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+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+**
+** http://oss.sgi.com/projects/FreeB
+**
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+**
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+**
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+*/
+
+/*
+ * tobezier.c++
+ *
+ */
+
+#include "glimports.h"
+#include "myassert.h"
+#include "mystdio.h"
+#include "mystring.h"
+#include "quilt.h"
+#include "knotvector.h"
+
+/* local type definitions */
+struct Breakpt { /* breakpoints */
+ Knot value; /* value */
+ int multi; /* multiplicity */
+ int def; /* deficit */
+};
+
+struct Knotspec { /* knotvector format */
+ long order; /* order of spline */
+ Knot_ptr inkbegin; /* input knot sequence */
+ Knot_ptr inkend; /* location after last knot */
+ Knot_ptr outkbegin; /* in-process knot subsequence */
+ Knot_ptr outkend; /* location after last knot */
+ Knot_ptr kleft; /* */
+ Knot_ptr kright; /* */
+ Knot_ptr kfirst; /* */
+ Knot_ptr klast; /* */
+ Knot_ptr sbegin; /* conversion factor values */
+ Breakpt * bbegin; /* in-process breakpoints */
+ Breakpt * bend; /* last breakpoint */
+ int ncoords; /* coordinates per control point */
+ int prestride; /* stride between input points */
+ int poststride; /* stride between output points */
+ int preoffset; /* scaled point offset */
+ int postoffset; /* scaled point offset */
+ int prewidth; /* width of dimension */
+ int postwidth; /* width of dimension */
+ int istransformed; /* was dimension transformed */
+ Knotspec * next; /* next knotspec */
+ Knotspec * kspectotrans; /* knotspec in transformation direction */
+
+ Knotspec( void );
+ ~Knotspec( void );
+ void factors( void );
+ void insert( REAL * );
+ void preselect();
+ void select( void );
+ void copy( INREAL *, REAL * );
+ void breakpoints( void );
+ void knots( void );
+ void transform( REAL * );
+ void showpts( REAL * );
+
+ void pt_io_copy( REAL *, INREAL * );
+ void pt_oo_copy( REAL *, REAL * );
+ void pt_oo_sum( REAL*, REAL*, REAL*, Knot, Knot );
+};
+
+struct Splinespec { /* a non-uniform tensor element */
+ Splinespec( int );
+ ~Splinespec(void);
+ Knotspec *kspec; /* format of each param. dir. */
+ int dim; /* domain dimension */
+ REAL * outcpts; /* Bezier control points */
+
+ void kspecinit( Knotvector & );
+ void kspecinit( Knotvector &, Knotvector & );
+ void select( void );
+ void layout( long );
+ void setupquilt( Quilt_ptr );
+ void copy( INREAL * );
+ void transform( void );
+};
+
+/*-----------------------------------------------------------------------------
+ * Quilt::toBezier - convert from NURBS to rational Bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Quilt::toBezier(
+ Knotvector& knotvector, /* a knot vector */
+ INREAL *ctlpts, /* input contol points */
+ long ncoords ) /* number of coordinates per control point */
+{
+ Splinespec spline( 1 );
+ spline.kspecinit( knotvector );
+ spline.select();
+ spline.layout( ncoords );
+ spline.setupquilt( this );
+ spline.copy( ctlpts );
+ spline.transform();
+}
+
+void
+Quilt::toBezier(
+ Knotvector& sknotvector, /* a knot vector */
+ Knotvector& tknotvector, /* a knot vector */
+ INREAL *ctlpts, /* input contol points */
+ long ncoords ) /* number of coordinates per control point */
+{
+ Splinespec spline( 2 );
+ spline.kspecinit( sknotvector, tknotvector );
+ spline.select();
+ spline.layout( ncoords );
+ spline.setupquilt( this );
+ spline.copy( ctlpts );
+ spline.transform();
+}
+Splinespec::Splinespec( int dimen )
+{
+ dim = dimen;
+}
+
+Splinespec::~Splinespec( void )
+{
+ /* Note: do NOT delete 'outcpts' here since its address (not contents)
+ * is copied in 'cpts' in this file in function Splinespec::setupquilt().
+ * This block of memory will eventually be deleted in file quilt.c++ in
+ * function Quilt::deleteMe() through 'cpts' so do NOT delete it here!
+ */
+ Knotspec *ktrav= kspec; //start at beginning of list
+ while (ktrav != 0) { //any items to delete?
