dll/opengl/mesa/src/glu/sgi/libnurbs/internals/tobezier.cc

   1 /*
   2 ** License Applicability. Except to the extent portions of this file are
   3 ** made subject to an alternative license as permitted in the SGI Free
   4 ** Software License B, Version 1.1 (the "License"), the contents of this
   5 ** file are subject only to the provisions of the License. You may not use
   6 ** this file except in compliance with the License. You may obtain a copy
   7 ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
   8 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
   9 **
  10 ** http://oss.sgi.com/projects/FreeB
  11 **
  12 ** Note that, as provided in the License, the Software is distributed on an
  13 ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
  14 ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
  15 ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
  16 ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
  17 **
  18 ** Original Code. The Original Code is: OpenGL Sample Implementation,
  19 ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
  20 ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
  21 ** Copyright in any portions created by third parties is as indicated
  22 ** elsewhere herein. All Rights Reserved.
  23 **
  24 ** Additional Notice Provisions: The application programming interfaces
  25 ** established by SGI in conjunction with the Original Code are The
  26 ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
  27 ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
  28 ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
  29 ** Window System(R) (Version 1.3), released October 19, 1998. This software
  30 ** was created using the OpenGL(R) version 1.2.1 Sample Implementation
  31 ** published by SGI, but has not been independently verified as being
  32 ** compliant with the OpenGL(R) version 1.2.1 Specification.
  33 */
  34
  35 /*
  36  * tobezier.c++
  37  *
  38  */
  39
  40 #include "glimports.h"
  41 #include "myassert.h"
  42 #include "mystdio.h"
  43 #include "mystring.h"
  44 #include "quilt.h"
  45 #include "knotvector.h"
  46
  47 /* local type definitions */
  48 struct Breakpt {                /* breakpoints  */
  49     Knot                value;          /* value        */
  50     int                 multi;          /* multiplicity */
  51     int                 def;            /* deficit */
  52 };
  53
  54 struct Knotspec {               /* knotvector format */
  55     long                order;          /* order of spline  */
  56     Knot_ptr            inkbegin;       /* input knot sequence */
  57     Knot_ptr            inkend;         /* location after last knot */
  58     Knot_ptr            outkbegin;      /* in-process knot subsequence */
  59     Knot_ptr            outkend;        /* location after last knot */
  60     Knot_ptr            kleft;          /* */
  61     Knot_ptr            kright;         /* */
  62     Knot_ptr            kfirst;         /* */
  63     Knot_ptr            klast;          /* */
  64     Knot_ptr            sbegin;         /* conversion factor values */
  65     Breakpt *           bbegin;         /* in-process breakpoints */
  66     Breakpt *           bend;           /* last breakpoint */
  67     int                 ncoords;        /* coordinates per control point */
  68     int                 prestride;      /* stride between input points */
  69     int                 poststride;     /* stride between output points */
  70     int                 preoffset;      /* scaled point offset  */
  71     int                 postoffset;     /* scaled point offset  */
  72     int                 prewidth;       /* width of dimension   */
  73     int                 postwidth;      /* width of dimension   */
  74     int                 istransformed;  /* was dimension transformed */
  75     Knotspec *          next;           /* next knotspec */
  76     Knotspec *          kspectotrans;   /* knotspec in transformation direction */
  77
  78                         Knotspec( void );
  79                         ~Knotspec( void );
  80     void                factors( void );
  81     void                insert( REAL * );
  82     void                preselect();
