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/* |
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================================================================== |
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Bias compensation for photon density estimates |
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|
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For background see: |
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R. Schregle, "Bias Compensation for Photon Maps", |
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Computer Graphics Forum, v22:n4, pp. 729-742, Dec. 2003. |
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|
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Roland Schregle ([email protected]) |
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(c) Fraunhofer Institute for Solar Energy Systems |
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================================================================== |
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|
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$Id: pmapbias.c,v 2.1 2015/02/24 19:39:26 greg Exp $ |
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*/ |
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|
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|
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#include "pmapbias.h" |
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#include "pmap.h" |
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#include "pmaprand.h" |
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|
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|
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|
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void squeuePartition (PhotonSQNode* squeue, unsigned lo, |
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unsigned mid, unsigned hi) |
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/* REVERSE Partition squeue such that all photons in |
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squeue-hi+1..squeue-mid are farther than the median at squeue-mid+1, |
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and those in squeue-mid+2..squeue-lo+1 are closer than the median. |
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This means that squeue points to the END of the queue, and the (1-based) |
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indices are offsets relative to it. This convoluted scheme is adopted |
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since the queue is initially a maxheap, so reverse sorting is expected |
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to be faster. */ |
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{ |
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unsigned l, h, p; |
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PhotonSQNode *lp, *hp, *pp; |
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float pivot, dist; |
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Photon* photon; |
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|
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while (hi > lo) { |
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/* Grab pivot node in middle as an educated guess, since our |
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queue is sorta sorted. */ |
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l = lo; |
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h = hi; |
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p = mid; |
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lp = squeue - lo + 1; |
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hp = squeue - hi + 1; |
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pp = squeue - p + 1; |
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pivot = pp -> dist; |
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|
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/* l & h converge, swapping elements out of order with respect to |
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pivot node. */ |
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while (l < h) { |
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while (lp -> dist <= pivot && l <= h && l < hi) |
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++l, --lp; |
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while (hp -> dist >= pivot && h >= l && h > lo) |
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--h, ++hp; |
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|
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if (l < h) { |
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/* Swap */ |
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photon = lp -> photon; |
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dist = lp -> dist; |
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lp -> photon = hp -> photon; |
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lp -> dist = hp -> dist; |
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hp -> photon = photon; |
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hp -> dist = dist; |
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} |
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} |
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|
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/* Swap convergence and pivot node */ |
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if (p > h) { |
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/* Need this otherwise shit happens! |
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Since lp -> dist > hp -> dist, we swap either l or p depending |
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on whether we're above or below p */ |
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h = l; |
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hp = lp; |
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} |
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|
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photon = hp -> photon; |
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dist = hp -> dist; |
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hp -> photon = pp -> photon; |
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hp -> dist = pivot; |
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pp -> photon = photon; |
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pp -> dist = dist; |
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if (h >= mid) |
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hi = h - 1; |
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if (h <= mid) |
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lo = h + 1; |
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} |
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|
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/* Once lo & hi have converged, we have found the median! */ |
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} |
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|
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|
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|
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void biasComp (PhotonMap* pmap, COLOR irrad) |
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/* Photon density estimate with bias compensation -- czech dis shit out! */ |
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{ |
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unsigned i, numLo, numHi, numMid; |
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PhotonSQNode *sq; |
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PhotonBCNode *hist; |
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float r, totalWeight = 0; |
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PhotonSQNode *squeueEnd; |
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PhotonBCNode *histEnd; |