+ Knotspec *deleteThis= ktrav; //remember to delete this
+ ktrav= ktrav->next; //go to next item if any
+ delete deleteThis; //delete it
+ }
+} /* ~Splinespec() */
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::kspecinit - initialize Splinespec structure
+ *
+ * Client: Quilt::toBezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::kspecinit( Knotvector& knotvector )
+{
+ kspec = new Knotspec;
+ kspec->inkbegin = knotvector.knotlist;
+ kspec->inkend = knotvector.knotlist + knotvector.knotcount;
+ kspec->prestride = (int) knotvector.stride;
+ kspec->order = knotvector.order;
+ kspec->next = NULL;
+}
+
+void
+Splinespec::kspecinit( Knotvector& sknotvector, Knotvector& tknotvector )
+{
+ kspec = new Knotspec;
+ Knotspec *tkspec = new Knotspec;
+
+ kspec->inkbegin = sknotvector.knotlist;
+ kspec->inkend = sknotvector.knotlist + sknotvector.knotcount;
+ kspec->prestride = (int) sknotvector.stride;
+ kspec->order = sknotvector.order;
+ kspec->next = tkspec;
+
+ tkspec->inkbegin = tknotvector.knotlist;
+ tkspec->inkend = tknotvector.knotlist + tknotvector.knotcount;
+ tkspec->prestride = (int) tknotvector.stride;
+ tkspec->order = tknotvector.order;
+ tkspec->next = NULL;
+}
+
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::select - select the subsegments to copy
+ *
+ * Client: gl_quilt_to_bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::select( )
+{
+ for( Knotspec *knotspec = kspec; knotspec; knotspec = knotspec->next ) {
+ knotspec->preselect();
+ knotspec->select();
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::layout -
+ *
+ * Client: gl_quilt_to_bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::layout( long ncoords )
+{
+
+ long stride = ncoords;
+ for( Knotspec *knotspec = kspec; knotspec; knotspec=knotspec->next ) {
+ knotspec->poststride = (int) stride;
+ stride *= ((knotspec->bend-knotspec->bbegin)*knotspec->order + knotspec->postoffset);
+ knotspec->preoffset *= knotspec->prestride;
+ knotspec->prewidth *= knotspec->poststride;
+ knotspec->postwidth *= knotspec->poststride;
+ knotspec->postoffset *= knotspec->poststride;
+ knotspec->ncoords = (int) ncoords;
+ }
+ outcpts = new REAL[stride];
+ assert( outcpts != 0 );
+}
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::copy - copy the control points of current subobject
+ *
+ * Client: gl_quilt_to_bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::copy( INREAL *incpts )
+{
+ kspec->copy( incpts, outcpts );
+}
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::setupquilt - assign all quilt variables from knotspec
+ *
+ * Client: gl_quilt_to_bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::setupquilt( Quilt_ptr quilt )
+{
+ Quiltspec_ptr qspec = quilt->qspec;
+ quilt->eqspec = qspec + dim;
+ for( Knotspec *knotspec = kspec; knotspec; knotspec=knotspec->next, qspec++ ) {
+ qspec->stride = knotspec->poststride;
+ qspec->width = knotspec->bend - knotspec->bbegin;
+ qspec->order = (int) knotspec->order;
+ qspec->offset = knotspec->postoffset;
+ qspec->index = 0;
+ qspec->bdry[0] = (knotspec->kleft == knotspec->kfirst) ? 1 : 0;
+ qspec->bdry[1] = (knotspec->kright == knotspec->klast) ? 1 : 0;
+ qspec->breakpoints = new Knot[qspec->width+1];
+ Knot_ptr k = qspec->breakpoints;
+ for( Breakpt *bk = knotspec->bbegin; bk <= knotspec->bend; bk++ )
+ *(k++) = bk->value;
+ }
+ quilt->cpts = outcpts;
+ quilt->next = 0;
+}
+
+/*-----------------------------------------------------------------------------
+ * Splinespec::transform - convert a spline to Bezier format
+ *
+ * Client: gl_quilt_to_bezier
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Splinespec::transform( void )
+{
+ Knotspec *knotspec;
+ for( knotspec = kspec; knotspec; knotspec=knotspec->next )
+ knotspec->istransformed = 0;
+
+ for( knotspec = kspec; knotspec; knotspec=knotspec->next ) {
+ for( Knotspec *kspec2 = kspec; kspec2; kspec2=kspec2->next )
+ kspec2->kspectotrans = knotspec;
+ kspec->transform( outcpts );
+ knotspec->istransformed = 1;
+ }
+}
+
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::Knotspec - constuct a knot spec
+ *-----------------------------------------------------------------------------
+ */
+
+Knotspec::Knotspec( void )
+{
+ bbegin = 0;
+ sbegin = 0;
+ outkbegin = 0;
