
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0.02624, 0.02682, 0.02731, 0.02774, 0.02812, 0.02846, 0.02877, 0.02905,
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0.02931, 0.02957, 0.02982, 0.03007, 0.03033, 0.03060, 0.03090, 0.03122,
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0.03158, 0.03196, 0.03236, 0.03280, 0.03326, 0.03375, 0.03427, 0.03481,
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0.03538, 0.03598, 0.03660, 0.03725, 0.03792, 0.03862, 0.03935, 0.04010,
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0.04087, 0.04167, 0.04250, 0.04335, 0.04423, 0.04512, 0.04605, 0.04699,
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0.04796, 0.04896, 0.04998, 0.05102, 0.05208, 0.05317, 0.05428, 0.05541,
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0.05657, 0.05774, 0.05894, 0.06016, 0.06140, 0.06267, 0.06395, 0.06526,
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0.06658, 0.06793, 0.06931, 0.07070, 0.07213, 0.07357, 0.07505, 0.07655,
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0.07808, 0.07964, 0.08123, 0.08284, 0.08447, 0.08613, 0.08780, 0.08949,
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0.09119, 0.09290, 0.09462, 0.09635, 0.09808, 0.09980, 0.10151, 0.10321,
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0.10488, 0.10653, 0.10815, 0.10972, 0.11125, 0.11273, 0.11415, 0.11553,
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0.11686, 0.11814, 0.11938, 0.12057, 0.12171, 0.12281, 0.12386, 0.12487,
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0.12583, 0.12675, 0.12762, 0.12844, 0.12922, 0.12994, 0.13062, 0.13125,
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0.13182, 0.13234, 0.13281, 0.13322, 0.13358, 0.13389, 0.13414, 0.13434,
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0.13448, 0.13456, 0.13459, 0.13456, 0.13447, 0.13433, 0.13413, 0.13387,
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0.13354, 0.13316, 0.13272, 0.13222, 0.13166, 0.13104, 0.13035, 0.12960,
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0.12879, 0.12792, 0.12698, 0.12598, 0.12492, 0.12380, 0.12261, 0.12136,
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0.12004, 0.11866, 0.11723, 0.11573, 0.11417, 0.11255, 0.11087, 0.10914,
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0.10735, 0.10550, 0.10361, 0.10165, 0.09964, 0.09758, 0.09546, 0.09329,
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0.09106, 0.08878, 0.08645, 0.08406, 0.08163, 0.07914, 0.07661, 0.07403,
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0.07140, 0.06874, 0.06604, 0.06329, 0.06052, 0.05770, 0.05487, 0.05199,
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0.04908, 0.04615, 0.04319, 0.04021, 0.03721, 0.03417, 0.03113, 0.02807,
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0.02499, 0.02189, 0.01879, 0.01567, 0.01255, 0.00942, 0.00628, 0.00314,
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0.00000
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};
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const fastf_t EPS3[] = {
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0.00000, 0.00165, 0.00330, 0.00493, 0.00653, 0.00810, 0.00963, 0.01110,
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0.01253, 0.01387, 0.01515, 0.01625, 0.01702, 0.01746, 0.01771, 0.01795,
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0.01824, 0.01858, 0.01893, 0.01922, 0.01943, 0.01951, 0.01945, 0.01926,
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0.01899, 0.01865, 0.01830, 0.01794, 0.01760, 0.01733, 0.01715, 0.01704,
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0.01702, 0.01706, 0.01715, 0.01727, 0.01742, 0.01759, 0.01777, 0.01798,
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0.01821, 0.01846, 0.01876, 0.01908, 0.01944, 0.01983, 0.02024, 0.02068,
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0.02114, 0.02161, 0.02211, 0.02261, 0.02313, 0.02365, 0.02419, 0.02474,
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0.02530, 0.02587, 0.02647, 0.02708, 0.02772, 0.02837, 0.02904, 0.02974,
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0.03046, 0.03119, 0.03195, 0.03271, 0.03350, 0.03429, 0.03510, 0.03593,
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0.03677, 0.03763, 0.03849, 0.03938, 0.04028, 0.04119, 0.04212, 0.04307,
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0.04404, 0.04502, 0.04602, 0.04704, 0.04808, 0.04914, 0.05021, 0.05130,
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0.05241, 0.05353, 0.05467, 0.05582, 0.05699, 0.05817, 0.05935, 0.06055,
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0.06174, 0.06294, 0.06414, 0.06534, 0.06653, 0.06772, 0.06890, 0.07006,
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0.07121, 0.07234, 0.07346, 0.07456, 0.07564, 0.07668, 0.07771, 0.07872,
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0.07970, 0.08064, 0.08155, 0.08244, 0.08327, 0.08406, 0.08480, 0.08550,
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0.08614, 0.08673, 0.08728, 0.08778, 0.08825, 0.08866, 0.08905, 0.08939,
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0.08968, 0.08995, 0.09017, 0.09034, 0.09048, 0.09057, 0.09062, 0.09061,
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0.09057, 0.09046, 0.09031, 0.09009, 0.08982, 0.08950, 0.08911, 0.08868,
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0.08819, 0.08765, 0.08707, 0.08643, 0.08576, 0.08504, 0.08427, 0.08346,
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0.08260, 0.08170, 0.08075, 0.07976, 0.07871, 0.07759, 0.07640, 0.07510,
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0.07368, 0.07216, 0.07047, 0.06864, 0.06664, 0.06448, 0.06220, 0.05982,
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0.05735, 0.05483, 0.05228, 0.04972, 0.04718, 0.04467, 0.04225, 0.03991,
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0.03766, 0.03548, 0.03338, 0.03135, 0.02939, 0.02752, 0.02569, 0.02394,
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0.02224, 0.02059, 0.01899, 0.01744, 0.01592, 0.01446, 0.01302, 0.01163,
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0.01026, 0.00892, 0.00761, 0.00630, 0.00502, 0.00376, 0.00250, 0.00124,
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0.00000
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};
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const fastf_t EPS4[] = {
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0.00000, 0.00145, 0.00290, 0.00433, 0.00574, 0.00712, 0.00847, 0.00978,
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0.01105, 0.01225, 0.01340, 0.01447, 0.01547, 0.01638, 0.01719, 0.01789,
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0.01847, 0.01893, 0.01924, 0.01940, 0.01940, 0.01924, 0.01893, 0.01850,
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0.01799, 0.01741, 0.01679, 0.01616, 0.01556, 0.01499, 0.01450, 0.01410,
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0.01379, 0.01356, 0.01340, 0.01331, 0.01327, 0.01328, 0.01333, 0.01340,
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0.01350, 0.01361, 0.01373, 0.01387, 0.01402, 0.01419, 0.01438, 0.01458,
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0.01480, 0.01504, 0.01530, 0.01558, 0.01588, 0.01620, 0.01654, 0.01689,
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0.01726, 0.01765, 0.01805, 0.01847, 0.01890, 0.01934, 0.01980, 0.02026,
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0.02074, 0.02124, 0.02174, 0.02226, 0.02279, 0.02334, 0.02390, 0.02447,
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0.02506, 0.02566, 0.02627, 0.02690, 0.02754, 0.02819, 0.02885, 0.02952,
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0.03020, 0.03089, 0.03160, 0.03231, 0.03304, 0.03378, 0.03453, 0.03530,
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0.03608, 0.03688, 0.03770, 0.03853, 0.03938, 0.04025, 0.04113, 0.04202,
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0.04293, 0.04386, 0.04479, 0.04574, 0.04670, 0.04767, 0.04866, 0.04966,
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0.05067, 0.05171, 0.05277, 0.05386, 0.05498, 0.05612, 0.05730, 0.05851,
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0.05976, 0.06103, 0.06231, 0.06362, 0.06493, 0.06625, 0.06758, 0.06889,
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0.07020, 0.07149, 0.07277, 0.07402, 0.07524, 0.07644, 0.07760, 0.07872,
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0.07979, 0.08082, 0.08180, 0.08272, 0.08359, 0.08440, 0.08515, 0.08585,
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0.08649, 0.08708, 0.08761, 0.08808, 0.08850, 0.08886, 0.08916, 0.08941,
|
