Candidates¶

class Candidates;¶

Public Functions¶

Candidates() = default;¶

void build(const CollisionMesh& mesh, const Eigen::MatrixXd& vertices, const double inflation_radius = 0, const BroadPhaseMethod broad_phase_method = DEFAULT_BROAD_PHASE_METHOD);¶

Initialize the set of discrete collision detection candidates.

Parameters:¶

const CollisionMesh &mesh¶: The surface of the collision mesh.
const Eigen::MatrixXd &vertices¶: Surface vertex positions (rowwise).
const double inflation_radius = 0¶: Amount to inflate the bounding boxes.
const BroadPhaseMethod broad_phase_method = DEFAULT_BROAD_PHASE_METHOD ¶: Broad phase method to use.

void build(const CollisionMesh& mesh, const Eigen::MatrixXd& vertices_t0, const Eigen::MatrixXd& vertices_t1, const double inflation_radius = 0, const BroadPhaseMethod broad_phase_method = DEFAULT_BROAD_PHASE_METHOD);¶

Initialize the set of continuous collision detection candidates.

Note

Assumes the trajectory is linear.

Parameters:¶

const CollisionMesh &mesh¶: The surface of the collision mesh.
const Eigen::MatrixXd &vertices_t0¶: Surface vertex starting positions (rowwise).
const Eigen::MatrixXd &vertices_t1¶: Surface vertex ending positions (rowwise).
const double inflation_radius = 0¶: Amount to inflate the bounding boxes.
const BroadPhaseMethod broad_phase_method = DEFAULT_BROAD_PHASE_METHOD ¶: Broad phase method to use.

size_t size() const;¶

bool empty() const;¶

void clear();¶

ContinuousCollisionCandidate& operator[](size_t i);¶

const ContinuousCollisionCandidate& operator[](size_t i) const;¶

bool is_step_collision_free(const CollisionMesh& mesh, const Eigen::MatrixXd& vertices_t0, const Eigen::MatrixXd& vertices_t1, const double min_distance = 0.0, const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const;¶

Determine if the step is collision free from the set of candidates.

Note

Assumes the trajectory is linear.

Parameters:¶

const CollisionMesh &mesh¶: The collision mesh.
const Eigen::MatrixXd &vertices_t0¶: Surface vertex starting positions (rowwise).
const Eigen::MatrixXd &vertices_t1¶: Surface vertex ending positions (rowwise).
const double min_distance = 0.0¶: The minimum distance allowable between any two elements.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: The narrow phase CCD algorithm to use.

Returns:¶

True if any collisions occur.

double compute_collision_free_stepsize(const CollisionMesh& mesh, const Eigen::MatrixXd& vertices_t0, const Eigen::MatrixXd& vertices_t1, const double min_distance = 0.0, const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const;¶

Computes a maximal step size that is collision free using the set of collision candidates.

Note

Assumes the trajectory is linear.

Parameters:¶

const CollisionMesh &mesh¶: The collision mesh.
const Eigen::MatrixXd &vertices_t0¶: Surface vertex starting positions (rowwise). Assumed to be intersection free.
const Eigen::MatrixXd &vertices_t1¶: Surface vertex ending positions (rowwise).
const double min_distance = 0.0¶: The minimum distance allowable between any two elements.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: The narrow phase CCD algorithm to use.

Returns:¶

A step-size \(\in [0, 1]\) that is collision free. A value of 1.0 if a full step and 0.0 is no step.

double compute_noncandidate_conservative_stepsize( const CollisionMesh& mesh, const Eigen::MatrixXd& displacements, const double dhat) const;¶

Computes a conservative bound on the largest-feasible step size for surface primitives not in collision.

Parameters:¶

const CollisionMesh &mesh¶: The collision mesh.
const Eigen::MatrixXd &displacements¶: Surface vertex displacements (rowwise).
const double dhat¶: Barrier activation distance.

double compute_cfl_stepsize(const CollisionMesh& mesh, const Eigen::MatrixXd& vertices_t0, const Eigen::MatrixXd& vertices_t1, const double dhat, const BroadPhaseMethod broad_phase_method = DEFAULT_BROAD_PHASE_METHOD, const double min_distance = 0.0, const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const;¶

Computes a CFL-inspired CCD maximum step step size.