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COLOR fluxLo, fluxMid, irradVar, irradAvg, p, d; |
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|
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if (!pmap -> biasCompHist) { |
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/* Allocate bias compensation history */ |
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numHi = pmap -> maxGather - pmap -> minGather; |
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for (i = pmap -> minGather + 1; numHi > 1; numHi >>= 1, ++i); |
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pmap -> biasCompHist = (PhotonBCNode*)malloc(i * sizeof(PhotonBCNode)); |
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if (!pmap -> biasCompHist) |
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error(USER, "can't allocate bias compensation history"); |
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} |
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|
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numLo = min(pmap -> minGather, pmap -> squeueEnd - 1); |
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numHi = min(pmap -> maxGather, pmap -> squeueEnd - 1); |
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sq = squeueEnd = pmap -> squeue + pmap -> squeueEnd - 1; |
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histEnd = pmap -> biasCompHist; |
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setcolor(fluxLo, 0, 0, 0); |
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|
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/* Partition to get numLo closest photons starting from END of queue */ |
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squeuePartition(squeueEnd, 1, numLo + 1, numHi); |
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|
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/* Get irradiance estimates (ignoring 1 / PI) using 1..numLo photons |
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and chuck in history. Queue is traversed BACKWARDS. */ |
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for (i = 1; i <= numLo; i++, sq--) { |
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/* Make sure furthest two photons are consecutive wrt distance */ |
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squeuePartition(squeueEnd, i, i + 1, numLo + 1); |
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getPhotonFlux(sq -> photon, irrad); |
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addcolor(fluxLo, irrad); |
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/* Average radius between furthest two photons to improve accuracy */ |
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r = 0.25 * (sq -> dist + (sq - 1) -> dist + |
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2 * sqrt(sq -> dist * (sq - 1) -> dist)); |
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/* Add irradiance and weight to history. Weights should increase |
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monotonically based on number of photons used for the estimate. */ |
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histEnd -> irrad [0] = fluxLo [0] / r; |
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histEnd -> irrad [1] = fluxLo [1] / r; |
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histEnd -> irrad [2] = fluxLo [2] / r; |
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totalWeight += histEnd++ -> weight = BIASCOMP_WGT((float)i); |
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} |
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|
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/* Compute expected value (average) and variance of irradiance based on |
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history for numLo photons. */ |
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setcolor(irradAvg, 0, 0, 0); |
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setcolor(irradVar, 0, 0, 0); |
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|
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for (hist = pmap -> biasCompHist; hist < histEnd; ++hist) |
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for (i = 0; i <= 2; ++i) { |
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irradAvg [i] += r = hist -> weight * hist -> irrad [i]; |
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irradVar [i] += r * hist -> irrad [i]; |
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} |
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|
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for (i = 0; i <= 2; ++i) { |
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r = irradAvg [i] /= totalWeight; |
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irradVar [i] = irradVar [i] / totalWeight - r * r; |
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} |
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|
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/* Do binary search within interval [numLo, numHi]. numLo is towards |
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the END of the queue. */ |
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while (numHi - numLo > 1) { |
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numMid = (numLo + numHi) >> 1; |
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/* Split interval to get numMid closest photons starting from the |
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END of the queue */ |
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squeuePartition(squeueEnd, numLo, numMid, numHi); |
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/* Make sure furthest two photons are consecutive wrt distance */ |
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squeuePartition(squeueEnd, numMid, numMid + 1, numHi); |
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copycolor(fluxMid, fluxLo); |
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sq = squeueEnd - numLo; |
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|
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/* Get irradiance for numMid photons (ignoring 1 / PI) */ |
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for (i = numLo; i < numMid; i++, sq--) { |
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getPhotonFlux(sq -> photon, irrad); |
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addcolor(fluxMid, irrad); |
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} |
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|
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/* Average radius between furthest two photons to improve accuracy */ |
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r = 0.25 * (sq -> dist + (sq + 1) -> dist + |
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2 * sqrt(sq -> dist * (sq + 1) -> dist)); |
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|
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/* Get deviation from current average, and probability that it's due |
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to noise from gaussian distribution based on current variance. Since |
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we are doing this for each colour channel we can also detect |
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chromatic bias. */ |
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for (i = 0; i <= 2; ++i) { |
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d [i] = irradAvg [i] - (irrad [i] = fluxMid [i] / r); |
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p [i] = exp(-0.5 * d [i] * d [i] / irradVar [i]); |
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} |
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|
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if (pmapRandom(pmap -> randState) < colorAvg(p)) { |
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/* Deviation is probably noise, so add mid irradiance to history */ |
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copycolor(histEnd -> irrad, irrad); |