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0.08959, 0.08972, 0.08978, 0.08978, 0.08972, 0.08959, 0.08940, 0.08914,
|
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0.08882, 0.08843, 0.08797, 0.08745, 0.08687, 0.08622, 0.08551, 0.08474,
|
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0.08390, 0.08300, 0.08203, 0.08101, 0.07991, 0.07876, 0.07752, 0.07622,
|
||||
0.07485, 0.07341, 0.07190, 0.07031, 0.06865, 0.06692, 0.06511, 0.06324,
|
||||
0.06130, 0.05929, 0.05723, 0.05509, 0.05290, 0.05064, 0.04834, 0.04597,
|
||||
0.04355, 0.04109, 0.03857, 0.03602, 0.03342, 0.03077, 0.02810, 0.02539,
|
||||
0.02264, 0.01988, 0.01708, 0.01427, 0.01144, 0.00858, 0.00573, 0.00287,
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0.00000
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||||
};
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const fastf_t EPS5[] = {
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0.00000, 0.00169, 0.00338, 0.00506, 0.00672, 0.00835, 0.00995, 0.01152,
|
||||
0.01304, 0.01450, 0.01591, 0.01719, 0.01822, 0.01896, 0.01952, 0.02004,
|
||||
0.02060, 0.02116, 0.02170, 0.02220, 0.02259, 0.02287, 0.02300, 0.02300,
|
||||
0.02289, 0.02270, 0.02245, 0.02215, 0.02184, 0.02154, 0.02126, 0.02101,
|
||||
0.02079, 0.02061, 0.02045, 0.02030, 0.02017, 0.02005, 0.01994, 0.01985,
|
||||
0.01979, 0.01972, 0.01969, 0.01966, 0.01966, 0.01968, 0.01971, 0.01975,
|
||||
0.01982, 0.01989, 0.01997, 0.02006, 0.02016, 0.02028, 0.02040, 0.02054,
|
||||
0.02067, 0.02083, 0.02099, 0.02116, 0.02135, 0.02155, 0.02175, 0.02198,
|
||||
0.02221, 0.02245, 0.02271, 0.02298, 0.02325, 0.02355, 0.02386, 0.02417,
|
||||
0.02450, 0.02484, 0.02519, 0.02555, 0.02592, 0.02630, 0.02670, 0.02710,
|
||||
0.02752, 0.02795, 0.02839, 0.02884, 0.02929, 0.02976, 0.03025, 0.03075,
|
||||
0.03126, 0.03178, 0.03232, 0.03287, 0.03343, 0.03401, 0.03461, 0.03522,
|
||||
0.03585, 0.03648, 0.03714, 0.03782, 0.03849, 0.03920, 0.03991, 0.04063,
|
||||
0.04136, 0.04213, 0.04290, 0.04369, 0.04451, 0.04535, 0.04622, 0.04712,
|
||||
0.04803, 0.04898, 0.04994, 0.05092, 0.05192, 0.05294, 0.05397, 0.05503,
|
||||
0.05610, 0.05721, 0.05833, 0.05949, 0.06067, 0.06187, 0.06309, 0.06434,
|
||||
0.06559, 0.06687, 0.06814, 0.06944, 0.07073, 0.07201, 0.07327, 0.07450,
|
||||
0.07571, 0.07689, 0.07801, 0.07908, 0.08009, 0.08104, 0.08194, 0.08277,
|
||||
0.08353, 0.08422, 0.08483, 0.08538, 0.08584, 0.08625, 0.08659, 0.08685,
|
||||
0.08706, 0.08720, 0.08729, 0.08732, 0.08728, 0.08716, 0.08691, 0.08654,
|
||||
0.08602, 0.08530, 0.08440, 0.08327, 0.08189, 0.08025, 0.07838, 0.07630,
|
||||
0.07403, 0.07162, 0.06908, 0.06647, 0.06378, 0.06107, 0.05836, 0.05568,
|
||||
0.05306, 0.05048, 0.04794, 0.04546, 0.04301, 0.04061, 0.03825, 0.03592,
|
||||
0.03363, 0.03137, 0.02914, 0.02694, 0.02477, 0.02262, 0.02049, 0.01838,
|
||||
0.01630, 0.01422, 0.01216, 0.01011, 0.00808, 0.00605, 0.00403, 0.00201,
|
||||
0.00000
|
||||
};
|
||||
|
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const fastf_t EPS6[] = {
|
||||
0.00000, 0.00149, 0.00297, 0.00444, 0.00589, 0.00734, 0.00875, 0.01013,
|
||||
0.01148, 0.01279, 0.01405, 0.01512, 0.01582, 0.01616, 0.01631, 0.01642,
|
||||
0.01659, 0.01681, 0.01705, 0.01729, 0.01751, 0.01767, 0.01778, 0.01784,
|
||||
0.01787, 0.01787, 0.01788, 0.01788, 0.01793, 0.01800, 0.01813, 0.01831,
|
||||
0.01854, 0.01881, 0.01912, 0.01945, 0.01981, 0.02018, 0.02056, 0.02095,
|
||||
0.02134, 0.02175, 0.02216, 0.02257, 0.02299, 0.02342, 0.02385, 0.02429,
|
||||
0.02475, 0.02521, 0.02569, 0.02619, 0.02670, 0.02722, 0.02777, 0.02832,
|
||||
0.02889, 0.02947, 0.03005, 0.03065, 0.03125, 0.03186, 0.03247, 0.03308,
|
||||
0.03370, 0.03432, 0.03495, 0.03559, 0.03625, 0.03692, 0.03759, 0.03828,
|
||||
0.03898, 0.03969, 0.04041, 0.04114, 0.04189, 0.04265, 0.04341, 0.04419,
|
||||
0.04496, 0.04574, 0.04651, 0.04729, 0.04804, 0.04879, 0.04953, 0.05026,
|
||||
0.05100, 0.05171, 0.05243, 0.05314, 0.05386, 0.05456, 0.05525, 0.05594,
|
||||
0.05661, 0.05728, 0.05793, 0.05858, 0.05921, 0.05981, 0.06039, 0.06096,
|
||||
0.06149, 0.06200, 0.06248, 0.06295, 0.06339, 0.06381, 0.06422, 0.06461,
|
||||
0.06498, 0.06533, 0.06566, 0.06597, 0.06626, 0.06651, 0.06675, 0.06695,
|
||||
0.06714, 0.06729, 0.06740, 0.06749, 0.06754, 0.06755, 0.06754, 0.06751,
|
||||
0.06743, 0.06734, 0.06720, 0.06704, 0.06686, 0.06666, 0.06642, 0.06615,
|
||||
0.06586, 0.06554, 0.06520, 0.06481, 0.06441, 0.06397, 0.06351, 0.06303,
|
||||
0.06252, 0.06198, 0.06142, 0.06083, 0.06022, 0.05960, 0.05896, 0.05830,
|
||||
0.05763, 0.05695, 0.05626, 0.05555, 0.05482, 0.05406, 0.05325, 0.05241,
|
||||
0.05152, 0.05057, 0.04956, 0.04848, 0.04734, 0.04615, 0.04490, 0.04362,
|
||||
0.04231, 0.04095, 0.03959, 0.03820, 0.03681, 0.03542, 0.03404, 0.03266,
|
||||
0.03129, 0.02993, 0.02857, 0.02723, 0.02589, 0.02455, 0.02322, 0.02190,
|
||||
0.02058, 0.01927, 0.01797, 0.01667, 0.01537, 0.01408, 0.01279, 0.01150,
|
||||
0.01021, 0.00893, 0.00765, 0.00637, 0.00509, 0.00382, 0.00254, 0.00127,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t EPS7[] = {
|
||||
0.00000, 0.00159, 0.00318, 0.00476, 0.00632, 0.00786, 0.00937, 0.01086,
|
||||
0.01231, 0.01372, 0.01507, 0.01623, 0.01702, 0.01743, 0.01761, 0.01776,
|
||||
0.01797, 0.01823, 0.01851, 0.01877, 0.01899, 0.01914, 0.01920, 0.01918,
|
||||
0.01911, 0.01898, 0.01885, 0.01871, 0.01858, 0.01850, 0.01846, 0.01848,
|
||||
0.01855, 0.01867, 0.01882, 0.01900, 0.01919, 0.01940, 0.01962, 0.01986,
|
||||
0.02010, 0.02036, 0.02062, 0.02088, 0.02115, 0.02144, 0.02174, 0.02205,
|
||||
0.02237, 0.02271, 0.02306, 0.02343, 0.02382, 0.02423, 0.02465, 0.02509,
|
||||
0.02555, 0.02602, 0.02650, 0.02699, 0.02749, 0.02800, 0.02850, 0.02902,
|
||||
0.02956, 0.03009, 0.03065, 0.03121, 0.03177, 0.03236, 0.03295, 0.03357,
|
||||
0.03420, 0.03484, 0.03550, 0.03618, 0.03688, 0.03760, 0.03833, 0.03908,
|
||||
0.03984, 0.04061, 0.04139, 0.04217, 0.04295, 0.04374, 0.04453, 0.04532,
|
||||
0.04612, 0.04691, 0.04772, 0.04852, 0.04932, 0.05013, 0.05094, 0.05172,
|
||||
0.05252, 0.05329, 0.05406, 0.05482, 0.05554, 0.05626, 0.05695, 0.05761,
|
||||
0.05824, 0.05884, 0.05942, 0.05997, 0.06049, 0.06099, 0.06147, 0.06193,
|
||||
0.06237, 0.06280, 0.06320, 0.06357, 0.06393, 0.06426, 0.06456, 0.06484,
|
||||
0.06508, 0.06530, 0.06548, 0.06564, 0.06576, 0.06585, 0.06591, 0.06595,
|
||||
0.06594, 0.06592, 0.06586, 0.06578, 0.06567, 0.06553, 0.06537, 0.06517,
|
||||
0.06496, 0.06470, 0.06442, 0.06410, 0.06376, 0.06339, 0.06299, 0.06257,
|
||||
0.06210, 0.06161, 0.06110, 0.06056, 0.06000, 0.05942, 0.05881, 0.05819,
|
||||
0.05756, 0.05691, 0.05625, 0.05557, 0.05487, 0.05413, 0.05336, 0.05254,
|
||||
0.05168, 0.05075, 0.04977, 0.04871, 0.04760, 0.04643, 0.04521, 0.04395,
|
||||
0.04265, 0.04132, 0.03997, 0.03860, 0.03722, 0.03584, 0.03446, 0.03309,
|
||||
0.03172, 0.03036, 0.02900, 0.02765, 0.02630, 0.02496, 0.02362, 0.02229,
|
||||
0.02095, 0.01963, 0.01831, 0.01699, 0.01567, 0.01436, 0.01304, 0.01173,
|
||||
0.01042, 0.00912, 0.00781, 0.00651, 0.00521, 0.00390, 0.00260, 0.00130,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t EPS8[] = {
|
||||
0.00000, 0.00148, 0.00296, 0.00443, 0.00588, 0.00733, 0.00874, 0.01014,
|
||||
0.01151, 0.01284, 0.01413, 0.01523, 0.01598, 0.01638, 0.01659, 0.01676,
|
||||
0.01700, 0.01728, 0.01756, 0.01783, 0.01804, 0.01816, 0.01819, 0.01811,
|
||||
0.01796, 0.01775, 0.01752, 0.01724, 0.01695, 0.01668, 0.01642, 0.01619,
|
||||
0.01599, 0.01581, 0.01567, 0.01556, 0.01548, 0.01543, 0.01541, 0.01541,
|
||||
0.01545, 0.01551, 0.01559, 0.01570, 0.01583, 0.01598, 0.01616, 0.01635,
|
||||
0.01657, 0.01682, 0.01708, 0.01737, 0.01769, 0.01802, 0.01837, 0.01874,
|
||||
0.01913, 0.01952, 0.01992, 0.02033, 0.02075, 0.02115, 0.02157, 0.02199,
|
||||
0.02241, 0.02285, 0.02329, 0.02376, 0.02423, 0.02472, 0.02522, 0.02575,
|
||||
0.02629, 0.02685, 0.02742, 0.02802, 0.02863, 0.02926, 0.02990, 0.03055,
|
||||
0.03122, 0.03188, 0.03254, 0.03322, 0.03388, 0.03455, 0.03523, 0.03591,
|
||||
0.03661, 0.03732, 0.03806, 0.03881, 0.03958, 0.04036, 0.04115, 0.04197,
|
||||
0.04278, 0.04361, 0.04445, 0.04527, 0.04610, 0.04692, 0.04772, 0.04851,
|
||||
0.04928, 0.05004, 0.05077, 0.05149, 0.05219, 0.05288, 0.05356, 0.05422,
|
||||
0.05487, 0.05550, 0.05612, 0.05670, 0.05728, 0.05782, 0.05834, 0.05884,
|
||||
0.05931, 0.05975, 0.06015, 0.06053, 0.06086, 0.06117, 0.06144, 0.06169,
|
||||
0.06190, 0.06210, 0.06227, 0.06241, 0.06254, 0.06263, 0.06271, 0.06275,
|
||||
0.06277, 0.06275, 0.06271, 0.06264, 0.06254, 0.06240, 0.06222, 0.06201,
|
||||
0.06176, 0.06147, 0.06115, 0.06077, 0.06037, 0.05994, 0.05948, 0.05899,
|
||||
0.05849, 0.05797, 0.05741, 0.05685, 0.05625, 0.05562, 0.05494, 0.05421,
|
||||
