gfx.cc

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    for (j = 0; j < nComps; ++j) {
      if (abs(colors[i].c[j] - colors[(i+1)&3].c[j]) > functionColorDelta) {
	break;
      }
    }
    if (j < nComps) {
      break;
    }
  }

  // center of the rectangle
  xM = 0.5 * (x0 + x1);
  yM = 0.5 * (y0 + y1);

  // the four corner colors are close (or we hit the recursive limit)
  // -- fill the rectangle; but require at least one subdivision
  // (depth==0) to avoid problems when the four outer corners of the
  // shaded region are the same color
  if ((i == 4 && depth > 0) || depth == functionMaxDepth) {

    // use the center color
    shading->getColor(xM, yM, &fillColor);
    state->setFillColor(&fillColor);
    out->updateFillColor(state);

    // fill the rectangle
    state->moveTo(x0 * matrix[0] + y0 * matrix[2] + matrix[4],
		  x0 * matrix[1] + y0 * matrix[3] + matrix[5]);
    state->lineTo(x1 * matrix[0] + y0 * matrix[2] + matrix[4],
		  x1 * matrix[1] + y0 * matrix[3] + matrix[5]);
    state->lineTo(x1 * matrix[0] + y1 * matrix[2] + matrix[4],
		  x1 * matrix[1] + y1 * matrix[3] + matrix[5]);
    state->lineTo(x0 * matrix[0] + y1 * matrix[2] + matrix[4],
		  x0 * matrix[1] + y1 * matrix[3] + matrix[5]);
    state->closePath();
    out->fill(state);
    state->clearPath();

  // the four corner colors are not close enough -- subdivide the
  // rectangle
  } else {

    // colors[0]       colorM0       colors[2]
    //   (x0,y0)       (xM,y0)       (x1,y0)
    //         +----------+----------+
    //         |          |          |
    //         |    UL    |    UR    |
    // color0M |       colorMM       | color1M
    // (x0,yM) +----------+----------+ (x1,yM)
    //         |       (xM,yM)       |
    //         |    LL    |    LR    |
    //         |          |          |
    //         +----------+----------+
    // colors[1]       colorM1       colors[3]
    //   (x0,y1)       (xM,y1)       (x1,y1)

    shading->getColor(x0, yM, &color0M);
    shading->getColor(x1, yM, &color1M);
    shading->getColor(xM, y0, &colorM0);
    shading->getColor(xM, y1, &colorM1);
    shading->getColor(xM, yM, &colorMM);

    // upper-left sub-rectangle
    colors2[0] = colors[0];
    colors2[1] = color0M;
    colors2[2] = colorM0;
    colors2[3] = colorMM;
    doFunctionShFill1(shading, x0, y0, xM, yM, colors2, depth + 1);
    
    // lower-left sub-rectangle
    colors2[0] = color0M;
    colors2[1] = colors[1];
    colors2[2] = colorMM;
    colors2[3] = colorM1;
    doFunctionShFill1(shading, x0, yM, xM, y1, colors2, depth + 1);
    
    // upper-right sub-rectangle
    colors2[0] = colorM0;
    colors2[1] = colorMM;
    colors2[2] = colors[2];
    colors2[3] = color1M;
    doFunctionShFill1(shading, xM, y0, x1, yM, colors2, depth + 1);

    // lower-right sub-rectangle
    colors2[0] = colorMM;
    colors2[1] = colorM1;
    colors2[2] = color1M;
    colors2[3] = colors[3];
    doFunctionShFill1(shading, xM, yM, x1, y1, colors2, depth + 1);
  }
}

void Gfx::doAxialShFill(GfxAxialShading *shading) {
  double xMin, yMin, xMax, yMax;
  double x0, y0, x1, y1;
  double dx, dy, mul;
  GBool dxZero, dyZero;
  double tMin, tMax, t, tx, ty;
  double s[4], sMin, sMax, tmp;
  double ux0, uy0, ux1, uy1, vx0, vy0, vx1, vy1;
  double t0, t1, tt;
  double ta[axialMaxSplits + 1];
  int next[axialMaxSplits + 1];
  GfxColor color0, color1;
  int nComps;
  int i, j, k, kk;

  if (out->useShadedFills() &&
      out->axialShadedFill(state, shading)) {
    return;
  }