Parameters:¶

const CollisionMesh &mesh¶: The collision mesh.
const Eigen::MatrixXd &vertices_t0¶: Surface vertex starting positions (rowwise).
const Eigen::MatrixXd &vertices_t1¶: Surface vertex ending positions (rowwise).
const double dhat¶: Barrier activation distance.
const double min_distance = 0.0¶: The minimum distance allowable between any two elements.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: The narrow phase CCD algorithm to use.

bool save_obj(const std::string& filename, const Eigen::MatrixXd& vertices, const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const;¶

Public Members¶

std::vector<VertexVertexCandidate> vv_candidates;¶

std::vector<EdgeVertexCandidate> ev_candidates;¶

std::vector<EdgeEdgeCandidate> ee_candidates;¶

std::vector<FaceVertexCandidate> fv_candidates;¶

Collision Stencil¶

class CollisionStencil;¶

A stencil representing a collision between at most four vertices.

Subclassed by ipc::Collision, ipc::ContinuousCollisionCandidate, ipc::FrictionCollision

Public Functions¶

virtual ~CollisionStencil() = default;¶

virtual int num_vertices() const = 0;¶: Get the number of vertices in the collision stencil.

inline int dim(const int ndof) const;¶

Get the dimension of the collision stencil.

Parameters:¶

const int ndof¶: Number of degrees of freedom in the stencil.

Returns:¶

The dimension of the collision stencil.

virtual std::array<long, 4> vertex_ids(const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const = 0;¶

Get the vertex IDs of the collision stencil.

Parameters:¶

const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

The vertex IDs of the collision stencil. Size is always 4, but elements i > num_vertices() are -1.

template <typename T> inline std::array<VectorMax3<T>, 4> vertices( const MatrixX<T>& vertices, const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const;¶

Get the vertex attributes of the collision stencil.

Template Parameters:¶

typename T¶: Type of the attributes

Parameters:¶

const MatrixX<T> &vertices¶: Vertex attributes
const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

The vertex positions of the collision stencil. Size is always 4, but elements i > num_vertices() are NaN.

template <typename T> inline VectorMax12<T> dof(const MatrixX<T>& X, const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const;¶

Select this stencil’s DOF from the full matrix of DOF.

Template Parameters:¶

typename T¶: Type of the DOF

Parameters:¶

const MatrixX<T> &X¶: Full matrix of DOF (rowwise).
const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

This stencil’s DOF.

virtual double compute_distance(const VectorMax12d& positions) const = 0;¶

Compute the distance of the stencil.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance of the stencil.

virtual VectorMax12d compute_distance_gradient( const VectorMax12d& positions) const = 0;¶

Compute the distance gradient of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance gradient of the stencil w.r.t. the stencil’s vertex positions.

virtual MatrixMax12d compute_distance_hessian( const VectorMax12d& positions) const = 0;¶

Compute the distance Hessian of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance Hessian of the stencil w.r.t. the stencil’s vertex positions.

Continuous Collision Candidate¶

class ContinuousCollisionCandidate : public virtual ipc::CollisionStencil;¶

Virtual class for candidates that support CCD.

Subclassed by ipc::EdgeEdgeCandidate, ipc::EdgeVertexCandidate, ipc::FaceVertexCandidate, ipc::VertexVertexCandidate

Public Functions¶

virtual ~ContinuousCollisionCandidate() = default;¶

virtual bool ccd(const VectorMax12d& vertices_t0, const VectorMax12d& vertices_t1, double& toi, const double min_distance = 0.0, const double tmax = 1.0, const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const = 0;¶

Perform narrow-phase CCD on the candidate.

Parameters:¶

const VectorMax12d &vertices_t0¶: [in] Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: [in] Stencil vertices at the end of the time step.
double &toi¶: [out] Computed time of impact (normalized).
const double min_distance = 0.0¶: [in] Minimum separation distance between primitives.
const double tmax = 1.0¶: [in] Maximum time (normalized) to look for collisions.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: [in] The narrow phase CCD algorithm to use.

Returns:¶

If the candidate had a collision over the time interval.

std::ostream& write_ccd_query(std::ostream& out, const VectorMax12d& vertices_t0, const VectorMax12d& vertices_t1) const;¶

Write the CCD query to a stream.

Parameters:¶

std::ostream &out¶: Stream to write to.
const VectorMax12d &vertices_t0¶: Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: Stencil vertices at the end of the time step.

Returns:¶

The stream.

Vertex-Vertex Candidate¶

class VertexVertexCandidate : public ipc::ContinuousCollisionCandidate;¶

Subclassed by ipc::VertexVertexCollision, ipc::VertexVertexFrictionCollision

Public Functions¶

VertexVertexCandidate(long vertex0_id, long vertex1_id);¶

inline virtual int num_vertices() const override;¶: Get the number of vertices in the collision stencil.

inline virtual std::array<long, 4> vertex_ids( const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const override;¶

Get the indices of the vertices.