0.05343, 0.05260, 0.05169, 0.05072, 0.04968, 0.04857, 0.04740, 0.04619,
|
||||
0.04494, 0.04365, 0.04234, 0.04098, 0.03962, 0.03824, 0.03685, 0.03546,
|
||||
0.03407, 0.03268, 0.03128, 0.02988, 0.02847, 0.02706, 0.02565, 0.02424,
|
||||
0.02282, 0.02141, 0.01999, 0.01857, 0.01715, 0.01573, 0.01430, 0.01287,
|
||||
0.01144, 0.01002, 0.00859, 0.00716, 0.00573, 0.00430, 0.00286, 0.00143,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI1[] = {
|
||||
0.15066, 0.15058, 0.15035, 0.14999, 0.14950, 0.14891, 0.14823, 0.14748,
|
||||
0.14668, 0.14583, 0.14497, 0.14410, 0.14323, 0.14238, 0.14155, 0.14074,
|
||||
0.13998, 0.13927, 0.13862, 0.13804, 0.13753, 0.13711, 0.13676, 0.13648,
|
||||
0.13627, 0.13610, 0.13598, 0.13590, 0.13584, 0.13579, 0.13576, 0.13573,
|
||||
0.13570, 0.13567, 0.13564, 0.13561, 0.13558, 0.13555, 0.13552, 0.13550,
|
||||
0.13547, 0.13544, 0.13542, 0.13539, 0.13536, 0.13533, 0.13529, 0.13525,
|
||||
0.13521, 0.13516, 0.13511, 0.13505, 0.13499, 0.13491, 0.13483, 0.13475,
|
||||
0.13465, 0.13454, 0.13442, 0.13428, 0.13414, 0.13398, 0.13381, 0.13363,
|
||||
0.13343, 0.13321, 0.13299, 0.13275, 0.13249, 0.13222, 0.13194, 0.13164,
|
||||
0.13133, 0.13100, 0.13065, 0.13028, 0.12988, 0.12947, 0.12903, 0.12857,
|
||||
0.12808, 0.12756, 0.12702, 0.12644, 0.12584, 0.12521, 0.12455, 0.12385,
|
||||
0.12313, 0.12238, 0.12160, 0.12079, 0.11994, 0.11907, 0.11817, 0.11724,
|
||||
0.11628, 0.11529, 0.11428, 0.11324, 0.11218, 0.11109, 0.10998, 0.10884,
|
||||
0.10768, 0.10650, 0.10530, 0.10407, 0.10283, 0.10157, 0.10029, 0.09899,
|
||||
0.09767, 0.09634, 0.09499, 0.09363, 0.09224, 0.09085, 0.08944, 0.08801,
|
||||
0.08657, 0.08512, 0.08365, 0.08217, 0.08068, 0.07917, 0.07766, 0.07614,
|
||||
0.07461, 0.07307, 0.07153, 0.06998, 0.06842, 0.06687, 0.06530, 0.06374,
|
||||
0.06217, 0.06060, 0.05904, 0.05747, 0.05591, 0.05435, 0.05280, 0.05125,
|
||||
0.04970, 0.04817, 0.04664, 0.04512, 0.04362, 0.04213, 0.04065, 0.03919,
|
||||
0.03774, 0.03631, 0.03490, 0.03350, 0.03213, 0.03077, 0.02943, 0.02811,
|
||||
0.02682, 0.02555, 0.02430, 0.02308, 0.02188, 0.02071, 0.01956, 0.01844,
|
||||
0.01735, 0.01630, 0.01527, 0.01428, 0.01331, 0.01239, 0.01149, 0.01062,
|
||||
0.00979, 0.00899, 0.00823, 0.00750, 0.00680, 0.00614, 0.00551, 0.00491,
|
||||
0.00435, 0.00382, 0.00332, 0.00286, 0.00244, 0.00205, 0.00169, 0.00137,
|
||||
0.00108, 0.00083, 0.00061, 0.00042, 0.00027, 0.00015, 0.00007, 0.00002,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI2[] = {
|
||||
0.25269, 0.25265, 0.25251, 0.25227, 0.25193, 0.25147, 0.25090, 0.25020,
|
||||
0.24937, 0.24841, 0.24730, 0.24605, 0.24467, 0.24321, 0.24170, 0.24016,
|
||||
0.23864, 0.23715, 0.23573, 0.23442, 0.23325, 0.23224, 0.23138, 0.23066,
|
||||
0.23006, 0.22956, 0.22916, 0.22884, 0.22858, 0.22836, 0.22818, 0.22802,
|
||||
0.22788, 0.22775, 0.22764, 0.22755, 0.22747, 0.22740, 0.22736, 0.22732,
|
||||
0.22730, 0.22729, 0.22730, 0.22731, 0.22733, 0.22736, 0.22739, 0.22742,
|
||||
0.22745, 0.22748, 0.22751, 0.22753, 0.22755, 0.22756, 0.22756, 0.22755,
|
||||
0.22753, 0.22751, 0.22747, 0.22742, 0.22736, 0.22729, 0.22720, 0.22709,
|
||||
0.22697, 0.22683, 0.22668, 0.22650, 0.22630, 0.22608, 0.22584, 0.22557,
|
||||
0.22528, 0.22497, 0.22462, 0.22426, 0.22386, 0.22345, 0.22300, 0.22253,
|
||||
0.22203, 0.22150, 0.22094, 0.22034, 0.21969, 0.21899, 0.21823, 0.21741,
|
||||
0.21652, 0.21554, 0.21449, 0.21334, 0.21211, 0.21081, 0.20941, 0.20795,
|
||||
0.20642, 0.20482, 0.20316, 0.20143, 0.19966, 0.19784, 0.19597, 0.19406,
|
||||
0.19210, 0.19009, 0.18805, 0.18597, 0.18385, 0.18169, 0.17950, 0.17727,
|
||||
0.17502, 0.17274, 0.17042, 0.16807, 0.16570, 0.16330, 0.16087, 0.15843,
|
||||
0.15596, 0.15347, 0.15095, 0.14842, 0.14588, 0.14331, 0.14073, 0.13812,
|
||||
0.13551, 0.13288, 0.13024, 0.12759, 0.12492, 0.12225, 0.11957, 0.11688,
|
||||
0.11418, 0.11149, 0.10878, 0.10608, 0.10338, 0.10068, 0.09798, 0.09529,
|
||||
0.09260, 0.08992, 0.08725, 0.08459, 0.08195, 0.07932, 0.07671, 0.07412,
|
||||
0.07155, 0.06900, 0.06648, 0.06398, 0.06151, 0.05907, 0.05666, 0.05428,
|
||||
0.05193, 0.04962, 0.04733, 0.04509, 0.04288, 0.04072, 0.03859, 0.03650,
|
||||
0.03446, 0.03247, 0.03051, 0.02861, 0.02674, 0.02493, 0.02317, 0.02147,
|
||||
0.01982, 0.01824, 0.01672, 0.01525, 0.01385, 0.01252, 0.01125, 0.01006,
|
||||
0.00892, 0.00786, 0.00686, 0.00593, 0.00506, 0.00426, 0.00353, 0.00287,
|
||||
0.00227, 0.00174, 0.00128, 0.00089, 0.00057, 0.00032, 0.00014, 0.00004,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI3[] = {
|
||||
0.17464, 0.17456, 0.17434, 0.17397, 0.17348, 0.17285, 0.17211, 0.17125,
|
||||
0.17030, 0.16923, 0.16808, 0.16682, 0.16542, 0.16391, 0.16236, 0.16086,
|
||||
0.15949, 0.15823, 0.15711, 0.15610, 0.15523, 0.15451, 0.15390, 0.15343,
|
||||
0.15305, 0.15278, 0.15258, 0.15246, 0.15239, 0.15235, 0.15235, 0.15237,
|
||||
0.15241, 0.15249, 0.15258, 0.15269, 0.15282, 0.15297, 0.15314, 0.15331,
|
||||
0.15350, 0.15370, 0.15389, 0.15408, 0.15427, 0.15445, 0.15464, 0.15482,
|
||||
0.15501, 0.15518, 0.15536, 0.15553, 0.15569, 0.15585, 0.15600, 0.15615,
|
||||
0.15629, 0.15643, 0.15655, 0.15667, 0.15678, 0.15688, 0.15697, 0.15705,
|
||||
0.15711, 0.15718, 0.15723, 0.15726, 0.15729, 0.15731, 0.15731, 0.15730,
|
||||
0.15728, 0.15724, 0.15719, 0.15713, 0.15704, 0.15694, 0.15682, 0.15669,
|
||||
0.15653, 0.15637, 0.15618, 0.15598, 0.15576, 0.15552, 0.15526, 0.15498,
|
||||
0.15466, 0.15431, 0.15393, 0.15351, 0.15305, 0.15255, 0.15200, 0.15141,
|
||||
0.15078, 0.15011, 0.14938, 0.14862, 0.14779, 0.14693, 0.14602, 0.14505,
|
||||
0.14402, 0.14295, 0.14181, 0.14063, 0.13940, 0.13812, 0.13680, 0.13544,
|
||||
0.13403, 0.13259, 0.13110, 0.12958, 0.12804, 0.12646, 0.12484, 0.12320,
|
||||
0.12154, 0.11984, 0.11813, 0.11638, 0.11461, 0.11281, 0.11100, 0.10915,
|
||||
0.10730, 0.10541, 0.10353, 0.10161, 0.09970, 0.09778, 0.09583, 0.09389,
|
||||
0.09194, 0.08998, 0.08800, 0.08601, 0.08401, 0.08201, 0.08000, 0.07798,
|
||||
0.07596, 0.07393, 0.07191, 0.06989, 0.06788, 0.06586, 0.06385, 0.06185,
|
||||
0.05986, 0.05787, 0.05589, 0.05392, 0.05196, 0.05001, 0.04807, 0.04615,
|
||||
0.04422, 0.04232, 0.04042, 0.03854, 0.03667, 0.03481, 0.03297, 0.03115,
|
||||
0.02937, 0.02762, 0.02590, 0.02423, 0.02260, 0.02101, 0.01949, 0.01802,
|
||||
0.01661, 0.01526, 0.01396, 0.01272, 0.01154, 0.01042, 0.00935, 0.00834,
|
||||
0.00739, 0.00650, 0.00566, 0.00489, 0.00416, 0.00350, 0.00289, 0.00234,
|
||||
0.00185, 0.00141, 0.00104, 0.00072, 0.00046, 0.00026, 0.00012, 0.00003,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI4[] = {
|
||||
0.16457, 0.16455, 0.16449, 0.16437, 0.16416, 0.16386, 0.16345, 0.16292,
|
||||
0.16223, 0.16139, 0.16037, 0.15916, 0.15779, 0.15631, 0.15475, 0.15316,
|
||||
0.15157, 0.15002, 0.14856, 0.14722, 0.14604, 0.14506, 0.14427, 0.14364,
|
||||
0.14316, 0.14281, 0.14257, 0.14242, 0.14235, 0.14233, 0.14236, 0.14241,
|
||||
0.14248, 0.14257, 0.14267, 0.14280, 0.14294, 0.14310, 0.14327, 0.14346,
|
||||
0.14366, 0.14387, 0.14410, 0.14433, 0.14457, 0.14481, 0.14506, 0.14530,
|
||||
0.14554, 0.14578, 0.14601, 0.14623, 0.14645, 0.14665, 0.14685, 0.14704,
|
||||
0.14722, 0.14740, 0.14757, 0.14774, 0.14790, 0.14806, 0.14821, 0.14835,
|
||||
0.14849, 0.14862, 0.14875, 0.14886, 0.14897, 0.14908, 0.14917, 0.14925,
|
||||
0.14933, 0.14940, 0.14945, 0.14950, 0.14954, 0.14957, 0.14959, 0.14961,
|
||||
0.14961, 0.14960, 0.14959, 0.14956, 0.14953, 0.14948, 0.14943, 0.14936,
|
||||
0.14928, 0.14918, 0.14908, 0.14896, 0.14883, 0.14869, 0.14853, 0.14835,
|
||||
0.14816, 0.14796, 0.14774, 0.14750, 0.14725, 0.14698, 0.14669, 0.14638,
|
||||
0.14606, 0.14571, 0.14533, 0.14494, 0.14452, 0.14407, 0.14360, 0.14310,
|
||||
0.14256, 0.14198, 0.14135, 0.14067, 0.13992, 0.13910, 0.13820, 0.13722,
|
||||
0.13615, 0.13498, 0.13371, 0.13237, 0.13094, 0.12943, 0.12787, 0.12624,
|
||||
0.12457, 0.12284, 0.12108, 0.11929, 0.11746, 0.11561, 0.11374, 0.11183,
|
||||
0.10988, 0.10790, 0.10590, 0.10386, 0.10180, 0.09970, 0.09758, 0.09542,
|
||||
0.09325, 0.09106, 0.08885, 0.08662, 0.08439, 0.08214, 0.07989, 0.07763,
|
||||
0.07537, 0.07311, 0.07085, 0.06859, 0.06633, 0.06407, 0.06182, 0.05957,
|
||||
0.05733, 0.05510, 0.05287, 0.05066, 0.04845, 0.04627, 0.04411, 0.04196,
|
||||
0.03983, 0.03773, 0.03566, 0.03362, 0.03160, 0.02963, 0.02769, 0.02579,
|
||||
0.02394, 0.02214, 0.02038, 0.01869, 0.01705, 0.01547, 0.01396, 0.01249,
|
||||
0.01111, 0.00980, 0.00856, 0.00740, 0.00631, 0.00531, 0.00439, 0.00356,
|
||||
0.00281, 0.00216, 0.00159, 0.00110, 0.00071, 0.00040, 0.00018, 0.00004,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI5[] = {
|
||||
0.18028, 0.18026, 0.18017, 0.17999, 0.17970, 0.17927, 0.17866, 0.17786,
|
||||
0.17684, 0.17558, 0.17403, 0.17233, 0.17077, 0.16944, 0.16824, 0.16708,
