#include <memory></memory>

#include <array></array>

#include "toonz/tdistort.h"

#include "traster.h"

#include "trastercm.h"

#include "tgeometry.h"

#include "tpixelutils.h"

#include <qlist></qlist>

//****************************************************************************************

//    Local namespace stuff

//****************************************************************************************

namespace {

inline double dist(const TPointD &a, const TPointD &b) { return norm(b - a); }

}

//========================================================================================

namespace {

typedef struct {

  TUINT32 val;

  double tot;

} BLOB24;

//---------------------------------------------------------------------------------

TPixelCM32 filterPixel(const TPointD &pos, const TRasterCM32P &rasIn) {

  TPointD distance = TPointD(

      areAlmostEqual(pos.x, tfloor(pos.x), 0.001) ? 0.0

                                                  : fabs(pos.x - tfloor(pos.x)),

      areAlmostEqual(pos.y, tfloor(pos.y), 0.001) ? 0.0 : fabs(pos.y -

                                                               tfloor(pos.y)));

  TPoint nearPos(tfloor(pos.x), tfloor(pos.y));

  if (distance == TPointD(0.0, 0.0)) {

    if (nearPos.x >= 0 && nearPos.x < rasIn->getLx() && nearPos.y >= 0 &&

        nearPos.y < rasIn->getLy())

      return rasIn->pixels(nearPos.y)[nearPos.x];

    else

      return TPixelCM32();

  }

  int i, j, k = 0;

  TPixelCM32 P[4];

  for (j = 0; j < 2; ++j)

    for (i         = 0; i < 2; ++i)

      P[i + 2 * j] = nearPos.x + i < rasIn->getLx() && nearPos.x + i >= 0 &&

                             nearPos.y + j < rasIn->getLy() &&

                             nearPos.y + j >= 0

                         ? rasIn->pixels(nearPos.y + j)[nearPos.x + i]

                         : TPixelCM32();

  if (P[0] == P[1] && P[1] == P[2] && P[2] == P[3]) return P[0];

  double w[4], sum = 0;

  for (j = 1; j >= 0; --j)

    for (i          = 1; i >= 0; --i)

      sum += w[k++] = fabs(distance.x - i) * fabs(distance.y - j);

  for (i = 0; i < 4; i++) w[i] /= sum;

  TPixelCM32 outPix;

  TUINT32 tone;

  double tone_tot = 0.0;

  BLOB24 currBlob, paintBlobs[4], inkBlobs[4];

  int paintBlobsSize = 0, inkBlobsSize = 0;

  // Doing the same thing in TRop::resample

  for (i = 0; i < 4; ++i) {

    // Build paint blobs and sort them

    tone = P[i].getTone();

    tone_tot += tone * w[i];

    currBlob.val = P[i].getPaint();

    currBlob.tot = tone * w[i];

    for (j = 0; j < paintBlobsSize; j++)

      if (paintBlobs[j].val == currBlob.val) break;

    if (j < paintBlobsSize)

      paintBlobs[j].tot += currBlob.tot;

    else

      paintBlobs[paintBlobsSize++] = currBlob;

    for (; j > 0 && paintBlobs[j].tot > paintBlobs[j - 1].tot; j--)

      std::swap(paintBlobs[j], paintBlobs[j - 1]);

    // Same for ink blobs

    currBlob.val = P[i].getInk();

    currBlob.tot = (TPixelCM32::getToneMask() - tone) * w[i];

    for (j = 0; j < inkBlobsSize; j++)

      if (inkBlobs[j].val == currBlob.val) break;

    if (j < inkBlobsSize)

      inkBlobs[j].tot += currBlob.tot;

    else

      inkBlobs[inkBlobsSize++] = currBlob;

    for (; j > 0 && inkBlobs[j].tot > inkBlobs[j - 1].tot; j--)

      std::swap(inkBlobs[j], inkBlobs[j - 1]);

  }

  tone = troundp(tone_tot);

  outPix.setPaint(paintBlobs[0].val);

  outPix.setInk(inkBlobs[0].val);

  outPix.setTone(tone);

  return outPix;

