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#ifndef lint |
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static const char RCSid[] = "$Id: bsdfrbf.c,v 2.25 2014/03/30 00:19:09 greg Exp $"; |
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#endif |
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/* |
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* Radial basis function representation for BSDF data. |
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* |
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* G. Ward |
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*/ |
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|
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/**************************************************************** |
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1) Collect samples into a grid using the Shirley-Chiu |
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angular mapping from a hemisphere to a square. |
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|
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2) Compute an adaptive quadtree by subdividing the grid so that |
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each leaf node has at least one sample up to as many |
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samples as fit nicely on a plane to within a certain |
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MSE tolerance. |
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|
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3) Place one Gaussian lobe at each leaf node in the quadtree, |
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sizing it to have a radius equal to the leaf size and |
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a volume equal to the energy in that node. |
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*****************************************************************/ |
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|
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#define _USE_MATH_DEFINES |
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#include <stdio.h> |
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#include <stdlib.h> |
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#include <string.h> |
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#include <math.h> |
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#include "bsdfrep.h" |
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|
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#ifndef RSCA |
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#define RSCA 2.0 /* radius scaling factor (empirical) */ |
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#endif |
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#ifndef SMOOTH_MSE |
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#define SMOOTH_MSE 5e-5 /* acceptable mean squared error */ |
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#endif |
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#ifndef SMOOTH_MSER |
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#define SMOOTH_MSER 0.03 /* acceptable relative MSE */ |
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#endif |
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#define MAX_RAD (GRIDRES/8) /* maximum lobe radius */ |
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|
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#define RBFALLOCB 10 /* RBF allocation block size */ |
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|
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/* loaded grid or comparison DSFs */ |
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GRIDVAL dsf_grid[GRIDRES][GRIDRES]; |
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|
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/* Start new DSF input grid */ |
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void |
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new_bsdf_data(double new_theta, double new_phi) |
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{ |
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if (!new_input_direction(new_theta, new_phi)) |
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exit(1); |
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memset(dsf_grid, 0, sizeof(dsf_grid)); |
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} |
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|
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/* Add BSDF data point */ |
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void |
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add_bsdf_data(double theta_out, double phi_out, double val, int isDSF) |
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{ |
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FVECT ovec; |
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int pos[2]; |
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|
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if (!output_orient) /* check output orientation */ |
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output_orient = 1 - 2*(theta_out > 90.); |
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else if (output_orient > 0 ^ theta_out < 90.) { |
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fputs("Cannot handle output angles on both sides of surface\n", |
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stderr); |
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exit(1); |
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} |
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ovec[2] = sin((M_PI/180.)*theta_out); |
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ovec[0] = cos((M_PI/180.)*phi_out) * ovec[2]; |
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ovec[1] = sin((M_PI/180.)*phi_out) * ovec[2]; |
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ovec[2] = sqrt(1. - ovec[2]*ovec[2]); |
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|
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if (!isDSF) |
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val *= COSF(ovec[2]); /* convert from BSDF to DSF */ |
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|
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/* update BSDF histogram */ |
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if (val < BSDF2BIG*ovec[2] && val > BSDF2SML*ovec[2]) |
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++bsdf_hist[histndx(val/ovec[2])]; |
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|
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pos_from_vec(pos, ovec); |
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|
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dsf_grid[pos[0]][pos[1]].sum.v += val; |
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dsf_grid[pos[0]][pos[1]].sum.n++; |
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} |
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|
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/* Compute minimum BSDF from histogram (does not clear) */ |
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static void |
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comp_bsdf_min() |
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{ |
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unsigned long cnt, target; |
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int i; |
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|
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cnt = 0; |
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for (i = HISTLEN; i--; ) |
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cnt += bsdf_hist[i]; |
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if (!cnt) { /* shouldn't happen */ |
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bsdf_min = 0; |
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return; |
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} |
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target = cnt/100; /* ignore bottom 1% */ |
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cnt = 0; |
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for (i = 0; cnt <= target; i++) |