|
||||
0.16586, 0.16461, 0.16334, 0.16208, 0.16085, 0.15968, 0.15859, 0.15759,
|
||||
0.15667, 0.15583, 0.15506, 0.15438, 0.15377, 0.15323, 0.15278, 0.15240,
|
||||
0.15207, 0.15179, 0.15156, 0.15135, 0.15115, 0.15097, 0.15079, 0.15063,
|
||||
0.15048, 0.15035, 0.15023, 0.15012, 0.15004, 0.14997, 0.14992, 0.14988,
|
||||
0.14985, 0.14983, 0.14982, 0.14982, 0.14982, 0.14983, 0.14985, 0.14986,
|
||||
0.14989, 0.14992, 0.14995, 0.14999, 0.15002, 0.15006, 0.15010, 0.15014,
|
||||
0.15019, 0.15023, 0.15027, 0.15032, 0.15036, 0.15041, 0.15046, 0.15050,
|
||||
0.15056, 0.15060, 0.15066, 0.15070, 0.15076, 0.15081, 0.15085, 0.15090,
|
||||
0.15095, 0.15098, 0.15101, 0.15103, 0.15106, 0.15108, 0.15108, 0.15109,
|
||||
0.15110, 0.15110, 0.15110, 0.15110, 0.15109, 0.15108, 0.15106, 0.15103,
|
||||
0.15100, 0.15096, 0.15090, 0.15084, 0.15076, 0.15068, 0.15059, 0.15050,
|
||||
0.15038, 0.15026, 0.15014, 0.14999, 0.14983, 0.14965, 0.14945, 0.14924,
|
||||
0.14900, 0.14875, 0.14847, 0.14817, 0.14784, 0.14750, 0.14712, 0.14671,
|
||||
0.14628, 0.14582, 0.14532, 0.14479, 0.14422, 0.14362, 0.14296, 0.14226,
|
||||
0.14149, 0.14065, 0.13974, 0.13875, 0.13768, 0.13652, 0.13526, 0.13391,
|
||||
0.13246, 0.13090, 0.12925, 0.12748, 0.12560, 0.12366, 0.12163, 0.11954,
|
||||
0.11738, 0.11520, 0.11298, 0.11074, 0.10848, 0.10618, 0.10386, 0.10150,
|
||||
0.09911, 0.09667, 0.09420, 0.09168, 0.08911, 0.08650, 0.08384, 0.08115,
|
||||
0.07840, 0.07562, 0.07280, 0.06994, 0.06704, 0.06412, 0.06117, 0.05820,
|
||||
0.05524, 0.05228, 0.04935, 0.04644, 0.04358, 0.04078, 0.03803, 0.03536,
|
||||
0.03277, 0.03026, 0.02785, 0.02551, 0.02327, 0.02112, 0.01906, 0.01710,
|
||||
0.01522, 0.01345, 0.01178, 0.01021, 0.00875, 0.00740, 0.00615, 0.00501,
|
||||
0.00397, 0.00306, 0.00226, 0.00158, 0.00101, 0.00057, 0.00025, 0.00006,
|
||||
0.00000
|
||||
};
|
||||
|
||||
const fastf_t PSI6[] = {
|
||||
0.15517, 0.15505, 0.15472, 0.15418, 0.15346, 0.15257, 0.15154, 0.15038,
|
||||
0.14911, 0.14776, 0.14634, 0.14493, 0.14363, 0.14249, 0.14146, 0.14058,
|
||||
0.13979, 0.13911, 0.13851, 0.13799, 0.13753, 0.13713, 0.13678, 0.13647,
|
||||
0.13620, 0.13596, 0.13576, 0.13559, 0.13543, 0.13531, 0.13521, 0.13512,
|
||||
0.13505, 0.13499, 0.13493, 0.13488, 0.13484, 0.13480, 0.13476, 0.13471,
|
||||
0.13468, 0.13463, 0.13460, 0.13456, 0.13452, 0.13447, 0.13442, 0.13438,
|
||||
0.13432, 0.13427, 0.13420, 0.13414, 0.13406, 0.13399, 0.13390, 0.13380,
|
||||
0.13371, 0.13360, 0.13348, 0.13336, 0.13322, 0.13307, 0.13292, 0.13276,
|
||||
0.13258, 0.13239, 0.13220, 0.13198, 0.13177, 0.13154, 0.13131, 0.13105,
|
||||
0.13079, 0.13051, 0.13020, 0.12989, 0.12955, 0.12917, 0.12878, 0.12836,
|
||||
0.12792, 0.12747, 0.12698, 0.12648, 0.12595, 0.12540, 0.12482, 0.12423,
|
||||
0.12361, 0.12295, 0.12228, 0.12158, 0.12085, 0.12009, 0.11932, 0.11851,
|
||||
0.11768, 0.11683, 0.11596, 0.11507, 0.11416, 0.11322, 0.11227, 0.11129,
|
||||
0.11030, 0.10928, 0.10825, 0.10720, 0.10614, 0.10505, 0.10395, 0.10284,
|
||||
0.10171, 0.10057, 0.09941, 0.09825, 0.09706, 0.09586, 0.09466, 0.09344,
|
||||
0.09221, 0.09096, 0.08972, 0.08845, 0.08718, 0.08590, 0.08462, 0.08332,
|
||||
0.08202, 0.08071, 0.07941, 0.07810, 0.07679, 0.07548, 0.07417, 0.07288,
|
||||
0.07158, 0.07029, 0.06902, 0.06775, 0.06650, 0.06525, 0.06402, 0.06278,
|
||||
0.06156, 0.06035, 0.05914, 0.05794, 0.05675, 0.05558, 0.05441, 0.05325,
|
||||
0.05210, 0.05096, 0.04983, 0.04872, 0.04761, 0.04650, 0.04539, 0.04428,
|
||||
0.04315, 0.04203, 0.04089, 0.03973, 0.03857, 0.03741, 0.03625, 0.03511,
|
||||
0.03399, 0.03291, 0.03186, 0.03086, 0.02991, 0.02902, 0.02820, 0.02745,
|
||||
0.02677, 0.02615, 0.02559, 0.02509, 0.02464, 0.02425, 0.02390, 0.02360,
|
||||
0.02333, 0.02311, 0.02293, 0.02277, 0.02265, 0.02256, 0.02248, 0.02244,
|
||||
0.02240, 0.02238, 0.02238, 0.02238, 0.02239, 0.02241, 0.02242, 0.02242,
|
||||
0.02243
|
||||
};
|
||||
|
||||
const fastf_t PSI7[] = {
|
||||
0.15365, 0.15354, 0.15318, 0.15263, 0.15188, 0.15098, 0.14993, 0.14876,
|
||||
0.14748, 0.14614, 0.14473, 0.14330, 0.14190, 0.14057, 0.13933, 0.13819,
|
||||
0.13717, 0.13626, 0.13544, 0.13472, 0.13407, 0.13349, 0.13296, 0.13249,
|
||||
0.13208, 0.13170, 0.13137, 0.13107, 0.13081, 0.13059, 0.13038, 0.13019,
|
||||
0.13004, 0.12990, 0.12978, 0.12969, 0.12962, 0.12956, 0.12953, 0.12951,
|
||||
0.12949, 0.12949, 0.12949, 0.12948, 0.12947, 0.12947, 0.12946, 0.12945,
|
||||
0.12944, 0.12943, 0.12942, 0.12941, 0.12940, 0.12939, 0.12938, 0.12937,
|
||||
0.12936, 0.12934, 0.12932, 0.12929, 0.12925, 0.12921, 0.12915, 0.12909,
|
||||
0.12902, 0.12894, 0.12885, 0.12876, 0.12865, 0.12853, 0.12841, 0.12827,
|
||||
0.12812, 0.12797, 0.12781, 0.12762, 0.12743, 0.12723, 0.12701, 0.12677,
|
||||
0.12652, 0.12625, 0.12596, 0.12567, 0.12535, 0.12500, 0.12464, 0.12424,
|
||||
0.12380, 0.12333, 0.12281, 0.12224, 0.12164, 0.12099, 0.12030, 0.11958,
|
||||
0.11883, 0.11805, 0.11724, 0.11641, 0.11554, 0.11466, 0.11375, 0.11282,
|
||||
0.11186, 0.11088, 0.10988, 0.10885, 0.10781, 0.10675, 0.10568, 0.10459,
|
||||
0.10349, 0.10237, 0.10124, 0.10009, 0.09893, 0.09776, 0.09657, 0.09537,
|
||||
0.09416, 0.09294, 0.09170, 0.09045, 0.08919, 0.08793, 0.08664, 0.08537,
|
||||
0.08407, 0.08277, 0.08147, 0.08017, 0.07886, 0.07755, 0.07625, 0.07495,
|
||||
0.07365, 0.07235, 0.07105, 0.06976, 0.06848, 0.06720, 0.06592, 0.06466,
|
||||
0.06340, 0.06215, 0.06091, 0.05967, 0.05846, 0.05724, 0.05604, 0.05485,
|
||||
0.05368, 0.05250, 0.05135, 0.05020, 0.04906, 0.04792, 0.04678, 0.04564,
|
||||
0.04450, 0.04333, 0.04216, 0.04098, 0.03978, 0.03859, 0.03740, 0.03623,
|
||||
0.03508, 0.03396, 0.03288, 0.03184, 0.03085, 0.02992, 0.02906, 0.02827,
|
||||
0.02754, 0.02688, 0.02628, 0.02573, 0.02524, 0.02480, 0.02440, 0.02406,
|
||||
0.02375, 0.02348, 0.02326, 0.02306, 0.02290, 0.02277, 0.02266, 0.02259,
|
||||
0.02252, 0.02247, 0.02245, 0.02242, 0.02242, 0.02242, 0.02242, 0.02242,
|
||||
0.02243
|
||||
};
|
||||
|
||||
const fastf_t PSI8[] = {
|
||||
0.14761, 0.14746, 0.14701, 0.14632, 0.14542, 0.14435, 0.14314, 0.14185,
|
||||
0.14052, 0.13916, 0.13785, 0.13662, 0.13554, 0.13460, 0.13376, 0.13296,
|
||||
0.13216, 0.13136, 0.13056, 0.12974, 0.12892, 0.12808, 0.12722, 0.12638,
|
||||
0.12555, 0.12476, 0.12406, 0.12342, 0.12288, 0.12247, 0.12219, 0.12204,
|
||||
0.12199, 0.12201, 0.12210, 0.12222, 0.12235, 0.12246, 0.12258, 0.12268,
|
||||
0.12279, 0.12289, 0.12300, 0.12310, 0.12321, 0.12331, 0.12343, 0.12354,
|
||||
0.12365, 0.12376, 0.12387, 0.12397, 0.12407, 0.12417, 0.12426, 0.12435,
|
||||
0.12443, 0.12451, 0.12459, 0.12466, 0.12472, 0.12478, 0.12484, 0.12488,
|
||||
0.12492, 0.12496, 0.12499, 0.12501, 0.12502, 0.12503, 0.12502, 0.12501,
|
||||
0.12499, 0.12495, 0.12491, 0.12487, 0.12481, 0.12474, 0.12466, 0.12457,
|
||||
0.12448, 0.12436, 0.12424, 0.12410, 0.12394, 0.12377, 0.12358, 0.12338,
|
||||
0.12316, 0.12292, 0.12266, 0.12237, 0.12206, 0.12174, 0.12137, 0.12099,
|
||||
0.12058, 0.12013, 0.11965, 0.11914, 0.11859, 0.11801, 0.11740, 0.11675,
|
||||
0.11607, 0.11534, 0.11459, 0.11379, 0.11297, 0.11211, 0.11122, 0.11031,
|
||||
0.10937, 0.10840, 0.10741, 0.10639, 0.10536, 0.10431, 0.10324, 0.10217,
|
||||
0.10107, 0.09995, 0.09881, 0.09766, 0.09650, 0.09532, 0.09412, 0.09292,
|
||||
0.09170, 0.09046, 0.08921, 0.08796, 0.08668, 0.08541, 0.08412, 0.08282,
|
||||
0.08151, 0.08020, 0.07889, 0.07755, 0.07622, 0.07489, 0.07354, 0.07220,
|
||||
0.07084, 0.06949, 0.06813, 0.06678, 0.06543, 0.06408, 0.06275, 0.06141,
|
||||
0.06009, 0.05879, 0.05749, 0.05621, 0.05494, 0.05367, 0.05240, 0.05113,
|
||||
0.04985, 0.04857, 0.04727, 0.04597, 0.04465, 0.04333, 0.04202, 0.04072,
|
||||
0.03943, 0.03818, 0.03695, 0.03577, 0.03463, 0.03355, 0.03252, 0.03156,
|
||||
0.03067, 0.02982, 0.02904, 0.02831, 0.02763, 0.02702, 0.02644, 0.02592,
|
||||
0.02544, 0.02500, 0.02461, 0.02426, 0.02394, 0.02365, 0.02341, 0.02320,
|
||||
0.02302, 0.02286, 0.02274, 0.02263, 0.02255, 0.02250, 0.02245, 0.02243,
|
||||
0.02242
|
||||
};
|
||||
|
||||
/*
|
||||
* Local Variables:
|
||||
* tab-width: 8
|
||||
* mode: C
|
||||
* indent-tabs-mode: t
|
||||
* c-file-style: "stroustrup"
|
||||
* End:
|
||||
* ex: shiftwidth=4 tabstop=8
|
||||
*/
|
||||
@@ -1,469 +0,0 @@
|
||||
/* N A C A . H
|
||||
* BRL-CAD
|
||||
*
|
||||
* Copyright (c) 2014-2021 United States Government as represented by
|
||||
* the U.S. Army Research Laboratory.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
*
|
||||
* 2. Redistributions in binary form must reproduce the above
|
||||
* copyright notice, this list of conditions and the following
|
||||
* disclaimer in the documentation and/or other materials provided
|
||||
* with the distribution.