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::copy - copy the control points along minor direction
+ *
+ * Client: Splinespec::copy
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::copy( INREAL *inpt, REAL *outpt )
+{
+ inpt = (INREAL *) (((char *) inpt) + preoffset);
+
+ if( next ) {
+ for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride ) {
+ next->copy( inpt, outpt );
+ inpt = (INREAL *) (((char *) inpt) + prestride);
+ }
+ } else {
+ for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride ) {
+ pt_io_copy( outpt, inpt );
+ inpt = (INREAL *) (((char *) inpt) + prestride);
+ }
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::showpts - print out points before transformation
+ *
+ * Client: Knotspec::select
+ *-----------------------------------------------------------------------------
+ */
+void
+Knotspec::showpts( REAL *outpt )
+{
+ if( next ) {
+ for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride )
+ next->showpts( outpt );
+ } else {
+ for( REAL *lpt=outpt+prewidth; outpt != lpt; outpt += poststride )
+ _glu_dprintf( "show %g %g %g\n", outpt[0], outpt[1], outpt[2] );
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::factors - precompute scale factors
+ * - overwrites knot vector, actual new knot vector is NOT produced
+ *
+ * Client: Knotspec::select
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::factors( void )
+{
+ Knot *mid = (outkend - 1) - order + bend->multi;
+ Knot_ptr fptr = sbegin;
+
+ for( Breakpt *bpt = bend; bpt >= bbegin; bpt-- ) {
+ mid -= bpt->multi; // last knot less than knot to insert
+ int def = bpt->def - 1; // number of knots to insert
+ if( def <= 0 ) continue;
+ Knot kv = bpt->value; // knot to insert
+
+ Knot *kf = (mid-def) + (order-1);
+ for( Knot *kl = kf + def; kl != kf; kl-- ) {
+ Knot *kh, *kt;
+ for( kt=kl, kh=mid; kt != kf; kh--, kt-- )
+ *(fptr++) = (kv - *kh) / (*kt - *kh);
+ *kl = kv;
+ }
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::insert - convert subobject in direction of kspec into Bezier
+ *
+ * Client: Knotspec::transform
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::insert( REAL *p )
+{
+ Knot_ptr fptr = sbegin;
+ REAL *srcpt = p + prewidth - poststride;
+ REAL *dstpt = p + postwidth + postoffset - poststride;
+ Breakpt *bpt = bend;
+
+ for( REAL *pend = srcpt - poststride*bpt->def; srcpt != pend; pend +=poststride ) {
+ REAL *p1 = srcpt;
+ for( REAL *p2 = srcpt-poststride; p2 != pend; p1 = p2, p2 -= poststride ) {
+ pt_oo_sum( p1, p1, p2, *fptr, 1.0-*fptr );
+ fptr++;
+ }
+ }
+
+ for( --bpt; bpt >= bbegin; bpt-- ) {
+
+ for( int multi = bpt->multi; multi > 0; multi-- ) {
+ pt_oo_copy( dstpt, srcpt );
+ dstpt -= poststride;
+ srcpt -= poststride;
+ }
+
+ for( REAL *pend = srcpt - poststride*bpt->def; srcpt != pend; pend +=poststride, dstpt-=poststride ) {
+ pt_oo_copy( dstpt, srcpt );
+ REAL *p1 = srcpt;
+
+ for( REAL *p2 = srcpt-poststride; p2 != pend; p1=p2, p2 -= poststride ) {
+ pt_oo_sum( p1, p1, p2, *fptr, 1.0-*fptr );
+ fptr++;
+ }
+ }
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::preselect - initialize kspec for processing
+ *
+ * Client: Splinespec::select
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::preselect( void )
+{
+ Knot kval;
+
+ /* position klast after last knot of "last" breakpoint */
+ for( klast = inkend - order, kval = *klast; klast != inkend; klast++ )
+ if( ! identical( *klast, kval ) ) break;
+
+ /* position kfirst after last knot of "first" breakpoint */
+ for( kfirst = inkbegin+order-1, kval= *kfirst; kfirst != inkend; kfirst++ )
+ if( ! identical( *kfirst, kval ) ) break;
+
+ /* compute multiplicity of first breakpoint */
+ Knot_ptr k;
+ for( k = kfirst - 1; k >= inkbegin; k-- )
+ if( ! identical( kval, *k ) ) break;
+ k++;
+
+ /* allocate space for breakpoints -
+ use worst case estimate on number of breakpoints */
+
+ bbegin = new Breakpt[(klast - kfirst)+1];
+ /* record multiplicity and value of first breakpoint */
+ bbegin->multi = kfirst - k;
+ bbegin->value = kval;
+ bend = bbegin;
+
+ kleft = kright = kfirst;
+}
+
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::select - Knotspec::select segments and precompute scale factors
+ *
+ * Client: Splinespec::select
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::select( void )
+{
+ breakpoints();
+ knots();
+ factors();
+
