src/rt/ambcomp.c

#ifndef lint
static const char       RCSid[] = "$Id: ambcomp.c,v 2.54 2014/05/09 04:55:19 greg Exp $";
#endif
/*
 * Routines to compute "ambient" values using Monte Carlo
 *
 *  Hessian calculations based on "Practical Hessian-Based Error Control
 *      for Irradiance Caching" by Schwarzhaupt, Wann Jensen, & Jarosz
 *      from ACM SIGGRAPH Asia 2012 conference proceedings.
 *
 *  Added book-keeping optimization to avoid calculations that would
 *      cancel due to traversal both directions on edges that are adjacent
 *      to same-valued triangles.  This cuts about half of Hessian math.
 *
 *  Declarations of external symbols in ambient.h
 */

#include "copyright.h"

#include  "ray.h"
#include  "ambient.h"
#include  "random.h"

#ifdef NEWAMB

extern void             SDsquare2disk(double ds[2], double seedx, double seedy);

                                /* vertex direction bit positions */
#define VDB_xy  0
#define VDB_y   01
#define VDB_x   02
#define VDB_Xy  03
#define VDB_xY  04
#define VDB_X   05
#define VDB_Y   06
#define VDB_XY  07
                                /* get opposite vertex direction bit */
#define VDB_OPP(f)      (~(f) & 07)
                                /* adjacent triangle vertex flags */
static const int  adjacent_trifl[8] = {
                        0,                      /* forbidden diagonal */
                        1<<VDB_x|1<<VDB_y|1<<VDB_Xy,
                        1<<VDB_y|1<<VDB_x|1<<VDB_xY,
                        1<<VDB_y|1<<VDB_Xy|1<<VDB_X,
                        1<<VDB_x|1<<VDB_xY|1<<VDB_Y,
                        1<<VDB_Xy|1<<VDB_X|1<<VDB_Y,
                        1<<VDB_xY|1<<VDB_Y|1<<VDB_X,
                        0,                      /* forbidden diagonal */
                };

typedef struct {
        COLOR   v;              /* hemisphere sample value */
        float   d;              /* reciprocal distance (1/rt) */
        FVECT   p;              /* intersection point */
} AMBSAMP;              /* sample value */

typedef struct {
        RAY     *rp;            /* originating ray sample */
        FVECT   ux, uy;         /* tangent axis unit vectors */
        int     ns;             /* number of samples per axis */
        COLOR   acoef;          /* division contribution coefficient */
        AMBSAMP sa[1];          /* sample array (extends struct) */
}  AMBHEMI;             /* ambient sample hemisphere */

#define ambndx(h,i,j)   ((i)*(h)->ns + (j))
#define ambsam(h,i,j)   (h)->sa[ambndx(h,i,j)]

typedef struct {
        FVECT   r_i, r_i1, e_i, rcp, rI2_eJ2;
        double  I1, I2;
        int     valid;
} FFTRI;                /* vectors and coefficients for Hessian calculation */


/* Get index for adjacent vertex */
static int
adjacent_verti(AMBHEMI *hp, int i, int j, int dbit)
{
        int     i0 = i*hp->ns + j;

        switch (dbit) {
        case VDB_y:     return(i0 - hp->ns);
        case VDB_x:     return(i0 - 1);
        case VDB_Xy:    return(i0 - hp->ns + 1);
        case VDB_xY:    return(i0 + hp->ns - 1);
        case VDB_X:     return(i0 + 1);
        case VDB_Y:     return(i0 + hp->ns);
                                /* the following should never occur */
        case VDB_xy:    return(i0 - hp->ns - 1);
        case VDB_XY:    return(i0 + hp->ns + 1);
        }
        return(-1);
}


/* Get vertex direction bit for the opposite edge to complete triangle */
static int
vdb_edge(int db1, int db2)
{
        switch (db1) {
        case VDB_x:     return(db2==VDB_y ? VDB_Xy : VDB_Y);
        case VDB_y:     return(db2==VDB_x ? VDB_xY : VDB_X);
        case VDB_X:     return(db2==VDB_Xy ? VDB_y : VDB_xY);
        case VDB_Y:     return(db2==VDB_xY ? VDB_x : VDB_Xy);
        case VDB_xY:    return(db2==VDB_x ? VDB_y : VDB_X);
        case VDB_Xy:    return(db2==VDB_y ? VDB_x : VDB_Y);
        }
        error(CONSISTENCY, "forbidden diagonal in vdb_edge()");
        return(-1);
}


static AMBHEMI *
inithemi(                       /* initialize sampling hemisphere */
        COLOR   ac,
        RAY     *r,
        double  wt
)
{
        AMBHEMI *hp;
        double  d;
        int     n, i;
                                        /* set number of divisions */
        if (ambacc <= FTINY &&
                        wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
                wt = d;                 /* avoid ray termination */
        n = sqrt(ambdiv * wt) + 0.5;
        i = 1 + 5*(ambacc > FTINY);     /* minimum number of samples */
        if (n < i)
                n = i;
                                        /* allocate sampling array */
        hp = (AMBHEMI *)malloc(sizeof(AMBHEMI) + sizeof(AMBSAMP)*(n*n - 1));
        if (hp == NULL)
                return(NULL);
        hp->rp = r;
        hp->ns = n;
                                        /* assign coefficient */
        copycolor(hp->acoef, ac);
        d = 1.0/(n*n);
        scalecolor(hp->acoef, d);
                                        /* make tangent plane axes */
        hp->uy[0] = 0.5 - frandom();
        hp->uy[1] = 0.5 - frandom();
        hp->uy[2] = 0.5 - frandom();
        for (i = 3; i--; )
                if ((-0.6 < r->ron[i]) & (r->ron[i] < 0.6))
                        break;
        if (i < 0)
                error(CONSISTENCY, "bad ray direction in inithemi");
        hp->uy[i] = 1.0;
        VCROSS(hp->ux, hp->uy, r->ron);
        normalize(hp->ux);
        VCROSS(hp->uy, r->ron, hp->ux);
                                        /* we're ready to sample */
        return(hp);
}