}

//---------------------------------------------------------------------------------

void resample(const TRasterCM32P &rasIn, TRasterCM32P &rasOut,

              const TDistorter &distorter, const TPoint &p) {

  if (rasOut->getLx() < 1 || rasOut->getLy() < 1 || rasIn->getLx() < 1 ||

      rasIn->getLy() < 1)

    return;

  std::unique_ptr<tpointd[]> preImages(new TPointD[distorter.maxInvCount()]);</tpointd[]>

  int x, y;

  int i;

  for (y = 0; y < rasOut->getLy(); y++) {

    TPixelCM32 *pix    = rasOut->pixels(y);

    TPixelCM32 *endPix = pix + rasOut->getLx();

    for (x = 0; pix != endPix; pix++, x++) {

      TPixelCM32 pixDown;

      int count = distorter.invMap(convert(p) + TPointD(x + 0.5, y + 0.5),

                                   preImages.get());

      for (i = count - 1; i >= 0; --i) {

        TPixelCM32 pixUp;

        TPointD preImage(preImages[i].x - 0.5, preImages[i].y - 0.5);

        if (preImage.x > -1 && preImage.y > -1 &&

            preImage.x < rasIn->getLx() + 1 && preImage.y < rasIn->getLy() + 1)

          pixUp = filterPixel(preImage, rasIn);

        pixDown.setPaint(pixUp.getPaint() ? pixUp.getPaint()

                                          : pixDown.getPaint());

        pixDown.setInk(pixUp.getInk() ? pixUp.getInk() : pixDown.getInk());

        pixDown.setTone(pixUp == TPixelCM32() ? pixDown.getTone()

                                              : pixUp.getTone());

      }

      *pix = pixDown;

    }

  }

}

//---------------------------------------------------------------------------------

template <typename channel_type="" pixel,="" typename=""></typename>

PIXEL closest_pixel(const TPointD &pos, const TRasterPT<pixel> &rasIn) {</pixel>

  TPoint nearPos(tround(pos.x), tround(pos.y));

  if (!rasIn->getBounds().contains(nearPos)) return PIXEL(0, 0, 0, 0);

  return rasIn->pixels(nearPos.y)[nearPos.x];

}

//---------------------------------------------------------------------------------

template <typename channel_type="" t,="" typename=""></typename>

void resampleClosestPixel(const TRasterPT<t> &rasIn, TRasterPT<t> &rasOut,</t></t>

                          const TDistorter &distorter, const TPoint &p) {

  if (rasOut->getLx() < 1 || rasOut->getLy() < 1 || rasIn->getLx() < 1 ||

      rasIn->getLy() < 1)

    return;

  std::unique_ptr<tpointd[]> preImages(new TPointD[distorter.maxInvCount()]);</tpointd[]>

  int x, y;

  int i;

  for (y = 0; y < rasOut->getLy(); y++) {

    T *pix    = rasOut->pixels(y);

    T *endPix = pix + rasOut->getLx();

    x = 0;

    for (; pix != endPix; pix++, x++) {

      T pixDown(0, 0, 0, 0);

      // preImages.clear();

      int count = distorter.invMap(convert(p) + TPointD(x + 0.5, y + 0.5),

                                   preImages.get());

      for (i = count - 1; i >= 0; --i) {

        T pixUp(0, 0, 0, 0);

        TPointD preImage(preImages[i].x - 0.5, preImages[i].y - 0.5);

        if (preImage.x > -1 && preImage.y > -1 &&

            preImage.x < rasIn->getLx() + 1 && preImage.y < rasIn->getLy() + 1)

          pixUp = closest_pixel<t, channel_type="">(preImage, rasIn);</t,>

        pixDown = pixUp;

      }

      *pix = pixDown;

    }

  }

}

//---------------------------------------------------------------------------------

TPixelCM32 closest_pixel(const TPointD &pos, const TRasterCM32P &rasIn) {

  TPoint nearPos(tround(pos.x), tround(pos.y));

  if (!rasIn->getBounds().contains(nearPos)) return TPixelCM32(0, 0, 255);

  return rasIn->pixels(nearPos.y)[nearPos.x];

}

//---------------------------------------------------------------------------------

void resampleClosestPixel(const TRasterCM32P &rasIn, TRasterCM32P &rasOut,

                          const TDistorter &distorter, const TPoint &p) {

  if (rasOut->getLx() < 1 || rasOut->getLy() < 1 || rasIn->getLx() < 1 ||

      rasIn->getLy() < 1)

    return;

  std::unique_ptr<tpointd[]> preImages(new TPointD[distorter.maxInvCount()]);</tpointd[]>

  int x, y;

  int i;

  for (y = 0; y < rasOut->getLy(); y++) {

    TPixelCM32 *pix    = rasOut->pixels(y);

