00001 /*<html><pre> -<a href="qh-user.htm" 00002 >-------------------------------</a><a name="TOP">-</a> 00003 00004 user.h 00005 user redefinable constants 00006 00007 see qh-user.htm. see COPYING for copyright information. 00008 00009 before reading any code, review qhull.h for data structure definitions and 00010 the "qh" macro. 00011 */ 00012 00013 #ifndef qhDEFuser 00014 #define qhDEFuser 1 00015 00016 /*============= data types and configuration macros ==========*/ 00017 00018 /*-<a href="qh-user.htm#TOC" 00019 >--------------------------------</a><a name="realT">-</a> 00020 00021 realT 00022 set the size of floating point numbers 00023 00024 qh_REALdigits 00025 maximimum number of significant digits 00026 00027 qh_REAL_1, qh_REAL_2n, qh_REAL_3n 00028 format strings for printf 00029 00030 qh_REALmax, qh_REALmin 00031 maximum and minimum (near zero) values 00032 00033 qh_REALepsilon 00034 machine roundoff. Maximum roundoff error for addition and multiplication. 00035 00036 notes: 00037 Select whether to store floating point numbers in single precision (float) 00038 or double precision (double). 00039 00040 Use 'float' to save about 8% in time and 25% in space. This is particularly 00041 help if high-d where convex hulls are space limited. Using 'float' also 00042 reduces the printed size of Qhull's output since numbers have 8 digits of 00043 precision. 00044 00045 Use 'double' when greater arithmetic precision is needed. This is needed 00046 for Delaunay triangulations and Voronoi diagrams when you are not merging 00047 facets. 00048 00049 If 'double' gives insufficient precision, your data probably includes 00050 degeneracies. If so you should use facet merging (done by default) 00051 or exact arithmetic (see imprecision section of manual, qh-impre.htm). 00052 You may also use option 'Po' to force output despite precision errors. 00053 00054 You may use 'long double', but many format statements need to be changed 00055 and you may need a 'long double' square root routine. S. Grundmann 00056 (sg@eeiwzb.et.tu-dresden.de) has done this. He reports that the code runs 00057 much slower with little gain in precision. 00058 00059 WARNING: on some machines, int f(){realT a= REALmax;return (a == REALmax);} 00060 returns False. Use (a > REALmax/2) instead of (a == REALmax). 00061 00062 REALfloat = 1 all numbers are 'float' type 00063 = 0 all numbers are 'double' type 00064 */ 00065 #define REALfloat 0 00066 00067 #if (REALfloat == 1) 00068 #define realT float 00069 #define REALmax FLT_MAX 00070 #define REALmin FLT_MIN 00071 #define REALepsilon FLT_EPSILON 00072 #define qh_REALdigits 8 /* maximum number of significant digits */ 00073 #define qh_REAL_1 "%6.8g " 00074 #define qh_REAL_2n "%6.8g %6.8g\n" 00075 #define qh_REAL_3n "%6.8g %6.8g %6.8g\n" 00076 00077 #elif (REALfloat == 0) 00078 #define realT double 00079 #define REALmax DBL_MAX 00080 #define REALmin DBL_MIN 00081 #define REALepsilon DBL_EPSILON 00082 #define qh_REALdigits 16 /* maximum number of significant digits */ 00083 #define qh_REAL_1 "%6.16g " 00084 #define qh_REAL_2n "%6.16g %6.16g\n" 00085 #define qh_REAL_3n "%6.16g %6.16g %6.16g\n" 00086 00087 #else 00088 #error unknown float option 00089 #endif 00090 00091 /*-<a href="qh-user.htm#TOC" 00092 >--------------------------------</a><a name="CPUclock">-</a> 00093 00094 qh_CPUclock 00095 define the clock() function for reporting the total time spent by Qhull 00096 returns CPU ticks as a 'long int' 00097 qh_CPUclock is only used for reporting the total time spent by Qhull 00098 00099 qh_SECticks 00100 the number of clock ticks per second 00101 00102 notes: 00103 looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds 00104 to define a custom clock, set