Collision Mesh¶

class CollisionMesh¶

A class for encapsolating the transformation/selections needed to go from a volumetric FE mesh to a surface collision mesh.

Public Functions

CollisionMesh() = default¶

Construct a new Collision Mesh object.

Collision Mesh objects are immutable, so use the other constructors.

CollisionMesh(const Eigen::MatrixXd& rest_positions,
    const Eigen::MatrixXi& edges = Eigen::MatrixXi(),
    const Eigen::MatrixXi& faces = Eigen::MatrixXi(),
    const Eigen::SparseMatrix<double>& displacement_map
    = Eigen::SparseMatrix<double>())¶

Construct a new Collision Mesh object directly from the collision mesh vertices.

Parameters:¶

const Eigen::MatrixXd &rest_positions¶

The vertices of the collision mesh at rest (#V × dim).

const Eigen::MatrixXi &edges = Eigen::MatrixXi()¶

The edges of the collision mesh (#E × 2).

const Eigen::MatrixXi &faces = Eigen::MatrixXi()¶

The faces of the collision mesh (#F × 3).

const Eigen::SparseMatrix<double> &displacement_map = Eigen::SparseMatrix<double>()¶

The displacement mapping from displacements on the full mesh to the collision mesh.

CollisionMesh(const std::vector<bool>& include_vertex,
    const Eigen::MatrixXd& full_rest_positions,
    const Eigen::MatrixXi& edges = Eigen::MatrixXi(),
    const Eigen::MatrixXi& faces = Eigen::MatrixXi(),
    const Eigen::SparseMatrix<double>& displacement_map
    = Eigen::SparseMatrix<double>())¶

Construct a new Collision Mesh object from a full mesh vertices.

Parameters:¶

const std::vector<bool> &include_vertex¶

Vector of bools indicating whether each vertex should be included in the collision mesh.

const Eigen::MatrixXd &full_rest_positions¶

The vertices of the full mesh at rest (#V × dim).

const Eigen::MatrixXi &edges = Eigen::MatrixXi()¶

The edges of the collision mesh indexed into the full mesh vertices (#E × 2).

const Eigen::MatrixXi &faces = Eigen::MatrixXi()¶

The faces of the collision mesh indexed into the full mesh vertices (#F × 3).

const Eigen::SparseMatrix<double> &displacement_map = Eigen::SparseMatrix<double>()¶

The displacement mapping from displacements on the full mesh to the collision mesh.

void init_adjacencies()¶

Initialize vertex-vertex and edge-vertex adjacencies.

void init_area_jacobians()¶

Initialize vertex and edge areas.

~CollisionMesh() = default¶

Destroy the Collision Mesh object.

inline size_t num_vertices() const¶

Get the number of vertices in the collision mesh.

inline size_t num_codim_vertices() const¶

Get the number of codimensional vertices in the collision mesh.

inline size_t num_codim_edges() const¶

Get the number of codimensional edges in the collision mesh.

inline size_t num_edges() const¶

Get the number of edges in the collision mesh.

inline size_t num_faces() const¶

Get the number of faces in the collision mesh.

inline size_t dim() const¶

Get the dimension of the mesh.

inline size_t ndof() const¶

Get the number of degrees of freedom in the collision mesh.

inline size_t full_num_vertices() const¶

Get the number of vertices in the full mesh.

inline size_t full_ndof() const¶

Get the number of degrees of freedom in the full mesh.

inline const Eigen::MatrixXd& rest_positions() const¶

Get the vertices of the collision mesh at rest (#V × dim).

inline const Eigen::VectorXi& codim_vertices() const¶

Get the indices of codimensional vertices of the collision mesh (#CV x 1).

inline const Eigen::VectorXi& codim_edges() const¶

Get the indices of codimensional edges of the collision mesh (#CE x 1).

inline const Eigen::MatrixXi& edges() const¶

Get the edges of the collision mesh (#E × 2).

inline const Eigen::MatrixXi& faces() const¶

Get the faces of the collision mesh (#F × 3).

inline const Eigen::MatrixXi& faces_to_edges() const¶

Get the mapping from faces to edges of the collision mesh (#F × 3).

Eigen::MatrixXd vertices(
    const Eigen::MatrixXd& full_positions) const¶

Compute the vertex positions from the positions of the full mesh.

Parameters:¶

const Eigen::MatrixXd &full_positions¶

The vertex positions of the full mesh (#FV × dim).

Returns:¶

The vertex positions of the collision mesh (#V × dim).

Eigen::MatrixXd displace_vertices(
    const Eigen::MatrixXd& full_displacements) const¶

Compute the vertex positions from vertex displacements on the full mesh.