    TPixelCM32 *endPix = pix + rasOut->getLx();

    x = 0;

    for (; pix != endPix; pix++, x++) {

      TPixelCM32 pixDown(0, 0, 255);

      int count = distorter.invMap(convert(p) + TPointD(x + 0.5, y + 0.5),

                                   preImages.get());

      for (i = count - 1; i >= 0; --i) {

        TPixelCM32 pixUp(0, 0, 255);

        TPointD preImage(preImages[i].x - 0.5, preImages[i].y - 0.5);

        if (preImage.x > -1 && preImage.y > -1 &&

            preImage.x < rasIn->getLx() + 1 && preImage.y < rasIn->getLy() + 1)

          pixUp = closest_pixel(preImage, rasIn);

        pixDown = pixUp;

      }

      *pix = pixDown;

    }

  }

}

//=================================================================================

template <typename channel_type="" pixel,="" typename=""></typename>

PIXEL filterPixel(double a, double b, PIXEL *lineSrc, int lineLength,

                  int lineWrap) {

  // Retrieve the interesting pixel interval

  double x0 = std::max(a, 0.0);

  double x1 = std::min(b, (double)lineLength);

  int x0Floor = tfloor(x0);

  int x0Ceil  = tceil(x0);

  int x1Floor = tfloor(x1);

  if (x0 >= x1) return PIXEL::Transparent;

  PIXEL *pix = lineSrc + x0Floor * lineWrap;

  // Build the sums

  double k, sumr = 0, sumg = 0, sumb = 0, summ = 0;

  // Fractionary part on the beginning

  if (x0Ceil > x0) {

    k = x0Ceil - x0;

    sumr += k * pix->r;

    sumg += k * pix->g;

    sumb += k * pix->b;

    summ += k * pix->m;

    pix += lineWrap;

  }

  // Intermediate pixels (ie when pixels contract)

  int x;

  for (x = x0Ceil; x < x1Floor; ++x, pix += lineWrap) {

    sumr += pix->r;

    sumg += pix->g;

    sumb += pix->b;

    summ += pix->m;

  }

  // Fractionary part on the end

  if (x1 < lineLength) {

    k = x1 - x;

    sumr += k * pix->r;

    sumg += k * pix->g;

    sumb += k * pix->b;

    summ += k * pix->m;

  }

  // Finally, divide per the total weight

  double length =

      b - a;  // 'transparent' pixels outside image range *are* considered

  sumr = sumr / length;

  sumg = sumg / length;

  sumb = sumb / length;

  summ = summ / length;

  return PIXEL(sumr, sumg, sumb, summ);

}

//---------------------------------------------------------------------------------

template <typename channel_type="" pixel,="" typename=""></typename>

PIXEL filterPixel(double a, double b, double c, double d,

                  const TRasterPT<pixel> &rasIn, PIXEL *temp) {</pixel>

  if (bool(a < b) == false && bool(b <= a) == false)

    return PIXEL::Transparent;  // NaNs

  else

    std::swap(a, b);

  if (bool(c < d) == false && bool(d <= c) == false)

    return PIXEL::Transparent;

  else

    std::swap(c, d);

  // Deal the magnification case, assuming that intervals have at least length

  // 1. This actually stands for:

  //  1. Their midpoint is bilinear filtered whenever their former length was

  //     less than 1 (see fractionary parts computing above).

  //  2. This behaviour is continuous with respect to interval lengths - that

  //     is, we pass from supersampling to subsampling in a smooth manner.

  if (b - a < 1) {

    double v = 0.5 * (a + b);

    a        = v - 0.5;

    b        = v + 0.5;

  }

  if (d - c < 1) {

    double v = 0.5 * (c + d);

    c        = v - 0.5;

    d        = v + 0.5;

  }

  // Now, filter each column in [a, b]

  double x0 = std::max(a, 0.0);

  double x1 = std::min(b, (double)rasIn->getLx());

  if (x0 >= x1) return PIXEL::Transparent;

  int xEnd = tceil(x1);

  for (int x = tfloor(x0); x < xEnd; ++x)

    temp[x]  = filterPixel<pixel, channel_type="">(</pixel,>

        c, d, rasIn->pixels(0) + x, rasIn->getLy(), rasIn->getWrap());