+ preoffset = kleft - (inkbegin + order);
+ postwidth = (int)((bend - bbegin) * order);
+ prewidth = (int)((outkend - outkbegin) - order);
+ postoffset = (bbegin->def > 1) ? (bbegin->def-1) : 0;
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::breakpoints - compute breakpoints for knotspec
+ *
+ * Client: Knotspec::select
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::breakpoints( void )
+{
+ Breakpt *ubpt = bbegin;
+ Breakpt *ubend = bend;
+ long nfactors = 0;
+
+ ubpt->value = ubend->value;
+ ubpt->multi = ubend->multi;
+
+ kleft = kright;
+
+ for( ; kright != klast; kright++ ) {
+ if ( identical(*kright,ubpt->value) ) {
+ (ubpt->multi)++;
+ } else {
+ ubpt->def = (int) (order - ubpt->multi);
+ nfactors += (ubpt->def * (ubpt->def - 1)) / 2;
+ (++ubpt)->value = *kright;
+ ubpt->multi = 1;
+ }
+ }
+ ubpt->def = (int) (order - ubpt->multi);
+ nfactors += (ubpt->def * (ubpt->def - 1)) / 2;
+
+ bend = ubpt;
+
+ if( nfactors ) {
+ sbegin = new Knot[nfactors];
+ } else {
+ sbegin = NULL;
+ }
+}
+
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::knots - copy relevant subsequence of knots into temporary area
+ *
+ * Client: Knotspec::select
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::knots( void )
+{
+ Knot_ptr inkpt = kleft - order;
+ Knot_ptr inkend = kright + bend->def;
+
+ /* allocate space for knots and factors */
+ outkbegin = new Knot[inkend-inkpt];
+ Knot_ptr outkpt;
+ for( outkpt = outkbegin; inkpt != inkend; inkpt++, outkpt++ )
+ *outkpt = *inkpt;
+
+ outkend = outkpt;
+}
+
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::transform - convert a spline along a given direction
+ *
+ * Client: Splienspec::transform
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::transform( REAL *p )
+{
+ if( next ) {
+ if( this == kspectotrans ) {
+ next->transform( p );
+ } else {
+ if( istransformed ) {
+ p += postoffset;
+ for( REAL *pend = p + postwidth; p != pend; p += poststride )
+ next->transform( p );
+ } else {
+ REAL *pend = p + prewidth;
+ for( ; p != pend; p += poststride )
+ next->transform( p );
+ }
+ }
+ } else {
+ if( this == kspectotrans ) {
+ insert( p );
+ } else {
+ if( istransformed ) {
+ p += postoffset;
+ for( REAL *pend = p + postwidth; p != pend; p += poststride )
+ kspectotrans->insert( p );
+ } else {
+ REAL *pend = p + prewidth;
+ for( ; p != pend; p += poststride )
+ kspectotrans->insert( p );
+ }
+ }
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * Knotspec::~Knotspec - free space alocated for knotspec
+ *-----------------------------------------------------------------------------
+ */
+
+Knotspec::~Knotspec( void )
+{
+ if( bbegin ) delete[] bbegin;
+ if( sbegin ) delete[] sbegin;
+ if( outkbegin ) delete[] outkbegin;
+}
+
+
+/*-----------------------------------------------------------------------------
+ * pt_io_copy - make internal copy of input cntrl pt. of x coords
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::pt_io_copy( REAL *topt, INREAL *frompt )
+{
+ switch( ncoords ) {
+ case 4:
+ topt[3] = (REAL) frompt[3];
+ case 3:
+ topt[2] = (REAL) frompt[2];
+ case 2:
+ topt[1] = (REAL) frompt[1];
+ case 1:
+ topt[0] = (REAL) frompt[0];
+ break;
+ default: {
+ for( int i = 0; i < ncoords; i++ )
+ *topt++ = (REAL) *frompt++;
+ }
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * pt_oo_copy - make internal copy of internal cntrl pt. of x coords
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::pt_oo_copy( REAL *topt, REAL *frompt )
+{
+ switch( ncoords ) {
+ case 4:
+ topt[3] = frompt[3];
+ case 3:
+ topt[2] = frompt[2];
+ case 2:
+ topt[1] = frompt[1];
+ case 1:
+ topt[0] = frompt[0];
+ break;
+ default:
+ memcpy( topt, frompt, ncoords * sizeof( REAL ) );
+ }
+}
+
+/*-----------------------------------------------------------------------------
+ * pt_oo_sum - compute affine combination of internal cntrl pts
+ *-----------------------------------------------------------------------------
+ */
+
+void
+Knotspec::pt_oo_sum( REAL *x, REAL *y, REAL *z, Knot a, Knot b )
+{
+ switch( ncoords ) {
+ case 4:
+ x[3] = a * y[3] + b * z[3];
+ case 3:
+ x[2] = a * y[2] + b * z[2];
+ case 2:
+ x[1] = a * y[1] + b * z[1];
+ case 1:
+ x[0] = a * y[0] + b * z[0];
+ break;
+ default: {
+ for( int i = 0; i < ncoords; i++ )
+ *x++ = a * *y++ + b * *z++;
+ }
+ }
+}