TangentialPotential¶

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

A tangential dissipative potential.

Subclassed by ipc::FrictionPotential, ipc::TangentialAdhesionPotential

Public Types¶

enum class DiffWRT : uint8_t;¶

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.

Eigen::VectorXd smooth_contact_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 double dmin = 0, const bool no_mu = false) const;¶

Eigen::SparseMatrix<double> smooth_contact_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 SmoothContactParameters& params, const DiffWRT wrt,
    const double dmin = 0, const bool no_mu = false) const;¶

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

VectorMaxNd smooth_contact_force(
    const TangentialCollision& collision,
    Eigen::ConstRef<VectorMaxNd> rest_positions,
    Eigen::ConstRef<VectorMaxNd> lagged_displacements,
    Eigen::ConstRef<VectorMaxNd> velocities,
    const bool no_mu = false,
    const bool no_contact_force_multiplier = false) const;¶

Eigen::MatrixXd smooth_contact_force_jacobian(
    const TangentialCollision& collision,
    Eigen::ConstRef<VectorMaxNd> rest_positions,
    Eigen::ConstRef<VectorMaxNd> lagged_displacements,
    Eigen::ConstRef<VectorMaxNd> velocities, const DiffWRT wrt,
    const bool no_mu) const;¶

MatrixMaxNd smooth_contact_force_jacobian_unit(
    const TangentialCollision& collision,
    Eigen::ConstRef<VectorMaxNd> lagged_positions,
    Eigen::ConstRef<VectorMaxNd> velocities, const DiffWRT wrt,
    const bool no_mu = false) const;¶

Compute the friction force Jacobian assuming the contact force magnitude being 1.

Parameters:¶

const TangentialCollision &collision¶

The collision

rest_positions

Rest positions of the vertices (rowwise).

lagged_displacements

Previous displacements of the vertices (rowwise).

Eigen::ConstRef<VectorMaxNd> velocities¶

Current displacements of the vertices (rowwise).

barrier_potential

Barrier potential (used for normal force magnitude).

barrier_stiffness

Barrier stiffness (used for normal force magnitude).

const DiffWRT wrt¶

Variable to differentiate the friction force with respect to.

dmin

Minimum distance (used for normal force magnitude).

Returns:¶

Friction force Jacobian

Protected Functions¶

virtual double mu_f0(
    const double x, const double mu_s, const double mu_k) const
    = 0;¶

Compute the value of the ∫ μ(y) f₁(y) dy, where f₁ is the first derivative of the smooth mollifier.

Parameters:¶

const double x¶

The tangential relative speed.

const double mu_s¶

Coefficient of static friction.

const double mu_k¶

Coefficient of kinetic friction.

Returns:¶

The value of the integral at x.

virtual double mu_f1_over_x(
    const double x, const double mu_s, const double mu_k) const
    = 0;¶

Compute the value of the [μ(y) f₁(y)] / x, where f₁ is the first derivative of the smooth mollifier.

Parameters:¶

const double x¶

The tangential relative speed.

const double mu_s¶

Coefficient of static friction.

const double mu_k¶

Coefficient of kinetic friction.

Returns:¶

The value of the product at x.

virtual double mu_f2_x_minus_mu_f1_over_x3(
    const double x, const double mu_s, const double mu_k) const
    = 0;¶

Compute the value of [(d/dx (μ(y) f₁(y))) x - μ(y) f₁(y)] / x³, where f₁ is the first derivative of the smooth mollifier.

Parameters:¶

const double x¶

The tangential relative speed.

const double mu_s¶

Coefficient of static friction.

const double mu_k¶

Coefficient of kinetic friction.

Returns:¶

The value of the derivative at x.

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

Check if the speed is dynamic.

Parameters:¶

const double speed¶

The tangential relative speed.

Returns:¶

True if the speed is dynamic, false otherwise.

Private Types¶

using Super = Potential<TangentialCollisions>;¶

using VectorMaxNd = Super::VectorMaxNd;¶

using MatrixMaxNd = Super::MatrixMaxNd;¶