qh_CLOCKtype to 0 00105 00106 if your system does not use clock() to return CPU ticks, replace 00107 qh_CPUclock with the corresponding function. It is converted 00108 to unsigned long to prevent wrap-around during long runs. 00109 00110 00111 Set qh_CLOCKtype to 00112 00113 1 for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond 00114 Note: may fail if more than 1 hour elapsed time 00115 00116 2 use qh_clock() with POSIX times() (see global.c) 00117 */ 00118 #define qh_CLOCKtype 1 /* change to the desired number */ 00119 00120 #if (qh_CLOCKtype == 1) 00121 00122 #if defined (CLOCKS_PER_SECOND) 00123 #define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */ 00124 #define qh_SECticks CLOCKS_PER_SECOND 00125 00126 #elif defined (CLOCKS_PER_SEC) 00127 #define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */ 00128 #define qh_SECticks CLOCKS_PER_SEC 00129 00130 #elif defined (CLK_TCK) 00131 #define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */ 00132 #define qh_SECticks CLK_TCK 00133 00134 #else 00135 #define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */ 00136 #define qh_SECticks 1E6 00137 #endif 00138 00139 #elif (qh_CLOCKtype == 2) 00140 #define qh_CPUclock qh_clock() /* return CPU clock */ 00141 #define qh_SECticks 100 00142 00143 #else /* qh_CLOCKtype == ? */ 00144 #error unknown clock option 00145 #endif 00146 00147 /*-<a href="qh-user.htm#TOC" 00148 >--------------------------------</a><a name="RANDOM">-</a> 00149 00150 qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed 00151 define random number generator 00152 00153 qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax. 00154 qh_RANDOMseed sets the random number seed for qh_RANDOMint 00155 00156 Set qh_RANDOMtype (default 5) to: 00157 1 for random() with 31 bits (UCB) 00158 2 for rand() with RAND_MAX or 15 bits (system 5) 00159 3 for rand() with 31 bits (Sun) 00160 4 for lrand48() with 31 bits (Solaris) 00161 5 for qh_rand() with 31 bits (included with Qhull) 00162 00163 notes: 00164 Random numbers are used by rbox to generate point sets. Random 00165 numbers are used by Qhull to rotate the input ('QRn' option), 00166 simulate a randomized algorithm ('Qr' option), and to simulate 00167 roundoff errors ('Rn' option). 00168 00169 Random number generators differ between systems. Most systems provide 00170 rand() but the period varies. The period of rand() is not critical 00171 since qhull does not normally use random numbers. 00172 00173 The default generator is Park & Miller's minimal standard random 00174 number generator [CACM 31:1195 '88]. It is included with Qhull. 00175 00176 If qh_RANDOMmax is wrong, qhull will report a warning and Geomview 00177 output will likely be invisible. 00178 */ 00179 #define qh_RANDOMtype 5 /* *** change to the desired number *** */ 00180 00181 #if (qh_RANDOMtype == 1) 00182 #define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, random()/MAX */ 00183 #define qh_RANDOMint random() 00184 #define qh_RANDOMseed_(seed) srandom(seed); 00185 00186 #elif (qh_RANDOMtype == 2) 00187 #ifdef RAND_MAX 00188 #define qh_RANDOMmax ((realT)RAND_MAX) 00189 #else 00190 #define qh_RANDOMmax ((realT)32767) /* 15 bits (System 5) */ 00191 #endif 00192 #define qh_RANDOMint rand() 00193 #define qh_RANDOMseed_(seed) srand((unsigned)seed); 00194 00195 #elif (qh_RANDOMtype == 3) 00196 #define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, Sun */ 00197 #define qh_RANDOMint rand() 00198 #define qh_RANDOMseed_(seed) srand((unsigned)seed); 00199 00200 #elif (qh_RANDOMtype == 4) 00201 #define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, lrand38()/MAX */ 00202 #define qh_RANDOMint lrand48() 00203 #define qh_RANDOMseed_(seed) srand48(seed); 