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IABSD.fr/xenocara/lib/libGLU/src/libnurbs/internals/mapdesc.cc

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  • Author : jsg
    Date : 2019-11-27 10:26:12
    Hash : f42e66cb
    Message : update to GLU 9.0.1 Among other minor changes this adds a stddef.h include for NULL required to build with Mesa 19.2 headers.

  • lib/libGLU/src/libnurbs/internals/mapdesc.cc
  • /*
    ** 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.
    */
    
    /*
     * mapdesc.c++
     *
     */
    
    #include <stdio.h>
    #include "glimports.h"
    #include "mystdio.h"
    #include "myassert.h"
    #include "mystring.h"
    #include "mymath.h"
    #include "backend.h"
    #include "nurbsconsts.h"
    #include "mapdesc.h"
    
    Mapdesc::Mapdesc( long _type, int _israt, int _ncoords, Backend& b ) 
        : backend( b )
    {
        type 		= _type;
        isrational 		= _israt;
        ncoords 		= _ncoords;
        hcoords		= _ncoords + (_israt ? 0 : 1 );
        inhcoords		= _ncoords - (_israt ? 1 : 0 );
        mask 		= ((1<<(inhcoords*2))-1);
        next		= 0;
    
        assert( hcoords <= MAXCOORDS );
        assert( inhcoords >= 1 );
    
        pixel_tolerance 	= 1.0;
        error_tolerance	= 1.0;
        bbox_subdividing	= N_NOBBOXSUBDIVISION;
        culling_method 	= N_NOCULLING;		
        sampling_method 	= N_NOSAMPLING;
        clampfactor 	= N_NOCLAMPING;
        minsavings 		= N_NOSAVINGSSUBDIVISION;
        s_steps  		= 0.0;
        t_steps 		= 0.0;
        maxrate 		= ( s_steps < 0.0 ) ? 0.0 : s_steps;
        maxsrate 		= ( s_steps < 0.0 ) ? 0.0 : s_steps;
        maxtrate 		= ( t_steps < 0.0 ) ? 0.0 : t_steps;
        identify( bmat );
        identify( cmat );
        identify( smat );
        for( int i = 0; i != inhcoords; i++ )
    	bboxsize[i] = 1.0;
    }
    
    void
    Mapdesc::setBboxsize( INREAL *mat )
    {
        for( int i = 0; i != inhcoords; i++ )
    	bboxsize[i] = (REAL) mat[i];
    }
    
    void
    Mapdesc::identify( REAL dest[MAXCOORDS][MAXCOORDS] )
    {
        memset( dest, 0, sizeof( REAL ) * MAXCOORDS * MAXCOORDS );
        for( int i=0; i != hcoords; i++ )
    	dest[i][i] = 1.0;
    }
    
    void
    Mapdesc::surfbbox( REAL bb[2][MAXCOORDS] )
    {
        backend.surfbbox( type, bb[0], bb[1] );
    }
    
    void 
    Mapdesc::copy( REAL dest[MAXCOORDS][MAXCOORDS], long n, INREAL *src,
    	long rstride, long cstride )
    {
        assert( n >= 0 );
        for( int i=0; i != n; i++ )
            for( int j=0; j != n; j++ )
    	    dest[i][j] = src[i*rstride + j*cstride];
    }
    
    /*--------------------------------------------------------------------------
     * copyPt - copy a homogeneous point
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::copyPt( REAL *d, REAL *s )
    {
        assert( hcoords > 0 );
        switch( hcoords  ) {
    	case 4: 
    	    d[3] = s[3];
    	    d[2] = s[2];
    	    d[1] = s[1];
    	    d[0] = s[0];
    	    break;
    	case 3: 
    	    d[2] = s[2];
    	    d[1] = s[1];
    	    d[0] = s[0];
    	    break;
    	case 2: 
    	    d[1] = s[1];
    	    d[0] = s[0];
    	    break;
    	case 1: 
    	    d[0] = s[0];
    	    break;
    	case 5: 
    	    d[4] = s[4];
    	    d[3] = s[3];
    	    d[2] = s[2];
    	    d[1] = s[1];
    	    d[0] = s[0];
    	    break;
    	default:
    	    memcpy( d, s, hcoords * sizeof( REAL ) );
    	    break;
        }
    }
    