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totalWeight += histEnd++ -> weight = BIASCOMP_WGT((float)numMid); |
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setcolor(irradAvg, 0, 0, 0); |
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setcolor(irradVar, 0, 0, 0); |
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|
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/* Update average and variance */ |
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for (hist = pmap -> biasCompHist; hist < histEnd; ++hist) |
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for (i = 0; i <= 2; i++) { |
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r = hist -> irrad [i]; |
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irradAvg [i] += hist -> weight * r; |
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irradVar [i] += hist -> weight * r * r; |
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} |
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|
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for (i = 0; i <= 2; i++) { |
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r = irradAvg [i] /= totalWeight; |
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irradVar [i] = irradVar [i] / totalWeight - r * r; |
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} |
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|
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/* Need more photons -- recurse on [numMid, numHi] */ |
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numLo = numMid; |
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copycolor(fluxLo, fluxMid); |
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} |
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else |
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/* Deviation is probably bias -- need fewer photons, |
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so recurse on [numLo, numMid] */ |
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numHi = numMid; |
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} |
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|
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--histEnd; |
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for (i = 0; i <= 2; i++) { |
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/* Estimated relative error */ |
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d [i] = histEnd -> irrad [i] / irradAvg [i] - 1; |
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|
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#ifdef BIASCOMP_BWIDTH |
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/* Return bandwidth instead of irradiance */ |
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irrad [i] = numHi / PI; |
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#else |
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/* 1 / PI required as ambient normalisation factor */ |
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irrad [i] = histEnd -> irrad [i] / (PI * PI); |
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#endif |
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} |
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|
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/* Update statistix */ |
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r = colorAvg(d); |
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if (r < pmap -> minError) |
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pmap -> minError = r; |
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if (r > pmap -> maxError) |
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pmap -> maxError = r; |
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pmap -> rmsError += r * r; |
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|
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if (numHi < pmap -> minGathered) |
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pmap -> minGathered = numHi; |
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if (numHi > pmap -> maxGathered) |
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pmap -> maxGathered = numHi; |
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|
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pmap -> totalGathered += numHi; |
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++pmap -> numDensity; |
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} |
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|
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|
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|
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void volumeBiasComp (PhotonMap* pmap, const RAY* ray, COLOR irrad) |
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/* Photon volume density estimate with bias compensation -- czech dis |
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shit out! */ |
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{ |
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unsigned i, numLo, numHi, numMid = 0; |
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PhotonSQNode *sq; |
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PhotonBCNode *hist; |
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const float gecc2 = ray -> gecc * ray -> gecc; |
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float r, totalWeight = 0; |
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PhotonSQNode *squeueEnd; |
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PhotonBCNode *histEnd; |
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COLOR fluxLo, fluxMid, irradVar, irradAvg, p, d; |
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|
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if (!pmap -> biasCompHist) { |
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/* Allocate bias compensation history */ |
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numHi = pmap -> maxGather - pmap -> minGather; |
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for (i = pmap -> minGather + 1; numHi > 1; numHi >>= 1, ++i); |
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pmap -> biasCompHist = (PhotonBCNode*)malloc(i * sizeof(PhotonBCNode)); |
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if (!pmap -> biasCompHist) |
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error(USER, "can't allocate bias compensation history"); |
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} |
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|
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numLo = min(pmap -> minGather, pmap -> squeueEnd - 1); |
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numHi = min(pmap -> maxGather, pmap -> squeueEnd - 1); |
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sq = squeueEnd = pmap -> squeue + pmap -> squeueEnd - 1; |
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histEnd = pmap -> biasCompHist; |
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setcolor(fluxLo, 0, 0, 0); |
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/* Partition to get numLo closest photons starting from END of queue */ |
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squeuePartition(squeueEnd, 1, numLo, numHi); |
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|
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/* Get irradiance estimates (ignoring constants) using 1..numLo photons |
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and chuck in history. Queue is traversed BACKWARDS. */ |
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for (i = 1; i <= numLo; i++, sq--) { |
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/* Make sure furthest two photons are consecutive wrt distance */ |
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squeuePartition(squeueEnd, i, i + 1, numHi); |
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|
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/* Compute phase function for inscattering from photon */ |
