TangentialPotential¶

class TangentialPotential
    : public ipc::Potential<TangentialCollisions>;¶

A tangential dissipative potential.

Subclassed by ipc::FrictionPotential, ipc::TangentialAdhesionPotential

Public Types¶

enum class DiffWRT;¶

Variable to differentiate the friction force with respect to.

Values:

enumerator REST_POSITIONS;¶

Differentiate w.r.t. rest positions.

enumerator LAGGED_DISPLACEMENTS;¶

Differentiate w.r.t. lagged displacements.

enumerator VELOCITIES;¶

Differentiate w.r.t. current velocities.

Public Functions¶

inline virtual ~TangentialPotential();¶

Eigen::VectorXd force(const TangentialCollisions& collisions,
    const CollisionMesh& mesh,
    Eigen::ConstRef<Eigen::MatrixXd> rest_positions,
    Eigen::ConstRef<Eigen::MatrixXd> lagged_displacements,
    Eigen::ConstRef<Eigen::MatrixXd> velocities,
    const NormalPotential& normal_potential,
    const double normal_stiffness, const double dmin = 0,
    const bool no_mu = false) const;¶

Compute the friction force from the given velocities.

Parameters:¶

const TangentialCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

Eigen::ConstRef<Eigen::MatrixXd> rest_positions¶

Rest positions of the vertices (rowwise).

Eigen::ConstRef<Eigen::MatrixXd> lagged_displacements¶

Previous displacements of the vertices (rowwise).

Eigen::ConstRef<Eigen::MatrixXd> velocities¶

Current displacements of the vertices (rowwise).

const NormalPotential &normal_potential¶

Normal potential (used for normal force magnitude).

const double normal_stiffness¶

Normal stiffness (used for normal force magnitude).

const double dmin = 0¶

Minimum distance (used for normal force magnitude).

const bool no_mu = false¶

whether to not multiply by mu

Returns:¶

The friction force.

Eigen::SparseMatrix<double> force_jacobian(
    const TangentialCollisions& collisions,
    const CollisionMesh& mesh,
    Eigen::ConstRef<Eigen::MatrixXd> rest_positions,
    Eigen::ConstRef<Eigen::MatrixXd> lagged_displacements,
    Eigen::ConstRef<Eigen::MatrixXd> velocities,
    const NormalPotential& normal_potential,
    const double normal_stiffness, const DiffWRT wrt,
    const double dmin = 0) const;¶

Compute the Jacobian of the friction force wrt the velocities.

Parameters:¶

const TangentialCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

Eigen::ConstRef<Eigen::MatrixXd> rest_positions¶

Rest positions of the vertices (rowwise).

Eigen::ConstRef<Eigen::MatrixXd> lagged_displacements¶

Previous displacements of the vertices (rowwise).

Eigen::ConstRef<Eigen::MatrixXd> velocities¶

Current displacements of the vertices (rowwise).

const NormalPotential &normal_potential¶

Normal potential (used for normal force magnitude).

const double normal_stiffness¶

Normal stiffness (used for normal force magnitude).

const DiffWRT wrt¶

The variable to take the derivative with respect to.

const double dmin = 0¶

Minimum distance (used for normal force magnitude).

Returns:¶

The Jacobian of the friction force wrt the velocities.

double operator()(const TangentialCollision& collision,
    Eigen::ConstRef<VectorMax12d> velocities) const override;¶

Compute the potential for a single collision.

Parameters:¶

const TangentialCollision &collision¶

The collision

Eigen::ConstRef<VectorMax12d> velocities¶

The collision stencil’s velocities.

Returns:¶

The potential.

VectorMax12d gradient(const TangentialCollision& collision,
    Eigen::ConstRef<VectorMax12d> velocities) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TangentialCollision &collision¶

The collision

Eigen::ConstRef<VectorMax12d> velocities¶

The collision stencil’s velocities.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const TangentialCollision& collision,
    Eigen::ConstRef<VectorMax12d> velocities,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const override;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const TangentialCollision &collision¶

The collision

Eigen::ConstRef<VectorMax12d> velocities¶

The collision stencil’s velocities.

const PSDProjectionMethod project_hessian_to_psd = PSDProjectionMethod::NONE¶

Whether to project the hessian to the positive semi-definite cone.

Returns:¶

The hessian of the potential.