    /*--------------------------------------------------------------------------
     * sumPt - compute affine combination of two homogeneous points
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::sumPt( REAL *dst, REAL *src1, REAL *src2, REAL alpha, REAL beta )
    {
        assert( hcoords > 0 );
        switch( hcoords  ) {
    	case 4: 
    	    dst[3] = src1[3] * alpha + src2[3] * beta;
    	    dst[2] = src1[2] * alpha + src2[2] * beta;
    	    dst[1] = src1[1] * alpha + src2[1] * beta;
    	    dst[0] = src1[0] * alpha + src2[0] * beta;
    	    break;
    	case 3: 
    	    dst[2] = src1[2] * alpha + src2[2] * beta;
    	    dst[1] = src1[1] * alpha + src2[1] * beta;
    	    dst[0] = src1[0] * alpha + src2[0] * beta;
    	    break;
    	case 2: 
    	    dst[1] = src1[1] * alpha + src2[1] * beta;
    	    dst[0] = src1[0] * alpha + src2[0] * beta;
    	    break;
    	case 1: 
    	    dst[0] = src1[0] * alpha + src2[0] * beta;
    	    break;
    	case 5: 
    	    dst[4] = src1[4] * alpha + src2[4] * beta;
    	    dst[3] = src1[3] * alpha + src2[3] * beta;
    	    dst[2] = src1[2] * alpha + src2[2] * beta;
    	    dst[1] = src1[1] * alpha + src2[1] * beta;
    	    dst[0] = src1[0] * alpha + src2[0] * beta;
    	    break;
    	default: {
    		for( int i = 0; i != hcoords; i++ )
    		    dst[i] = src1[i] * alpha + src2[i] * beta;
                }
    	    break;
        }
    }
    
    /*--------------------------------------------------------------------------
     * clipbits - compute bit-vector indicating point/window position
     *		       of a (transformed) homogeneous point
     *--------------------------------------------------------------------------
     */
    unsigned int
    Mapdesc::clipbits( REAL *p )
    {
        assert( inhcoords >= 0 );
        assert( inhcoords <= 3 );
    
        int nc = inhcoords;
        REAL pw = p[nc];
        REAL nw = -pw;
        unsigned int bits = 0;
    
        if( pw == 0.0 ) return mask;
    
        if( pw > 0.0 ) {
    	switch( nc ) {
    	case 3:
    	    if( p[2] <= pw ) bits |= (1<<5);
    	    if( p[2] >= nw ) bits |= (1<<4);
    	    if( p[1] <= pw ) bits |= (1<<3);
    	    if( p[1] >= nw ) bits |= (1<<2);
    	    if( p[0] <= pw ) bits |= (1<<1);
    	    if( p[0] >= nw ) bits |= (1<<0);
                return bits;
    	case 2:
    	    if( p[1] <= pw ) bits |= (1<<3);
    	    if( p[1] >= nw ) bits |= (1<<2);
    	    if( p[0] <= pw ) bits |= (1<<1);
    	    if( p[0] >= nw ) bits |= (1<<0);
                return bits;
    	case 1:
    	    if( p[0] <= pw ) bits |= (1<<1);
    	    if( p[0] >= nw ) bits |= (1<<0);
                return bits;
    	default: {
    		int bit = 1;
    		for( int i=0; i<nc; i++ ) {
    		    if( p[i] >= nw ) bits |= bit; 
    		    bit <<= 1;
    		    if( p[i] <= pw ) bits |= bit; 
    		    bit <<= 1;
    		}
    		abort();
    		break;
    	    }
    	}
        } else { 
    	switch( nc ) {
    	case 3:
    	    if( p[2] <= nw ) bits |= (1<<5);
    	    if( p[2] >= pw ) bits |= (1<<4);
    	    if( p[1] <= nw ) bits |= (1<<3);
    	    if( p[1] >= pw ) bits |= (1<<2);
    	    if( p[0] <= nw ) bits |= (1<<1);
    	    if( p[0] >= pw ) bits |= (1<<0);
                return bits;
    	case 2:
    	    if( p[1] <= nw ) bits |= (1<<3);
    	    if( p[1] >= pw ) bits |= (1<<2);
    	    if( p[0] <= nw ) bits |= (1<<1);
    	    if( p[0] >= pw ) bits |= (1<<0);
                return bits;
    	case 1:
    	    if( p[0] <= nw ) bits |= (1<<1);
    	    if( p[0] >= pw ) bits |= (1<<0);
                return bits;
    	default: {
    		int bit = 1; 
    		for( int i=0; i<nc; i++ ) {
    		    if( p[i] >= pw ) bits |= bit; 
    		    bit <<= 1;
    		    if( p[i] <= nw ) bits |= bit; 
    		    bit <<= 1;
    		}
    		abort();
    		break;
    	    }
    	}
        }
        return bits;
    }
    