  // Then, filter temp

  return filterPixel<pixel, channel_type="">(a, b, temp, rasIn->getLx(), 1);</pixel,>

}

//---------------------------------------------------------------------------------

template <typename channel_type="" t,="" typename=""></typename>

void resample(const TRasterPT<t> &rasIn, TRasterPT<t> &rasOut,</t></t>

              const TDistorter &distorter, const TPoint &p) {

  if (rasOut->getLx() < 1 || rasOut->getLy() < 1 || rasIn->getLx() < 1 ||

      rasIn->getLy() < 1)

    return;

  int invsCount = distorter.maxInvCount();

  // Allocate buffers

  std::array<std::unique_ptr<tpointd[]>, 2> invs = {</std::unique_ptr<tpointd[]>

      std::unique_ptr<tpointd[]>(</tpointd[]>

          new TPointD[invsCount * (rasOut->getLx() + 1)]),

      std::unique_ptr<tpointd[]>(</tpointd[]>

          new TPointD[invsCount * (rasOut->getLx() + 1)]),

  };

  std::array<std::unique_ptr<int[]>, 2> counts = {</std::unique_ptr<int[]>

      std::unique_ptr<int[]>(new int[rasOut->getLx() + 1]),</int[]>

      std::unique_ptr<int[]>(new int[rasOut->getLx() + 1]),</int[]>

  };

  std::unique_ptr<t[]> temp(new T[rasIn->getLx()]);</t[]>

  TPointD shift(convert(p) + TPointD(0.5, 0.5));

  // Fill in the first inverses (lower edge of output image)

  {

    TPointD *currOldInv = invs[0].get();

    int *oldCounts      = counts[0].get();

    for (int x     = 0; x <= rasOut->getLx(); currOldInv += invsCount, ++x)

      oldCounts[x] = distorter.invMap(shift + TPointD(x, 0.0), currOldInv);

  }

  // For each output row

  for (int y = 0; y < rasOut->getLy(); ++y) {

    // Alternate inverse buffers

    TPointD *oldInvs = invs[y % 2].get();

    TPointD *newInvs = invs[(y + 1) % 2].get();

    int *oldCounts   = counts[y % 2].get();

    int *newCounts   = counts[(y + 1) % 2].get();

    // Build the new inverses

    {

      TPointD *currNewInv = newInvs;

      for (int x = 0; x <= rasOut->getLx(); currNewInv += invsCount, ++x)

        newCounts[x] =

            distorter.invMap(shift + TPointD(x, y + 1.0), currNewInv);

    }

    // Filter each pixel in the row

    T *pix              = rasOut->pixels(y);

    TPointD *currOldInv = oldInvs;

    TPointD *currNewInv = newInvs;

    for (int x = 0; x < rasOut->getLx();

         currOldInv += invsCount, currNewInv += invsCount, ++x, ++pix) {

      T pixDown(0, 0, 0, 0);

      int count = std::min({oldCounts[x], oldCounts[x + 1], newCounts[x]});

      for (int i = 0; i < count; ++i) {

        T pixUp(0, 0, 0, 0);

        pixUp = filterPixel<t, channel_type="">(</t,>

            currOldInv[i].x - 0.5, (currOldInv + invsCount)[i].x - 0.5,

            currOldInv[i].y - 0.5, currNewInv[i].y - 0.5, rasIn, temp.get());

        pixDown = overPix(pixDown, pixUp);

      }

      *pix = pixDown;

    }

  }

}

}  // namespace

//==============================================================================================

void distort(TRasterP &outRas, const TRasterP &inRas,

             const TDistorter &distorter, const TPoint &dstPos,

             const TRop::ResampleFilterType &filter) {

  TRaster32P inRas32      = inRas;

  TRaster64P inRas64      = inRas;

  TRasterCM32P inRasCM32  = inRas;

  TRaster32P outRas32     = outRas;

  TRaster64P outRas64     = outRas;

  TRasterCM32P outRasCM32 = outRas;

  if (filter == TRop::Bilinear) {

    if (inRas32)

      ::resample<tpixel32, uchar="">(inRas32, outRas32, distorter, dstPos);</tpixel32,>

    else if (inRas64)

      ::resample<tpixel64, ushort="">(inRas64, outRas64, distorter, dstPos);</tpixel64,>

    else if (inRasCM32 && outRasCM32)