00204 00205 #elif (qh_RANDOMtype == 5) 00206 #define qh_RANDOMmax ((realT)2147483646UL) /* 31 bits, qh_rand/MAX */ 00207 #define qh_RANDOMint qh_rand() 00208 #define qh_RANDOMseed_(seed) qh_srand(seed); 00209 /* unlike rand(), never returns 0 */ 00210 00211 #else 00212 #error: unknown random option 00213 #endif 00214 00215 /*-<a href="qh-user.htm#TOC" 00216 >--------------------------------</a><a name="ORIENTclock">-</a> 00217 00218 qh_ORIENTclock 00219 0 for inward pointing normals by Geomview convention 00220 */ 00221 #define qh_ORIENTclock 0 00222 00223 00224 /*========= performance related constants =========*/ 00225 00226 /*-<a href="qh-user.htm#TOC" 00227 >--------------------------------</a><a name="HASHfactor">-</a> 00228 00229 qh_HASHfactor 00230 total hash slots / used hash slots. Must be at least 1.1. 00231 00232 notes: 00233 =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy 00234 */ 00235 #define qh_HASHfactor 2 00236 00237 /*-<a href="qh-user.htm#TOC" 00238 >--------------------------------</a><a name="VERIFYdirect">-</a> 00239 00240 qh_VERIFYdirect 00241 with 'Tv' verify all points against all facets if op count is smaller 00242 00243 notes: 00244 if greater, calls qh_check_bestdist() instead 00245 */ 00246 #define qh_VERIFYdirect 1000000 00247 00248 /*-<a href="qh-user.htm#TOC" 00249 >--------------------------------</a><a name="INITIALsearch">-</a> 00250 00251 qh_INITIALsearch 00252 if qh_INITIALmax, search points up to this dimension 00253 */ 00254 #define qh_INITIALsearch 6 00255 00256 /*-<a href="qh-user.htm#TOC" 00257 >--------------------------------</a><a name="INITIALmax">-</a> 00258 00259 qh_INITIALmax 00260 if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex 00261 00262 notes: 00263 from points with non-zero determinants 00264 use option 'Qs' to override (much slower) 00265 */ 00266 #define qh_INITIALmax 8 00267 00268 /*-<a href="qh-user.htm#TOC" 00269 >--------------------------------</a><a name="JOGGLEdefault">-</a> 00270 00271 qh_JOGGLEdefault 00272 default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault 00273 00274 notes: 00275 rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16 00276 rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults 00277 rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults 00278 rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults 00279 rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults 00280 rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults 00281 rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults 00282 rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults 00283 rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults 00284 the later have about 20 points per facet, each of which may interfere 00285 00286 pick a value large enough to avoid retries on most inputs 00287 */ 00288 #define qh_JOGGLEdefault 30000.0 00289 00290 /*-<a href="qh-user.htm#TOC" 00291 >--------------------------------</a><a name="JOGGLEincrease">-</a> 00292 00293 qh_JOGGLEincrease 00294 factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain 00295 */ 00296 #define qh_JOGGLEincrease 10.0 00297 00298 /*-<a href="qh-user.htm#TOC" 00299 >--------------------------------</a><a name="JOGGLEretry">-</a> 00300 00301 qh_JOGGLEretry 00302 if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax 00303 00304 notes: 00305 try twice at the original value in case of bad luck the first time 00306 */ 00307 #define qh_JOGGLEretry 2 00308 00309 /*-<a href="qh-user.htm#TOC" 00310 >--------------------------------</a><a name="JOGGLEagain">-</a> 00311 00312 qh_JOGGLEagain 00313 every following qh_JOGGLEagain, increase qh.JOGGLEmax 00314 00315 notes: 00316 1 is OK since it's