Parameters:¶

const Eigen::MatrixXd &full_displacements¶

The vertex displacements on the full mesh (#FV × dim).

Returns:¶

The vertex positions of the collision mesh (#V × dim).

Eigen::MatrixXd map_displacements(
    const Eigen::MatrixXd& full_displacements) const¶

Map vertex displacements on the full mesh to vertex displacements on the collision mesh.

Parameters:¶

const Eigen::MatrixXd &full_displacements¶

The vertex displacements on the full mesh (#FV × dim).

Returns:¶

The vertex displacements on the collision mesh (#V × dim).

inline size_t to_full_vertex_id(const size_t id) const¶

Map a vertex ID to the corresponding vertex ID in the full mesh.

Parameters:¶

const size_t id¶

Vertex ID in the collision mesh.

Returns:¶

Vertex ID in the full mesh.

Eigen::VectorXd to_full_dof(const Eigen::VectorXd& x) const¶

Map a vector quantity on the collision mesh to the full mesh.

This is useful for mapping gradients from the collision mesh to the full mesh (i.e., applies the chain-rule).

Parameters:¶

const Eigen::VectorXd &x¶

Vector quantity on the collision mesh with size equal to ndof().

Returns:¶

Vector quantity on the full mesh with size equal to full_ndof().

Eigen::SparseMatrix<double> to_full_dof(
    const Eigen::SparseMatrix<double>& X) const¶

Map a matrix quantity on the collision mesh to the full mesh.

This is useful for mapping Hessians from the collision mesh to the full mesh (i.e., applies the chain-rule).

Parameters:¶

const Eigen::SparseMatrix<double> &X¶

Matrix quantity on the collision mesh with size equal to ndof() × ndof().

Returns:¶

Matrix quantity on the full mesh with size equal to full_ndof() × full_ndof().

inline const std::vector<unordered_set<int>>&
vertex_vertex_adjacencies() const¶

Get the vertex-vertex adjacency matrix.

inline const std::vector<unordered_set<int>>&
vertex_edge_adjacencies() const¶

Get the vertex-edge adjacency matrix.

inline const std::vector<unordered_set<int>>&
edge_vertex_adjacencies() const¶

Get the edge-vertex adjacency matrix.

inline bool are_adjacencies_initialized() const¶

Determine if the adjacencies have been initialized by calling init_adjacencies().

inline bool is_vertex_on_boundary(const int vi) const¶

Is a vertex on the boundary of the collision mesh?

Parameters:¶

const int vi¶

Vertex ID.

Returns:¶

True if the vertex is on the boundary of the collision mesh.

inline double vertex_area(const size_t vi) const¶

Get the barycentric area of a vertex.

Parameters:¶

const size_t vi¶

Vertex ID.

Returns:¶

Barycentric area of vertex vi.

inline const Eigen::VectorXd& vertex_areas() const¶

Get the barycentric area of the vertices.

inline const Eigen::SparseVector<double>& vertex_area_gradient(
    const size_t vi) const¶

Get the gradient of the barycentric area of a vertex wrt the rest positions of all points.

Parameters:¶

const size_t vi¶

Vertex ID.

Returns:¶

Gradient of the barycentric area of vertex vi wrt the rest positions of all points.

inline double edge_area(const size_t ei) const¶

Get the barycentric area of an edge.

Parameters:¶

const size_t ei¶

Edge ID.

Returns:¶

Barycentric area of edge ei.

inline const Eigen::VectorXd& edge_areas() const¶

Get the barycentric area of the edges.

inline const Eigen::SparseVector<double>& edge_area_gradient(
    const size_t ei) const¶

Get the gradient of the barycentric area of an edge wrt the rest positions of all points.

Parameters:¶

const size_t ei¶

Edge ID.

Returns:¶

Gradient of the barycentric area of edge ei wrt the rest positions of all points.

inline bool are_area_jacobians_initialized() const¶

Determine if the area Jacobians have been initialized by calling init_area_jacobians().

Public Members

std::function<bool(size_t, size_t)> can_collide
    = default_can_collide¶

A function that takes two vertex IDs and returns true if the vertices (and faces or edges containing the vertices) can collide.

By default all primitives can collide with all other primitives.

Public Static Functions

static inline CollisionMesh build_from_full_mesh(
    const Eigen::MatrixXd& full_rest_positions,
    const Eigen::MatrixXi& edges,
    const Eigen::MatrixXi& faces = Eigen::MatrixXi())¶

Helper function that automatically builds include_vertex using construct_is_on_surface.

