Function SmoothGeneric

libs/geometry/smoothing.cpp:11–45

double constexpr kEps = 1e-5;

void SmoothGeneric(m2::PointD const & pt0, m2::PointD const & pt1, m2::PointD const & pt2, m2::PointD const & pt3,
                   double alpha, size_t pointsCount, std::vector<m2::PointD> & path)
{
  if (pt0.EqualDxDy(pt1, kEps) || pt1.EqualDxDy(pt2, kEps) || pt2.EqualDxDy(pt3, kEps))
    return;

  auto const calcNextT = [alpha](double prevT, m2::PointD const & prevP, m2::PointD const & nextP)
  {
    auto const dx = nextP.x - prevP.x;
    auto const dy = nextP.y - prevP.y;
    return pow(dx * dx + dy * dy, alpha * 0.5) + prevT;
  };

  double const t0 = 0.0;
  double const t1 = calcNextT(t0, pt0, pt1);
  double const t2 = calcNextT(t1, pt1, pt2);
  double const t3 = calcNextT(t2, pt2, pt3);

  size_t partsCount = pointsCount + 1;
  for (size_t i = 1; i < partsCount; ++i)
  {
    double const t = t1 + (t2 - t1) * i / partsCount;

    auto const a1 = pt0 * (t1 - t) / (t1 - t0) + pt1 * (t - t0) / (t1 - t0);
    auto const a2 = pt1 * (t2 - t) / (t2 - t1) + pt2 * (t - t1) / (t2 - t1);
    auto const a3 = pt2 * (t3 - t) / (t3 - t2) + pt3 * (t - t2) / (t3 - t2);

    auto const b1 = a1 * (t2 - t) / (t2 - t0) + a2 * (t - t0) / (t2 - t0);
    auto const b2 = a2 * (t3 - t) / (t3 - t1) + a3 * (t - t1) / (t3 - t1);

    auto const pt = b1 * (t2 - t) / (t2 - t1) + b2 * (t - t1) / (t2 - t1);
    if (!path.back().EqualDxDy(pt, kEps) && !pt2.EqualDxDy(pt, kEps))
      path.push_back(pt);
  }
}

// The same as SmoothGeneric but optimized for alpha == 0.0.
void SmoothUniform(m2::PointD const & pt0, m2::PointD const & pt1, m2::PointD const & pt2, m2::PointD const & pt3,