/* Sample ambient division and apply weighting coefficient */
static int
getambsamp(RAY *arp, AMBHEMI *hp, int i, int j, int n)
{
        int     hlist[3], ii;
        double  spt[2], zd;
                                        /* ambient coefficient for weight */
        if (ambacc > FTINY)
                setcolor(arp->rcoef, AVGREFL, AVGREFL, AVGREFL);
        else
                copycolor(arp->rcoef, hp->acoef);
        if (rayorigin(arp, AMBIENT, hp->rp, arp->rcoef) < 0)
                return(0);
        if (ambacc > FTINY) {
                multcolor(arp->rcoef, hp->acoef);
                scalecolor(arp->rcoef, 1./AVGREFL);
        }
        hlist[0] = hp->rp->rno;
        hlist[1] = j;
        hlist[2] = i;
        multisamp(spt, 2, urand(ilhash(hlist,3)+n));
        if (!n) {                       /* avoid border samples for n==0 */
                if ((spt[0] < 0.1) | (spt[0] >= 0.9))
                        spt[0] = 0.1 + 0.8*frandom();
                if ((spt[1] < 0.1) | (spt[1] >= 0.9))
                        spt[1] = 0.1 + 0.8*frandom();
        }
        SDsquare2disk(spt, (j+spt[1])/hp->ns, (i+spt[0])/hp->ns);
        zd = sqrt(1. - spt[0]*spt[0] - spt[1]*spt[1]);
        for (ii = 3; ii--; )
                arp->rdir[ii] = spt[0]*hp->ux[ii] +
                                spt[1]*hp->uy[ii] +
                                zd*hp->rp->ron[ii];
        checknorm(arp->rdir);
        dimlist[ndims++] = ambndx(hp,i,j) + 90171;
        rayvalue(arp);                  /* evaluate ray */
        ndims--;                        /* apply coefficient */
        multcolor(arp->rcol, arp->rcoef);
        return(1);
}


static AMBSAMP *
ambsample(                              /* initial ambient division sample */
        AMBHEMI *hp,
        int     i,
        int     j
)
{
        AMBSAMP *ap = &ambsam(hp,i,j);
        RAY     ar;
                                        /* generate hemispherical sample */
        if (!getambsamp(&ar, hp, i, j, 0) || ar.rt <= FTINY) {
                memset(ap, 0, sizeof(AMBSAMP));
                return(NULL);
        }
        ap->d = 1.0/ar.rt;              /* limit vertex distance */
        if (ar.rt > 10.0*thescene.cusize)
                ar.rt = 10.0*thescene.cusize;
        VSUM(ap->p, ar.rorg, ar.rdir, ar.rt);
        copycolor(ap->v, ar.rcol);
        return(ap);
}


/* Estimate errors based on ambient division differences */
static float *
getambdiffs(AMBHEMI *hp)
{
        float   *earr = (float *)calloc(hp->ns*hp->ns, sizeof(float));
        float   *ep;
        AMBSAMP *ap;
        double  b, d2;
        int     i, j;

        if (earr == NULL)               /* out of memory? */
                return(NULL);
                                        /* compute squared neighbor diffs */
        for (ap = hp->sa, ep = earr, i = 0; i < hp->ns; i++)
            for (j = 0; j < hp->ns; j++, ap++, ep++) {
                b = bright(ap[0].v);
                if (i) {                /* from above */
                        d2 = b - bright(ap[-hp->ns].v);
                        d2 *= d2;
                        ep[0] += d2;
                        ep[-hp->ns] += d2;
                }
                if (!j) continue;
                                        /* from behind */
                d2 = b - bright(ap[-1].v);
                d2 *= d2;
                ep[0] += d2;
                ep[-1] += d2;
                if (!i) continue;
                                        /* diagonal */
                d2 = b - bright(ap[-hp->ns-1].v);
                d2 *= d2;
                ep[0] += d2;
                ep[-hp->ns-1] += d2;
            }
                                        /* correct for number of neighbors */
        earr[0] *= 8./3.;
        earr[hp->ns-1] *= 8./3.;
        earr[(hp->ns-1)*hp->ns] *= 8./3.;
        earr[(hp->ns-1)*hp->ns + hp->ns-1] *= 8./3.;
        for (i = 1; i < hp->ns-1; i++) {
                earr[i*hp->ns] *= 8./5.;
                earr[i*hp->ns + hp->ns-1] *= 8./5.;
        }
        for (j = 1; j < hp->ns-1; j++) {
                earr[j] *= 8./5.;
                earr[(hp->ns-1)*hp->ns + j] *= 8./5.;
        }
        return(earr);
}


/* Perform super-sampling on hemisphere (introduces bias) */
static void
ambsupersamp(double acol[3], AMBHEMI *hp, int cnt)
{
        float   *earr = getambdiffs(hp);
        double  e2rem = 0;
        AMBSAMP *ap;
        RAY     ar;
        double  asum[3];
        float   *ep;
        int     i, j, n, nss;

        if (earr == NULL)               /* just skip calc. if no memory */
                return;
                                        /* accumulate estimated variances */
        for (ep = earr + hp->ns*hp->ns; ep > earr; )
                e2rem += *--ep;
        ep = earr;                      /* perform super-sampling */
        for (ap = hp->sa, i = 0; i < hp->ns; i++)
            for (j = 0; j < hp->ns; j++, ap++) {
                if (e2rem <= FTINY)
                        goto done;      /* nothing left to do */
                nss = *ep/e2rem*cnt + frandom();
                asum[0] = asum[1] = asum[2] = 0.0;
                for (n = 1; n <= nss; n++) {
                        if (!getambsamp(&ar, hp, i, j, n)) {
                                nss = n-1;
                                break;
                        }
                        addcolor(asum, ar.rcol);
                }
                if (nss) {              /* update returned ambient value */
                        const double    ssf = 1./(nss + 1.);
                        for (n = 3; n--; )
                                acol[n] += ssf*asum[n] +
                                                (ssf - 1.)*colval(ap->v,n);
                }
                e2rem -= *ep++;         /* update remainders */
                cnt -= nss;
        }
done:
        free(earr);
}