      ::resample(inRasCM32, outRasCM32, distorter, dstPos);

    else

      assert(0);

  } else if (filter == TRop::ClosestPixel) {

    if (inRas32)

      ::resampleClosestPixel<tpixel32, uchar="">(inRas32, outRas32, distorter,</tpixel32,>

                                              dstPos);

    else if (inRas64)

      ::resampleClosestPixel<tpixel64, ushort="">(inRas64, outRas64, distorter,</tpixel64,>

                                               dstPos);

    else if (inRasCM32 && outRasCM32)

      ::resampleClosestPixel(inRasCM32, outRasCM32, distorter, dstPos);

    else

      assert(0);

  } else

    assert(0);

}

//================================================================================================

//

// BilinearDistorterBase

//

//================================================================================================

BilinearDistorterBase::BilinearDistorterBase(

    const TPointD &p00s, const TPointD &p10s, const TPointD &p01s,

    const TPointD &p11s, const TPointD &p00d, const TPointD &p10d,

    const TPointD &p01d, const TPointD &p11d)

    : TQuadDistorter(p00s, p10s, p01s, p11s, p00d, p10d, p01d, p11d)

{

  m_A = p00d;

  m_B = p10d - p00d;

  m_C = p01d - p00d;

  m_D = p11d - p01d - p10d + p00d;

  m_a  = m_D.x * m_C.y - m_C.x * m_D.y;

  m_b0 = m_B.x * m_C.y - m_C.x * m_B.y;

}

//--------------------------------------------------------------------------------

inline TPointD BilinearDistorterBase::map(const TPointD &p) const {

  double t = (p.x - m_p00s.x) / (m_p10s.x - m_p00s.x);

  double s = (p.y - m_p00s.y) / (m_p01s.y - m_p00s.y);

  return (1 - s) * (1 - t) * m_p00d + (1 - s) * t * m_p10d +

         s * (1 - t) * m_p01d + s * t * m_p11d;

}

//--------------------------------------------------------------------------------

int BilinearDistorterBase::invMap(const TPointD &p, TPointD *results) const {

  // See the book "Digital Image Warping" by G. Wolberg

  double b = m_D.x * (m_A.y - p.y) + m_D.y * (p.x - m_A.x) + m_b0;

  double c = m_B.x * (m_A.y - p.y) + m_B.y * (p.x - m_A.x);

  if (fabs(m_a) > 0.001) {

    // If delta <0, the points cannot be inverse-mapped

    double delta = sq(b) - 4.0 * m_a * c;

    if (delta < 0) return 0;

    double sqrtDelta = sqrt(delta);

    double k         = 0.5 / m_a;

    double v1        = k * (-b + sqrtDelta);

    double v2        = k * (-b - sqrtDelta);

    double u1, u2;

    double den = m_B.x + m_D.x * v1;

    if (fabs(den) > 0.01)

      u1 = (p.x - m_A.x - m_C.x * v1) / den;

    else

      u1 = (p.y - m_A.y - m_C.y * v1) / (m_B.y + m_D.y * v1);

    den = m_B.x + m_D.x * v2;

    if (fabs(den) > 0.01)

      u2 = (p.x - m_A.x - m_C.x * v2) / den;

    else

      u2 = (p.y - m_A.y - m_C.y * v2) / (m_B.y + m_D.y * v2);

    TPointD difP10_P00 = m_p10s - m_p00s;

    TPointD difP01_P00 = m_p01s - m_p00s;

    results[0] = m_p00s + u1 * difP10_P00 + v1 * difP01_P00;

    results[1] = m_p00s + u2 * difP10_P00 + v2 * difP01_P00;

    return 2;

  } else {

    // The equation reduces to first order.

    double v = -c / b;

    double u = (p.x - m_A.x - m_C.x * v) / (m_B.x + m_D.x * v);

    results[0] = m_p00s + u * (m_p10s - m_p00s) + v * (m_p01s - m_p00s);

    return 1;

  }

}

//================================================================================================

//

// BilinearDistorter

//

//================================================================================================

BilinearDistorter::BilinearDistorter(const TPointD &p00s, const TPointD &p10s,

                                     const TPointD &p01s, const TPointD &p11s,

                                     const TPointD &p00d, const TPointD &p10d,

                                     const TPointD &p01d, const TPointD &p11d)