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if (gecc2 <= FTINY) |
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r = 1; |
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else { |
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r = DOT(ray -> rdir, sq -> photon -> norm) / 127; |
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r = 1 + gecc2 - 2 * ray -> gecc * r; |
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r = (1 - gecc2) / (r * sqrt(r)); |
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} |
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|
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getPhotonFlux(sq -> photon, irrad); |
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scalecolor(irrad, r); |
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addcolor(fluxLo, irrad); |
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/* Average radius between furthest two photons to improve accuracy */ |
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r = 0.25 * (sq -> dist + (sq - 1) -> dist + |
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2 * sqrt(sq -> dist * (sq - 1) -> dist)); |
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r *= sqrt(r); |
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/* Add irradiance and weight to history. Weights should increase |
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monotonically based on number of photons used for the estimate. */ |
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histEnd -> irrad [0] = fluxLo [0] / r; |
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histEnd -> irrad [1] = fluxLo [1] / r; |
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histEnd -> irrad [2] = fluxLo [2] / r; |
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totalWeight += histEnd++ -> weight = BIASCOMP_WGT((float)i); |
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} |
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|
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/* Compute expected value (average) and variance of irradiance based on |
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history for numLo photons. */ |
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setcolor(irradAvg, 0, 0, 0); |
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setcolor(irradVar, 0, 0, 0); |
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|
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for (hist = pmap -> biasCompHist; hist < histEnd; ++hist) |
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for (i = 0; i <= 2; ++i) { |
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irradAvg [i] += r = hist -> weight * hist -> irrad [i]; |
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irradVar [i] += r * hist -> irrad [i]; |
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} |
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|
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for (i = 0; i <= 2; ++i) { |
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r = irradAvg [i] /= totalWeight; |
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irradVar [i] = irradVar [i] / totalWeight - r * r; |
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} |
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|
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/* Do binary search within interval [numLo, numHi]. numLo is towards |
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the END of the queue. */ |
| 330 |
while (numHi - numLo > 1) { |
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numMid = (numLo + numHi) >> 1; |
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/* Split interval to get numMid closest photons starting from the |
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END of the queue */ |
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squeuePartition(squeueEnd, numLo, numMid, numHi); |
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/* Make sure furthest two photons are consecutive wrt distance */ |
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squeuePartition(squeueEnd, numMid, numMid + 1, numHi); |
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copycolor(fluxMid, fluxLo); |
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sq = squeueEnd - numLo; |
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|
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/* Get irradiance for numMid photons (ignoring constants) */ |
| 341 |
for (i = numLo; i < numMid; i++, sq--) { |
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/* Compute phase function for inscattering from photon */ |
| 343 |
if (gecc2 <= FTINY) |
| 344 |
r = 1; |
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else { |
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r = DOT(ray -> rdir, sq -> photon -> norm) / 127; |
| 347 |
r = 1 + gecc2 - 2 * ray -> gecc * r; |
| 348 |
r = (1 - gecc2) / (r * sqrt(r)); |
| 349 |
} |
| 350 |
|
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getPhotonFlux(sq -> photon, irrad); |
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scalecolor(irrad, r); |
| 353 |
addcolor(fluxMid, irrad); |
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} |
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|
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/* Average radius between furthest two photons to improve accuracy */ |
| 357 |
r = 0.25 * (sq -> dist + (sq + 1) -> dist + |
| 358 |
2 * sqrt(sq -> dist * (sq + 1) -> dist)); |
| 359 |
r *= sqrt(r); |
| 360 |
|
| 361 |
/* Get deviation from current average, and probability that it's due |
| 362 |
to noise from gaussian distribution based on current variance. Since |
| 363 |
we are doing this for each colour channel we can also detect |
| 364 |
chromatic bias. */ |
| 365 |
for (i = 0; i <= 2; ++i) { |
| 366 |
d [i] = irradAvg [i] - (irrad [i] = fluxMid [i] / r); |
| 367 |
p [i] = exp(-0.5 * d [i] * d [i] / irradVar [i]); |
| 368 |
} |
| 369 |
|
| 370 |
if (pmapRandom(pmap -> randState) < colorAvg(p)) { |
| 371 |
/* Deviation is probably noise, so add mid irradiance to history */ |
| 372 |
copycolor(histEnd -> irrad, irrad); |
| 373 |
totalWeight += histEnd++ -> weight = BIASCOMP_WGT((float)numMid); |
| 374 |
setcolor(irradAvg, 0, 0, 0); |
| 375 |
setcolor(irradVar, 0, 0, 0); |
| 376 |
|
| 377 |
/* Update average and variance */ |
| 378 |
for (hist = pmap -> biasCompHist; hist < histEnd; ++hist) |
| 379 |
for (i = 0; i <= 2; i++) { |
| 380 |
r = hist -> irrad [i]; |
| 381 |
irradAvg [i] += hist -> weight * r; |
| 382 |
irradVar [i] += hist -> weight * r * r; |
| 383 |
} |
| 384 |
for (i = 0; i <= 2; i++) { |
| 385 |
r = irradAvg [i] /= totalWeight; |
| 386 |
irradVar [i] = irradVar [i] / totalWeight - r * r; |
| 387 |
} |
| 388 |
|
| 389 |
/* Need more photons -- recurse on [numMid, numHi] */ |
| 390 |
numLo = numMid; |
| 391 |
copycolor(fluxLo, fluxMid); |
| 392 |
} |
| 393 |
else |
| 394 |
/* Deviation is probably bias -- need fewer photons, |
| 395 |
so recurse on [numLo, numMid] */ |
| 396 |
numHi = numMid; |
| 397 |
} |
| 398 |
|
| 399 |
--histEnd; |
| 400 |
for (i = 0; i <= 2; i++) { |
| 401 |
/* Estimated relative error */ |
| 402 |
d [i] = histEnd -> irrad [i] / irradAvg [i] - 1; |
| 403 |
/* Divide by 4 / 3 * PI for search volume (r^3 already accounted |
| 404 |
for) and phase function normalization factor 1 / (4 * PI) */ |
| 405 |
irrad [i] = histEnd -> irrad [i] * 3 / (16 * PI * PI); |
| 406 |
} |
| 407 |
|
| 408 |
/* Update statistix */ |
| 409 |
r = colorAvg(d); |
| 410 |
if (r < pmap -> minError) |
| 411 |
pmap -> minError = r; |
| 412 |
if (r > pmap -> maxError) |
| 413 |
pmap -> maxError = r; |
| 414 |
pmap -> rmsError += r * r; |
| 415 |
|
| 416 |
if (numMid < pmap -> minGathered) |
| 417 |
pmap -> minGathered = numMid; |
| 418 |
if (numMid > pmap -> maxGathered) |
| 419 |
pmap -> maxGathered = numMid; |
| 420 |
|
| 421 |
pmap -> totalGathered += numMid; |
| 422 |
++pmap -> numDensity; |
| 423 |
} |
| 424 |
|