/* Compute vertex flags, indicating farthest in each direction */
static uby8 *
vertex_flags(AMBHEMI *hp)
{
        uby8    *vflags = (uby8 *)calloc(hp->ns*hp->ns, sizeof(uby8));
        uby8    *vf;
        AMBSAMP *ap;
        int     i, j;

        if (vflags == NULL)
                error(SYSTEM, "out of memory in vertex_flags()");
        vf = vflags;
        ap = hp->sa;            /* compute farthest along first row */
        for (j = 0; j < hp->ns-1; j++, vf++, ap++)
                if (ap[0].d <= ap[1].d)
                        vf[0] |= 1<<VDB_X;
                else
                        vf[1] |= 1<<VDB_x;
        ++vf; ++ap;
                                /* flag subsequent rows */
        for (i = 1; i < hp->ns; i++) {
            for (j = 0; j < hp->ns-1; j++, vf++, ap++) {
                if (ap[0].d <= ap[-hp->ns].d)   /* row before */
                        vf[0] |= 1<<VDB_y;
                else
                        vf[-hp->ns] |= 1<<VDB_Y;
                if (ap[0].d <= ap[1-hp->ns].d)  /* diagonal we care about */
                        vf[0] |= 1<<VDB_Xy;
                else
                        vf[1-hp->ns] |= 1<<VDB_xY;
                if (ap[0].d <= ap[1].d)         /* column after */
                        vf[0] |= 1<<VDB_X;
                else
                        vf[1] |= 1<<VDB_x;
            }
            if (ap[0].d <= ap[-hp->ns].d)       /* final column edge */
                vf[0] |= 1<<VDB_y;
            else
                vf[-hp->ns] |= 1<<VDB_Y;
            ++vf; ++ap;
        }
        return(vflags);
}


/* Return brightness of farthest ambient sample */
static double
back_ambval(AMBHEMI *hp, int i, int j, int dbit1, int dbit2, const uby8 *vflags)
{
        const int       v0 = ambndx(hp,i,j);
        const int       tflags = (1<<dbit1 | 1<<dbit2);
        int             v1, v2;

        if ((vflags[v0] & tflags) == tflags)    /* is v0 the farthest? */
                return(colval(hp->sa[v0].v,CIEY));
        v1 = adjacent_verti(hp, i, j, dbit1);
        if (vflags[v0] & 1<<dbit2)              /* v1 farthest if v0>v2 */
                return(colval(hp->sa[v1].v,CIEY));
        v2 = adjacent_verti(hp, i, j, dbit2);
        if (vflags[v0] & 1<<dbit1)              /* v2 farthest if v0>v1 */
                return(colval(hp->sa[v2].v,CIEY));
                                                /* else check if v1>v2 */
        if (vflags[v1] & 1<<vdb_edge(dbit1,dbit2))
                return(colval(hp->sa[v1].v,CIEY));
        return(colval(hp->sa[v2].v,CIEY));
}


/* Compute vectors and coefficients for Hessian/gradient calcs */
static void
comp_fftri(FFTRI *ftp, AMBHEMI *hp, int i, int j, int dbit, const uby8 *vflags)
{
        const int       i0 = ambndx(hp,i,j);
        double          rdot_cp, dot_e, dot_er, rdot_r, rdot_r1, J2;
        int             i1, ii;

        ftp->valid = 0;                 /* check if we can skip this edge */
        ii = adjacent_trifl[dbit];
        if ((vflags[i0] & ii) == ii)    /* cancels if vertex used as value */
                return;
        i1 = adjacent_verti(hp, i, j, dbit);
        ii = adjacent_trifl[VDB_OPP(dbit)];
        if ((vflags[i1] & ii) == ii)    /* on either end (for both triangles) */
                return;
                                        /* else go ahead with calculation */
        VSUB(ftp->r_i, hp->sa[i0].p, hp->rp->rop);
        VSUB(ftp->r_i1, hp->sa[i1].p, hp->rp->rop);
        VSUB(ftp->e_i, hp->sa[i1].p, hp->sa[i0].p);
        VCROSS(ftp->rcp, ftp->r_i, ftp->r_i1);
        rdot_cp = 1.0/DOT(ftp->rcp,ftp->rcp);
        dot_e = DOT(ftp->e_i,ftp->e_i);
        dot_er = DOT(ftp->e_i, ftp->r_i);
        rdot_r = 1.0/DOT(ftp->r_i,ftp->r_i);
        rdot_r1 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
        ftp->I1 = acos( DOT(ftp->r_i, ftp->r_i1) * sqrt(rdot_r*rdot_r1) ) *
                        sqrt( rdot_cp );
        ftp->I2 = ( DOT(ftp->e_i, ftp->r_i1)*rdot_r1 - dot_er*rdot_r +
                        dot_e*ftp->I1 )*0.5*rdot_cp;
        J2 =  ( 0.5*(rdot_r - rdot_r1) - dot_er*ftp->I2 ) / dot_e;
        for (ii = 3; ii--; )
                ftp->rI2_eJ2[ii] = ftp->I2*ftp->r_i[ii] + J2*ftp->e_i[ii];
        ftp->valid++;
}


/* Compose 3x3 matrix from two vectors */
static void
compose_matrix(FVECT mat[3], FVECT va, FVECT vb)
{
        mat[0][0] = 2.0*va[0]*vb[0];
        mat[1][1] = 2.0*va[1]*vb[1];
        mat[2][2] = 2.0*va[2]*vb[2];
        mat[0][1] = mat[1][0] = va[0]*vb[1] + va[1]*vb[0];
        mat[0][2] = mat[2][0] = va[0]*vb[2] + va[2]*vb[0];
        mat[1][2] = mat[2][1] = va[1]*vb[2] + va[2]*vb[1];
}


/* Compute partial 3x3 Hessian matrix for edge */
static void
comp_hessian(FVECT hess[3], FFTRI *ftp, FVECT nrm)
{
        FVECT   ncp;
        FVECT   m1[3], m2[3], m3[3], m4[3];
        double  d1, d2, d3, d4;
        double  I3, J3, K3;
        int     i, j;