    : TQuadDistorter(p00s, p10s, p01s, p11s, p00d, p10d, p01d, p11d) {

  m_refToSource.m_p00 = p00s;

  m_refToSource.m_p10 = p10s;

  m_refToSource.m_p01 = p01s;

  m_refToSource.m_p11 = p11s;

  m_refToDest.m_p00   = p00d;

  m_refToDest.m_p10   = p10d;

  m_refToDest.m_p01   = p01d;

  m_refToDest.m_p11   = p11d;

  m_refToSource.m_A = p00s;

  m_refToSource.m_B = p10s - p00s;

  m_refToSource.m_C = p01s - p00s;

  m_refToSource.m_D = p11s - p01s - p10s + p00s;

  m_refToDest.m_A   = p00d;

  m_refToDest.m_B   = p10d - p00d;

  m_refToDest.m_C   = p01d - p00d;

  m_refToDest.m_D   = p11d - p01d - p10d + p00d;

  m_refToSource.m_a = m_refToSource.m_D.x * m_refToSource.m_C.y -

                      m_refToSource.m_C.x * m_refToSource.m_D.y;

  m_refToSource.m_b0 = m_refToSource.m_B.x * m_refToSource.m_C.y -

                       m_refToSource.m_C.x * m_refToSource.m_B.y;

  m_refToDest.m_a = m_refToDest.m_D.x * m_refToDest.m_C.y -

                    m_refToDest.m_C.x * m_refToDest.m_D.y;

  m_refToDest.m_b0 = m_refToDest.m_B.x * m_refToDest.m_C.y -

                     m_refToDest.m_C.x * m_refToDest.m_B.y;

}

//---------------------------------------------------------------------------------

BilinearDistorter::~BilinearDistorter() {}

//--------------------------------------------------------------------------------

TPointD BilinearDistorter::map(const TPointD &p) const {

  TPointD sourceToRefPoints[2];

  int returnCount = m_refToSource.invMap(p, sourceToRefPoints);

  if (returnCount > 0) return m_refToDest.map(sourceToRefPoints[0]);

  return TConsts::napd;

}

//--------------------------------------------------------------------------------

inline int BilinearDistorter::invMap(const TPointD &p, TPointD *results) const {

  int returnCount = m_refToDest.invMap(p, results);

  for (int i   = 0; i < returnCount; ++i)

    results[i] = m_refToSource.map(results[i]);

  return returnCount;

}

//--------------------------------------------------------------------------------

inline TPointD BilinearDistorter::Base::map(const TPointD &p) const {

  return (1 - p.y) * (1 - p.x) * m_p00 + (1 - p.y) * p.x * m_p10 +

         p.y * (1 - p.x) * m_p01 + p.y * p.x * m_p11;

}

//--------------------------------------------------------------------------------

int BilinearDistorter::Base::invMap(const TPointD &p, TPointD *results) const {

  // See the book "Digital Image Warping" by G. Wolberg

  double b = m_D.x * (m_A.y - p.y) + m_D.y * (p.x - m_A.x) + m_b0;

  double c = m_B.x * (m_A.y - p.y) + m_B.y * (p.x - m_A.x);

  if (fabs(m_a) > 0.001) {

    // If delta <0, the points cannot be inverse-mapped

    double delta = sq(b) - 4.0 * m_a * c;

    if (delta < 0) return 0;

    double sqrtDelta = sqrt(delta);

    double k         = 0.5 / m_a;

    double v1        = k * (-b + sqrtDelta);

    double v2        = k * (-b - sqrtDelta);

    double u1, u2;

    double den = m_B.x + m_D.x * v1;

    if (fabs(den) > 0.01)

      u1 = (p.x - m_A.x - m_C.x * v1) / den;

    else

      u1 = (p.y - m_A.y - m_C.y * v1) / (m_B.y + m_D.y * v1);

    den = m_B.x + m_D.x * v2;

    if (fabs(den) > 0.01)

      u2 = (p.x - m_A.x - m_C.x * v2) / den;

    else

      u2 = (p.y - m_A.y - m_C.y * v2) / (m_B.y + m_D.y * v2);

    results[0] = TPointD(u1, v1);

    results[1] = TPointD(u2, v2);

    return 2;

  } else {

    // The equation reduces to first order.

    double v = -c / b;

    double u = (p.x - m_A.x - m_C.x * v) / (m_B.x + m_D.x * v);

    results[0] = TPointD(u, v);

    return 1;