already failed qh_JOGGLEretry times 00317 */ 00318 #define qh_JOGGLEagain 1 00319 00320 /*-<a href="qh-user.htm#TOC" 00321 >--------------------------------</a><a name="JOGGLEmaxincrease">-</a> 00322 00323 qh_JOGGLEmaxincrease 00324 maximum qh.JOGGLEmax due to qh_JOGGLEincrease 00325 relative to qh.MAXwidth 00326 00327 notes: 00328 qh.joggleinput will retry at this value until qh_JOGGLEmaxretry 00329 */ 00330 #define qh_JOGGLEmaxincrease 1e-2 00331 00332 /*-<a href="qh-user.htm#TOC" 00333 >--------------------------------</a><a name="JOGGLEmaxretry">-</a> 00334 00335 qh_JOGGLEmaxretry 00336 stop after qh_JOGGLEmaxretry attempts 00337 */ 00338 #define qh_JOGGLEmaxretry 100 00339 00340 /*========= memory constants =========*/ 00341 00342 /*-<a href="qh-user.htm#TOC" 00343 >--------------------------------</a><a name="MEMalign">-</a> 00344 00345 qh_MEMalign 00346 memory alignment for qh_meminitbuffers() in global.c 00347 00348 notes: 00349 to avoid bus errors, memory allocation must consider alignment requirements. 00350 malloc() automatically takes care of alignment. Since mem.c manages 00351 its own memory, we need to explicitly specify alignment in 00352 qh_meminitbuffers(). 00353 00354 A safe choice is sizeof(double). sizeof(float) may be used if doubles 00355 do not occur in data structures and pointers are the same size. Be careful 00356 of machines (e.g., DEC Alpha) with large pointers. 00357 00358 If using gcc, best alignment is 00359 #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *)) 00360 */ 00361 #define qh_MEMalign fmax_(sizeof(realT), sizeof(void *)) 00362 00363 /*-<a href="qh-user.htm#TOC" 00364 >--------------------------------</a><a name="MEMbufsize">-</a> 00365 00366 qh_MEMbufsize 00367 size of additional memory buffers 00368 00369 notes: 00370 used for qh_meminitbuffers() in global.c 00371 */ 00372 #define qh_MEMbufsize 0x10000 /* allocate 64K memory buffers */ 00373 00374 /*-<a href="qh-user.htm#TOC" 00375 >--------------------------------</a><a name="MEMinitbuf">-</a> 00376 00377 qh_MEMinitbuf 00378 size of initial memory buffer 00379 00380 notes: 00381 use for qh_meminitbuffers() in global.c 00382 */ 00383 #define qh_MEMinitbuf 0x20000 /* initially allocate 128K buffer */ 00384 00385 /*-<a href="qh-user.htm#TOC" 00386 >--------------------------------</a><a name="INFINITE">-</a> 00387 00388 qh_INFINITE 00389 on output, indicates Voronoi center at infinity 00390 */ 00391 #define qh_INFINITE -10.101 00392 00393 /*-<a href="qh-user.htm#TOC" 00394 >--------------------------------</a><a name="DEFAULTbox">-</a> 00395 00396 qh_DEFAULTbox 00397 default box size (Geomview expects 0.5) 00398 */ 00399 #define qh_DEFAULTbox 0.5 00400 00401 /*======= conditional compilation ============================*/ 00402 00403 /*-<a href="qh-user.htm#TOC" 00404 >--------------------------------</a><a name="compiler">-</a> 00405 00406 __cplusplus 00407 defined by C++ compilers 00408 00409 __MSC_VER 00410 defined by Microsoft Visual C++ 00411 00412 __MWERKS__ && __POWERPC__ 00413 defined by Metrowerks when compiling for the Power Macintosh 00414 00415 __STDC__ 00416 defined for strict ANSI C 00417 */ 00418 00419 /*-<a href="qh-user.htm#TOC" 00420 >--------------------------------</a><a name="COMPUTEfurthest">-</a> 00421 00422 qh_COMPUTEfurthest 00423 compute furthest distance to an outside point instead of storing it with the facet 00424 =1 to compute furthest 00425 00426 notes: 00427 computing furthest saves memory but costs time 00428 about 40% more distance tests for partitioning 00429 removes facet->furthestdist 00430 */ 00431 #define qh_COMPUTEfurthest 0 00432 00433 /*-<a href="qh-user.htm#TOC" 00434 >--------------------------------</a><a name="KEEPstatistics">-</a> 00435 00436 qh_KEEPstatistics 00437 =0 removes most of statistic gathering and reporting 00438 00439 notes: 00440 if 0, code size is reduced by about 4%. 