        if (!ftp->valid) {              /* preemptive test */
                memset(hess, 0, sizeof(FVECT)*3);
                return;
        }
                                        /* compute intermediate coefficients */
        d1 = 1.0/DOT(ftp->r_i,ftp->r_i);
        d2 = 1.0/DOT(ftp->r_i1,ftp->r_i1);
        d3 = 1.0/DOT(ftp->e_i,ftp->e_i);
        d4 = DOT(ftp->e_i, ftp->r_i);
        I3 = ( DOT(ftp->e_i, ftp->r_i1)*d2*d2 - d4*d1*d1 + 3.0/d3*ftp->I2 )
                        / ( 4.0*DOT(ftp->rcp,ftp->rcp) );
        J3 = 0.25*d3*(d1*d1 - d2*d2) - d4*d3*I3;
        K3 = d3*(ftp->I2 - I3/d1 - 2.0*d4*J3);
                                        /* intermediate matrices */
        VCROSS(ncp, nrm, ftp->e_i);
        compose_matrix(m1, ncp, ftp->rI2_eJ2);
        compose_matrix(m2, ftp->r_i, ftp->r_i);
        compose_matrix(m3, ftp->e_i, ftp->e_i);
        compose_matrix(m4, ftp->r_i, ftp->e_i);
        d1 = DOT(nrm, ftp->rcp);
        d2 = -d1*ftp->I2;
        d1 *= 2.0;
        for (i = 3; i--; )              /* final matrix sum */
            for (j = 3; j--; ) {
                hess[i][j] = m1[i][j] + d1*( I3*m2[i][j] + K3*m3[i][j] +
                                                2.0*J3*m4[i][j] );
                hess[i][j] += d2*(i==j);
                hess[i][j] *= -1.0/PI;
            }
}


/* Reverse hessian calculation result for edge in other direction */
static void
rev_hessian(FVECT hess[3])
{
        int     i;

        for (i = 3; i--; ) {
                hess[i][0] = -hess[i][0];
                hess[i][1] = -hess[i][1];
                hess[i][2] = -hess[i][2];
        }
}


/* Add to radiometric Hessian from the given triangle */
static void
add2hessian(FVECT hess[3], FVECT ehess1[3],
                FVECT ehess2[3], FVECT ehess3[3], double v)
{
        int     i, j;

        for (i = 3; i--; )
            for (j = 3; j--; )
                hess[i][j] += v*( ehess1[i][j] + ehess2[i][j] + ehess3[i][j] );
}


/* Compute partial displacement form factor gradient for edge */
static void
comp_gradient(FVECT grad, FFTRI *ftp, FVECT nrm)
{
        FVECT   ncp;
        double  f1;
        int     i;

        if (!ftp->valid) {              /* preemptive test */
                memset(grad, 0, sizeof(FVECT));
                return;
        }
        f1 = 2.0*DOT(nrm, ftp->rcp);
        VCROSS(ncp, nrm, ftp->e_i);
        for (i = 3; i--; )
                grad[i] = (0.5/PI)*( ftp->I1*ncp[i] + f1*ftp->rI2_eJ2[i] );
}


/* Reverse gradient calculation result for edge in other direction */
static void
rev_gradient(FVECT grad)
{
        grad[0] = -grad[0];
        grad[1] = -grad[1];
        grad[2] = -grad[2];
}


/* Add to displacement gradient from the given triangle */
static void
add2gradient(FVECT grad, FVECT egrad1, FVECT egrad2, FVECT egrad3, double v)
{
        int     i;

        for (i = 3; i--; )
                grad[i] += v*( egrad1[i] + egrad2[i] + egrad3[i] );
}


/* Compute anisotropic radii and eigenvector directions */
static void
eigenvectors(FVECT uv[2], float ra[2], FVECT hessian[3])
{
        double  hess2[2][2];
        FVECT   a, b;
        double  evalue[2], slope1, xmag1;
        int     i;
                                        /* project Hessian to sample plane */
        for (i = 3; i--; ) {
                a[i] = DOT(hessian[i], uv[0]);
                b[i] = DOT(hessian[i], uv[1]);
        }
        hess2[0][0] = DOT(uv[0], a);
        hess2[0][1] = DOT(uv[0], b);
        hess2[1][0] = DOT(uv[1], a);
        hess2[1][1] = DOT(uv[1], b);
                                        /* compute eigenvalue(s) */
        i = quadratic(evalue, 1.0, -hess2[0][0]-hess2[1][1],
                        hess2[0][0]*hess2[1][1]-hess2[0][1]*hess2[1][0]);
        if (i == 1)                     /* double-root (circle) */
                evalue[1] = evalue[0];
        if (!i || ((evalue[0] = fabs(evalue[0])) <= FTINY*FTINY) |
                        ((evalue[1] = fabs(evalue[1])) <= FTINY*FTINY) ) {
                ra[0] = ra[1] = maxarad;
                return;
        }
        if (evalue[0] > evalue[1]) {
                ra[0] = sqrt(sqrt(4.0/evalue[0]));
                ra[1] = sqrt(sqrt(4.0/evalue[1]));
                slope1 = evalue[1];
        } else {
                ra[0] = sqrt(sqrt(4.0/evalue[1]));
                ra[1] = sqrt(sqrt(4.0/evalue[0]));
                slope1 = evalue[0];
        }
                                        /* compute unit eigenvectors */
        if (fabs(hess2[0][1]) <= FTINY)
                return;                 /* uv OK as is */
        slope1 = (slope1 - hess2[0][0]) / hess2[0][1];
        xmag1 = sqrt(1.0/(1.0 + slope1*slope1));
        for (i = 3; i--; ) {
                b[i] = xmag1*uv[0][i] + slope1*xmag1*uv[1][i];
                a[i] = slope1*xmag1*uv[0][i] - xmag1*uv[1][i];
        }
        VCOPY(uv[0], a);
        VCOPY(uv[1], b);
}