    /*--------------------------------------------------------------------------
     * xformRational - transform a homogeneous point
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformRational( Maxmatrix mat, REAL *d, REAL *s )
    {
        assert( hcoords >= 0 );
    
        if( hcoords == 3 ) {
    	REAL x = s[0];
    	REAL y = s[1];
    	REAL z = s[2];
    	d[0] = x*mat[0][0]+y*mat[1][0]+z*mat[2][0];
    	d[1] = x*mat[0][1]+y*mat[1][1]+z*mat[2][1];
    	d[2] = x*mat[0][2]+y*mat[1][2]+z*mat[2][2];
        } else if( hcoords == 4 ) {
    	REAL x = s[0];
    	REAL y = s[1];
    	REAL z = s[2];
    	REAL w = s[3];
    	d[0] = x*mat[0][0]+y*mat[1][0]+z*mat[2][0]+w*mat[3][0];
    	d[1] = x*mat[0][1]+y*mat[1][1]+z*mat[2][1]+w*mat[3][1];
    	d[2] = x*mat[0][2]+y*mat[1][2]+z*mat[2][2]+w*mat[3][2];
    	d[3] = x*mat[0][3]+y*mat[1][3]+z*mat[2][3]+w*mat[3][3];
        } else {
    	for( int i=0; i != hcoords; i++ ) {
    	    d[i] = 0;
    	    for( int j = 0; j != hcoords; j++ )
    		d[i] += s[j] * mat[j][i];
    	}
        }
    }
    
    /*--------------------------------------------------------------------------
     * xformNonrational - transform a inhomogeneous point to a homogeneous point
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformNonrational( Maxmatrix mat, REAL *d, REAL *s )
    {
        if( inhcoords == 2 ) {
    	REAL x = s[0];
    	REAL y = s[1];
    	d[0] = x*mat[0][0]+y*mat[1][0]+mat[2][0];
    	d[1] = x*mat[0][1]+y*mat[1][1]+mat[2][1];
    	d[2] = x*mat[0][2]+y*mat[1][2]+mat[2][2];
        } else if( inhcoords == 3 ) {
    	REAL x = s[0];
    	REAL y = s[1];
    	REAL z = s[2];
    	d[0] = x*mat[0][0]+y*mat[1][0]+z*mat[2][0]+mat[3][0];
    	d[1] = x*mat[0][1]+y*mat[1][1]+z*mat[2][1]+mat[3][1];
    	d[2] = x*mat[0][2]+y*mat[1][2]+z*mat[2][2]+mat[3][2];
    	d[3] = x*mat[0][3]+y*mat[1][3]+z*mat[2][3]+mat[3][3];
        } else {
            assert( inhcoords >= 0 );
    	for( int i=0; i != hcoords; i++ ) {
    	    d[i] = mat[inhcoords][i];
    	    for( int j = 0; j < inhcoords; j++ )
    		d[i] += s[j] * mat[j][i];
    	}
        }
    }
    
    /*--------------------------------------------------------------------------
     * xformAndCullCheck - transform a set of points that may be EITHER 
     *	homogeneous or inhomogeneous depending on the map description and
     *	check if they are either completely inside, completely outside, 
     *	or intersecting the viewing frustrum.
     *--------------------------------------------------------------------------
     */
    int
    Mapdesc::xformAndCullCheck( 
        REAL *pts, int uorder, int ustride, int vorder, int vstride )
    {
        assert( uorder > 0 );
        assert( vorder > 0 );
    
        unsigned int inbits = mask;
        unsigned int outbits = 0;
    