00441 */ 00442 #define qh_KEEPstatistics 1 00443 00444 /*-<a href="qh-user.htm#TOC" 00445 >--------------------------------</a><a name="MAXoutside">-</a> 00446 00447 qh_MAXoutside 00448 record outer plane for each facet 00449 =1 to record facet->maxoutside 00450 00451 notes: 00452 this takes a realT per facet and slightly slows down qhull 00453 it produces better outer planes for geomview output 00454 */ 00455 #define qh_MAXoutside 1 00456 00457 /*-<a href="qh-user.htm#TOC" 00458 >--------------------------------</a><a name="NOmerge">-</a> 00459 00460 qh_NOmerge 00461 disables facet merging if defined 00462 00463 notes: 00464 This saves about 10% space. 00465 00466 Unless 'Q0' 00467 qh_NOmerge sets 'QJ' to avoid precision errors 00468 00469 #define qh_NOmerge 00470 00471 see: 00472 <a href="mem.h#NOmem">qh_NOmem</a> in mem.c 00473 00474 see user.c/user_eg.c for removing io.o 00475 */ 00476 00477 /*-<a href="qh-user.htm#TOC" 00478 >--------------------------------</a><a name="NOtrace">-</a> 00479 00480 qh_NOtrace 00481 no tracing if defined 00482 00483 notes: 00484 This saves about 5% space. 00485 00486 #define qh_NOtrace 00487 */ 00488 00489 /*-<a href="qh-user.htm#TOC" 00490 >--------------------------------</a><a name="QHpointer">-</a> 00491 00492 qh_QHpointer 00493 access global data with pointer or static structure 00494 00495 qh_QHpointer = 1 access globals via a pointer to allocated memory 00496 enables qh_saveqhull() and qh_restoreqhull() 00497 costs about 8% in time and 2% in space 00498 00499 = 0 qh_qh and qh_qhstat are static data structures 00500 only one instance of qhull() can be active at a time 00501 default value 00502 00503 notes: 00504 all global variables for qhull are in qh, qhmem, and qhstat 00505 qh is defined in qhull.h 00506 qhmem is defined in mem.h 00507 qhstat is defined in stat.h 00508 00509 see: 00510 user_eg.c for an example 00511 */ 00512 #define qh_QHpointer 0 00513 #if 0 /* sample code */ 00514 qhT *oldqhA, *oldqhB; 00515 00516 exitcode= qh_new_qhull (dim, numpoints, points, ismalloc, 00517 flags, outfile, errfile); 00518 /* use results from first call to qh_new_qhull */ 00519 oldqhA= qh_save_qhull(); 00520 exitcode= qh_new_qhull (dimB, numpointsB, pointsB, ismalloc, 00521 flags, outfile, errfile); 00522 /* use results from second call to qh_new_qhull */ 00523 oldqhB= qh_save_qhull(); 00524 qh_restore_qhull (&oldqhA); 00525 /* use results from first call to qh_new_qhull */ 00526 qh_freeqhull (qh_ALL); /* frees all memory used by first call */ 00527 qh_restore_qhull (&oldqhB); 00528 /* use results from second call to qh_new_qhull */ 00529 qh_freeqhull (!qh_ALL); /* frees long memory used by second call */ 00530 qh_memfreeshort (&curlong, &totlong); /* frees short memory and memory allocator */ 00531 #endif 00532 00533 /*-<a href="qh-user.htm#TOC" 00534 >--------------------------------</a><a name="QUICKhelp">-</a> 00535 00536 qh_QUICKhelp 00537 =1 to use abbreviated help messages, e.g., for degenerate inputs 00538 */ 00539 #define qh_QUICKhelp 0 00540 00541 /* ============ -merge constants- ==================== 00542 00543 These constants effect facet merging. You probably will not need 00544 to modify these. They effect the performance of facet merging. 