static void
ambHessian(                             /* anisotropic radii & pos. gradient */
        AMBHEMI *hp,
        FVECT   uv[2],                  /* returned */
        float   ra[2],                  /* returned (optional) */
        float   pg[2]                   /* returned (optional) */
)
{
        static char     memerrmsg[] = "out of memory in ambHessian()";
        FVECT           (*hessrow)[3] = NULL;
        FVECT           *gradrow = NULL;
        uby8            *vflags;
        FVECT           hessian[3];
        FVECT           gradient;
        FFTRI           fftr;
        int             i, j;
                                        /* be sure to assign unit vectors */
        VCOPY(uv[0], hp->ux);
        VCOPY(uv[1], hp->uy);
                        /* clock-wise vertex traversal from sample POV */
        if (ra != NULL) {               /* initialize Hessian row buffer */
                hessrow = (FVECT (*)[3])malloc(sizeof(FVECT)*3*(hp->ns-1));
                if (hessrow == NULL)
                        error(SYSTEM, memerrmsg);
                memset(hessian, 0, sizeof(hessian));
        } else if (pg == NULL)          /* bogus call? */
                return;
        if (pg != NULL) {               /* initialize form factor row buffer */
                gradrow = (FVECT *)malloc(sizeof(FVECT)*(hp->ns-1));
                if (gradrow == NULL)
                        error(SYSTEM, memerrmsg);
                memset(gradient, 0, sizeof(gradient));
        }
                                        /* get vertex position flags */
        vflags = vertex_flags(hp);
                                        /* compute first row of edges */
        for (j = 0; j < hp->ns-1; j++) {
                comp_fftri(&fftr, hp, 0, j, VDB_X, vflags);
                if (hessrow != NULL)
                        comp_hessian(hessrow[j], &fftr, hp->rp->ron);
                if (gradrow != NULL)
                        comp_gradient(gradrow[j], &fftr, hp->rp->ron);
        }
                                        /* sum each row of triangles */
        for (i = 0; i < hp->ns-1; i++) {
            FVECT       hesscol[3];     /* compute first vertical edge */
            FVECT       gradcol;
            comp_fftri(&fftr, hp, i, 0, VDB_Y, vflags);
            if (hessrow != NULL)
                comp_hessian(hesscol, &fftr, hp->rp->ron);
            if (gradrow != NULL)
                comp_gradient(gradcol, &fftr, hp->rp->ron);
            for (j = 0; j < hp->ns-1; j++) {
                FVECT   hessdia[3];     /* compute triangle contributions */
                FVECT   graddia;
                double  backg;
                backg = back_ambval(hp, i, j, VDB_X, VDB_Y, vflags);
                                        /* diagonal (inner) edge */
                comp_fftri(&fftr, hp, i, j+1, VDB_xY, vflags);
                if (hessrow != NULL) {
                    comp_hessian(hessdia, &fftr, hp->rp->ron);
                    rev_hessian(hesscol);
                    add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
                }
                if (gradrow != NULL) {
                    comp_gradient(graddia, &fftr, hp->rp->ron);
                    rev_gradient(gradcol);
                    add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
                }
                                        /* initialize edge in next row */
                comp_fftri(&fftr, hp, i+1, j+1, VDB_x, vflags);
                if (hessrow != NULL)
                    comp_hessian(hessrow[j], &fftr, hp->rp->ron);
                if (gradrow != NULL)
                    comp_gradient(gradrow[j], &fftr, hp->rp->ron);
                                        /* new column edge & paired triangle */
                backg = back_ambval(hp, i+1, j+1, VDB_x, VDB_y, vflags);
                comp_fftri(&fftr, hp, i, j+1, VDB_Y, vflags);
                if (hessrow != NULL) {
                    comp_hessian(hesscol, &fftr, hp->rp->ron);
                    rev_hessian(hessdia);
                    add2hessian(hessian, hessrow[j], hessdia, hesscol, backg);
                    if (i < hp->ns-2)
                        rev_hessian(hessrow[j]);
                }
                if (gradrow != NULL) {
                    comp_gradient(gradcol, &fftr, hp->rp->ron);
                    rev_gradient(graddia);
                    add2gradient(gradient, gradrow[j], graddia, gradcol, backg);
                    if (i < hp->ns-2)
                        rev_gradient(gradrow[j]);
                }
            }
        }
                                        /* release row buffers */
        if (hessrow != NULL) free(hessrow);
        if (gradrow != NULL) free(gradrow);
        free(vflags);
        
        if (ra != NULL)                 /* extract eigenvectors & radii */
                eigenvectors(uv, ra, hessian);
        if (pg != NULL) {               /* tangential position gradient */
                pg[0] = DOT(gradient, uv[0]);
                pg[1] = DOT(gradient, uv[1]);
        }
}


/* Compute direction gradient from a hemispherical sampling */
static void
ambdirgrad(AMBHEMI *hp, FVECT uv[2], float dg[2])
{
        AMBSAMP *ap;
        double  dgsum[2];
        int     n;
        FVECT   vd;
        double  gfact;

        dgsum[0] = dgsum[1] = 0.0;      /* sum values times -tan(theta) */
        for (ap = hp->sa, n = hp->ns*hp->ns; n--; ap++) {
                                        /* use vector for azimuth + 90deg */
                VSUB(vd, ap->p, hp->rp->rop);
                                        /* brightness over cosine factor */
                gfact = colval(ap->v,CIEY) / DOT(hp->rp->ron, vd);
                                        /* sine = proj_radius/vd_length */
                dgsum[0] -= DOT(uv[1], vd) * gfact;
                dgsum[1] += DOT(uv[0], vd) * gfact;
        }
        dg[0] = dgsum[0] / (hp->ns*hp->ns);
        dg[1] = dgsum[1] / (hp->ns*hp->ns);
}


/* Compute potential light leak direction flags for cache value */
static uint32
ambcorral(AMBHEMI *hp, FVECT uv[2], const double r0, const double r1)
{
        const double    max_d = 1.0/(minarad*ambacc + 0.001);
        const double    ang_res = 0.5*PI/(hp->ns-1);
        const double    ang_step = ang_res/((int)(16/PI*ang_res) + (1+FTINY));
        double          avg_d = 0;
        uint32          flgs = 0;
        int             i, j;
                                        /* don't bother for a few samples */
        if (hp->ns < 12)
                return(0);
                                        /* check distances overhead */
        for (i = hp->ns*3/4; i-- > hp->ns>>2; )
            for (j = hp->ns*3/4; j-- > hp->ns>>2; )
                avg_d += ambsam(hp,i,j).d;
        avg_d *= 4.0/(hp->ns*hp->ns);
        if (avg_d*r0 >= 1.0)            /* ceiling too low for corral? */
                return(0);
        if (avg_d >= max_d)             /* insurance */
                return(0);
                                        /* else circle around perimeter */
        for (i = 0; i < hp->ns; i++)
            for (j = 0; j < hp->ns; j += !i|(i==hp->ns-1) ? 1 : hp->ns-1) {
                AMBSAMP *ap = &ambsam(hp,i,j);
                FVECT   vec;
                double  u, v;
                double  ang, a1;
                int     abp;
                if ((ap->d <= FTINY) | (ap->d >= max_d))
                        continue;       /* too far or too near */
                VSUB(vec, ap->p, hp->rp->rop);
                u = DOT(vec, uv[0]) * ap->d;
                v = DOT(vec, uv[1]) * ap->d;
                if ((r0*r0*u*u + r1*r1*v*v) * ap->d*ap->d <= 1.0)
                        continue;       /* occluder outside ellipse */
                ang = atan2a(v, u);     /* else set direction flags */
                for (a1 = ang-.5*ang_res; a1 <= ang+.5*ang_res; a1 += ang_step)
                        flgs |= 1L<<(int)(16/PI*(a1 + 2.*PI*(a1 < 0)));
            }
        return(flgs);
}


