height_map.cc
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29 
32 
33 #include <cmath>
34 
35 namespace towr {
36 
39 {
40  switch (type) {
41  case FlatID: return std::make_shared<FlatGround>(); break;
42  case BlockID: return std::make_shared<Block>(); break;
43  case StairsID: return std::make_shared<Stairs>(); break;
44  case GapID: return std::make_shared<Gap>(); break;
45  case SlopeID: return std::make_shared<Slope>(); break;
46  case ChimneyID: return std::make_shared<Chimney>(); break;
47  case ChimneyLRID: return std::make_shared<ChimneyLR>(); break;
48  default: assert(false); break;
49  }
50 }
51 
52 double
53 HeightMap::GetDerivativeOfHeightWrt (Dim2D dim, double x, double y) const
54 {
55  switch (dim) {
56  case X: return GetHeightDerivWrtX(x,y);
57  case Y: return GetHeightDerivWrtY(x,y);
58  default: assert(false); // derivative dimension not implemented
59  }
60 }
61 
63 HeightMap::GetNormalizedBasis (Direction basis, double x, double y) const
64 {
65  return GetBasis(basis, x, y).normalized();
66 }
67 
69 HeightMap::GetBasis (Direction basis, double x, double y,
70  const DimDerivs& deriv) const
71 {
72  switch (basis) {
73  case Normal: return GetNormal(x,y, deriv);
74  case Tangent1: return GetTangent1(x,y, deriv);
75  case Tangent2: return GetTangent2(x,y, deriv);
76  default: assert(false); // basis does not exist
77  }
78 }
79 
82  double x, double y) const
83 {
84  // inner derivative
85  Vector3d dv_wrt_dim = GetBasis(basis, x, y, {dim});
86 
87  // outer derivative
88  Vector3d v = GetBasis(basis, x,y, {});
90  return dn_norm_wrt_n.cwiseProduct(dv_wrt_dim);
91 }
92 
94 HeightMap::GetNormal(double x, double y, const DimDerivs& deriv) const
95 {
96  Vector3d n;
97 
98  bool basis_requested = deriv.empty();
99 
100  for (auto dim : {X_,Y_}) {
101  if (basis_requested)
102  n(dim) = -GetDerivativeOfHeightWrt(dim, x, y);
103  else
104  n(dim) = -GetSecondDerivativeOfHeightWrt(dim, deriv.front(), x, y);
105  }
106 
107  n(Z) = basis_requested? 1.0 : 0.0;
108 
109  return n;
110 }
111 
113 HeightMap::GetTangent1 (double x, double y, const DimDerivs& deriv) const
114 {
115  Vector3d tx;
116 
117  bool basis_requested = deriv.empty();
118 
119  tx(X) = basis_requested? 1.0 : 0.0;
120  tx(Y) = 0.0;
121  tx(Z) = basis_requested? GetDerivativeOfHeightWrt(X_, x, y)
122  : GetSecondDerivativeOfHeightWrt(X_, deriv.front(), x, y);
123 
124  return tx;
125 }
126 
128 HeightMap::GetTangent2 (double x, double y, const DimDerivs& deriv) const
129 {
130  Vector3d ty;
131 
132  bool basis_requested = deriv.empty();
133 
134  ty(X) = 0.0;
135  ty(Y) = basis_requested? 1.0 : 0.0;
136  ty(Z) = basis_requested? GetDerivativeOfHeightWrt(Y_, x,y)
137  : GetSecondDerivativeOfHeightWrt(Y_, deriv.front(), x, y);
138  return ty;
139 }
140 
143  const Vector3d& v, int idx) const
144 {
145  // see notebook or
146  // http://blog.mmacklin.com/2012/05/
147  return 1/v.squaredNorm()*(v.norm() * Vector3d::Unit(idx) - v(idx)*v.normalized());
148 }
149 
150 double
152  double x, double y) const
153 {
154  if (dim1 == X_) {
155  if (dim2 == X_) return GetHeightDerivWrtXX(x,y);
156  if (dim2 == Y_) return GetHeightDerivWrtXY(x,y);
157  } else {
158  if (dim2 == X_) return GetHeightDerivWrtYX(x,y);
159  if (dim2 == Y_) return GetHeightDerivWrtYY(x,y);
160  }
161 
162  assert(false); // second derivative not specified.
163 }
164 
165 } /* namespace towr */
TerrainID
Terrains IDs corresponding for factory method.
Definition: height_map.h:79
Vector3d GetDerivativeOfNormalizedBasisWrt(Direction direction, Dim2D dim, double x, double y) const
How the terrain normal/tangent vectors change when moving in x or y.
Definition: height_map.cc:81
Vector3d GetTangent1(double x, double y, const DimDerivs &={}) const
Definition: height_map.cc:113
double GetSecondDerivativeOfHeightWrt(Dim2D dim1, Dim2D dim2, double x, double y) const
Definition: height_map.cc:151
Vector3d GetNormal(double x, double y, const DimDerivs &={}) const
Definition: height_map.cc:94
static HeightMap::Ptr MakeTerrain(TerrainID type)
Definition: height_map.cc:38
virtual double GetHeightDerivWrtXY(double x, double y) const
Definition: height_map.h:168
Vector3d GetNormalizedBasis(Direction direction, double x, double y) const
Returns either the vector normal or tangent to the terrain patch.
Definition: height_map.cc:63
Eigen::Vector3d Vector3d
Definition: height_map.h:74
virtual double GetHeightDerivWrtY(double x, double y) const
Definition: height_map.h:164
std::vector< Dim2D > DimDerivs
dimensional derivatives
Definition: height_map.h:139
virtual double GetHeightDerivWrtXX(double x, double y) const
Definition: height_map.h:167
virtual double GetHeightDerivWrtX(double x, double y) const
Definition: height_map.h:163
double GetDerivativeOfHeightWrt(Dim2D dim, double x, double y) const
How the height value changes at a 2D position in direction dim.
Definition: height_map.cc:53
Vector3d GetDerivativeOfNormalizedVectorWrtNonNormalizedIndex(const Vector3d &non_normalized, int index) const
Definition: height_map.cc:142
virtual double GetHeightDerivWrtYY(double x, double y) const
Definition: height_map.h:170
virtual double GetHeightDerivWrtYX(double x, double y) const
Definition: height_map.h:169
Vector3d GetBasis(Direction direction, double x, double y, const DimDerivs &dim_deriv={}) const
returns either the terrain normal/tangent or its derivative.
Definition: height_map.cc:69
std::shared_ptr< HeightMap > Ptr
Definition: height_map.h:73
Vector3d GetTangent2(double x, double y, const DimDerivs &={}) const
Definition: height_map.cc:128


towr
Author(s): Alexander W. Winkler
autogenerated on Mon Feb 28 2022 23:54:22