  // get the clip region bbox
  state->getUserClipBBox(&xMin, &yMin, &xMax, &yMax);

  // compute min and max t values, based on the four corners of the
  // clip region bbox
  shading->getCoords(&x0, &y0, &x1, &y1);
  dx = x1 - x0;
  dy = y1 - y0;
  dxZero = fabs(dx) < 0.01;
  dyZero = fabs(dy) < 0.01;
  if (dxZero && dyZero) {
    tMin = tMax = 0;
  } else {
    mul = 1 / (dx * dx + dy * dy);
    tMin = tMax = ((xMin - x0) * dx + (yMin - y0) * dy) * mul;
    t = ((xMin - x0) * dx + (yMax - y0) * dy) * mul;
    if (t < tMin) {
      tMin = t;
    } else if (t > tMax) {
      tMax = t;
    }
    t = ((xMax - x0) * dx + (yMin - y0) * dy) * mul;
    if (t < tMin) {
      tMin = t;
    } else if (t > tMax) {
      tMax = t;
    }
    t = ((xMax - x0) * dx + (yMax - y0) * dy) * mul;
    if (t < tMin) {
      tMin = t;
    } else if (t > tMax) {
      tMax = t;
    }
    if (tMin < 0 && !shading->getExtend0()) {
      tMin = 0;
    }
    if (tMax > 1 && !shading->getExtend1()) {
      tMax = 1;
    }
  }

  // get the function domain
  t0 = shading->getDomain0();
  t1 = shading->getDomain1();

  // Traverse the t axis and do the shading.
  //
  // For each point (tx, ty) on the t axis, consider a line through
  // that point perpendicular to the t axis:
  //
  //     x(s) = tx + s * -dy   -->   s = (x - tx) / -dy
  //     y(s) = ty + s * dx    -->   s = (y - ty) / dx
  //
  // Then look at the intersection of this line with the bounding box
  // (xMin, yMin, xMax, yMax).  In the general case, there are four
  // intersection points:
  //
  //     s0 = (xMin - tx) / -dy
  //     s1 = (xMax - tx) / -dy
  //     s2 = (yMin - ty) / dx
  //     s3 = (yMax - ty) / dx
  //
  // and we want the middle two s values.
  //
  // In the case where dx = 0, take s0 and s1; in the case where dy =
  // 0, take s2 and s3.
  //
  // Each filled polygon is bounded by two of these line segments
  // perpdendicular to the t axis.
  //
  // The t axis is bisected into smaller regions until the color
  // difference across a region is small enough, and then the region
  // is painted with a single color.

  // set up: require at least one split to avoid problems when the two
  // ends of the t axis have the same color
  nComps = shading->getColorSpace()->getNComps();
  ta[0] = tMin;
  next[0] = axialMaxSplits / 2;
  ta[axialMaxSplits / 2] = 0.5 * (tMin + tMax);
  next[axialMaxSplits / 2] = axialMaxSplits;
  ta[axialMaxSplits] = tMax;

  // compute the color at t = tMin
  if (tMin < 0) {
    tt = t0;
  } else if (tMin > 1) {
    tt = t1;
  } else {
    tt = t0 + (t1 - t0) * tMin;
  }
  shading->getColor(tt, &color0);

  // compute the coordinates of the point on the t axis at t = tMin;
  // then compute the intersection of the perpendicular line with the
  // bounding box
  tx = x0 + tMin * dx;
  ty = y0 + tMin * dy;
  if (dxZero && dyZero) {
    sMin = sMax = 0;
  } else if (dxZero) {
    sMin = (xMin - tx) / -dy;
    sMax = (xMax - tx) / -dy;
    if (sMin > sMax) { tmp = sMin; sMin = sMax; sMax = tmp; }
  } else if (dyZero) {
    sMin = (yMin - ty) / dx;
    sMax = (yMax - ty) / dx;
    if (sMin > sMax) { tmp = sMin; sMin = sMax; sMax = tmp; }
  } else {
    s[0] = (yMin - ty) / dx;
    s[1] = (yMax - ty) / dx;
    s[2] = (xMin - tx) / -dy;
    s[3] = (xMax - tx) / -dy;
    for (j = 0; j < 3; ++j) {
      kk = j;
      for (k = j + 1; k < 4; ++k) {
	if (s[k] < s[kk]) {
	  kk = k;
	}
      }
      tmp = s[j]; s[j] = s[kk]; s[kk] = tmp;
    }
    sMin = s[1];
    sMax = s[2];
  }
  ux0 = tx - sMin * dy;
  uy0 = ty + sMin * dx;
  vx0 = tx - sMax * dy;
  vy0 = ty + sMax * dx;