Parameters:¶

const Eigen::MatrixXd &full_rest_positions¶

The full vertices at rest (#FV × dim).

const Eigen::MatrixXi &edges¶

The edge matrix of mesh (#E × 2).

const Eigen::MatrixXi &faces = Eigen::MatrixXi()¶

The face matrix of mesh (#F × 3).

Returns:¶

Constructed CollisionMesh.

static std::vector<bool> construct_is_on_surface(
    const long num_vertices, const Eigen::MatrixXi& edges,
    const Eigen::VectorXi& codim_vertices = Eigen::VectorXi())¶

Construct a vector of bools indicating whether each vertex is on the surface.

Parameters:¶

const long num_vertices¶

The number of vertices in the mesh.

const Eigen::MatrixXi &edges¶

The surface edges of the mesh (#E × 2).

const Eigen::VectorXi &codim_vertices = Eigen::VectorXi()¶

The indices of codimensional vertices (#CV x 1).

Returns:¶

A vector of bools indicating whether each vertex is on the surface.

static Eigen::MatrixXi construct_faces_to_edges(
    const Eigen::MatrixXi& faces, const Eigen::MatrixXi& edges)¶

Construct a matrix that maps from the faces’ edges to rows in the edges matrix.

Parameters:¶

const Eigen::MatrixXi &faces¶

The face matrix of mesh (#F × 3).

const Eigen::MatrixXi &edges¶

The edge matrix of mesh (#E × 2).

Returns:¶

Matrix that maps from the faces’ edges to rows in the edges matrix.

Protected Functions

void init_codim_vertices()¶

void init_codim_edges()¶

void init_selection_matrices(const int dim)¶

Initialize the selection matrix from full vertices/DOF to collision vertices/DOF.

void init_areas()¶

Initialize vertex and edge areas.

Protected Attributes

Eigen::MatrixXd m_full_rest_positions¶

The full vertex positions at rest (#FV × dim).

Eigen::MatrixXd m_rest_positions¶

The vertex positions at rest (#V × dim).

Eigen::VectorXi m_codim_vertices¶

The indices of codimensional vertices (#CV x 1).

Eigen::VectorXi m_codim_edges¶

The indices of codimensional edges (#CE x 1).

Eigen::MatrixXi m_edges¶

Edges as rows of indicies into vertices (#E × 2).

Eigen::MatrixXi m_faces¶

Triangular faces as rows of indicies into vertices (#F × 3).

Eigen::MatrixXi m_faces_to_edges¶

Map from faces edges to rows of edges (#F × 3).

Eigen::VectorXi m_full_vertex_to_vertex¶

Map from full vertices to collision vertices.

Note

Negative values indicate full vertex is dropped.

Eigen::VectorXi m_vertex_to_full_vertex¶

Map from collision vertices to full vertices.

Eigen::SparseMatrix<double> m_select_vertices¶

Selection matrix S ∈ ℝ^{collision×full} for vertices.

Eigen::SparseMatrix<double> m_select_dof¶

Selection matrix S ∈ ℝ^{(dim*collision)×(dim*full)} for DOF.

Eigen::SparseMatrix<double> m_displacement_map¶

Mapping from full displacements to collision displacements.

Note

this is premultiplied by m_select_vertices

Eigen::SparseMatrix<double> m_displacement_dof_map¶

Mapping from full displacements DOF to collision displacements DOF.

Note

this is premultiplied by m_select_dof

std::vector<unordered_set<int>> m_vertex_vertex_adjacencies¶

Vertices adjacent to vertices.

std::vector<unordered_set<int>> m_vertex_edge_adjacencies¶

Edges adjacent to vertices.

std::vector<unordered_set<int>> m_edge_vertex_adjacencies¶

Vertices adjacent to edges.

std::vector<bool> m_is_vertex_on_boundary¶

Is vertex on the boundary of the triangle mesh in 3D or polyline in 2D?

Eigen::VectorXd m_vertex_areas¶

Vertex areas 2D: 1/2 sum of length of connected edges 3D: 1/3 sum of area of connected triangles.

Eigen::VectorXd m_edge_areas¶

Edge areas 3D: 1/3 sum of area of connected triangles.

std::vector<Eigen::SparseVector<double>> m_vertex_area_jacobian¶

The rows of the Jacobian of the vertex areas vector.

std::vector<Eigen::SparseVector<double>> m_edge_area_jacobian¶

The rows of the Jacobian of the edge areas vector.

Protected Static Functions

static Eigen::SparseMatrix<double> vertex_matrix_to_dof_matrix(
    const Eigen::SparseMatrix<double>& M_V, int dim)¶

Convert a matrix meant for M_V * vertices to M_dof * x by duplicating the entries dim times.

Private Static Functions

static inline int default_can_collide(size_t, size_t)¶

By default all primitives can collide with all other primitives.