|
||||
*
|
||||
* 3. The name of the author may not be used to endorse or promote
|
||||
* products derived from this software without specific prior written
|
||||
* permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
|
||||
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
|
||||
* GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
||||
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
||||
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
/** @file naca.h
|
||||
*
|
||||
* BRL-CAD's translation of the calculation of coordinates for NACA airfoils is
|
||||
* based on the public domain program naca456 written by Ralph Carmichael of
|
||||
* Public Domain Aeronautical Software (PDAS):
|
||||
*
|
||||
* http://www.pdas.com/naca456.html
|
||||
*
|
||||
* naca456 is in turn based off of earlier work by several authors at NASA,
|
||||
* documented in reports NASA TM X-3284, NASA TM X-3069 and NASA TM 4741. The
|
||||
* program naca456 is documented in the paper:
|
||||
*
|
||||
* Carmichael, Ralph L.: Algorithm for Calculating Coordinates of Cambered NACA
|
||||
* Airfoils At Specified Chord Locations. AIAA Paper 2001-5235, November 2001.
|
||||
*
|
||||
* Disclaimer, per the PDAS distribution:
|
||||
*
|
||||
* Although many of the works contained herein were developed by national
|
||||
* laboratories or their contractors, neither the U.S. Government nor Public
|
||||
* Domain Aeronautical Software make any warranty as to the accuracy or
|
||||
* appropriateness of the procedure to any particular application.
|
||||
*
|
||||
* The programs and descriptions have been collected and reproduced with great
|
||||
* care and attention to accuracy, but no guarantee or warranty is implied. All
|
||||
* programs are offered AS IS and Public Domain Aeronautical Software does not
|
||||
* give any express or implied warranty of any kind and any implied warranties are
|
||||
* disclaimed. Public Domain Aeronautical Software will not be liable for any
|
||||
* direct, indirect, special, incidental, or consequential damages arising out of
|
||||
* any use of this software. In no case should the results of any computational
|
||||
* scheme be used as a substitute for sound engineering practice and judgment.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "common.h"
|
||||
|
||||
#include "vmath.h"
|
||||
|
||||
|
||||
/* The array in this structure should be 1-indexed */
|
||||
struct fortran_array {
|
||||
int n;
|
||||
fastf_t *nums;
|
||||
};
|
||||
#define SIZE(array) array->n
|
||||
#define INDEX(array, n) array->nums[n]
|
||||
#define ALLOCATE(array, _n) do { \
|
||||
array = (struct fortran_array *)malloc(sizeof(struct fortran_array)); \
|
||||
array->nums = (fastf_t *)malloc(sizeof(fastf_t) * (_n + 1)); \
|
||||
array->n = _n; \
|
||||
} while (0);
|
||||
#define DEALLOCATE(array) do { \
|
||||
free(array->nums); \
|
||||
free(array); \
|
||||
} while (0);
|
||||
#define SLICE(new, array, start, end) do { \
|
||||
new = (struct fortran_array *)malloc(sizeof(struct fortran_array)); \
|
||||
new->n = (end - start) + 1; \
|
||||
new->nums = array->nums + start - 1; \
|
||||
} while (0);
|
||||
#define COPY(new, array, start, end) do { \
|
||||
VMOVEN(F2C(new), F2CI(array, start), (end - start) + 1); \
|
||||
} while (0);
|
||||
|
||||
#define F2C(array) F2CI(array, 1)
|
||||
#define F2CI(array, indx) (array->nums + indx)
|
||||
|
||||
#define C2F(array, carray, n) do { \
|
||||
ALLOCATE(array, n); \
|
||||
VMOVEN(array->nums + 1, carray, n); \
|
||||
} while (0);
|
||||
|
||||
#define SIGNUM(x) ((x > 0) - (x < 0))
|
||||
#define SIGN(a, b) (a * SIGNUM(b))
|
||||
|
||||
/**
|
||||
* Evaluate a cubic polynomial and its 1st, 2nd, and 3rd derivatives
|
||||
* at a specified point. The cubic is defined by the function and the
|
||||
* 1st derivative at two points. The cubic isi mapped onto [0,1] for
|
||||
* some savings in computation. If no derivatives are wanted, it is
|
||||
* probably preferable to use the evaluateCubic function.
|
||||
*
|
||||
* Any of f, fp, fpp, and fppp may be null.
|
||||
*
|
||||
* @param[in] a a at first point
|
||||
* @param[in] fa f(a) at first point
|
||||
* @param[in] fpa f'(a) at first point
|
||||
* @param[in] b b at second point
|
||||
* @param[in] fb f(b) at second point
|
||||
* @param[in] fpb f'(b) at second point
|
||||
* @param[in] u The point to evaluate the function at.
|
||||
* @param[out] f f(u)
|
||||
* @param[out] fp f'(u), f''(u), f'''(u)
|
||||
* @param[out] fpp f''(u), f'''(u)
|
||||
* @param[out] fppp f'''(u)
|
||||
*/
|
||||
extern void EvaluateCubicAndDerivs(fastf_t a, fastf_t fa, fastf_t fpa,
|
||||
fastf_t b, fastf_t fb, fastf_t fpb,
|
||||
fastf_t u,
|
||||
fastf_t *f, fastf_t *fp, fastf_t *fpp, fastf_t *fppp);
|
||||
|
||||
/**
|
||||
* Compute the cubic spline with endpoint conditions chosen by FMM
|
||||
* (from the book Forsyth, Malcolm & Moler)
|
||||
*/
|
||||
extern void FMMspline(struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp);
|
||||
|
||||
/**
|
||||
* Interpolate in a cubic spline at one point
|
||||
*
|
||||
* @param[in] x Defines the cubic spline
|
||||
* @param[in] y Defines the cubic spline
|
||||
* @param[in] yp Defines the cubic spline
|
||||
* @param[in] u Point where spline is to be evaluated
|
||||
* @param[out] f f(u)
|
||||
* @param[out] fp f'(u), f''(u), f'''(u)
|
||||
* @param[out] fpp f''(u), f'''(u)
|
||||
* @param[out] fppp f'''(u)
|
||||
*/
|
||||
extern void PClookup(struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp,
|
||||
fastf_t u,
|
||||
fastf_t *f, fastf_t *fp, fastf_t *fpp, fastf_t *fppp);
|
||||
|
||||
/**
|
||||
* Find a value of x corresponding to a value of fbar of the cubic
|
||||
* spline defined by arrays x, f, fp. f is the value of the spline at
|
||||
* x and fp is the first derivative.
|
||||
*
|
||||
* The spline is searched for an interval that crosses the specified
|
||||
* value. Then Brent's method is used for finding the zero.
|
||||
*/
|
||||
extern void SplineZero(struct fortran_array *x, struct fortran_array *f, struct fortran_array *fp,
|
||||
fastf_t fbar, fastf_t tol,
|
||||
fastf_t *xbar, int *errCode);
|
||||
|
||||
/**
|
||||
* Use polynomial evaluation for table lookup. Find points ahead and
|
||||
* behind evaluation point to match order of interpolation desired.
|
||||
*
|
||||
* @param[in] x Data tables
|
||||
* @param[in] y Data tables
|
||||
* @param[in] order Order of interpolation (1 = linear, 2 = quadratic ...)
|
||||
* @param[in] u x-coord where function is to be evaluated
|
||||
*/
|
||||
extern fastf_t TableLookup(struct fortran_array *x, struct fortran_array *y, int order, fastf_t u);
|
||||
|
||||
|
||||
|
||||
/**
|
||||
* Add the computed thickness and camber to get a cambered airfoil.
|
||||
*
|
||||
* NOTE - The dimension of xupper, ... must not be less than that of x.
|
||||
*
|
||||
* Note on param thick: note this the half-thickness
|
||||
*/
|
||||
void CombineThicknessAndCamber(struct fortran_array *x, struct fortran_array *thick, struct fortran_array *y, struct fortran_array *yp,
|
||||
struct fortran_array *xupper, struct fortran_array *yupper, struct fortran_array *xlower, struct fortran_array *ylower);
|
||||
|
||||
/**
|
||||
* Compute the r and k1 factors used in the calculation of ordinates
|
||||
* of a three-digit mean line.
|
||||
*
|
||||
* REF: Table, upper left of p.8 of NASA Technical Memorandum 4741
|
||||
*
|
||||
* @param[in] x x-coor of max. camber ( in [0,0.25] )
|
||||
* @param[out] r factor used by MeanLine3
|
||||
* @param[out] k1 factor used by MeanLine3
|
||||
*/
|
||||
void GetRk1(fastf_t x, fastf_t *r, fastf_t *k1);
|
||||
|
||||
/**
|
||||
* Compute the r, k1, and k2 factors used in the calculation of
|
||||
* ordinates of a three-digit-reflex mean line
|
||||
*
|
||||
* REF - Table, upper right, of p.8 of NASA Technical Memorandum 4741.
|
||||
*
|
||||
* NOTE - This is really the correct equation for k2. It was printed
|
||||
* incorrectly on p. 9 of NASA TM X-3284 in 1976 and then changed
|
||||
* (incorrectly!!) on p.8 of NASA TM 4741 in 1995. Eastman Jacobs had
|
||||
* it right the first time on p.522 of NACA Report 537 in 1935.
|
||||
*
|
||||
* @param[in] x x-coor of maximum camber ( in [0,0.25] )
|
||||
* @param[out] r factor used by MeanLine3R
|
||||
* @param[out] k1 factor used by MeanLine3R
|
||||
* @param[out] k2 factor used by MeanLine3R
|
||||
*/
|
||||
void GetRk1k2(fastf_t x, fastf_t *r, fastf_t *k1, fastf_t *k2);
|
||||
|
||||
/**
|
||||
* Compute the upper and lower coordinates of an airfoil defined by the
|
||||
* thickness (x,yt) and the mean line (x,ymean,ymeanp)
|
||||
*/
|
||||
void InterpolateCombinedAirfoil(struct fortran_array *x, struct fortran_array *yt, struct fortran_array *ymean, struct fortran_array *ymeanp,
|
||||
struct fortran_array *yu, struct fortran_array *yl,
|
||||
struct fortran_array *yup, struct fortran_array *ylp);
|
||||
|
||||
/**
|
||||
* Using the airfoil defined by (xupper, yupper) for upper surface and
|
||||
* (xlower, ylower) for the lower surface, interpolate at each point
|
||||
* of array x to yield yu and yup on upper surface and yl and ylp on
|
||||
* lower.
|
||||
*
|
||||
* NOTE - xupper and xlower do not need to be the same size.
|
||||
*/
|
||||
void InterpolateUpperAndLower(struct fortran_array *xupper, struct fortran_array *yupper,
|
||||
struct fortran_array *xlower, struct fortran_array *ylower,
|
||||
struct fortran_array *x,
|
||||
struct fortran_array *yu, struct fortran_array *yl,
|
||||
struct fortran_array *yup, struct fortran_array *ylp);
|
||||
|
||||
/**
|
||||
* Compute the leading edge radius of a 4-digit thickness
|
||||
* distribution
|
||||
*
|
||||
* @param[in] toc maximum value of t/c
|
||||
*/
|
||||
fastf_t LeadingEdgeRadius4(fastf_t toc);
|
||||
|
||||
/**
|
||||
* Compute the leading edge radius of a 4-digit-modified thickness
|
||||
* distribution from the thickness and the le index.