  83     void                select( void );
  84     void                copy( INREAL *, REAL * );
  85     void                breakpoints( void );
  86     void                knots( void );
  87     void                transform( REAL * );
  88     void                showpts( REAL * );
  89
  90     void                pt_io_copy( REAL *, INREAL * );
  91     void                pt_oo_copy( REAL *, REAL * );
  92     void                pt_oo_sum( REAL*, REAL*, REAL*, Knot, Knot );
  93 };
  94
  95 struct Splinespec {             /* a non-uniform tensor element */
  96                         Splinespec( int );
  97                         ~Splinespec(void);
  98     Knotspec            *kspec; /* format of each param. dir. */
  99     int                 dim;            /* domain dimension */
 100     REAL *              outcpts;        /* Bezier control points */
 101
 102     void                kspecinit( Knotvector & );
 103     void                kspecinit( Knotvector &, Knotvector & );
 104     void                select( void );
 105     void                layout( long );
 106     void                setupquilt( Quilt_ptr );
 107     void                copy( INREAL * );
 108     void                transform( void );
 109 };
 110
 111 /*-----------------------------------------------------------------------------
 112  * Quilt::toBezier - convert from NURBS to rational Bezier
 113  *-----------------------------------------------------------------------------
 114  */
 115
 116 void
 117 Quilt::toBezier(
 118     Knotvector& knotvector,     /* a knot vector */
 119     INREAL *ctlpts,             /* input contol points */
 120     long ncoords )              /* number of coordinates per control point */
 121 {
 122     Splinespec spline( 1 );
 123     spline.kspecinit( knotvector );
 124     spline.select();
 125     spline.layout( ncoords );
 126     spline.setupquilt( this );
 127     spline.copy( ctlpts );
 128     spline.transform();
 129 }
 130
 131 void
 132 Quilt::toBezier(
 133     Knotvector& sknotvector,    /* a knot vector */
 134     Knotvector& tknotvector,    /* a knot vector */
 135     INREAL *ctlpts,             /* input contol points */
 136     long ncoords )              /* number of coordinates per control point */
 137 {
 138     Splinespec spline( 2 );
 139     spline.kspecinit( sknotvector, tknotvector );
 140     spline.select();
 141     spline.layout( ncoords );
 142     spline.setupquilt( this );
 143     spline.copy( ctlpts );
 144     spline.transform();
 145 }
 146 Splinespec::Splinespec( int dimen )
 147 {
 148     dim = dimen;
 149 }
 150
 151 Splinespec::~Splinespec( void )
 152 {
 153     /* Note: do NOT delete 'outcpts' here since its address (not contents)
 154      * is copied in 'cpts' in this file in function Splinespec::setupquilt().
 155      * This block of memory will eventually be deleted in file quilt.c++ in
 156      * function Quilt::deleteMe() through 'cpts' so do NOT delete it here!
 157      */
 158     Knotspec *ktrav= kspec;         //start at beginning of list
 159     while (ktrav != 0) {            //any items to delete?
 160        Knotspec *deleteThis= ktrav; //remember to delete this
 161        ktrav= ktrav->next;          //go to next item if any
 162        delete deleteThis;           //delete it
 163     }
 164 } /* ~Splinespec() */
 165
 166 /*-----------------------------------------------------------------------------
 167  * Splinespec::kspecinit - initialize Splinespec structure
 168  *
 169  * Client: Quilt::toBezier
 170  *-----------------------------------------------------------------------------
 171  */
 172
 173 void
 174 Splinespec::kspecinit( Knotvector& knotvector )
 175 {
 176     kspec = new Knotspec;
 177     kspec->inkbegin = knotvector.knotlist;
 178     kspec->inkend = knotvector.knotlist + knotvector.knotcount;
 179     kspec->prestride = (int) knotvector.stride;
 180     kspec->order = knotvector.order;
 181     kspec->next = NULL;
 182 }
 183
 184 void
 185 Splinespec::kspecinit( Knotvector& sknotvector, Knotvector& tknotvector )
 186 {
 187     kspec = new Knotspec;
 188     Knotspec *tkspec = new Knotspec;
 189
 190     kspec->inkbegin = sknotvector.knotlist;