  i = 0;
  while (i < axialMaxSplits) {

    // bisect until color difference is small enough or we hit the
    // bisection limit
    j = next[i];
    while (j > i + 1) {
      if (ta[j] < 0) {
	tt = t0;
      } else if (ta[j] > 1) {
	tt = t1;
      } else {
	tt = t0 + (t1 - t0) * ta[j];
      }
      shading->getColor(tt, &color1);
      for (k = 0; k < nComps; ++k) {
	if (abs(color1.c[k] - color0.c[k]) > axialColorDelta) {
	  break;
	}
      }
      if (k == nComps) {
	break;
      }
      k = (i + j) / 2;
      ta[k] = 0.5 * (ta[i] + ta[j]);
      next[i] = k;
      next[k] = j;
      j = k;
    }

    // use the average of the colors of the two sides of the region
    for (k = 0; k < nComps; ++k) {
      color0.c[k] = (color0.c[k] + color1.c[k]) / 2;
    }

    // compute the coordinates of the point on the t axis; then
    // compute the intersection of the perpendicular line with the
    // bounding box
    tx = x0 + ta[j] * dx;
    ty = y0 + ta[j] * dy;
    if (dxZero && dyZero) {
      sMin = sMax = 0;
    } else if (dxZero) {
      sMin = (xMin - tx) / -dy;
      sMax = (xMax - tx) / -dy;
      if (sMin > sMax) { tmp = sMin; sMin = sMax; sMax = tmp; }
    } else if (dyZero) {
      sMin = (yMin - ty) / dx;
      sMax = (yMax - ty) / dx;
      if (sMin > sMax) { tmp = sMin; sMin = sMax; sMax = tmp; }
    } else {
      s[0] = (yMin - ty) / dx;
      s[1] = (yMax - ty) / dx;
      s[2] = (xMin - tx) / -dy;
      s[3] = (xMax - tx) / -dy;
      for (j = 0; j < 3; ++j) {
	kk = j;
	for (k = j + 1; k < 4; ++k) {
	  if (s[k] < s[kk]) {
	    kk = k;
	  }
	}
	tmp = s[j]; s[j] = s[kk]; s[kk] = tmp;
      }
      sMin = s[1];
      sMax = s[2];
    }
    ux1 = tx - sMin * dy;
    uy1 = ty + sMin * dx;
    vx1 = tx - sMax * dy;
    vy1 = ty + sMax * dx;

    // set the color
    state->setFillColor(&color0);
    out->updateFillColor(state);

    // fill the region
    state->moveTo(ux0, uy0);
    state->lineTo(vx0, vy0);
    state->lineTo(vx1, vy1);
    state->lineTo(ux1, uy1);
    state->closePath();
    out->fill(state);
    state->clearPath();

    // set up for next region
    ux0 = ux1;
    uy0 = uy1;
    vx0 = vx1;
    vy0 = vy1;
    color0 = color1;
    i = next[i];
  }
}

void Gfx::doRadialShFill(GfxRadialShading *shading) {
  double xMin, yMin, xMax, yMax;
  double x0, y0, r0, x1, y1, r1, t0, t1;
  int nComps;
  GfxColor colorA, colorB;
  double xa, ya, xb, yb, ra, rb;
  double ta, tb, sa, sb;
  double sz, xz, yz, sMin, sMax;
  GBool enclosed;
  int ia, ib, k, n;
  double *ctm;
  double theta, alpha, angle, t;

  if (out->useShadedFills() &&
      out->radialShadedFill(state, shading)) {
    return;
  }

  // get the shading info
  shading->getCoords(&x0, &y0, &r0, &x1, &y1, &r1);
  t0 = shading->getDomain0();
  t1 = shading->getDomain1();
  nComps = shading->getColorSpace()->getNComps();