  }

}

//=================================================================================

//

// TPerspect

//

//=================================================================================

PerspectiveDistorter::TPerspect::TPerspect()

    : a11(1.0)

    , a12(0.0)

    , a13(0.0)

    , a21(0.0)

    , a22(1.0)

    , a23(0.0)

    , a31(0.0)

    , a32(0.0)

    , a33(1.0) {}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect::TPerspect(double p11, double p12, double p13,

                                           double p21, double p22, double p23,

                                           double p31, double p32, double p33)

    : a11(p11)

    , a12(p12)

    , a13(p13)

    , a21(p21)

    , a22(p22)

    , a23(p23)

    , a31(p31)

    , a32(p32)

    , a33(p33) {}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect::TPerspect(const TPerspect &p)

    : a11(p.a11)

    , a12(p.a12)

    , a13(p.a13)

    , a21(p.a21)

    , a22(p.a22)

    , a23(p.a23)

    , a31(p.a31)

    , a32(p.a32)

    , a33(p.a33) {}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect::~TPerspect() {}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect &PerspectiveDistorter::TPerspect::operator=(

    const PerspectiveDistorter::TPerspect &p) {

  a11 = p.a11;

  a12 = p.a12;

  a13 = p.a13;

  a21 = p.a21;

  a22 = p.a22;

  a23 = p.a23;

  a31 = p.a31;

  a32 = p.a32;

  a33 = p.a33;

  return *this;

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect PerspectiveDistorter::TPerspect::operator*(

    const PerspectiveDistorter::TPerspect &p) const {

  return PerspectiveDistorter::TPerspect(

      a11 * p.a11 + a12 * p.a21 + a13 * p.a31,

      a11 * p.a12 + a12 * p.a22 + a13 * p.a32,

      a11 * p.a13 + a12 * p.a23 + a13 * p.a33,

      a21 * p.a11 + a22 * p.a21 + a23 * p.a31,

      a21 * p.a12 + a22 * p.a22 + a23 * p.a32,

      a21 * p.a13 + a22 * p.a23 + a23 * p.a33,

      a31 * p.a11 + a32 * p.a21 + a33 * p.a31,

      a31 * p.a12 + a32 * p.a22 + a33 * p.a32,

      a31 * p.a13 + a32 * p.a23 + a33 * p.a33);

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect PerspectiveDistorter::TPerspect::operator*(

    const TAffine &aff) const {

  return operator*(TPerspect(aff.a11, aff.a12, aff.a13, aff.a21, aff.a22,

                             aff.a23, 0.0, 0.0, 1.0));

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect operator*(

    const TAffine &aff, const PerspectiveDistorter::TPerspect &p) {

  return PerspectiveDistorter::TPerspect(aff.a11, aff.a12, aff.a13, aff.a21,

                                         aff.a22, aff.a23, 0.0, 0.0, 1.0) *

         p;

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect PerspectiveDistorter::TPerspect::operator*=(

    const PerspectiveDistorter::TPerspect &p) {

  return *this * p;

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::TPerspect PerspectiveDistorter::TPerspect::inv() const {

  return TPerspect(

      a22 * a33 - a23 * a32, a13 * a32 - a12 * a33, a12 * a23 - a13 * a22,

      a23 * a31 - a21 * a33, a11 * a33 - a13 * a31, a13 * a21 - a11 * a23,

      a21 * a32 - a22 * a31, a12 * a31 - a11 * a32, a11 * a22 - a12 * a21);

}

//---------------------------------------------------------------------------------

double PerspectiveDistorter::TPerspect::det() const {

  return a11 * a22 * a33 + a12 * a23 * a31 + a13 * a21 * a32 - a13 * a22 * a31 -

         a11 * a23 * a32 - a12 * a21 * a33;

}

//---------------------------------------------------------------------------------

bool PerspectiveDistorter::TPerspect::operator==(

    const PerspectiveDistorter::TPerspect &p) const {

  return a11 == p.a11 && a12 == p.a12 && a13 == p.a13 && a21 == p.a21 &&

         a22 == p.a22 && a23 == p.a23 && a31 == p.a31 && a32 == p.a32 &&

         a33 == p.a33;

}

//---------------------------------------------------------------------------------

bool PerspectiveDistorter::TPerspect::operator!=(

    const PerspectiveDistorter::TPerspect &p) const {

  return !(*this == p);