        REAL *p = pts;
        for( REAL *pend = p + uorder * ustride; p != pend; p += ustride ) {
            REAL *q = p;
            for( REAL *qend = q + vorder * vstride; q != qend; q += vstride ) {
        	    REAL cpts[MAXCOORDS];
    	    xformCulling( cpts, q );
    	    unsigned int bits = clipbits( cpts );
    	    outbits |= bits;
    	    inbits &= bits;
    	    if( ( outbits == (unsigned int)mask ) && ( inbits != (unsigned int)mask ) ) return CULL_ACCEPT;
    	} 
        }
    
        if( outbits != (unsigned int)mask ) {
    	return CULL_TRIVIAL_REJECT;
        } else if( inbits == (unsigned int)mask ) {
    	return CULL_TRIVIAL_ACCEPT;
        } else {
    	return CULL_ACCEPT;
        }
    }
    
    /*--------------------------------------------------------------------------
     * cullCheck - check if a set of homogeneous transformed points are 
     *	either completely inside, completely outside, 
     *	or intersecting the viewing frustrum.
     *--------------------------------------------------------------------------
     */
    int
    Mapdesc::cullCheck( REAL *pts, int uorder, int ustride, int vorder, int vstride )
    {
        unsigned int inbits = mask;
        unsigned int outbits  = 0;
    
        REAL *p = pts;
        for( REAL *pend = p + uorder * ustride; p != pend; p += ustride ) {
            REAL *q = p;
            for( REAL *qend = q + vorder * vstride; q != qend; q += vstride ) {
    	    unsigned int bits = clipbits( q );
    	    outbits |= bits;
    	    inbits &= bits;
    	    if( ( outbits == (unsigned int)mask ) && ( inbits != (unsigned int)mask ) ) return CULL_ACCEPT;
    	} 
        }
    
        if( outbits != (unsigned int)mask ) {
    	return CULL_TRIVIAL_REJECT;
        } else if( inbits == (unsigned int)mask ) {
    	return CULL_TRIVIAL_ACCEPT;
        } else {
    	return CULL_ACCEPT;
        }
    }
    
    /*--------------------------------------------------------------------------
     * cullCheck - check if a set of homogeneous transformed points are 
     *	either completely inside, completely outside, 
     *	or intersecting the viewing frustrum.
     *--------------------------------------------------------------------------
     */
    int
    Mapdesc::cullCheck( REAL *pts, int order, int stride )
    {
        unsigned int inbits = mask;
        unsigned int outbits  = 0;
    
        REAL *p = pts;
        for( REAL *pend = p + order * stride; p != pend; p += stride ) {
    	unsigned int bits = clipbits( p );
    	outbits |= bits;
    	inbits &= bits;
    	if( ( outbits == (unsigned int)mask ) && ( inbits != (unsigned int)mask ) ) return CULL_ACCEPT;
        }
    
        if( outbits != (unsigned int)mask ) {
    	return CULL_TRIVIAL_REJECT;
        } else if( inbits == (unsigned int)mask ) {
    	return CULL_TRIVIAL_ACCEPT;
        } else {
    	return CULL_ACCEPT;
        }
    }
    
    /*--------------------------------------------------------------------------
     * xformSampling - transform a set of points that may be EITHER 
     *	homogeneous or inhomogeneous depending on the map description 
     *	into sampling space 
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformSampling( REAL *pts, int order, int stride, REAL *sp, int outstride )
    {
        xformMat( smat, pts, order, stride, sp, outstride );
    }
    
    void
    Mapdesc::xformBounding( REAL *pts, int order, int stride, REAL *sp, int outstride )
    {
        xformMat( bmat, pts, order, stride, sp, outstride );
    }
    
    /*--------------------------------------------------------------------------
     * xformCulling - transform a set of points that may be EITHER 
     *	homogeneous or inhomogeneous depending on the map description 
     *	into culling space 
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformCulling( REAL *pts, int order, int stride, REAL *cp, int outstride )
    {
        xformMat( cmat, pts, order, stride, cp, outstride );
    }
    