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cnt += bsdf_hist[i]; |
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bsdf_min = histval(i-1); |
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} |
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|
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/* Determine if the given region is empty of grid samples */ |
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static int |
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empty_region(int x0, int x1, int y0, int y1) |
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{ |
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int x, y; |
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|
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if (dsf_grid[x][y].sum.n) |
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return(0); |
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return(1); |
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} |
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|
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/* Determine if the given region is smooth enough to be a single lobe */ |
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static int |
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smooth_region(int x0, int x1, int y0, int y1) |
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{ |
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RREAL rMtx[3][3]; |
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FVECT xvec; |
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double A, B, C, nvs, sqerr; |
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int x, y, n; |
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/* compute planar regression */ |
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memset(rMtx, 0, sizeof(rMtx)); |
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memset(xvec, 0, sizeof(xvec)); |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if ((n = dsf_grid[x][y].sum.n) > 0) { |
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double z = dsf_grid[x][y].sum.v; |
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rMtx[0][0] += x*x*(double)n; |
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rMtx[0][1] += x*y*(double)n; |
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rMtx[0][2] += x*(double)n; |
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rMtx[1][1] += y*y*(double)n; |
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rMtx[1][2] += y*(double)n; |
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rMtx[2][2] += (double)n; |
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xvec[0] += x*z; |
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xvec[1] += y*z; |
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xvec[2] += z; |
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} |
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rMtx[1][0] = rMtx[0][1]; |
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rMtx[2][0] = rMtx[0][2]; |
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rMtx[2][1] = rMtx[1][2]; |
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nvs = rMtx[2][2]; |
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if (SDinvXform(rMtx, rMtx) != SDEnone) |
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return(1); /* colinear values */ |
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A = DOT(rMtx[0], xvec); |
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B = DOT(rMtx[1], xvec); |
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C = DOT(rMtx[2], xvec); |
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sqerr = 0.0; /* compute mean squared error */ |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if ((n = dsf_grid[x][y].sum.n) > 0) { |
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double d = A*x + B*y + C - dsf_grid[x][y].sum.v/n; |
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sqerr += n*d*d; |
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} |
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if (sqerr <= nvs*SMOOTH_MSE) /* below absolute MSE threshold? */ |
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return(1); |
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/* OR below relative MSE threshold? */ |
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return(sqerr*nvs <= xvec[2]*xvec[2]*SMOOTH_MSER); |
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} |
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|
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/* Create new lobe based on integrated samples in region */ |
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static int |
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create_lobe(RBFVAL *rvp, int x0, int x1, int y0, int y1) |
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{ |
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double vtot = 0.0; |
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int nv = 0; |
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double wxsum = 0.0, wysum = 0.0, wtsum = 0.0; |
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double rad; |
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int x, y; |
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/* compute average for region */ |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if (dsf_grid[x][y].sum.n) { |
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const double v = dsf_grid[x][y].sum.v; |
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const int n = dsf_grid[x][y].sum.n; |
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|
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if (v > 0) { |
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double wt = v / (double)n; |
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wxsum += wt * x; |
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wysum += wt * y; |
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wtsum += wt; |
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} |
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vtot += v; |
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nv += n; |
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} |
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if (!nv) { |
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fprintf(stderr, "%s: internal - missing samples in create_lobe\n", |
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progname); |
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exit(1); |
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} |
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if (vtot <= 0) /* only create positive lobes */ |
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return(0); |
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/* peak value based on integral */ |
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vtot *= (x1-x0)*(y1-y0)*(2.*M_PI/GRIDRES/GRIDRES)/(double)nv; |
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rad = (RSCA/(double)GRIDRES)*(x1-x0); |
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rvp->peak = vtot / ((2.*M_PI) * rad*rad); |
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rvp->crad = ANG2R(rad); /* put peak at centroid */ |
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rvp->gx = (int)(wxsum/wtsum + .5); |
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rvp->gy = (int)(wysum/wtsum + .5); |
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return(1); |
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} |
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|
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/* Recursive function to build radial basis function representation */ |
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static int |
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build_rbfrep(RBFVAL **arp, int *np, int x0, int x1, int y0, int y1) |
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{ |
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int xmid = (x0+x1)>>1; |
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int ymid = (y0+y1)>>1; |
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int branched[4]; |