Parameters:¶

const Eigen::MatrixXi &edges¶: edge matrix of mesh
const Eigen::MatrixXi &faces¶: face matrix of mesh

Returns:¶

List of vertex indices

virtual double compute_distance( const VectorMax12d& positions) const override;¶

Compute the distance of the stencil.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance of the stencil.

virtual VectorMax12d compute_distance_gradient( const VectorMax12d& positions) const override;¶

Compute the distance gradient of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance gradient of the stencil w.r.t. the stencil’s vertex positions.

virtual MatrixMax12d compute_distance_hessian( const VectorMax12d& positions) const override;¶

Compute the distance Hessian of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance Hessian of the stencil w.r.t. the stencil’s vertex positions.

Perform narrow-phase CCD on the candidate.

Parameters:¶

const VectorMax12d &vertices_t0¶: [in] Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: [in] Stencil vertices at the end of the time step.
double &toi¶: [out] Computed time of impact (normalized).
const double min_distance = 0.0¶: [in] Minimum separation distance between primitives.
const double tmax = 1.0¶: [in] Maximum time (normalized) to look for collisions.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: [in] The narrow phase CCD algorithm to use.

Returns:¶

If the candidate had a collision over the time interval.

bool operator==(const VertexVertexCandidate& other) const;¶

bool operator!=(const VertexVertexCandidate& other) const;¶

bool operator<(const VertexVertexCandidate& other) const;¶: Compare EdgeVertexCandidates for sorting.

Public Members¶

long vertex0_id;¶: ID of the first vertex.

long vertex1_id;¶: ID of the second vertex.

Friends¶

template <typename H> inline friend H AbslHashValue(H h, const VertexVertexCandidate& vv);¶

Edge-Vertex Candidate¶

class EdgeVertexCandidate : public ipc::ContinuousCollisionCandidate;¶

Subclassed by ipc::EdgeVertexCollision, ipc::EdgeVertexFrictionCollision

Public Functions¶

EdgeVertexCandidate(long edge_id, long vertex_id);¶

inline virtual int num_vertices() const override;¶: Get the number of vertices in the collision stencil.

inline virtual std::array<long, 4> vertex_ids( const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const override;¶

Get the vertex IDs of the collision stencil.

Parameters:¶

const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

The vertex IDs of the collision stencil. Size is always 4, but elements i > num_vertices() are -1.

virtual double compute_distance( const VectorMax12d& positions) const override;¶

Compute the distance of the stencil.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance of the stencil.

virtual VectorMax12d compute_distance_gradient( const VectorMax12d& positions) const override;¶

Compute the distance gradient of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance gradient of the stencil w.r.t. the stencil’s vertex positions.

virtual MatrixMax12d compute_distance_hessian( const VectorMax12d& positions) const override;¶

Compute the distance Hessian of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance Hessian of the stencil w.r.t. the stencil’s vertex positions.

Perform narrow-phase CCD on the candidate.

Parameters:¶

const VectorMax12d &vertices_t0¶: [in] Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: [in] Stencil vertices at the end of the time step.
double &toi¶: [out] Computed time of impact (normalized).
const double min_distance = 0.0¶: [in] Minimum separation distance between primitives.
const double tmax = 1.0¶: [in] Maximum time (normalized) to look for collisions.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: [in] The narrow phase CCD algorithm to use.

Returns:¶

If the candidate had a collision over the time interval.

inline virtual PointEdgeDistanceType known_dtype() const;¶

bool operator==(const EdgeVertexCandidate& other) const;¶

bool operator!=(const EdgeVertexCandidate& other) const;¶

bool operator<(const EdgeVertexCandidate& other) const;¶: Compare EdgeVertexCandidates for sorting.

Public Members¶

long edge_id;¶: ID of the edge.

long vertex_id;¶: ID of the vertex.

Friends¶

template <typename H> inline friend H AbslHashValue(H h, const EdgeVertexCandidate& ev);¶

Edge-Edge Candidate¶

class EdgeEdgeCandidate : public ipc::ContinuousCollisionCandidate;¶

Subclassed by ipc::EdgeEdgeCollision, ipc::EdgeEdgeFrictionCollision

Public Functions¶

EdgeEdgeCandidate(long edge0_id, long edge1_id);¶

inline virtual int num_vertices() const override;¶: Get the number of vertices in the collision stencil.

inline virtual std::array<long, 4> vertex_ids( const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const override;¶

Get the vertex IDs of the collision stencil.

Parameters:¶

const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

The vertex IDs of the collision stencil. Size is always 4, but elements i > num_vertices() are -1.

virtual double compute_distance( const VectorMax12d& positions) const override;¶

Compute the distance of the stencil.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance of the stencil.

virtual VectorMax12d compute_distance_gradient( const VectorMax12d& positions) const override;¶

Compute the distance gradient of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance gradient of the stencil w.r.t. the stencil’s vertex positions.

virtual MatrixMax12d compute_distance_hessian( const VectorMax12d& positions) const override;¶

Compute the distance Hessian of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance Hessian of the stencil w.r.t. the stencil’s vertex positions.