    /*--------------------------------------------------------------------------
     * xformCulling - transform a set of points that may be EITHER 
     *	homogeneous or inhomogeneous depending on the map description 
     *	into culling space 
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformCulling( REAL *pts, 
        int uorder, int ustride,
        int vorder, int vstride, 
        REAL *cp, int outustride, int outvstride )
    {
        xformMat( cmat, pts, uorder, ustride, vorder, vstride, cp, outustride, outvstride );
    }
    
    /*--------------------------------------------------------------------------
     * xformSampling - transform a set of points that may be EITHER 
     *	homogeneous or inhomogeneous depending on the map description 
     *	into sampling space 
     *--------------------------------------------------------------------------
     */
    void
    Mapdesc::xformSampling( REAL *pts, 
        int uorder, int ustride, 
        int vorder, int vstride, 
        REAL *sp, int outustride, int outvstride )
    {
        xformMat( smat, pts, uorder, ustride, vorder, vstride, sp, outustride, outvstride );
    }
    
    void
    Mapdesc::xformBounding( REAL *pts, 
        int uorder, int ustride, 
        int vorder, int vstride, 
        REAL *sp, int outustride, int outvstride )
    {
        xformMat( bmat, pts, uorder, ustride, vorder, vstride, sp, outustride, outvstride );
    }
    
    void
    Mapdesc::xformMat( 
        Maxmatrix	mat, 
        REAL *	pts, 
        int 	order, 
        int 	stride,
        REAL *	cp, 
        int 	outstride )
    {
        if( isrational ) {
    	REAL *pend = pts + order * stride;
    	for( REAL *p = pts ; p != pend; p += stride ) {
    	    xformRational( mat, cp, p );
    	    cp += outstride;
    	}       
        } else {
    	REAL *pend = pts + order * stride;
    	for( REAL *p = pts ; p != pend; p += stride ) {
    	    xformNonrational( mat, cp, p );
    	    cp += outstride;
    	}	
        }
    }
    
    void
    Mapdesc::xformMat( Maxmatrix mat, REAL *pts, 
        int uorder, int ustride, 
        int vorder, int vstride, 
        REAL *cp, int outustride, int outvstride )
    {
        if( isrational ) {
    	REAL *pend = pts + uorder * ustride;
    	for( REAL *p = pts ; p != pend; p += ustride ) {
    	    REAL *cpts2 = cp;
    	    REAL *qend = p + vorder * vstride;
    	    for( REAL *q = p; q != qend; q += vstride ) {
    		xformRational( mat, cpts2, q );
    		cpts2 += outvstride;
    	    } 
    	    cp += outustride;
    	}
        } else {
    	REAL *pend = pts + uorder * ustride;
    	for( REAL *p = pts ; p != pend; p += ustride ) {
    	    REAL *cpts2 = cp;
    	    REAL *qend = p + vorder * vstride;
    	    for( REAL *q = p; q != qend; q += vstride ) {
    		xformNonrational( mat, cpts2, q );
    		cpts2 += outvstride;
    	    } 
    	    cp += outustride;
    	}
        }
    }
    
    /*--------------------------------------------------------------------------
     * subdivide - subdivide a curve along an isoparametric line
     *--------------------------------------------------------------------------
     */
    
    void
    Mapdesc::subdivide( REAL *src, REAL *dst, REAL v, int stride, int order )
    {
        REAL mv = 1.0 - v;
    
        for( REAL *send=src+stride*order; src!=send; send-=stride, dst+=stride ) {
    	copyPt( dst, src );
    	REAL *qpnt = src + stride;
    	for( REAL *qp=src; qpnt!=send; qp=qpnt, qpnt+=stride )
    	    sumPt( qp, qp, qpnt, mv, v );
        }
    }
    
    /*--------------------------------------------------------------------------
     * subdivide - subdivide a patch along an isoparametric line
     *--------------------------------------------------------------------------
     */
    
    void
    Mapdesc::subdivide( REAL *src, REAL *dst, REAL v, 
        int so, int ss, int to, int ts  )
    {
        REAL mv = 1.0 - v;
    
        for( REAL *slast = src+ss*so; src != slast; src += ss, dst += ss ) {
    	REAL *sp = src;
    	REAL *dp = dst;
            for( REAL *send = src+ts*to; sp != send; send -= ts, dp += ts ) {
    	    copyPt( dp, sp );
    	    REAL *qp = sp;
    	    for( REAL *qpnt = sp+ts; qpnt != send; qp = qpnt, qpnt += ts )
    	        sumPt( qp, qp, qpnt, mv, v );
    	}
        }
    }
    