|
||||
*
|
||||
* NOTE - leIndex is coded as fastf_t, although it is usually integer.
|
||||
*
|
||||
* @param[in] toc maximum value of t/c
|
||||
* @param[in] leIndex leading edge index
|
||||
*/
|
||||
fastf_t LeadingEdgeRadius4M(fastf_t toc, fastf_t leIndex);
|
||||
|
||||
/**
|
||||
* Compute the leading edge radius of a 6- or 6A-series thickness
|
||||
* distribution.
|
||||
*
|
||||
* @param[in] family family
|
||||
* @param[in] toc maximum value of t/c
|
||||
*/
|
||||
fastf_t LeadingEdgeRadius6(fastf_t family, fastf_t toc);
|
||||
|
||||
/**
|
||||
* Calculates a table of x-values to be used for the output. They are
|
||||
* very dense at the nose, less dense on the forward airfoil and much
|
||||
* less dense on the aft airfoil.
|
||||
*/
|
||||
void LoadX(int denCode, int nx, struct fortran_array *x);
|
||||
|
||||
/**
|
||||
* Compute displacement and slope of the NACA 2-digit mean line.
|
||||
*
|
||||
* NOTE - E.g., a NACA Mean Line 64 has cmax = 0.06 and xmax = 0.4.
|
||||
*
|
||||
* REF - Eq 6.4, p.114 of Abbot and von Doenhoff
|
||||
*
|
||||
* @param[in] cmax max. camber as fraction of chord
|
||||
* @param[in] xmaxc fraction of chord where the camber is max.
|
||||
* @param[in] x x
|
||||
* @param[out] ym ym
|
||||
* @param[out] ymp ymp
|
||||
*/
|
||||
void MeanLine2(fastf_t cmax,
|
||||
fastf_t xmaxc,
|
||||
struct fortran_array *x,
|
||||
struct fortran_array *ym, struct fortran_array *ymp);
|
||||
|
||||
/**
|
||||
* Compute displacement and slope of the NACA 3-digit mean line.
|
||||
* EXAMPLE - A 210 mean line has design CL=0.3 and max camber at 5 percent
|
||||
* (first digit is 2/3 CL in tenths; second digit is twice x of max
|
||||
* camber in percent chord; third digit, zero, indicates non reflexed)
|
||||
*
|
||||
* REF - Eq. 6.6 p.115 of Abbot and von Doenhoff
|
||||
*
|
||||
* NOTE - The constant 1.8
|
||||
*
|
||||
* @param[in] cl design lift coefficient
|
||||
* @param[in] xmaxc x-coor of maximum camber
|
||||
* @param[in] x x
|
||||
* @param[out] ym ym
|
||||
* @param[out] ymp ymp
|
||||
*/
|
||||
void MeanLine3(fastf_t cl,
|
||||
fastf_t xmaxc,
|
||||
struct fortran_array *x,
|
||||
struct fortran_array *ym, struct fortran_array *ymp);
|
||||
|
||||
/**
|
||||
* Compute displacement and slope of the NACA 3-digit reflex mean line
|
||||
*
|
||||
* NOTE - The constant 1.8 appears in the final calculation. This
|
||||
* comes from the fact that the basic equation is given for cl = 0.3
|
||||
* and that there is a 6 in the denominator, so one finally multiplies
|
||||
* by (cl/0.3)/6
|
||||
*
|
||||
* REF - p.8 of NASA Technical Memorandum 474 and NACA Report 537.
|
||||
*
|
||||
* @param[in] cl design lift coefficient
|
||||
* @param[in] xmaxc x-coor of maximum camber
|
||||
* @param[in] x x
|
||||
* @param[out] ym ym
|
||||
* @param[out] ymp ymp
|
||||
*/
|
||||
void MeanLine3Reflex(fastf_t cl,
|
||||
fastf_t xmaxc,
|
||||
struct fortran_array *x,
|
||||
struct fortran_array *ym, struct fortran_array *ymp);
|
||||
|
||||
/**
|
||||
* Compute the displacement and slope of a 6-series mean line.
|
||||
*
|
||||
* REF - EQ. 4-26 and 4-27, p.74 of Abbott and von Doenhoff.
|
||||
*
|
||||
* @param[in] a chordwise extent of uniform loading 0 <= a <= 1
|
||||
* @param[in] cl design CL of the mean line
|
||||
* @param[out] x fraction of chord
|
||||
* @param[out] ym y-coord of meanline
|
||||
* @param[out] ymp dy/dx of mean line
|
||||
*/
|
||||
void MeanLine6(fastf_t a, fastf_t cl, struct fortran_array *x, struct fortran_array *ym, struct fortran_array *ymp);
|
||||
|
||||
/**
|
||||
* Compute the displacement and slope of a modified six-series mean
|
||||
* line as designed for use with the 6A-series profiles
|
||||
*
|
||||
* REF - p.210 of NACA Report 903 (Larry Loftin).
|
||||
*
|
||||
* NOTE - a is not an input variable; it is always 0.8 for this mean line.
|
||||
*
|
||||
* @param[in] cl the design lift coefficient
|
||||
* @param[in] x fraction of chord
|
||||
* @param[out] ym y-coor of meanline
|
||||
* @param[out] ymp dy/dx of mean line
|
||||
*/
|
||||
void MeanLine6M(fastf_t cl, struct fortran_array *x, struct fortran_array *ym, struct fortran_array *ymp);
|
||||
|
||||
/**
|
||||
* Define the shape of an airfoil parametrically using s, the
|
||||
* inscribed arc length, s. s = 0 at the trailing edge, then
|
||||
* increases by moving forward along the upper surface, then around
|
||||
* the nose and rearward along the lower surface. The final value of
|
||||
* s is somewhat greater than 2.
|
||||
*/
|
||||
void ParametrizeAirfoil(struct fortran_array *xupper, struct fortran_array *yupper, struct fortran_array *xlower, struct fortran_array *ylower,
|
||||
struct fortran_array *s, struct fortran_array *x, struct fortran_array *y);
|
||||
|
||||
/**
|
||||
* Compute the scale factor used to multiply the epsilon and psi
|
||||
* functions to get the proper thickness/chord for the mapping of a
|
||||
* six-series airfoil (or 6A).
|
||||
*
|
||||
* REF - Discussed in AIAA-2001-5235
|
||||
*
|
||||
* @param[in] family 1 = 63, 2 = 64, 3 = 65, 4 = 66, 5 = 67,
|
||||
* 6 = 63A, 7 = 64A, 8 = 65A
|
||||
* @param[in] tc desired t/c (fraction, not percent)
|
||||
*/
|
||||
fastf_t ScaleFactor(int family, fastf_t tc);
|
||||
|
||||
/**
|
||||
* Set the data points that define a 6-series or 6A-series thickness
|
||||
* distribution. User has no control of the spacing of xt - it
|
||||
* depends on phi, eps, psi
|
||||
*
|
||||
* @param[in] family 1 = 63, 2 = 64, 3 = 65, 4 = 66, 5 = 67,
|
||||
* 6 = 63A, 7 = 64A, 8 = 65A
|
||||
* @param[in] tc max value of t / c
|
||||
* @param[out] xt xt
|
||||
* @param[out] yt yt
|
||||
*/
|
||||
void SetSixDigitPoints(int family, fastf_t tc, struct fortran_array *xt, struct fortran_array *yt);
|
||||
|
||||
/**
|
||||
* Compute the values of y, dy/dx, d2y/dx2 at each point of x.
|
||||
*/
|
||||
void Thickness4(fastf_t toc, struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp, struct fortran_array *ypp);
|
||||
|
||||
/**
|
||||
* Compute the thickness distribution (and derivatives) of a NACA
|
||||
* 4-digit-modified section.
|
||||
*
|
||||
* NOTE - First digit after dash is l.e. index; 2nd is loc of max thickness
|
||||
*
|
||||
* @param[in] toc toc
|
||||
* @param[in] leIndex leading edge index
|
||||
* @param[in] xmaxt x-coor of maximum thickness (fraction of chord)
|
||||
* @param[in] x x
|
||||
* @param[out] y y
|
||||
* @param[out] yp yp
|
||||
* @param[out] ypp ypp
|
||||
*/
|
||||
void Thickness4M(fastf_t toc, fastf_t leIndex, fastf_t xmaxt,
|
||||
struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp, struct fortran_array *ypp);
|
||||
|
||||
/**
|
||||
* Compute the values of y, dy/dx, d2y/d2x at each point of x. The
|
||||
* equation used gives an airfoil that is very similar to the
|
||||
* four-digit airfoil profile, but has a sharp trailing edge. This
|
||||
* airfoil does not have any NACA blessing, so it is strictly
|
||||
* unofficial. Lots of folks want to compute a four-digit section,
|
||||
* but are using a theory that assumes a zero trailing edge.
|
||||
*/
|
||||
void Thickness4sharpTE(fastf_t toc, struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp, struct fortran_array *ypp);
|
||||
|
||||
/**
|
||||
* Compute the values of y, dy/dx, d2y/dx2 at each poitn of x by
|
||||
* interpolation in the tables computed by xxxx.
|
||||
*/
|
||||
void Thickness6(int family, fastf_t toc, struct fortran_array *x,
|
||||
struct fortran_array *y, struct fortran_array *yp, struct fortran_array *ypp);
|
||||
|
||||
|
||||
|
||||
extern const fastf_t EPS1[];
|
||||
extern const fastf_t EPS2[];
|
||||
extern const fastf_t EPS3[];
|
||||
extern const fastf_t EPS4[];
|
||||
extern const fastf_t EPS5[];
|
||||
extern const fastf_t EPS6[];
|
||||
extern const fastf_t EPS7[];
|
||||
extern const fastf_t EPS8[];
|
||||
extern const fastf_t PSI1[];
|
||||
extern const fastf_t PSI2[];
|
||||
extern const fastf_t PSI3[];
|
||||
extern const fastf_t PSI4[];
|
||||
extern const fastf_t PSI5[];
|
||||
extern const fastf_t PSI6[];
|
||||
extern const fastf_t PSI7[];
|
||||
extern const fastf_t PSI8[];
|
||||
|
||||
/*
|
||||
* Local Variables:
|
||||
* tab-width: 8
|
||||
* mode: C
|
||||
* indent-tabs-mode: t
|
||||
* c-file-style: "stroustrup"
|
||||
* End:
|
||||
* ex: shiftwidth=4 tabstop=8
|
||||
*/
|
||||
@@ -1,89 +0,0 @@
|
||||
/* N A C A 4 5 6 . C
|
||||
* BRL-CAD
|
||||
*
|
||||
* Copyright (c) 2014-2021 United States Government as represented by
|
||||
* the U.S. Army Research Laboratory.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
*
|
||||
* 2. Redistributions in binary form must reproduce the above
|
||||
* copyright notice, this list of conditions and the following
|
||||
* disclaimer in the documentation and/or other materials provided
|
||||
* with the distribution.
|
||||
*
|
||||
* 3. The name of the author may not be used to endorse or promote
|
||||
* products derived from this software without specific prior written
|
||||
* permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
|
||||
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
|
||||
* GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
||||
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
||||
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
/** @file naca456.c
|
||||
*
|
||||
* BRL-CAD's translation of the calculation of coordinates for NACA airfoils is
|
||||
* based on the public domain program naca456 written by Ralph Carmichael of
|
||||
* Public Domain Aeronautical Software (PDAS):
|
||||
*
|
||||
* http://www.pdas.com/naca456.html
|
||||
*
|
||||
* naca456 is in turn based off of earlier work by several authors at NASA,
|
||||
* documented in reports NASA TM X-3284, NASA TM X-3069 and NASA TM 4741. The
|
||||
* program naca456 is documented in the paper:
|
||||
*
|
||||
* Carmichael, Ralph L.: Algorithm for Calculating Coordinates of Cambered NACA
|
||||
* Airfoils At Specified Chord Locations. AIAA Paper 2001-5235, November 2001.
|
||||
*
|
||||
* Disclaimer, per the PDAS distribution:
|
||||
*
|
||||
* Although many of the works contained herein were developed by national
|
||||
* laboratories or their contractors, neither the U.S. Government nor Public
|
||||
* Domain Aeronautical Software make any warranty as to the accuracy or
|
||||
* appropriateness of the procedure to any particular application.
|
||||
*
|
||||
* The programs and descriptions have been collected and reproduced with great
|
||||
* care and attention to accuracy, but no guarantee or warranty is implied. All
|
||||
* programs are offered AS IS and Public Domain Aeronautical Software does not
|
||||
* give any express or implied warranty of any kind and any implied warranties are
|
||||
* disclaimed. Public Domain Aeronautical Software will not be liable for any
|
||||
* direct, indirect, special, incidental, or consequential damages arising out of
|
||||
* any use of this software. In no case should the results of any computational
|
||||
* scheme be used as a substitute for sound engineering practice and judgment.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "naca.h"
|
||||
#include "bu/app.h"
|
||||
|
||||
int
|
||||
main(int argc, const char **argv)
|
||||
{
|
||||
bu_setprogname(argv[0]);
|
||||
if (!argc || !argv)
|
||||
return 1;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
/*
|
||||
* Local Variables:
|
||||
* tab-width: 8
|
||||
* mode: C
|
||||
* indent-tabs-mode: t
|
||||
* c-file-style: "stroustrup"
|
||||
* End:
|
||||
* ex: shiftwidth=4 tabstop=8
|
||||
*/
|
||||
File diff suppressed because it is too large.