}

//---------------------------------------------------------------------------------

bool PerspectiveDistorter::TPerspect::isIdentity(double err) const {

  return ((a11 - 1.0) * (a11 - 1.0) + (a22 - 1.0) * (a22 - 1.0) +

          (a33 - 1.0) * (a33 - 1.0) + a12 * a12 + a13 * a13 + a21 * a21 +

          a23 * a23 + a31 * a31 + a32 * a32) < err;

}

//---------------------------------------------------------------------------------

TPointD PerspectiveDistorter::TPerspect::operator*(const TPointD &p) const {

  double den = (a31 * p.x + a32 * p.y + a33);

  double x   = (a11 * p.x + a12 * p.y + a13) / den;

  double y   = (a21 * p.x + a22 * p.y + a23) / den;

  return TPointD(x, y);

}

//---------------------------------------------------------------------------------

T3DPointD PerspectiveDistorter::TPerspect::operator*(const T3DPointD &p) const {

  return T3DPointD(a11 * p.x + a12 * p.y + a13 * p.z,

                   a21 * p.x + a22 * p.y + a23 * p.z,

                   a31 * p.x + a32 * p.y + a33 * p.z);

}

//---------------------------------------------------------------------------------

TRectD PerspectiveDistorter::TPerspect::operator*(const TRectD &rect) const {

  if (rect != TConsts::infiniteRectD) {

    TPointD p1 = *this * rect.getP00(), p2 = *this * rect.getP01(),

            p3 = *this * rect.getP10(), p4 = *this * rect.getP11();

    return TRectD(

        std::min({p1.x, p2.x, p3.x, p4.x}), std::min({p1.y, p2.y, p3.y, p4.y}),

        std::max({p1.x, p2.x, p3.x, p4.x}), std::max({p1.y, p2.y, p3.y, p4.y}));

  } else

    return TConsts::infiniteRectD;

}

//================================================================================================

//

// PerspectiveDistorter

//

//================================================================================================

PerspectiveDistorter::PerspectiveDistorter(

    const TPointD &p00s, const TPointD &p10s, const TPointD &p01s,

    const TPointD &p11s, const TPointD &p00d, const TPointD &p10d,

    const TPointD &p01d, const TPointD &p11d)

    : TQuadDistorter(p00s, p10s, p01s, p11s, p00d, p10d, p01d, p11d) {

  computeMatrix();

}

//---------------------------------------------------------------------------------

PerspectiveDistorter::~PerspectiveDistorter() {}

//---------------------------------------------------------------------------------

void PerspectiveDistorter::computeMatrix() {

  // Since source and destination points are intended in hundreds of pixels in

  // their refs,

  // and inverting makes squares with respect to their elements' size, we'd

  // better put the

  // quadrilaterals in more numerically stable references before inversions.

  double srcSize = std::max({dist(m_p00s, m_p10s), dist(m_p00s, m_p01s),

                             dist(m_p10s, m_p11s), dist(m_p01s, m_p11s)});

  double dstSize = std::max({dist(m_p00d, m_p10d), dist(m_p00d, m_p01d),

                             dist(m_p10d, m_p11d), dist(m_p01d, m_p11d)});

  TAffine toSrcNormalizedRef(TScale(1.0 / srcSize) * TTranslation(-m_p00s));

  TAffine toSrcRef(TTranslation(m_p00s) * TScale(srcSize));

  TAffine toDstNormalizedRef(TScale(1.0 / dstSize) * TTranslation(-m_p00d));

  TAffine toDstRef(TTranslation(m_p00d) * TScale(dstSize));

  TPointD p00s;

  TPointD p10s(toSrcNormalizedRef * m_p10s);

  TPointD p01s(toSrcNormalizedRef * m_p01s);

  TPointD p11s(toSrcNormalizedRef * m_p11s);

  TPointD p00d;

  TPointD p10d(toDstNormalizedRef * m_p10d);

  TPointD p01d(toDstNormalizedRef * m_p01d);

  TPointD p11d(toDstNormalizedRef * m_p11d);

  // compute a matrix from (0,0), (1,0), (1,1), (0,1) to m_startPoints.

  TPerspect m1 = computeSquareToMatrix(p00s, p10s, p01s, p11s);

  // compute a matrix from (0,0), (1,0), (1,1), (0,1) to m_endPoints.