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int nadded, nleaves; |
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/* need to make this a leaf? */ |
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if (empty_region(x0, xmid, y0, ymid) || |
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empty_region(xmid, x1, y0, ymid) || |
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empty_region(x0, xmid, ymid, y1) || |
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empty_region(xmid, x1, ymid, y1)) |
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return(0); |
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/* add children (branches+leaves) */ |
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if ((branched[0] = build_rbfrep(arp, np, x0, xmid, y0, ymid)) < 0) |
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return(-1); |
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if ((branched[1] = build_rbfrep(arp, np, xmid, x1, y0, ymid)) < 0) |
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return(-1); |
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if ((branched[2] = build_rbfrep(arp, np, x0, xmid, ymid, y1)) < 0) |
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return(-1); |
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if ((branched[3] = build_rbfrep(arp, np, xmid, x1, ymid, y1)) < 0) |
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return(-1); |
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nadded = branched[0] + branched[1] + branched[2] + branched[3]; |
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nleaves = !branched[0] + !branched[1] + !branched[2] + !branched[3]; |
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if (!nleaves) /* nothing but branches? */ |
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return(nadded); |
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/* combine 4 leaves into 1? */ |
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if ((nleaves == 4) & (x1-x0 <= MAX_RAD) && |
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smooth_region(x0, x1, y0, y1)) |
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return(0); |
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/* need more array space? */ |
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if ((*np+nleaves-1)>>RBFALLOCB != (*np-1)>>RBFALLOCB) { |
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*arp = (RBFVAL *)realloc(*arp, |
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sizeof(RBFVAL)*(*np+nleaves-1+(1<<RBFALLOCB))); |
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if (*arp == NULL) |
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return(-1); |
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} |
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/* create lobes for leaves */ |
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if (!branched[0] && create_lobe(*arp+*np, x0, xmid, y0, ymid)) { |
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++(*np); ++nadded; |
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} |
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if (!branched[1] && create_lobe(*arp+*np, xmid, x1, y0, ymid)) { |
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++(*np); ++nadded; |
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} |
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if (!branched[2] && create_lobe(*arp+*np, x0, xmid, ymid, y1)) { |
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++(*np); ++nadded; |
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} |
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if (!branched[3] && create_lobe(*arp+*np, xmid, x1, ymid, y1)) { |
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++(*np); ++nadded; |
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} |
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return(nadded); |
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} |
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|
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/* Count up filled nodes and build RBF representation from current grid */ |
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RBFNODE * |
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make_rbfrep() |
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{ |
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RBFNODE *newnode; |
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RBFVAL *rbfarr; |
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int nn; |
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/* compute minimum BSDF */ |
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comp_bsdf_min(); |
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/* create RBF node list */ |
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rbfarr = NULL; nn = 0; |
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if (build_rbfrep(&rbfarr, &nn, 0, GRIDRES, 0, GRIDRES) <= 0) { |
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if (nn) |
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goto memerr; |
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fprintf(stderr, |
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"%s: warning - skipping bad incidence (%.1f,%.1f)\n", |
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progname, theta_in_deg, phi_in_deg); |
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return(NULL); |
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} |
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/* (re)allocate RBF array */ |
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newnode = (RBFNODE *)realloc(rbfarr, |
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sizeof(RBFNODE) + sizeof(RBFVAL)*(nn-1)); |
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if (newnode == NULL) |
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goto memerr; |
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/* copy computed lobes into RBF node */ |
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memmove(newnode->rbfa, newnode, sizeof(RBFVAL)*nn); |
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newnode->ord = -1; |
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newnode->next = NULL; |
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newnode->ejl = NULL; |
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newnode->invec[2] = sin((M_PI/180.)*theta_in_deg); |
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newnode->invec[0] = cos((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
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newnode->invec[1] = sin((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
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newnode->invec[2] = input_orient*sqrt(1. - newnode->invec[2]*newnode->invec[2]); |
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newnode->vtotal = .0; |
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newnode->nrbf = nn; |
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/* compute sum for normalization */ |
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while (nn-- > 0) |
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newnode->vtotal += rbf_volume(&newnode->rbfa[nn]); |
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#ifdef DEBUG |
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fprintf(stderr, "Built RBF with %d lobes\n", newnode->nrbf); |
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fprintf(stderr, "Integrated DSF at (%.1f,%.1f) deg. is %.2f\n", |
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get_theta180(newnode->invec), get_phi360(newnode->invec), |
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newnode->vtotal); |
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#endif |
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insert_dsf(newnode); |
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return(newnode); |
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memerr: |
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fprintf(stderr, "%s: Out of memory in make_rbfrep()\n", progname); |
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exit(1); |
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} |