    
    #define sign(x)	((x > 0) ? 1 : ((x < 0.0) ? -1 : 0))
    
    /*--------------------------------------------------------------------------
     * project - project a set of homogeneous coordinates into inhomogeneous ones
     *--------------------------------------------------------------------------
     */
    int
    Mapdesc::project( REAL *src, int rstride, int cstride, 
    	          REAL *dest, int trstride, int tcstride,
    		  int nrows, int ncols )
    {
        int s = sign( src[inhcoords] );
        REAL *rlast = src + nrows * rstride;
        REAL *trptr = dest;
        for( REAL *rptr=src; rptr != rlast; rptr+=rstride, trptr+=trstride ) {
    	REAL *clast = rptr + ncols * cstride;
    	REAL *tcptr = trptr;
    	for( REAL *cptr = rptr; cptr != clast; cptr+=cstride, tcptr+=tcstride ) {
    	    REAL *coordlast = cptr + inhcoords;
    	    if( sign( *coordlast ) != s ) return 0;
    	    REAL *tcoord = tcptr;
    	    for( REAL *coord = cptr; coord != coordlast; coord++, tcoord++ ) {
    		*tcoord = *coord / *coordlast;
    	    }
    	}
        }
        return 1;
    }
    
    /*--------------------------------------------------------------------------
     * project - project a set of homogeneous coordinates into inhomogeneous ones
     *--------------------------------------------------------------------------
     */
    int
    Mapdesc::project( REAL *src, int stride, REAL *dest, int tstride, int ncols )
    {
        int s = sign( src[inhcoords] );
    
        REAL *clast = src + ncols * stride;
        for( REAL *cptr = src, *tcptr = dest; cptr != clast; cptr+=stride, tcptr+=tstride ) {
    	REAL *coordlast = cptr + inhcoords;
    	if( sign( *coordlast ) != s ) return 0;
    	for( REAL *coord = cptr, *tcoord = tcptr; coord != coordlast; coord++, tcoord++ ) 
    	    *tcoord = *coord / *coordlast;
        }
    
        return 1;
    }
    
    int
    Mapdesc::bboxTooBig( 
        REAL *p, 
        int	 rstride,
        int	 cstride,
        int	 nrows,
        int	 ncols,
        REAL bb[2][MAXCOORDS] )
    {
        REAL bbpts[MAXORDER][MAXORDER][MAXCOORDS];
        const int trstride = sizeof(bbpts[0]) / sizeof(REAL);
        const int tcstride = sizeof(bbpts[0][0]) / sizeof(REAL); 
    
        // points have been transformed, therefore they are homogeneous
        // project points
        int val = project( p, rstride, cstride, 
    	     &bbpts[0][0][0], trstride, tcstride, nrows, ncols );
        if( val == 0 ) return -1;
    
        // compute bounding box
        bbox( bb, &bbpts[0][0][0], trstride, tcstride, nrows, ncols );
    
        // find out if bounding box can't fit in unit cube
        if( bbox_subdividing == N_BBOXROUND ) {
    	for( int k=0; k != inhcoords; k++ )
    	    if( ceilf(bb[1][k]) - floorf(bb[0][k]) > bboxsize[k] ) return 1;
        } else {
    	for( int k=0; k != inhcoords; k++ )
    	    if( bb[1][k] - bb[0][k] > bboxsize[k] ) return 1;
        }
        return 0;  
    }
    
    void
    Mapdesc::bbox( 
        REAL bb[2][MAXCOORDS], 
        REAL *p, 
        int	 rstride,
        int	 cstride,
        int	 nrows,
        int	 ncols )
    {
        int k;
        for( k=0; k != inhcoords; k++ )
    	 bb[0][k] = bb[1][k] = p[k];
    
        for( int i=0; i != nrows; i++ ) 
    	for( int j=0; j != ncols; j++ ) 
    	    for( k=0; k != inhcoords; k++ ) {
    		REAL x = p[i*rstride + j*cstride + k];
    		if(  x < bb[0][k] ) bb[0][k] = x;
    		else if( x > bb[1][k] ) bb[1][k] = x;
    	    }
    }
    