  // Compute the point at which r(s) = 0; check for the enclosed
  // circles case; and compute the angles for the tangent lines.
  if (x0 == x1 && y0 == y1) {
    enclosed = gTrue;
    theta = 0; // make gcc happy
    sz = 0; // make gcc happy
  } else if (r0 == r1) {
    enclosed = gFalse;
    theta = 0;
    sz = 0; // make gcc happy
  } else {
    sz = -r0 / (r1 - r0);
    xz = x0 + sz * (x1 - x0);
    yz = y0 + sz * (y1 - y0);
    enclosed = (xz - x0) * (xz - x0) + (yz - y0) * (yz - y0) <= r0 * r0;
    theta = asin(r0 / sqrt((x0 - xz) * (x0 - xz) + (y0 - yz) * (y0 - yz)));
    if (r0 > r1) {
      theta = -theta;
    }
  }
  if (enclosed) {
    alpha = 0;
  } else {
    alpha = atan2(y1 - y0, x1 - x0);
  }

  // compute the (possibly extended) s range
  state->getUserClipBBox(&xMin, &yMin, &xMax, &yMax);
  if (enclosed) {
    sMin = 0;
    sMax = 1;
  } else {
    sMin = 1;
    sMax = 0;
    // solve for x(s) + r(s) = xMin
    if ((x1 + r1) - (x0 + r0) != 0) {
      sa = (xMin - (x0 + r0)) / ((x1 + r1) - (x0 + r0));
      if (sa < sMin) {
	sMin = sa;
      } else if (sa > sMax) {
	sMax = sa;
      }
    }
    // solve for x(s) - r(s) = xMax
    if ((x1 - r1) - (x0 - r0) != 0) {
      sa = (xMax - (x0 - r0)) / ((x1 - r1) - (x0 - r0));
      if (sa < sMin) {
	sMin = sa;
      } else if (sa > sMax) {
	sMax = sa;
      }
    }
    // solve for y(s) + r(s) = yMin
    if ((y1 + r1) - (y0 + r0) != 0) {
      sa = (yMin - (y0 + r0)) / ((y1 + r1) - (y0 + r0));
      if (sa < sMin) {
	sMin = sa;
      } else if (sa > sMax) {
	sMax = sa;
      }
    }
    // solve for y(s) - r(s) = yMax
    if ((y1 - r1) - (y0 - r0) != 0) {
      sa = (yMax - (y0 - r0)) / ((y1 - r1) - (y0 - r0));
      if (sa < sMin) {
	sMin = sa;
      } else if (sa > sMax) {
	sMax = sa;
      }
    }
    // check against sz
    if (r0 < r1) {
      if (sMin < sz) {
	sMin = sz;
      }
    } else if (r0 > r1) {
      if (sMax > sz) {
	sMax = sz;
      }
    }
    // check the 'extend' flags
    if (!shading->getExtend0() && sMin < 0) {
      sMin = 0;
    }
    if (!shading->getExtend1() && sMax > 1) {
      sMax = 1;
    }
  }

  // compute the number of steps into which circles must be divided to
  // achieve a curve flatness of 0.1 pixel in device space for the
  // largest circle (note that "device space" is 72 dpi when generating
  // PostScript, hence the relatively small 0.1 pixel accuracy)
  ctm = state->getCTM();
  t = fabs(ctm[0]);
  if (fabs(ctm[1]) > t) {
    t = fabs(ctm[1]);
  }
  if (fabs(ctm[2]) > t) {
    t = fabs(ctm[2]);
  }
  if (fabs(ctm[3]) > t) {
    t = fabs(ctm[3]);
  }
  if (r0 > r1) {
    t *= r0;
  } else {
    t *= r1;
  }
  if (t < 1) {
    n = 3;
  } else {
    n = (int)(M_PI / acos(1 - 0.1 / t));
    if (n < 3) {
      n = 3;
    } else if (n > 200) {
      n = 200;
    }
  }

  // setup for the start circle
  ia = 0;
  sa = sMin;
  ta = t0 + sa * (t1 - t0);
  xa = x0 + sa * (x1 - x0);
  ya = y0 + sa * (y1 - y0);
  ra = r0 + sa * (r1 - r0);
  if (ta < t0) {
    shading->getColor(t0, &colorA);
  } else if (ta > t1) {
    shading->getColor(t1, &colorA);
  } else {
    shading->getColor(ta, &colorA);
  }

  // fill the circles
  while (ia < radialMaxSplits) {