 191     kspec->inkend = sknotvector.knotlist + sknotvector.knotcount;
 192     kspec->prestride = (int) sknotvector.stride;
 193     kspec->order = sknotvector.order;
 194     kspec->next = tkspec;
 195
 196     tkspec->inkbegin = tknotvector.knotlist;
 197     tkspec->inkend = tknotvector.knotlist + tknotvector.knotcount;
 198     tkspec->prestride = (int) tknotvector.stride;
 199     tkspec->order = tknotvector.order;
 200     tkspec->next = NULL;
 201 }
 202
 203
 204 /*-----------------------------------------------------------------------------
 205  * Splinespec::select - select the subsegments to copy
 206  *
 207  * Client: gl_quilt_to_bezier
 208  *-----------------------------------------------------------------------------
 209  */
 210
 211 void
 212 Splinespec::select( )
 213 {
 214     for( Knotspec *knotspec = kspec; knotspec; knotspec = knotspec->next ) {
 215         knotspec->preselect();
 216         knotspec->select();
 217     }
 218 }
 219
 220 /*-----------------------------------------------------------------------------
 221  * Splinespec::layout -
 222  *
 223  * Client: gl_quilt_to_bezier
 224  *-----------------------------------------------------------------------------
 225  */
 226
 227 void
 228 Splinespec::layout( long ncoords )
 229 {
 230
 231     long stride = ncoords;
 232     for( Knotspec *knotspec = kspec; knotspec; knotspec=knotspec->next ) {
 233         knotspec->poststride = (int) stride;
 234         stride *= ((knotspec->bend-knotspec->bbegin)*knotspec->order + knotspec->postoffset);
 235         knotspec->preoffset  *= knotspec->prestride;
 236         knotspec->prewidth  *= knotspec->poststride;
 237         knotspec->postwidth *= knotspec->poststride;
 238         knotspec->postoffset *= knotspec->poststride;
 239         knotspec->ncoords = (int) ncoords;
 240     }
 241     outcpts = new REAL[stride];
 242     assert( outcpts != 0 );
 243 }
 244
 245 /*-----------------------------------------------------------------------------
 246  * Splinespec::copy - copy the control points of current subobject
 247  *
 248  * Client: gl_quilt_to_bezier
 249  *-----------------------------------------------------------------------------
 250  */
 251
 252 void
 253 Splinespec::copy( INREAL *incpts )
 254 {
 255     kspec->copy( incpts, outcpts );
 256 }
 257
 258 /*-----------------------------------------------------------------------------
 259  * Splinespec::setupquilt - assign all quilt variables from knotspec
 260  *
 261  * Client: gl_quilt_to_bezier
 262  *-----------------------------------------------------------------------------
 263  */
 264
 265 void
 266 Splinespec::setupquilt( Quilt_ptr quilt )
 267 {
 268     Quiltspec_ptr qspec = quilt->qspec;
 269     quilt->eqspec = qspec + dim;
 270     for( Knotspec *knotspec = kspec; knotspec; knotspec=knotspec->next, qspec++ ) {
 271         qspec->stride   = knotspec->poststride;
 272         qspec->width    = knotspec->bend - knotspec->bbegin;
 273         qspec->order    = (int) knotspec->order;
 274         qspec->offset   = knotspec->postoffset;
 275         qspec->index    = 0;
 276         qspec->bdry[0]  = (knotspec->kleft == knotspec->kfirst) ? 1 : 0;
 277         qspec->bdry[1]  = (knotspec->kright == knotspec->klast) ? 1 : 0;
 278         qspec->breakpoints = new Knot[qspec->width+1];
 279         Knot_ptr k =  qspec->breakpoints;
 280         for( Breakpt *bk = knotspec->bbegin; bk <= knotspec->bend; bk++ )
 281             *(k++) = bk->value;
 282     }
 283     quilt->cpts = outcpts;
 284     quilt->next = 0;
 285 }
 286
 287 /*-----------------------------------------------------------------------------
 288  * Splinespec::transform - convert a spline to Bezier format
 289  *
 290  * Client: gl_quilt_to_bezier
 291  *-----------------------------------------------------------------------------
 292  */
 293
 294 void
 295 Splinespec::transform( void )
 296 {
 297     Knotspec *knotspec;
 298     for( knotspec = kspec; knotspec; knotspec=knotspec->next )
 299         knotspec->istransformed = 0;
 300
 301     for( knotspec = kspec; knotspec; knotspec=knotspec->next ) {
 302         for( Knotspec *kspec2 = kspec; kspec2; kspec2=kspec2->next )
 303             kspec2->kspectotrans = knotspec;
 304         kspec->transform( outcpts );