    /*--------------------------------------------------------------------------
     * calcVelocityRational - calculate upper bound on first partial derivative 
     *	of a homogeneous set of points and bounds on each row of points.
     *--------------------------------------------------------------------------
     */
    REAL
    Mapdesc::calcVelocityRational( REAL *p, int stride, int ncols )
    {
        REAL tmp[MAXORDER][MAXCOORDS];
    
        assert( ncols <= MAXORDER );
    
        const int tstride = sizeof(tmp[0]) / sizeof(REAL); 
    
        if( project( p, stride, &tmp[0][0], tstride, ncols ) ) {
    	return calcPartialVelocity( &tmp[0][0], tstride, ncols, 1, 1.0 );
        } else { /* XXX */
    	return calcPartialVelocity( &tmp[0][0], tstride, ncols, 1, 1.0 );
        }
    }
    
    /*--------------------------------------------------------------------------
     * calcVelocityNonrational - calculate upper bound on  first partial 
     *	derivative of a inhomogeneous set of points.
     *--------------------------------------------------------------------------
     */
    REAL
    Mapdesc::calcVelocityNonrational( REAL *pts, int stride, int ncols )
    {
        return calcPartialVelocity( pts, stride, ncols, 1, 1.0 );
    }
    
    int
    Mapdesc::isProperty( long property )
    {
        switch ( property ) {
    	case N_PIXEL_TOLERANCE:
    	case N_ERROR_TOLERANCE:
    	case N_CULLING:
    	case N_BBOX_SUBDIVIDING:
    	case N_S_STEPS:
    	case N_T_STEPS:
            case N_SAMPLINGMETHOD:
            case N_CLAMPFACTOR:
            case N_MINSAVINGS:
    	    return 1;
    	default:
    	    return 0;
        }
    }
    
    REAL
    Mapdesc::getProperty( long property )
    {
        switch ( property ) {
    	case N_PIXEL_TOLERANCE:
    	    return pixel_tolerance;
    	case N_ERROR_TOLERANCE:
    	    return error_tolerance;
    	case N_CULLING:
    	    return culling_method;
    	case N_BBOX_SUBDIVIDING:
    	    return bbox_subdividing;
    	case N_S_STEPS:
    	    return s_steps;
    	case N_T_STEPS:
    	    return t_steps;
            case N_SAMPLINGMETHOD:
    	    return sampling_method;
            case N_CLAMPFACTOR:
    	    return clampfactor;
            case N_MINSAVINGS:
    	    return minsavings;
    	default:
    	    abort();
    	    return -1; //not necessary, needed to shut up compiler
        }
    }
    
    void
    Mapdesc::setProperty( long property, REAL value )
    {
    
        switch ( property ) {
    	case N_PIXEL_TOLERANCE:
    	    pixel_tolerance = value;
    	    break;
    	case N_ERROR_TOLERANCE:
    	    error_tolerance = value;
    	    break;
    	case N_CULLING:
    	    culling_method = value;
    	    break;
    	case N_BBOX_SUBDIVIDING:
    	    if( value <= 0.0 ) value = N_NOBBOXSUBDIVISION;
    	    bbox_subdividing = value;
    	    break;
    	case N_S_STEPS:
    	    if( value < 0.0 ) value = 0.0;
    	    s_steps = value;
    	    maxrate = ( value < 0.0 ) ? 0.0 : value;
    	    maxsrate = ( value < 0.0 ) ? 0.0 : value;
    	    break;
    	case N_T_STEPS:
    	    if( value < 0.0 ) value = 0.0;
    	    t_steps = value;
    	    maxtrate = ( value < 0.0 ) ? 0.0 : value;
    	    break;
    	case N_SAMPLINGMETHOD:
    	    sampling_method = value;
    	    break;
    	case N_CLAMPFACTOR:
    	    if( value <= 0.0 ) value = N_NOCLAMPING;
    	    clampfactor = value;
    	    break;
    	case N_MINSAVINGS:
    	    if( value <= 0.0 ) value = N_NOSAVINGSSUBDIVISION;
    	    minsavings = value;
    	    break;
    	default:
    	    abort();
    	    break;
        }
    }