00545 */ 00546 00547 /*-<a href="qh-user.htm#TOC" 00548 >--------------------------------</a><a name="DIMmergeVertex">-</a> 00549 00550 qh_DIMmergeVertex 00551 max dimension for vertex merging (it is not effective in high-d) 00552 */ 00553 #define qh_DIMmergeVertex 6 00554 00555 /*-<a href="qh-user.htm#TOC" 00556 >--------------------------------</a><a name="DIMreduceBuild">-</a> 00557 00558 qh_DIMreduceBuild 00559 max dimension for vertex reduction during build (slow in high-d) 00560 */ 00561 #define qh_DIMreduceBuild 5 00562 00563 /*-<a href="qh-user.htm#TOC" 00564 >--------------------------------</a><a name="BESTcentrum">-</a> 00565 00566 qh_BESTcentrum 00567 if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster) 00568 else, qh_findbestneighbor() tests all vertices (much better merges) 00569 00570 qh_BESTcentrum2 00571 if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums 00572 */ 00573 #define qh_BESTcentrum 20 00574 #define qh_BESTcentrum2 2 00575 00576 /*-<a href="qh-user.htm#TOC" 00577 >--------------------------------</a><a name="BESTnonconvex">-</a> 00578 00579 qh_BESTnonconvex 00580 if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges. 00581 00582 notes: 00583 It is needed because qh_findbestneighbor is slow for large facets 00584 */ 00585 #define qh_BESTnonconvex 15 00586 00587 /*-<a href="qh-user.htm#TOC" 00588 >--------------------------------</a><a name="MAXnewmerges">-</a> 00589 00590 qh_MAXnewmerges 00591 if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums. 00592 00593 notes: 00594 It is needed because postmerge can merge many facets at once 00595 */ 00596 #define qh_MAXnewmerges 2 00597 00598 /*-<a href="qh-user.htm#TOC" 00599 >--------------------------------</a><a name="MAXnewcentrum">-</a> 00600 00601 qh_MAXnewcentrum 00602 if <= dim+n vertices (n approximates the number of merges), 00603 reset the centrum in qh_updatetested() and qh_mergecycle_facets() 00604 00605 notes: 00606 needed to reduce cost and because centrums may move too much if 00607 many vertices in high-d 00608 */ 00609 #define qh_MAXnewcentrum 5 00610 00611 /*-<a href="qh-user.htm#TOC" 00612 >--------------------------------</a><a name="COPLANARratio">-</a> 00613 00614 qh_COPLANARratio 00615 for 3-d+ merging, qh.MINvisible is n*premerge_centrum 00616 00617 notes: 00618 for non-merging, it's DISTround 00619 */ 00620 #define qh_COPLANARratio 3 00621 00622 /*-<a href="qh-user.htm#TOC" 00623 >--------------------------------</a><a name="DISToutside">-</a> 00624 00625 qh_DISToutside 00626 When is a point clearly outside of a facet? 00627 Stops search in qh_findbestnew or qh_partitionall 00628 qh_findbest uses qh.MINoutside since since it is only called if no merges. 00629 00630 notes: 00631 'Qf' always searches for best facet 00632 if !qh.MERGING, same as qh.MINoutside. 00633 if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved 00634 [Note: Zdelvertextot occurs normally with interior points] 00635 RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv 00636 When there is a sharp edge, need to move points to a 00637 clearly good facet; otherwise may be lost in another partitioning. 00638 if too big then O(n^2) behavior for partitioning in cone 00639 if very small then important points not processed 00640 Needed in qh_partitionall for 00641 RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv 00642 Needed in qh_findbestnew for many instances of 00643 RBOX 1000 s Z1 G1e-13 t | QHULL Tv 00644 00645 See: 00646 qh_DISToutside -- when is a point clearly outside of a facet 00647 qh_SEARCHdist -- when is facet coplanar with the best facet? 00648 qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint() 00649 */ 00650 #define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \ 00651 fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside)) 00652 00653 /*-<a href="qh-user.htm#TOC" 00654 >--------------------------------</a><a name="RATIOnearinside">-</a> 00655 00656 qh_RATIOnearinside 00657 ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for 00658 qh_check_maxout(). 