Load diff
@@ -1,485 +0,0 @@
|
||||
/* S P L P R O C S . C
|
||||
* BRL-CAD
|
||||
*
|
||||
* Copyright (c) 2014-2021 United States Government as represented by
|
||||
* the U.S. Army Research Laboratory.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
*
|
||||
* 2. Redistributions in binary form must reproduce the above
|
||||
* copyright notice, this list of conditions and the following
|
||||
* disclaimer in the documentation and/or other materials provided
|
||||
* with the distribution.
|
||||
*
|
||||
* 3. The name of the author may not be used to endorse or promote
|
||||
* products derived from this software without specific prior written
|
||||
* permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
|
||||
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
|
||||
* GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
||||
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
||||
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
/** @file splprocs.c
|
||||
*
|
||||
* BRL-CAD's translation of the calculation of coordinates for NACA airfoils is
|
||||
* based on the public domain program naca456 written by Ralph Carmichael of
|
||||
* Public Domain Aeronautical Software (PDAS):
|
||||
*
|
||||
* http://www.pdas.com/naca456.html
|
||||
*
|
||||
* naca456 is in turn based off of earlier work by several authors at NASA,
|
||||
* documented in reports NASA TM X-3284, NASA TM X-3069 and NASA TM 4741. The
|
||||
* program naca456 is documented in the paper:
|
||||
*
|
||||
* Carmichael, Ralph L.: Algorithm for Calculating Coordinates of Cambered NACA
|
||||
* Airfoils At Specified Chord Locations. AIAA Paper 2001-5235, November 2001.
|
||||
*
|
||||
* Disclaimer, per the PDAS distribution:
|
||||
*
|
||||
* Although many of the works contained herein were developed by national
|
||||
* laboratories or their contractors, neither the U.S. Government nor Public
|
||||
* Domain Aeronautical Software make any warranty as to the accuracy or
|
||||
* appropriateness of the procedure to any particular application.
|
||||
*
|
||||
* The programs and descriptions have been collected and reproduced with great
|
||||
* care and attention to accuracy, but no guarantee or warranty is implied. All
|
||||
* programs are offered AS IS and Public Domain Aeronautical Software does not
|
||||
* give any express or implied warranty of any kind and any implied warranties are
|
||||
* disclaimed. Public Domain Aeronautical Software will not be liable for any
|
||||
* direct, indirect, special, incidental, or consequential damages arising out of
|
||||
* any use of this software. In no case should the results of any computational
|
||||
* scheme be used as a substitute for sound engineering practice and judgment.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "common.h"
|
||||
|
||||
#include <stdlib.h>
|
||||
|
||||
#include "bu/defines.h"
|
||||
#include "vmath.h"
|
||||
#include "bn.h"
|
||||
|
||||
#include "naca.h"
|
||||
|
||||
static fastf_t Zeroin(fastf_t ax, fastf_t bx, fastf_t (*f)(fastf_t x), fastf_t tol);
|
||||
|
||||
/* Globals for EvaluateCubic (g prefix for global) */
|
||||
fastf_t ga, gfa, gfpa;
|
||||
fastf_t gb, gfb, gfpb;
|
||||
|
||||
/**
|
||||
* Evaluate a cubic polynomial defined by the function and the first
|
||||
* derivative at two points.
|
||||
*
|
||||
* @param[in] u The point to evaluate the function at.
|
||||
*/
|
||||
static fastf_t
|
||||
EvaluateCubic(fastf_t u)
|
||||
{
|
||||
fastf_t d = (gfb - gfa) / (gb - ga);
|
||||
fastf_t t = (u - ga) / (gb - ga);
|
||||
fastf_t p = 1.0 - t;
|
||||
return p * gfa + t * gfb - p * t * (gb - ga) * (p * (d - gfpa) - t * (d - gfpb));
|
||||
}
|
||||
|
||||
void
|
||||
EvaluateCubicAndDerivs(fastf_t a, fastf_t fa, fastf_t fpa,
|
||||
fastf_t b, fastf_t fb, fastf_t fpb,
|
||||
fastf_t u,
|
||||
fastf_t *f, fastf_t *fp, fastf_t *fpp, fastf_t *fppp)
|
||||
{
|
||||
/* The "magic" matrix */
|
||||
const mat_t magic = {2.0, -2.0, 1.0, 1.0,
|
||||
-3.0, 3.0, -2.0, -1.0,
|
||||
0.0, 0.0, 1.0, 0.0,
|
||||
1.0, 0.0, 0.0, 0.0};
|
||||
|
||||
hvect_t coef, rhs;
|
||||
fastf_t h, t;
|
||||
|
||||
HSET(rhs, fa, fb, fpa * (b - a), fpb * (b - a));
|
||||
bn_matXvec(coef, magic, rhs);
|
||||
|
||||
/* CAUTION - these are not the coefficients of the cubic in the
|
||||
* original coordinates. This is the cubic on [0,1] from the
|
||||
* mapping t=(x-a)/(b-a). That is why the h terms appear in the
|
||||
* derivatives
|
||||
*/
|
||||
h = 1.0/(b - a);
|
||||
t = (u - a) * h;
|
||||
if (f) { *f = coef[3] + t * (coef[2] + t * (coef[1] + t * coef[0])); }
|
||||
if (fp) { *fp = h * (coef[2] + t * (2.0 * coef[1] + t * 3.0 * coef[0])); }
|
||||
if (fpp) { *fpp = h * h * (2.0 * coef[1] + t * 6.0 * coef[0]); }
|
||||
if (fppp) { *fppp = h * h * h * 6.0 * coef[0]; }
|
||||
}
|
||||
|
||||
|
||||
void
|
||||
FMMspline(struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp)
|
||||
{
|
||||
int i, n;
|
||||
fastf_t deriv1, deriv2;
|
||||
struct fortran_array *dx, *dy, *delta, *dd, *alpha, *beta, *sigma, *tmp;
|
||||
|
||||
/* y and yp must be at least this size */
|
||||
n = SIZE(x);
|
||||
if (n < 2) {
|
||||
INDEX(yp, 1) = 0.0;
|
||||
return;
|
||||
}
|
||||
ALLOCATE(dx, n - 1);
|
||||
ALLOCATE(dy, n - 1);
|
||||
ALLOCATE(delta, n - 1);
|
||||
VSUB2N(F2C(dx), F2CI(dx, 2), F2C(x), n - 1);
|
||||
VSUB2N(F2C(dy), F2CI(dy, 2), F2C(y), n - 1);
|
||||
for (i = 1; i <= n; i++) {
|
||||
INDEX(delta, i) = INDEX(dy, i) / INDEX(dx, i);
|
||||
}
|
||||
if (n == 2) {
|
||||
INDEX(yp, 1) = INDEX(delta, 1);
|
||||
INDEX(yp, 2) = INDEX(delta, 2);
|
||||
DEALLOCATE(dx);
|
||||
DEALLOCATE(dy);
|
||||
DEALLOCATE(delta);
|
||||
return;
|
||||
}
|
||||
ALLOCATE(dd, n - 2);
|
||||
VSUB2N(F2C(dd), F2CI(delta, 2), F2C(delta), n - 2);
|
||||
if (n == 3) {
|
||||
deriv2 = INDEX(dd, 1) / (INDEX(x, 3) - INDEX(x, 1));
|
||||
deriv1 = INDEX(delta, 1) - deriv2 * INDEX(dx, 1);
|
||||
INDEX(yp, 1) = deriv1;
|
||||
INDEX(yp, 2) = deriv1 + deriv2 * INDEX(dx, 1);
|
||||
INDEX(yp, 3) = deriv1 + deriv2 * (INDEX(x, 3) - INDEX(x, 1));
|
||||
DEALLOCATE(dx);
|
||||
DEALLOCATE(dy);
|
||||
DEALLOCATE(delta);
|
||||
DEALLOCATE(dd);
|
||||
}
|
||||
/* This gets rid of the trivial cases n = 1, 2, 3. Assume from here on n > 3 */
|
||||
|
||||
ALLOCATE(alpha, n);
|
||||
ALLOCATE(beta, n);
|
||||
ALLOCATE(sigma, n);
|
||||
ALLOCATE(tmp, n);
|
||||
INDEX(alpha, 1) = -INDEX(dx, 1);
|
||||
VADD2N(F2CI(alpha, 2), F2CI(dx, 1), F2CI(dx, 2), n - 2);
|
||||
VSCALEN(F2CI(alpha, 2), F2CI(alpha, 2), 2.0, n - 2);
|
||||
/* Serial loop, fwd elimination */
|
||||
for (i = 2; i <= n - 1; i ++) {
|
||||
INDEX(alpha, i) = INDEX(alpha, i) - INDEX(dx, i - 1) * INDEX(dx, i - 1) / INDEX(alpha, i - 1);
|
||||
}
|
||||
INDEX(alpha, n) = -INDEX(dx, n - 1) - INDEX(dx, n - 1) * INDEX(dx, n - 1) / INDEX(alpha, n - 1);
|
||||
|
||||
INDEX(beta, 1) = INDEX(dd, 2) / (INDEX(x, 4) - INDEX(x, 2)) - INDEX(dd, 1) / (INDEX(x, 3) - INDEX(x, 1));
|
||||
INDEX(beta, 1) = INDEX(beta, 1) * INDEX(dx, 1) * INDEX(dx, 1) / (INDEX(x, 4) - INDEX(x, 1));
|
||||
SLICE(tmp, beta, 2, n-1);
|
||||
COPY(tmp, dd, 1, n - 2);
|
||||
INDEX(beta, n) = INDEX(dd, n - 2) / (INDEX(x, n) - INDEX(x, n - 2)) - INDEX(dd, n - 3) / (INDEX(x, n - 1 ) - INDEX(x, n - 3));
|
||||
INDEX(beta, n) = -INDEX(beta, n) * INDEX(dx, n - 1) * INDEX(dx, n - 1) / (INDEX(x, n) - INDEX(x, n - 3));
|
||||
/* Serial loop, fwd elimination */
|
||||
for (i = 2; i <= n; i++) {
|
||||
INDEX(beta, i) = INDEX(beta, i) - INDEX(dx, i - 1) * INDEX(beta, i - 1) / INDEX(alpha, i - 1);
|
||||
}
|
||||
|
||||
INDEX(sigma, n) = INDEX(beta, n) / INDEX(alpha, n);
|
||||
/* Reverse order serial loop, back substitution */
|
||||
for (i = n - 1; i <= 1; i--) {
|
||||
INDEX(sigma, i) = (INDEX(beta, i) - INDEX(dx, i) * INDEX(sigma, i + 1)) / INDEX(alpha, i);
|
||||
}
|
||||
|
||||
for (i = 1; i <= n - 1; i++) {
|
||||
INDEX(yp, i) = INDEX(delta, i) - INDEX(dx, i) * (INDEX(sigma, i) + INDEX(sigma, i) + INDEX(sigma, i + 1));
|
||||
}
|
||||
INDEX(yp, n) = INDEX(yp, n - 1) + INDEX(dx, n - 1) * 3.0 * (INDEX(sigma, n) + INDEX(sigma, n - 1));
|
||||
|
||||
DEALLOCATE(dx);
|
||||
DEALLOCATE(dy);
|
||||
DEALLOCATE(delta);
|
||||
DEALLOCATE(alpha);
|
||||
DEALLOCATE(beta);
|
||||
DEALLOCATE(sigma);
|
||||
DEALLOCATE(dd);
|
||||
return;
|
||||
}
|
||||
|
||||
/**
|
||||
* Compute the value of the interpolating polynomial thru x- and
|
||||
* y-arrays at the x-value of u, using Lagrange's equation.
