template<class T>
class drake::geometry::VolumeMesh< T >
VolumeMesh represents a tetrahedral volume mesh.
- Template Parameters
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| T | The underlying scalar type for coordinates, e.g., double or AutoDiffXd. Must be a valid Eigen scalar. |
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A collection of type traits to enable mesh consumers to be templated on mesh type.
Each mesh type provides specific definitions of vertex, element, and barycentric coordinates. For VolumeMesh, an element is a tetrahedron.
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| using | ScalarType = T |
| template<typename U = T> |
| using | Barycentric = Vector<U, kVertexPerElement> |
| | Type of barycentric coordinates on a tetrahedral element.
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| static constexpr int | kVertexPerElement = 4 |
| | Number of vertices per element.
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| class | VolumeMeshTester< T > |
| | VolumeMesh (std::vector< VolumeElement > &&elements, std::vector< Vector3< T > > &&vertices) |
| | Constructor from a vector of vertices and from a vector of elements.
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| const VolumeElement & | element (int e) const |
| const Vector3< T > & | vertex (int v) const |
| | Returns the vertex identified by a given index.
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| const Vector3< T > & | inward_normal (int e, int f) const |
| | Returns the inward facing normal of face f of element e.
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| const Vector3< T > & | edge_vector (int e, int a, int b) const |
| | Returns p_AB_M, the position vector from vertex A to vertex B in M, where A and B are specified by the element local indices a and b of element e.
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| const std::vector< Vector3< T > > & | vertices () const |
| const std::vector< VolumeElement > & | tetrahedra () const |
| int | num_elements () const |
| | Returns the number of tetrahedral elements in the mesh.
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| int | num_vertices () const |
| | Returns the number of vertices in the mesh.
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| T | CalcTetrahedronVolume (int e) const |
| | Calculates volume of a tetrahedral element.
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| T | CalcVolume () const |
| | Calculates the volume of this mesh by taking the sum of the volume of each tetrahedral element.
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| template<typename C> |
| Barycentric< promoted_numerical_t< T, C > > | CalcBarycentric (const Vector3< C > &p_MQ, int e) const |
| | Calculate barycentric coordinates with respect to the tetrahedron e of the point Q.
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| bool | Equal (const VolumeMesh< T > &mesh, double vertex_tolerance=0) const |
| | Checks to see whether the given VolumeMesh object is equal via deep comparison (up to a tolerance).
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| template<typename FieldValue> |
| std::optional< Vector3< promoted_numerical_t< T, FieldValue > > > | MaybeCalcGradientVectorOfLinearField (const std::array< FieldValue, 4 > &field_value, int e) const |
| | Calculates the gradient ∇u of a linear field u on the tetrahedron e.
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| template<typename FieldValue> |
| Vector3< promoted_numerical_t< T, FieldValue > > | CalcGradientVectorOfLinearField (const std::array< FieldValue, 4 > &field_value, int e) const |
| | Like MaybeCalcGradientVectorOfLinearField, but throws if the geometry is degenerate.
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| void | TransformVertices (const math::RigidTransform< T > &transform) |
| | Transforms the vertices of this mesh from its initial frame M to the new frame N.
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| void | SetAllPositions (const Eigen::Ref< const VectorX< T > > &p_MVs) |
| | Updates the position of all vertices in the mesh.
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template<class T>
template<typename U = T>
Type of barycentric coordinates on a tetrahedral element.
Barycentric coordinates (b₀, b₁, b₂, b₃) satisfy b₀ + b₁ + b₂ + b₃ = 1. It corresponds to a position in the space. If all bᵢ >= 0, it corresponds to a position inside the tetrahedron or on the faces of the tetrahedron. If some bᵢ < 0, it corresponds to a position outside the tetrahedron. Technically we could calculate one of the bᵢ from the others; however, there is no standard way to omit one of the coordinates.
template<class T>
template<typename FieldValue>
| std::optional< Vector3< promoted_numerical_t< T, FieldValue > > > MaybeCalcGradientVectorOfLinearField |
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const std::array< FieldValue, 4 > & | field_value, |
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int | e ) const |
Calculates the gradient ∇u of a linear field u on the tetrahedron e.
Field u is defined by the four field values field_value[i] at the i-th vertex of the tetrahedron. The gradient ∇u is expressed in the coordinates frame of this mesh M.
If the return value is std::nullopt, the tetrahedron is degenerate, and no reliable gradient could be computed.
The return type depends on both the mesh's vertex position scalar type T and the given field's scalar type FieldValue. See promoted_numerical_t for details.
template<class T>
| void SetAllPositions |
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const Eigen::Ref< const VectorX< T > > & | p_MVs | ) |
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Updates the position of all vertices in the mesh.
Each sequential triple in p_MVs (e.g., 3i, 3i + 1, 3i + 2), i ∈ ℤ, is interpreted as a position vector associated with the iᵗʰ vertex. The position values are interpreted to be measured and expressed in the same frame as the mesh to be deformed.
- Parameters
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| p_MVs | Vertex positions for the mesh's N vertices flattened into a vector (where each position vector is measured and expressed in the mesh's original frame). |
- Exceptions
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