 305         knotspec->istransformed = 1;
 306     }
 307 }
 308
 309
 310 /*-----------------------------------------------------------------------------
 311  * Knotspec::Knotspec -  constuct a knot spec
 312  *-----------------------------------------------------------------------------
 313  */
 314
 315 Knotspec::Knotspec( void )
 316 {
 317     bbegin = 0;
 318     sbegin = 0;
 319     outkbegin = 0;
 320 }
 321
 322 /*-----------------------------------------------------------------------------
 323  * Knotspec::copy -  copy the control points along minor direction
 324  *
 325  * Client: Splinespec::copy
 326  *-----------------------------------------------------------------------------
 327  */
 328
 329 void
 330 Knotspec::copy( INREAL *inpt, REAL *outpt )
 331 {
 332     inpt = (INREAL *) (((char *) inpt) + preoffset);
 333
 334     if( next ) {
 335         for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride ) {
 336             next->copy( inpt, outpt );
 337             inpt = (INREAL *) (((char *) inpt) + prestride);
 338         }
 339    } else {
 340         for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride ) {
 341             pt_io_copy( outpt, inpt );
 342             inpt = (INREAL *) (((char *) inpt) + prestride);
 343         }
 344      }
 345 }
 346
 347 /*-----------------------------------------------------------------------------
 348  * Knotspec::showpts - print out points before transformation
 349  *
 350  * Client: Knotspec::select
 351  *-----------------------------------------------------------------------------
 352  */
 353 void
 354 Knotspec::showpts( REAL *outpt )
 355 {
 356     if( next ) {
 357         for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride )
 358             next->showpts( outpt );
 359     } else {
 360         for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride )
 361             _glu_dprintf(  "show %g %g %g\n", outpt[0], outpt[1], outpt[2] );
 362     }
 363 }
 364
 365 /*-----------------------------------------------------------------------------
 366  * Knotspec::factors - precompute scale factors
 367  *         - overwrites knot vector, actual new knot vector is NOT produced
 368  *
 369  * Client: Knotspec::select
 370  *-----------------------------------------------------------------------------
 371  */
 372
 373 void
 374 Knotspec::factors( void )
 375 {
 376     Knot *mid = (outkend - 1) - order + bend->multi;
 377     Knot_ptr fptr = sbegin;
 378
 379     for( Breakpt *bpt = bend; bpt >= bbegin; bpt-- ) {
 380         mid -= bpt->multi;              // last knot less than knot to insert
 381         int def = bpt->def - 1;         // number of knots to insert
 382         if( def <= 0 ) continue;
 383         Knot kv = bpt->value;           // knot to insert
 384
 385         Knot *kf = (mid-def) + (order-1);
 386         for( Knot *kl = kf + def; kl != kf; kl-- ) {
 387             Knot *kh, *kt;
 388             for( kt=kl, kh=mid; kt != kf; kh--, kt-- )
 389                 *(fptr++) = (kv - *kh) / (*kt - *kh);
 390             *kl = kv;
 391         }
 392     }
 393 }
 394
 395 /*-----------------------------------------------------------------------------
 396  * Knotspec::insert - convert subobject in direction of kspec into Bezier
 397  *
 398  * Client: Knotspec::transform
 399  *-----------------------------------------------------------------------------
 400  */
 401
 402 void
 403 Knotspec::insert( REAL *p )
 404 {
 405     Knot_ptr fptr = sbegin;
 406     REAL *srcpt = p + prewidth - poststride;
 407     REAL *dstpt = p + postwidth + postoffset - poststride;
 408     Breakpt *bpt = bend;
 409
 410    for( REAL *pend = srcpt - poststride*bpt->def; srcpt != pend; pend +=poststride ) {
 411         REAL *p1 = srcpt;
 412         for( REAL *p2 = srcpt-poststride; p2 != pend; p1 = p2, p2 -= poststride ) {
 413             pt_oo_sum( p1, p1, p2, *fptr, 1.0-*fptr );
 414             fptr++;
 415         }
 416     }
 417
 418     for( --bpt; bpt >= bbegin; bpt-- ) {
 419
 420         for( int multi = bpt->multi; multi > 0; multi-- ) {
 421             pt_oo_copy( dstpt, srcpt );
 422             dstpt -= poststride;
 423             srcpt -= poststride;
 424         }