Perform narrow-phase CCD on the candidate.

Parameters:¶

const VectorMax12d &vertices_t0¶: [in] Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: [in] Stencil vertices at the end of the time step.
double &toi¶: [out] Computed time of impact (normalized).
const double min_distance = 0.0¶: [in] Minimum separation distance between primitives.
const double tmax = 1.0¶: [in] Maximum time (normalized) to look for collisions.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: [in] The narrow phase CCD algorithm to use.

Returns:¶

If the candidate had a collision over the time interval.

inline virtual EdgeEdgeDistanceType known_dtype() const;¶

bool operator==(const EdgeEdgeCandidate& other) const;¶

bool operator!=(const EdgeEdgeCandidate& other) const;¶

bool operator<(const EdgeEdgeCandidate& other) const;¶: Compare EdgeEdgeCandidates for sorting.

Public Members¶

long edge0_id;¶: ID of the first edge.

long edge1_id;¶: ID of the second edge.

Friends¶

template <typename H> inline friend H AbslHashValue(H h, const EdgeEdgeCandidate& ee);¶

Edge-Face Candidate¶

class EdgeFaceCandidate;¶

Candidate for intersection between edge and face.

Not included in Candidates because it is not a collision candidate.

Public Functions¶

EdgeFaceCandidate(long edge_id, long face_id);¶

bool operator==(const EdgeFaceCandidate& other) const;¶

bool operator!=(const EdgeFaceCandidate& other) const;¶

bool operator<(const EdgeFaceCandidate& other) const;¶: Compare EdgeFaceCandidate for sorting.

Public Members¶

long edge_id;¶: ID of the edge.

long face_id;¶: ID of the face.

Friends¶

template <typename H> inline friend H AbslHashValue(H h, const EdgeFaceCandidate& fv);¶

Face-Vertex Candidate¶

class FaceVertexCandidate : public ipc::ContinuousCollisionCandidate;¶

Subclassed by ipc::FaceVertexCollision, ipc::FaceVertexFrictionCollision

Public Functions¶

FaceVertexCandidate(long face_id, long vertex_id);¶

inline virtual int num_vertices() const override;¶: Get the number of vertices in the collision stencil.

inline virtual std::array<long, 4> vertex_ids( const Eigen::MatrixXi& edges, const Eigen::MatrixXi& faces) const override;¶

Get the vertex IDs of the collision stencil.

Parameters:¶

const Eigen::MatrixXi &edges¶: Collision mesh edges
const Eigen::MatrixXi &faces¶: Collision mesh faces

Returns:¶

The vertex IDs of the collision stencil. Size is always 4, but elements i > num_vertices() are -1.

virtual double compute_distance( const VectorMax12d& positions) const override;¶

Compute the distance of the stencil.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance of the stencil.

virtual VectorMax12d compute_distance_gradient( const VectorMax12d& positions) const override;¶

Compute the distance gradient of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance gradient of the stencil w.r.t. the stencil’s vertex positions.

virtual MatrixMax12d compute_distance_hessian( const VectorMax12d& positions) const override;¶

Compute the distance Hessian of the stencil w.r.t.

the stencil’s vertex positions.

Note

positions can be computed as stencil.dof(vertices, edges, faces)

Parameters:¶

const VectorMax12d &positions¶: Stencil’s vertex positions.

Returns:¶

Distance Hessian of the stencil w.r.t. the stencil’s vertex positions.

Perform narrow-phase CCD on the candidate.

Parameters:¶

const VectorMax12d &vertices_t0¶: [in] Stencil vertices at the start of the time step.
const VectorMax12d &vertices_t1¶: [in] Stencil vertices at the end of the time step.
double &toi¶: [out] Computed time of impact (normalized).
const double min_distance = 0.0¶: [in] Minimum separation distance between primitives.
const double tmax = 1.0¶: [in] Maximum time (normalized) to look for collisions.
const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD¶: [in] The narrow phase CCD algorithm to use.

Returns:¶

If the candidate had a collision over the time interval.

inline virtual PointTriangleDistanceType known_dtype() const;¶

bool operator==(const FaceVertexCandidate& other) const;¶

bool operator!=(const FaceVertexCandidate& other) const;¶

bool operator<(const FaceVertexCandidate& other) const;¶: Compare FaceVertexCandidate for sorting.

Public Members¶

long face_id;¶: ID of the face.

long vertex_id;¶: ID of the vertex.

Friends¶

template <typename H> inline friend H AbslHashValue(H h, const FaceVertexCandidate& fv);¶