height_map.cc

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#include <towr/terrain/height_map.h>
#include <towr/terrain/examples/height_map_examples.h>

#include <cmath>

namespace towr {

HeightMap::Ptr
HeightMap::MakeTerrain (TerrainID type)
{
  switch (type) {
    case FlatID:      return std::make_shared<FlatGround>(); break;
    case BlockID:     return std::make_shared<Block>(); break;
    case StairsID:    return std::make_shared<Stairs>(); break;
    case GapID:       return std::make_shared<Gap>(); break;
    case SlopeID:     return std::make_shared<Slope>(); break;
    case ChimneyID:   return std::make_shared<Chimney>(); break;
    case ChimneyLRID: return std::make_shared<ChimneyLR>(); break;
    default: assert(false); break;
  }
}

double
HeightMap::GetDerivativeOfHeightWrt (Dim2D dim, double x, double y) const
{
  switch (dim) {
    case X: return GetHeightDerivWrtX(x,y);
    case Y: return GetHeightDerivWrtY(x,y);
    default: assert(false); // derivative dimension not implemented
  }
}

HeightMap::Vector3d
HeightMap::GetNormalizedBasis (Direction basis, double x, double y) const
{
  return GetBasis(basis, x, y).normalized();
}

HeightMap::Vector3d
HeightMap::GetBasis (Direction basis, double x, double y,
                                  const DimDerivs& deriv) const
{
  switch (basis) {
    case Normal:   return GetNormal(x,y, deriv);
    case Tangent1: return GetTangent1(x,y, deriv);
    case Tangent2: return GetTangent2(x,y, deriv);
    default: assert(false); // basis does not exist
  }
}

HeightMap::Vector3d
HeightMap::GetDerivativeOfNormalizedBasisWrt (Direction basis, Dim2D dim,
                                              double x, double y) const
{
  // inner derivative
  Vector3d dv_wrt_dim = GetBasis(basis, x, y, {dim});

  // outer derivative
  Vector3d v = GetBasis(basis, x,y, {});
  Vector3d dn_norm_wrt_n = GetDerivativeOfNormalizedVectorWrtNonNormalizedIndex(v, dim);
  return dn_norm_wrt_n.cwiseProduct(dv_wrt_dim);
}

HeightMap::Vector3d
HeightMap::GetNormal(double x, double y, const DimDerivs& deriv) const
{
  Vector3d n;

  bool basis_requested = deriv.empty();

  for (auto dim : {X_,Y_}) {
    if (basis_requested)
      n(dim) = -GetDerivativeOfHeightWrt(dim, x, y);
    else
      n(dim) = -GetSecondDerivativeOfHeightWrt(dim, deriv.front(), x, y);
  }

  n(Z) = basis_requested? 1.0 : 0.0;

  return n;
}

HeightMap::Vector3d
HeightMap::GetTangent1 (double x, double y, const DimDerivs& deriv) const
{
  Vector3d tx;

  bool basis_requested = deriv.empty();

  tx(X) = basis_requested? 1.0 : 0.0;
  tx(Y) = 0.0;
  tx(Z) = basis_requested? GetDerivativeOfHeightWrt(X_, x, y)
                         : GetSecondDerivativeOfHeightWrt(X_, deriv.front(), x, y);

  return tx;
}

HeightMap::Vector3d
HeightMap::GetTangent2 (double x, double y, const DimDerivs& deriv) const
{
  Vector3d ty;

  bool basis_requested = deriv.empty();

  ty(X) = 0.0;
  ty(Y) = basis_requested? 1.0 : 0.0;
  ty(Z) = basis_requested? GetDerivativeOfHeightWrt(Y_, x,y)
                         : GetSecondDerivativeOfHeightWrt(Y_, deriv.front(), x, y);
  return ty;
}

HeightMap::Vector3d
HeightMap::GetDerivativeOfNormalizedVectorWrtNonNormalizedIndex (
    const Vector3d& v, int idx) const
{
  // see notebook or
  // http://blog.mmacklin.com/2012/05/
  return 1/v.squaredNorm()*(v.norm() * Vector3d::Unit(idx) - v(idx)*v.normalized());
}

double
HeightMap::GetSecondDerivativeOfHeightWrt (Dim2D dim1, Dim2D dim2,
                                           double x, double y) const
{
  if (dim1 == X_) {
    if (dim2 == X_) return GetHeightDerivWrtXX(x,y);
    if (dim2 == Y_) return GetHeightDerivWrtXY(x,y);
  } else {
    if (dim2 == X_) return GetHeightDerivWrtYX(x,y);
    if (dim2 == Y_) return GetHeightDerivWrtYY(x,y);
  }

  assert(false); // second derivative not specified.
}

} /* namespace towr */