VectorMax12d force(const TangentialCollision& collision,
    Eigen::ConstRef<VectorMax12d> rest_positions,
    Eigen::ConstRef<VectorMax12d> lagged_displacements,
    Eigen::ConstRef<VectorMax12d> velocities,
    const NormalPotential& normal_potential,
    const double normal_stiffness, const double dmin = 0,
    const bool no_mu = false) const;¶

Compute the friction force.

Parameters:¶

const TangentialCollision &collision¶

The collision

Eigen::ConstRef<VectorMax12d> rest_positions¶

Rest positions of the vertices (rowwise).

Eigen::ConstRef<VectorMax12d> lagged_displacements¶

Previous displacements of the vertices (rowwise).

Eigen::ConstRef<VectorMax12d> velocities¶

Current displacements of the vertices (rowwise).

const NormalPotential &normal_potential¶

Normal potential (used for normal force magnitude).

const double normal_stiffness¶

Normal stiffness (used for normal force magnitude).

const double dmin = 0¶

Minimum distance (used for normal force magnitude).

const bool no_mu = false¶

Whether to not multiply by mu

Returns:¶

Friction force

MatrixMax12d force_jacobian(const TangentialCollision& collision,
    Eigen::ConstRef<VectorMax12d> rest_positions,
    Eigen::ConstRef<VectorMax12d> lagged_displacements,
    Eigen::ConstRef<VectorMax12d> velocities,
    const NormalPotential& normal_potential,
    const double normal_stiffness, const DiffWRT wrt,
    const double dmin = 0) const;¶

Compute the friction force Jacobian.

Parameters:¶

const TangentialCollision &collision¶

The collision

Eigen::ConstRef<VectorMax12d> rest_positions¶

Rest positions of the vertices (rowwise).

Eigen::ConstRef<VectorMax12d> lagged_displacements¶

Previous displacements of the vertices (rowwise).

Eigen::ConstRef<VectorMax12d> velocities¶

Current displacements of the vertices (rowwise).

const NormalPotential &normal_potential¶

Normal potential (used for normal force magnitude).

const double normal_stiffness¶

Noraml stiffness (used for normal force magnitude).

const DiffWRT wrt¶

Variable to differentiate the friction force with respect to.

const double dmin = 0¶

Minimum distance (used for normal force magnitude).

Returns:¶

Friction force Jacobian

Eigen::VectorXd gradient(const TCollisions& collisions,
    const CollisionMesh& mesh,
    Eigen::ConstRef<Eigen::MatrixXd> X) const;¶

Compute the gradient of the potential.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

Eigen::ConstRef<Eigen::MatrixXd> X¶

Degrees of freedom of the collision mesh (e.g., vertices or velocities).

Returns:¶

The gradient of the potential w.r.t. X. This will have a size of |X|.

virtual VectorMax12d gradient(const TCollision& collision,
    Eigen::ConstRef<VectorMax12d> x) const
    = 0;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> x¶

The collision stencil’s degrees of freedom.

Returns:¶

The gradient of the potential.

Eigen::SparseMatrix<double> hessian(const TCollisions& collisions,
    const CollisionMesh& mesh, Eigen::ConstRef<Eigen::MatrixXd> X,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const;¶

Compute the hessian of the potential.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

Eigen::ConstRef<Eigen::MatrixXd> X¶

Degrees of freedom of the collision mesh (e.g., vertices or velocities).

const PSDProjectionMethod project_hessian_to_psd = PSDProjectionMethod::NONE¶

Make sure the hessian is positive semi-definite.

Returns:¶

The Hessian of the potential w.r.t. X. This will have a size of |X|×|X|.

virtual MatrixMax12d hessian(const TCollision& collision,
    Eigen::ConstRef<VectorMax12d> x,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const
    = 0;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> x¶

The collision stencil’s degrees of freedom.

const PSDProjectionMethod project_hessian_to_psd = PSDProjectionMethod::NONE¶

Whether to project the hessian to the positive semi-definite cone.

Returns:¶

The hessian of the potential.

Protected Functions¶

virtual double f0(const double x) const = 0;¶

virtual double f1_over_x(const double x) const = 0;¶

virtual double f2_x_minus_f1_over_x3(const double x) const = 0;¶

virtual bool is_dynamic(const double speed) const = 0;¶

Private Types¶

using Super = Potential;¶