int
doambient(                              /* compute ambient component */
        COLOR   rcol,                   /* input/output color */
        RAY     *r,
        double  wt,
        FVECT   uv[2],                  /* returned (optional) */
        float   ra[2],                  /* returned (optional) */
        float   pg[2],                  /* returned (optional) */
        float   dg[2],                  /* returned (optional) */
        uint32  *crlp                   /* returned (optional) */
)
{
        AMBHEMI *hp = inithemi(rcol, r, wt);
        int     cnt;
        FVECT   my_uv[2];
        double  d, K, acol[3];
        AMBSAMP *ap;
        int     i, j;
                                        /* check/initialize */
        if (hp == NULL)
                return(0);
        if (uv != NULL)
                memset(uv, 0, sizeof(FVECT)*2);
        if (ra != NULL)
                ra[0] = ra[1] = 0.0;
        if (pg != NULL)
                pg[0] = pg[1] = 0.0;
        if (dg != NULL)
                dg[0] = dg[1] = 0.0;
        if (crlp != NULL)
                *crlp = 0;
                                        /* sample the hemisphere */
        acol[0] = acol[1] = acol[2] = 0.0;
        cnt = 0;
        for (i = hp->ns; i--; )
                for (j = hp->ns; j--; )
                        if ((ap = ambsample(hp, i, j)) != NULL) {
                                addcolor(acol, ap->v);
                                ++cnt;
                        }
        if (!cnt) {
                setcolor(rcol, 0.0, 0.0, 0.0);
                free(hp);
                return(0);              /* no valid samples */
        }
        if (cnt < hp->ns*hp->ns) {      /* incomplete sampling? */
                copycolor(rcol, acol);
                free(hp);
                return(-1);             /* return value w/o Hessian */
        }
        cnt = ambssamp*wt + 0.5;        /* perform super-sampling? */
        if (cnt > 8)
                ambsupersamp(acol, hp, cnt);
        copycolor(rcol, acol);          /* final indirect irradiance/PI */
        if ((ra == NULL) & (pg == NULL) & (dg == NULL)) {
                free(hp);
                return(-1);             /* no radius or gradient calc. */
        }
        if ((d = bright(acol)) > FTINY) {       /* normalize Y values */
                d = 0.99*(hp->ns*hp->ns)/d;
                K = 0.01;
        } else {                        /* or fall back on geometric Hessian */
                K = 1.0;
                pg = NULL;
                dg = NULL;
                crlp = NULL;
        }
        ap = hp->sa;                    /* relative Y channel from here on... */
        for (i = hp->ns*hp->ns; i--; ap++)
                colval(ap->v,CIEY) = bright(ap->v)*d + K;

        if (uv == NULL)                 /* make sure we have axis pointers */
                uv = my_uv;
                                        /* compute radii & pos. gradient */
        ambHessian(hp, uv, ra, pg);

        if (dg != NULL)                 /* compute direction gradient */
                ambdirgrad(hp, uv, dg);

        if (ra != NULL) {               /* scale/clamp radii */
                if (pg != NULL) {
                        if (ra[0]*(d = fabs(pg[0])) > 1.0)
                                ra[0] = 1.0/d;
                        if (ra[1]*(d = fabs(pg[1])) > 1.0)
                                ra[1] = 1.0/d;
                        if (ra[0] > ra[1])
                                ra[0] = ra[1];
                }
                if (ra[0] < minarad) {
                        ra[0] = minarad;
                        if (ra[1] < minarad)
                                ra[1] = minarad;
                }
                ra[0] *= d = 1.0/sqrt(sqrt(wt));
                if ((ra[1] *= d) > 2.0*ra[0])
                        ra[1] = 2.0*ra[0];
                if (ra[1] > maxarad) {
                        ra[1] = maxarad;
                        if (ra[0] > maxarad)
                                ra[0] = maxarad;
                }
                                        /* flag encroached directions */
                if ((wt >= 0.5-FTINY) & (crlp != NULL))
                        *crlp = ambcorral(hp, uv, ra[0]*ambacc, ra[1]*ambacc);
                if (pg != NULL) {       /* cap gradient if necessary */
                        d = pg[0]*pg[0]*ra[0]*ra[0] + pg[1]*pg[1]*ra[1]*ra[1];
                        if (d > 1.0) {
                                d = 1.0/sqrt(d);
                                pg[0] *= d;
                                pg[1] *= d;
                        }
                }
        }
        free(hp);                       /* clean up and return */
        return(1);
}


#else /* ! NEWAMB */


void
inithemi(                       /* initialize sampling hemisphere */
        AMBHEMI  *hp,
        COLOR ac,
        RAY  *r,
        double  wt
)
{
        double  d;
        int  i;
                                        /* set number of divisions */
        if (ambacc <= FTINY &&
                        wt > (d = 0.8*intens(ac)*r->rweight/(ambdiv*minweight)))
                wt = d;                 /* avoid ray termination */
        hp->nt = sqrt(ambdiv * wt / PI) + 0.5;
        i = ambacc > FTINY ? 3 : 1;     /* minimum number of samples */
        if (hp->nt < i)
                hp->nt = i;
        hp->np = PI * hp->nt + 0.5;
                                        /* set number of super-samples */
        hp->ns = ambssamp * wt + 0.5;
                                        /* assign coefficient */
        copycolor(hp->acoef, ac);
        d = 1.0/(hp->nt*hp->np);
        scalecolor(hp->acoef, d);
                                        /* make axes */
        VCOPY(hp->uz, r->ron);
        hp->uy[0] = hp->uy[1] = hp->uy[2] = 0.0;
        for (i = 0; i < 3; i++)
                if (hp->uz[i] < 0.6 && hp->uz[i] > -0.6)
                        break;
        if (i >= 3)
                error(CONSISTENCY, "bad ray direction in inithemi");
        hp->uy[i] = 1.0;
        fcross(hp->ux, hp->uy, hp->uz);
        normalize(hp->ux);
        fcross(hp->uy, hp->uz, hp->ux);
}