 425
 426         for( REAL *pend = srcpt - poststride*bpt->def; srcpt != pend; pend +=poststride, dstpt-=poststride ) {
 427             pt_oo_copy( dstpt, srcpt );
 428             REAL *p1 = srcpt;
 429
 430             for( REAL *p2 = srcpt-poststride; p2 != pend; p1=p2, p2 -= poststride ) {
 431                 pt_oo_sum( p1, p1, p2, *fptr, 1.0-*fptr );
 432                 fptr++;
 433             }
 434         }
 435     }
 436 }
 437
 438 /*-----------------------------------------------------------------------------
 439  * Knotspec::preselect - initialize kspec for processing
 440  *
 441  * Client: Splinespec::select
 442  *-----------------------------------------------------------------------------
 443  */
 444
 445 void
 446 Knotspec::preselect( void )
 447 {
 448     Knot kval;
 449
 450     /* position klast after last knot of "last" breakpoint */
 451     for( klast = inkend - order, kval = *klast; klast != inkend; klast++ )
 452         if( ! identical( *klast, kval ) ) break;
 453
 454     /* position kfirst after last knot of "first" breakpoint */
 455     for( kfirst = inkbegin+order-1, kval= *kfirst;  kfirst != inkend; kfirst++ )
 456         if( ! identical( *kfirst, kval ) ) break;
 457
 458     /* compute multiplicity of first breakpoint */
 459     Knot_ptr k;
 460     for( k  = kfirst - 1; k >= inkbegin; k-- )
 461         if( ! identical( kval, *k ) ) break;
 462     k++;
 463
 464     /* allocate space for breakpoints -
 465        use worst case estimate on number of breakpoints */
 466
 467     bbegin = new Breakpt[(klast - kfirst)+1];
 468     /* record multiplicity and value of first breakpoint */
 469     bbegin->multi = kfirst - k;
 470     bbegin->value = kval;
 471     bend = bbegin;
 472
 473     kleft = kright = kfirst;
 474 }
 475
 476
 477 /*-----------------------------------------------------------------------------
 478  * Knotspec::select - Knotspec::select segments and precompute scale factors
 479  *
 480  * Client: Splinespec::select
 481  *-----------------------------------------------------------------------------
 482  */
 483
 484 void
 485 Knotspec::select( void )
 486 {
 487     breakpoints();
 488     knots();
 489     factors();
 490
 491     preoffset   = kleft - (inkbegin + order);
 492     postwidth   = (int)((bend - bbegin) * order);
 493     prewidth    = (int)((outkend - outkbegin) - order);
 494     postoffset  = (bbegin->def > 1) ? (bbegin->def-1) : 0;
 495 }
 496
 497 /*-----------------------------------------------------------------------------
 498  * Knotspec::breakpoints - compute breakpoints for knotspec
 499  *
 500  * Client: Knotspec::select
 501  *-----------------------------------------------------------------------------
 502  */
 503
 504 void
 505 Knotspec::breakpoints( void )
 506 {
 507     Breakpt *ubpt       = bbegin;
 508     Breakpt *ubend      = bend;
 509     long    nfactors    = 0;
 510
 511     ubpt->value = ubend->value;
 512     ubpt->multi = ubend->multi;
 513
 514     kleft = kright;
 515
 516     for( ; kright != klast; kright++ ) {
 517         if ( identical(*kright,ubpt->value) ) {
 518             (ubpt->multi)++;
 519         } else {
 520             ubpt->def = (int) (order - ubpt->multi);
 521             nfactors += (ubpt->def * (ubpt->def - 1)) / 2;
 522             (++ubpt)->value = *kright;
 523             ubpt->multi = 1;
 524         }
 525     }
 526     ubpt->def = (int) (order - ubpt->multi);
 527     nfactors += (ubpt->def * (ubpt->def - 1)) / 2;
 528
 529     bend = ubpt;
 530
 531     if( nfactors ) {
 532         sbegin = new Knot[nfactors];
 533     } else {
 534         sbegin = NULL;
 535     }
 536 }
 537
 538
 539 /*-----------------------------------------------------------------------------
 540  * Knotspec::knots - copy relevant subsequence of knots into temporary area
 541  *
 542  * Client: Knotspec::select
 543  *-----------------------------------------------------------------------------
 544  */
 545
 546 void
 547 Knotspec::knots( void )
 548 {
 549     Knot_ptr inkpt = kleft - order;
 550     Knot_ptr inkend = kright  + bend->def;
 551
 552     /* allocate space for knots and factors */
 553     outkbegin = new Knot[inkend-inkpt];
 554     Knot_ptr outkpt;