00659 00660 notes: 00661 This is overkill since do not know the correct value. 00662 It effects whether 'Qc' reports all coplanar points 00663 Not used for 'd' since non-extreme points are coplanar 00664 */ 00665 #define qh_RATIOnearinside 5 00666 00667 /*-<a href="qh-user.htm#TOC" 00668 >--------------------------------</a><a name="SEARCHdist">-</a> 00669 00670 qh_SEARCHdist 00671 When is a facet coplanar with the best facet? 00672 qh_findbesthorizon: all coplanar facets of the best facet need to be searched. 00673 00674 See: 00675 qh_DISToutside -- when is a point clearly outside of a facet 00676 qh_SEARCHdist -- when is facet coplanar with the best facet? 00677 qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint() 00678 */ 00679 #define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \ 00680 (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar))); 00681 00682 /*-<a href="qh-user.htm#TOC" 00683 >--------------------------------</a><a name="USEfindbestnew">-</a> 00684 00685 qh_USEfindbestnew 00686 Always use qh_findbestnew for qh_partitionpoint, otherwise use 00687 qh_findbestnew if merged new facet or sharpnewfacets. 00688 00689 See: 00690 qh_DISToutside -- when is a point clearly outside of a facet 00691 qh_SEARCHdist -- when is facet coplanar with the best facet? 00692 qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint() 00693 */ 00694 #define qh_USEfindbestnew (zzval_(Ztotmerge) > 50) 00695 00696 /*-<a href="qh-user.htm#TOC" 00697 >--------------------------------</a><a name="WIDEcoplanar">-</a> 00698 00699 qh_WIDEcoplanar 00700 n*MAXcoplanar or n*MINvisible for a WIDEfacet 00701 00702 if vertex is further than qh.WIDEfacet from the hyperplane 00703 then its ridges are not counted in computing the area, and 00704 the facet's centrum is frozen. 00705 00706 notes: 00707 qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar, 00708 qh_WIDEcoplanar * qh.MINvisible); 00709 */ 00710 #define qh_WIDEcoplanar 6 00711 00712 /*-<a href="qh-user.htm#TOC" 00713 >--------------------------------</a><a name="MAXnarrow">-</a> 00714 00715 qh_MAXnarrow 00716 max. cosine in initial hull that sets qh.NARROWhull 00717 00718 notes: 00719 If qh.NARROWhull, the initial partition does not make 00720 coplanar points. If narrow, a coplanar point can be 00721 coplanar to two facets of opposite orientations and 00722 distant from the exact convex hull. 00723 00724 Conservative estimate. Don't actually see problems until it is -1.0 00725 */ 00726 #define qh_MAXnarrow -0.99999999 00727 00728 /*-<a href="qh-user.htm#TOC" 00729 >--------------------------------</a><a name="WARNnarrow">-</a> 00730 00731 qh_WARNnarrow 00732 max. cosine in initial hull to warn about qh.NARROWhull 00733 00734 notes: 00735 this is a conservative estimate. 00736 Don't actually see problems until it is -1.0. See qh-impre.htm 00737 */ 00738 #define qh_WARNnarrow -0.999999999999999 00739 00740 /*-<a href="qh-user.htm#TOC" 00741 >--------------------------------</a><a name="ZEROdelaunay">-</a> 00742 00743 qh_ZEROdelaunay 00744 a zero Delaunay facet occurs for input sites coplanar with their convex hull 00745 the last normal coefficient of a zero Delaunay facet is within 00746 qh_ZEROdelaunay * qh.ANGLEround of 0 00747 00748 notes: 00749 qh_ZEROdelaunay does not allow for joggled input ('QJ'). 00750 00751 You can avoid zero Delaunay facets by surrounding the input with a box. 00752 00753 Use option 'PDk:-n' to explicitly define zero Delaunay facets 00754 k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation) 00755 n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12') 00756 */ 00757 #define qh_ZEROdelaunay 2 00758 00759 #endif /* qh_DEFuser */ 00760 00761 00762
1.7.1