int
divsample(                              /* sample a division */
        AMBSAMP  *dp,
        AMBHEMI  *h,
        RAY  *r
)
{
        RAY  ar;
        int  hlist[3];
        double  spt[2];
        double  xd, yd, zd;
        double  b2;
        double  phi;
        int  i;
                                        /* ambient coefficient for weight */
        if (ambacc > FTINY)
                setcolor(ar.rcoef, AVGREFL, AVGREFL, AVGREFL);
        else
                copycolor(ar.rcoef, h->acoef);
        if (rayorigin(&ar, AMBIENT, r, ar.rcoef) < 0)
                return(-1);
        if (ambacc > FTINY) {
                multcolor(ar.rcoef, h->acoef);
                scalecolor(ar.rcoef, 1./AVGREFL);
        }
        hlist[0] = r->rno;
        hlist[1] = dp->t;
        hlist[2] = dp->p;
        multisamp(spt, 2, urand(ilhash(hlist,3)+dp->n));
        zd = sqrt((dp->t + spt[0])/h->nt);
        phi = 2.0*PI * (dp->p + spt[1])/h->np;
        xd = tcos(phi) * zd;
        yd = tsin(phi) * zd;
        zd = sqrt(1.0 - zd*zd);
        for (i = 0; i < 3; i++)
                ar.rdir[i] =    xd*h->ux[i] +
                                yd*h->uy[i] +
                                zd*h->uz[i];
        checknorm(ar.rdir);
        dimlist[ndims++] = dp->t*h->np + dp->p + 90171;
        rayvalue(&ar);
        ndims--;
        multcolor(ar.rcol, ar.rcoef);   /* apply coefficient */
        addcolor(dp->v, ar.rcol);
                                        /* use rt to improve gradient calc */
        if (ar.rt > FTINY && ar.rt < FHUGE)
                dp->r += 1.0/ar.rt;
                                        /* (re)initialize error */
        if (dp->n++) {
                b2 = bright(dp->v)/dp->n - bright(ar.rcol);
                b2 = b2*b2 + dp->k*((dp->n-1)*(dp->n-1));
                dp->k = b2/(dp->n*dp->n);
        } else
                dp->k = 0.0;
        return(0);
}


static int
ambcmp(                                 /* decreasing order */
        const void *p1,
        const void *p2
)
{
        const AMBSAMP   *d1 = (const AMBSAMP *)p1;
        const AMBSAMP   *d2 = (const AMBSAMP *)p2;

        if (d1->k < d2->k)
                return(1);
        if (d1->k > d2->k)
                return(-1);
        return(0);
}


static int
ambnorm(                                /* standard order */
        const void *p1,
        const void *p2
)
{
        const AMBSAMP   *d1 = (const AMBSAMP *)p1;
        const AMBSAMP   *d2 = (const AMBSAMP *)p2;
        int     c;

        if ( (c = d1->t - d2->t) )
                return(c);
        return(d1->p - d2->p);
}


double
doambient(                              /* compute ambient component */
        COLOR  rcol,
        RAY  *r,
        double  wt,
        FVECT  pg,
        FVECT  dg
)
{
        double  b, d=0;
        AMBHEMI  hemi;
        AMBSAMP  *div;
        AMBSAMP  dnew;
        double  acol[3];
        AMBSAMP  *dp;
        double  arad;
        int  divcnt;
        int  i, j;
                                        /* initialize hemisphere */
        inithemi(&hemi, rcol, r, wt);
        divcnt = hemi.nt * hemi.np;
                                        /* initialize */
        if (pg != NULL)
                pg[0] = pg[1] = pg[2] = 0.0;
        if (dg != NULL)
                dg[0] = dg[1] = dg[2] = 0.0;
        setcolor(rcol, 0.0, 0.0, 0.0);
        if (divcnt == 0)
                return(0.0);
                                        /* allocate super-samples */
        if (hemi.ns > 0 || pg != NULL || dg != NULL) {
                div = (AMBSAMP *)malloc(divcnt*sizeof(AMBSAMP));
                if (div == NULL)
                        error(SYSTEM, "out of memory in doambient");
        } else
                div = NULL;
                                        /* sample the divisions */
        arad = 0.0;
        acol[0] = acol[1] = acol[2] = 0.0;
        if ((dp = div) == NULL)
                dp = &dnew;
        divcnt = 0;
        for (i = 0; i < hemi.nt; i++)
                for (j = 0; j < hemi.np; j++) {
                        dp->t = i; dp->p = j;
                        setcolor(dp->v, 0.0, 0.0, 0.0);
                        dp->r = 0.0;
                        dp->n = 0;
                        if (divsample(dp, &hemi, r) < 0) {
                                if (div != NULL)
                                        dp++;
                                continue;
                        }
                        arad += dp->r;
                        divcnt++;
                        if (div != NULL)
                                dp++;
                        else
                                addcolor(acol, dp->v);
                }
        if (!divcnt) {
                if (div != NULL)
                        free((void *)div);
                return(0.0);            /* no samples taken */
        }
        if (divcnt < hemi.nt*hemi.np) {
                pg = dg = NULL;         /* incomplete sampling */
                hemi.ns = 0;
        } else if (arad > FTINY && divcnt/arad < minarad) {
                hemi.ns = 0;            /* close enough */
        } else if (hemi.ns > 0) {       /* else perform super-sampling? */
                comperrs(div, &hemi);                   /* compute errors */
                qsort(div, divcnt, sizeof(AMBSAMP), ambcmp);    /* sort divs */
                                                /* super-sample */
                for (i = hemi.ns; i > 0; i--) {
                        dnew = *div;
                        if (divsample(&dnew, &hemi, r) < 0) {
                                dp++;
                                continue;
                        }
                        dp = div;               /* reinsert */
                        j = divcnt < i ? divcnt : i;
                        while (--j > 0 && dnew.k < dp[1].k) {
                                *dp = *(dp+1);
                                dp++;
                        }
                        *dp = dnew;
                }
                if (pg != NULL || dg != NULL)   /* restore order */
                        qsort(div, divcnt, sizeof(AMBSAMP), ambnorm);
        }
                                        /* compute returned values */
        if (div != NULL) {
                arad = 0.0;             /* note: divcnt may be < nt*np */
                for (i = hemi.nt*hemi.np, dp = div; i-- > 0; dp++) {
                        arad += dp->r;
                        if (dp->n > 1) {
                                b = 1.0/dp->n;
                                scalecolor(dp->v, b);
                                dp->r *= b;
                                dp->n = 1;
                        }
                        addcolor(acol, dp->v);
                }
                b = bright(acol);
                if (b > FTINY) {
                        b = 1.0/b;      /* compute & normalize gradient(s) */
                        if (pg != NULL) {
                                posgradient(pg, div, &hemi);
                                for (i = 0; i < 3; i++)
                                        pg[i] *= b;
                        }
                        if (dg != NULL) {
                                dirgradient(dg, div, &hemi);
                                for (i = 0; i < 3; i++)
                                        dg[i] *= b;
                        }
                }
                free((void *)div);
        }
        copycolor(rcol, acol);
        if (arad <= FTINY)
                arad = maxarad;
        else
                arad = (divcnt+hemi.ns)/arad;
        if (pg != NULL) {               /* reduce radius if gradient large */
                d = DOT(pg,pg);
                if (d*arad*arad > 1.0)
                        arad = 1.0/sqrt(d);
        }
        if (arad < minarad) {
                arad = minarad;
                if (pg != NULL && d*arad*arad > 1.0) {  /* cap gradient */
                        d = 1.0/arad/sqrt(d);
                        for (i = 0; i < 3; i++)
                                pg[i] *= d;
                }
        }
        if ((arad /= sqrt(wt)) > maxarad)
                arad = maxarad;
        return(arad);
}