 555     for( outkpt = outkbegin; inkpt != inkend; inkpt++, outkpt++ )
 556         *outkpt = *inkpt;
 557
 558     outkend = outkpt;
 559 }
 560
 561
 562 /*-----------------------------------------------------------------------------
 563  * Knotspec::transform -        convert a spline along a given direction
 564  *
 565  * Client: Splienspec::transform
 566  *-----------------------------------------------------------------------------
 567  */
 568
 569 void
 570 Knotspec::transform( REAL *p )
 571 {
 572    if( next ) {
 573         if( this == kspectotrans ) {
 574             next->transform( p );
 575         } else {
 576             if( istransformed ) {
 577                 p += postoffset;
 578                 for( REAL *pend = p + postwidth; p != pend; p += poststride )
 579                     next->transform( p );
 580             } else {
 581                 REAL *pend = p + prewidth;
 582                 for( ; p != pend; p += poststride )
 583                     next->transform( p );
 584             }
 585         }
 586    } else {
 587         if( this == kspectotrans ) {
 588             insert( p );
 589         } else {
 590             if( istransformed ) {
 591                 p += postoffset;
 592                 for( REAL *pend = p + postwidth; p != pend; p += poststride )
 593                     kspectotrans->insert( p );
 594             } else {
 595                 REAL *pend = p + prewidth;
 596                 for( ; p != pend; p += poststride )
 597                     kspectotrans->insert( p );
 598             }
 599         }
 600    }
 601 }
 602
 603 /*-----------------------------------------------------------------------------
 604  * Knotspec::~Knotspec - free space alocated for knotspec
 605  *-----------------------------------------------------------------------------
 606  */
 607
 608 Knotspec::~Knotspec( void )
 609 {
 610     if( bbegin ) delete[] bbegin;
 611     if( sbegin ) delete[] sbegin;
 612     if( outkbegin ) delete[] outkbegin;
 613 }
 614
 615
 616 /*-----------------------------------------------------------------------------
 617  * pt_io_copy - make internal copy of input cntrl pt. of x coords
 618  *-----------------------------------------------------------------------------
 619  */
 620
 621 void
 622 Knotspec::pt_io_copy( REAL *topt, INREAL *frompt )
 623 {
 624     switch( ncoords ) {
 625     case 4:
 626         topt[3] = (REAL) frompt[3];
 627     case 3:
 628         topt[2] = (REAL) frompt[2];
 629     case 2:
 630         topt[1] = (REAL) frompt[1];
 631     case 1:
 632         topt[0] = (REAL) frompt[0];
 633         break;
 634     default: {
 635             for( int i = 0; i < ncoords; i++ )
 636                 *topt++ = (REAL) *frompt++;
 637         }
 638     }
 639 }
 640
 641 /*-----------------------------------------------------------------------------
 642  * pt_oo_copy - make internal copy of internal cntrl pt. of x coords
 643  *-----------------------------------------------------------------------------
 644  */
 645
 646 void
 647 Knotspec::pt_oo_copy( REAL *topt, REAL *frompt )
 648 {
 649     switch( ncoords ) {
 650     case 4:
 651         topt[3] = frompt[3];
 652     case 3:
 653         topt[2] = frompt[2];
 654     case 2:
 655         topt[1] = frompt[1];
 656     case 1:
 657         topt[0] = frompt[0];
 658         break;
 659     default:
 660         memcpy( topt, frompt, ncoords * sizeof( REAL ) );
 661     }
 662 }
 663
 664 /*-----------------------------------------------------------------------------
 665  * pt_oo_sum - compute affine combination of internal cntrl pts
 666  *-----------------------------------------------------------------------------
 667  */
 668
 669 void
 670 Knotspec::pt_oo_sum( REAL *x, REAL *y, REAL *z, Knot a, Knot b )
 671 {
 672     switch( ncoords ) {
 673     case 4:
 674         x[3] = a * y[3]  +  b * z[3];
 675     case 3:
 676         x[2] = a * y[2]  +  b * z[2];
 677     case 2:
 678         x[1] = a * y[1]  +  b * z[1];
 679     case 1:
 680         x[0] = a * y[0]  +  b * z[0];
 681         break;
 682     default: {
 683           for( int i = 0; i < ncoords; i++ )
 684               *x++ = a * *y++   +   b * *z++;
 685     }
 686     }
 687 }