|
||||
*
|
||||
* @param[in] x Tables of coordinates
|
||||
* @param[in] y Tables of coordinates
|
||||
* @param[in] u value of x-coordinate for interpolation
|
||||
*/
|
||||
static double
|
||||
InterpolatePolynomial(struct fortran_array *x, struct fortran_array *y, fastf_t u)
|
||||
{
|
||||
int n = SIZE(x);
|
||||
struct fortran_array *du;
|
||||
fastf_t sum = 0.0;
|
||||
int i, j;
|
||||
ALLOCATE(du, n);
|
||||
VSETALLN(F2C(du), u, n);
|
||||
VSUB2N(F2C(du), F2C(du), F2C(x), n);
|
||||
for (j = 1; j <= n; j++) {
|
||||
fastf_t fact = 1.0;
|
||||
for (i = 1; i <= n; i++) {
|
||||
if (i != j) {
|
||||
fact = fact * INDEX(du, i) / (INDEX(x, j) - INDEX(x, i));
|
||||
}
|
||||
}
|
||||
sum = sum + INDEX(y, j) * fact;
|
||||
}
|
||||
return sum;
|
||||
}
|
||||
|
||||
/**
|
||||
* Search a sorted (increasing) array to find the interval bounding a
|
||||
* given number. If n is the size of the array a
|
||||
* return 0 if number x is less than a(1)
|
||||
* return n if x > a(n)
|
||||
* return i if a(i) <= x < a(i+1)
|
||||
* If x is exactly equal to a(n), return n
|
||||
*
|
||||
* @param[in] xtab Input array
|
||||
* @param[in] x Input number
|
||||
*/
|
||||
static int
|
||||
Lookup(struct fortran_array *xtab, fastf_t x)
|
||||
{
|
||||
int i;
|
||||
int j, k, n;
|
||||
n = SIZE(xtab);
|
||||
if (n <= 0) {
|
||||
return -1;
|
||||
}
|
||||
|
||||
if (x < INDEX(xtab, 1)) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
if (x > INDEX(xtab, n)) {
|
||||
return n;
|
||||
}
|
||||
|
||||
i = 1;
|
||||
j = SIZE(xtab);
|
||||
while (1) {
|
||||
if (j <= i + 1) { break; }
|
||||
k = (i + j)/2; /* Integer division */
|
||||
if (x < INDEX(xtab, k)) {
|
||||
j = k;
|
||||
} else {
|
||||
i = k;
|
||||
}
|
||||
}
|
||||
|
||||
return i;
|
||||
}
|
||||
|
||||
void
|
||||
PClookup(struct fortran_array *x, struct fortran_array *y, struct fortran_array *yp,
|
||||
fastf_t u,
|
||||
fastf_t *f, fastf_t *fp, fastf_t *fpp, fastf_t *fppp)
|
||||
{
|
||||
fastf_t ud, a, fa, fpa, b, fb, fpb;
|
||||
int k;
|
||||
|
||||
k = Lookup(x, u);
|
||||
V_MIN(k, SIZE(x)-1);
|
||||
V_MAX(k, 1);
|
||||
a = INDEX(x, k);
|
||||
fa = INDEX(y, k);
|
||||
fpa = INDEX(yp, k);
|
||||
b = INDEX(x, k + 1);
|
||||
fb = INDEX(y, k + 1);
|
||||
fpb = INDEX(yp, k + 1);
|
||||
ud = u;
|
||||
EvaluateCubicAndDerivs(a, fa, fpa, b, fb, fpb, ud, f, fp, fpp, fppp);
|
||||
}
|
||||
|
||||
void
|
||||
SplineZero(struct fortran_array *x, struct fortran_array *f, struct fortran_array *fp,
|
||||
fastf_t fbar, fastf_t tol,
|
||||
fastf_t *xbar, int *errCode)
|
||||
{
|
||||
int k, n;
|
||||
struct fortran_array *fLocal;
|
||||
|
||||
n = SIZE(x);
|
||||
|
||||
/* Look for an exact match. Could happen... */
|
||||
for (k = 1; k <= n; k++) {
|
||||
if (fabs(INDEX(f, k) - fbar) < tol) {
|
||||
*xbar = INDEX(x, k);
|
||||
*errCode = 0;
|
||||
return;
|
||||
}
|
||||
}
|
||||
|
||||
ALLOCATE(fLocal, n);
|
||||
VSETALLN(F2C(fLocal), fbar, n);
|
||||
VSUB2N(F2C(fLocal), F2C(f), F2C(fLocal), n);
|
||||
/* Look for a zero of fLocal */
|
||||
|
||||
for (k = 2; k <= n; k++) {
|
||||
if (INDEX(fLocal, k - 1) * INDEX(fLocal, k) < 0.0) break;
|
||||
}
|
||||
if (k == n + 1) { /* No crossing could be found */
|
||||
*errCode = 1;
|
||||
DEALLOCATE(fLocal);
|
||||
return;
|
||||
}
|
||||
|
||||
*errCode = 0;
|
||||
/* Set the global variables for EvaluateCubic */
|
||||
ga = INDEX(x, k - 1);
|
||||
gfa = INDEX(fLocal, k - 1);
|
||||
gfpa = INDEX(fp, k - 1);
|
||||
gb = INDEX(x, k);
|
||||
gfb = INDEX(fLocal, k);
|
||||
gfpb = INDEX(fp, k);
|
||||
DEALLOCATE(fLocal);
|
||||
*xbar = Zeroin(ga, gb, EvaluateCubic, tol);
|
||||
}
|
||||
|
||||
fastf_t
|
||||
TableLookup(struct fortran_array *x, struct fortran_array *y, int order, fastf_t u)
|
||||
{
|
||||
int j, m;
|
||||
/* Used for the parameters to InterpolatePolynomial */
|
||||
struct fortran_array *xp, *yp;
|
||||
|
||||
m = order + 1;
|
||||
V_MIN(m, SIZE(x)); /* number of points used for interpolating poly */
|
||||
j = Lookup(x, u);
|
||||
j = j - (m / 2 - 1);
|
||||
V_MIN(j, 1 + SIZE(x) - m); /* j + m - 1 must not exceed SIZE(x) */
|
||||
V_MIN(j, 1); /* j must be positive */
|
||||
/* Use points j through j + m - 1 for interpolation (m points) */
|
||||
SLICE(xp, x, j, j + m - 1);
|
||||
SLICE(yp, y, j, j + m - 1);
|
||||
return InterpolatePolynomial(xp, yp, u);
|
||||
}
|
||||
|
||||
/**
|
||||
* Compute a zero of f in the interval (ax, bx)
|
||||
*
|
||||
* ax and bx are the lift and right endpoints of the interval, tol is
|
||||
* the desired interval of uncertainty.
|
||||
*
|
||||
* @param[in] ax left endpoint of interval
|
||||
* @param[in] bx right endpoint of interval
|
||||
* @param[in] tol desired interval of uncertainty
|
||||
*/
|
||||
static fastf_t
|
||||
Zeroin(fastf_t ax, fastf_t bx, fastf_t (*f)(fastf_t x), fastf_t tol)
|
||||
{
|
||||
const int MAX_ITER = 500;
|
||||
int k;
|
||||
fastf_t a, b, c, eps, fa, fb, fc, tol1, xm, p, r, s, tmp;
|
||||
|
||||
fastf_t d = 0.0;
|
||||
fastf_t e = 0.0;
|
||||
fastf_t q = 0.0;
|
||||
|
||||
eps = SMALL_FASTF;
|
||||
a = ax; /* initialization */
|
||||
b = bx;
|
||||
fa = f(a);
|
||||
fb = f(b); /* should test that fa and fb have opposite signs */
|
||||
c = b;
|
||||
fc = fb;
|
||||
e = b - a;
|
||||
|
||||
for (k = 1; k <= MAX_ITER; k++) { /* begin iteration */
|
||||
if (((fb > 0.0) && (fc > 0.0)) || ((fb < 0.0 && fc < 0.0))) {
|
||||
c = a;
|
||||
fc = fa;
|
||||
d = b - a;
|
||||
e = d;
|
||||
}
|
||||
|
||||
if (fabs(fc) < fabs(fb)) {
|
||||
a = b;
|
||||
b = c;
|
||||
c = a;
|
||||
fa = fb;
|
||||
fb = fc;
|
||||
fc = fa;
|
||||
}
|
||||
|
||||
tol1 = 2.0 * eps * fabs(b) + 0.5 * tol; /* convergence test */
|
||||
xm = 0.5 * (c - b);
|
||||
if ((fabs(xm) <= tol1) || (NEAR_ZERO(fb, tol))) {
|
||||
return b;
|
||||
}
|
||||
|
||||
/* Is bisection necessary */
|
||||
if ((fabs(e) <= tol1) && (fabs(fa) > fabs(fb))) {
|
||||
s = fb / fa; /* is quadratic interpolation possible? */
|
||||
if (NEAR_EQUAL(a, c, tol)) {
|
||||
s = fb / fa; /* Use linear interpolation */
|
||||
p = 2.0 * xm * s;
|
||||
q = 1.0 - s;
|
||||
} else {
|
||||
q = fa / fc; /* Use inverse quadratic interpolation */
|
||||
r = fb / fc;
|
||||
s = fb / fa;
|
||||
p = s * (2.0 * xm * q * (q - r) - (b - a) * (r - 1.0));
|
||||
q = (q - 1.0) * (r - 1.0) * (s - 1.0);
|
||||
}
|
||||
|
||||
if (p > 0.0) { q = -q; } /* adjust signs */
|
||||
p = fabs(p);
|
||||
|
||||
tmp = 3.0 * xm * q - fabs(tol1 * q);
|
||||
V_MIN(tmp, fabs(e * q));
|
||||
if (p + p < tmp) {
|
||||
e = d; /* Use interpolation */
|
||||
d = p / q;
|
||||
} else {
|
||||
d = xm; /* Use bisection */
|
||||
e = d;
|
||||
}
|
||||
} else {
|
||||
d = xm; /* Use bisection */
|
||||
e = d;
|
||||
}
|
||||
|
||||
a = b;
|
||||
fa = fb;
|
||||
if (fabs(d) > tol1) {
|
||||
b = b + d;
|
||||
} else {
|
||||
b = b + SIGN(tol1, xm);
|
||||
}
|
||||
fb = f(b);
|
||||
}
|
||||
|
||||
return b; /* but this is a bad return. Max iterations exceeded */
|
||||
}
|
||||
|
||||
/*
|
||||
* Local Variables:
|
||||
* tab-width: 8
|
||||
* mode: C
|
||||
* indent-tabs-mode: t
|
||||
* c-file-style: "stroustrup"
|
||||
* End:
|
||||
* ex: shiftwidth=4 tabstop=8
|
||||
*/
|
||||
Reference in new issue
Block a user