void
comperrs(                       /* compute initial error estimates */
        AMBSAMP  *da,   /* assumes standard ordering */
        AMBHEMI  *hp
)
{
        double  b, b2;
        int  i, j;
        AMBSAMP  *dp;
                                /* sum differences from neighbors */
        dp = da;
        for (i = 0; i < hp->nt; i++)
                for (j = 0; j < hp->np; j++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in comperrs");
#endif
                        b = bright(dp[0].v);
                        if (i > 0) {            /* from above */
                                b2 = bright(dp[-hp->np].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[-hp->np].k += b2;
                        }
                        if (j > 0) {            /* from behind */
                                b2 = bright(dp[-1].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[-1].k += b2;
                        } else {                /* around */
                                b2 = bright(dp[hp->np-1].v) - b;
                                b2 *= b2 * 0.25;
                                dp[0].k += b2;
                                dp[hp->np-1].k += b2;
                        }
                        dp++;
                }
                                /* divide by number of neighbors */
        dp = da;
        for (j = 0; j < hp->np; j++)            /* top row */
                (dp++)->k *= 1.0/3.0;
        if (hp->nt < 2)
                return;
        for (i = 1; i < hp->nt-1; i++)          /* central region */
                for (j = 0; j < hp->np; j++)
                        (dp++)->k *= 0.25;
        for (j = 0; j < hp->np; j++)            /* bottom row */
                (dp++)->k *= 1.0/3.0;
}


void
posgradient(                                    /* compute position gradient */
        FVECT  gv,
        AMBSAMP  *da,                   /* assumes standard ordering */
        AMBHEMI  *hp
)
{
        int  i, j;
        double  nextsine, lastsine, b, d;
        double  mag0, mag1;
        double  phi, cosp, sinp, xd, yd;
        AMBSAMP  *dp;

        xd = yd = 0.0;
        for (j = 0; j < hp->np; j++) {
                dp = da + j;
                mag0 = mag1 = 0.0;
                lastsine = 0.0;
                for (i = 0; i < hp->nt; i++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in posgradient");
#endif
                        b = bright(dp->v);
                        if (i > 0) {
                                d = dp[-hp->np].r;
                                if (dp[0].r > d) d = dp[0].r;
                                                        /* sin(t)*cos(t)^2 */
                                d *= lastsine * (1.0 - (double)i/hp->nt);
                                mag0 += d*(b - bright(dp[-hp->np].v));
                        }
                        nextsine = sqrt((double)(i+1)/hp->nt);
                        if (j > 0) {
                                d = dp[-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d * (nextsine - lastsine) *
                                                (b - bright(dp[-1].v));
                        } else {
                                d = dp[hp->np-1].r;
                                if (dp[0].r > d) d = dp[0].r;
                                mag1 += d * (nextsine - lastsine) *
                                                (b - bright(dp[hp->np-1].v));
                        }
                        dp += hp->np;
                        lastsine = nextsine;
                }
                mag0 *= 2.0*PI / hp->np;
                phi = 2.0*PI * (double)j/hp->np;
                cosp = tcos(phi); sinp = tsin(phi);
                xd += mag0*cosp - mag1*sinp;
                yd += mag0*sinp + mag1*cosp;
        }
        for (i = 0; i < 3; i++)
                gv[i] = (xd*hp->ux[i] + yd*hp->uy[i])*(hp->nt*hp->np)/PI;
}


void
dirgradient(                                    /* compute direction gradient */
        FVECT  gv,
        AMBSAMP  *da,                   /* assumes standard ordering */
        AMBHEMI  *hp
)
{
        int  i, j;
        double  mag;
        double  phi, xd, yd;
        AMBSAMP  *dp;

        xd = yd = 0.0;
        for (j = 0; j < hp->np; j++) {
                dp = da + j;
                mag = 0.0;
                for (i = 0; i < hp->nt; i++) {
#ifdef  DEBUG
                        if (dp->t != i || dp->p != j)
                                error(CONSISTENCY,
                                        "division order in dirgradient");
#endif
                                                        /* tan(t) */
                        mag += bright(dp->v)/sqrt(hp->nt/(i+.5) - 1.0);
                        dp += hp->np;
                }
                phi = 2.0*PI * (j+.5)/hp->np + PI/2.0;
                xd += mag * tcos(phi);
                yd += mag * tsin(phi);
        }
        for (i = 0; i < 3; i++)
                gv[i] = xd*hp->ux[i] + yd*hp->uy[i];
}

#endif  /* ! NEWAMB */
Revision:	2.55
Committed:	Fri May 9 16:05:09 2014 UTC (9 years, 11 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.54:	+29 -21 lines
Log Message:	Better fix for previous bug and include diagonals in error est. (NEWAMB)