Potentials¶

Generic Potential¶

template <class TCollisions> class Potential;¶

Inheritence diagram for ipc::Potential:

Base class for potentials.

Template Parameters:¶

class TCollisions¶

The type of the collisions.

Public Functions¶

Potential() = default;¶

virtual ~Potential() = default;¶

double operator()(const TCollisions& collisions,
    const CollisionMesh& mesh, const Eigen::MatrixXd& X) const;¶

Compute the potential for a set of collisions.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

const Eigen::MatrixXd &X¶

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

Returns:¶

The potential for a set of collisions.

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

Compute the gradient of the potential.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

const 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|.

Eigen::SparseMatrix<double> hessian(const TCollisions& collisions,
    const CollisionMesh& mesh, const 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.

const 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 double operator()(
    const TCollision& collision, const VectorMax12d& x) const
    = 0;¶

Compute the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

const VectorMax12d &x¶

The collision stencil’s degrees of freedom.

Returns:¶

The potential.

virtual VectorMax12d gradient(
    const TCollision& collision, const VectorMax12d& x) const
    = 0;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

const VectorMax12d &x¶

The collision stencil’s degrees of freedom.

Returns:¶

The gradient of the potential.

virtual MatrixMax12d hessian(const TCollision& collision,
    const 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.

const VectorMax12d &x¶

The collision stencil’s degrees of freedom.

Returns:¶

The hessian of the potential.

Protected Types¶

using TCollision = typename TCollisions::value_type;¶

Normal Potentials¶

class NormalPotential : public ipc::Potential<NormalCollisions>;¶

Inheritence diagram for ipc::NormalPotential:

Collaboration diagram for ipc::NormalPotential:

Base class for distance-based potentials.

Subclassed by ipc::BarrierPotential, ipc::NormalAdhesionPotential

Public Functions¶

NormalPotential() = default;¶

virtual ~NormalPotential() = default;¶

Eigen::SparseMatrix<double> shape_derivative(
    const NormalCollisions& collisions, const CollisionMesh& mesh,
    const Eigen::MatrixXd& vertices) const;¶

Compute the shape derivative of the potential.

Parameters:¶

const NormalCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

const Eigen::MatrixXd &vertices¶

Vertices of the collision mesh.

Throws:¶

std::runtime_error – If the collision collisions were not built with shape derivatives enabled.

Returns:¶

The derivative of the force with respect to X, the rest vertices.

double operator()(const NormalCollision& collision,
    const VectorMax12d& positions) const override;¶

Compute the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The potential.

VectorMax12d gradient(const NormalCollision& collision,
    const VectorMax12d& positions) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const NormalCollision& collision,
    const VectorMax12d& positions,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const override;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The hessian of the potential.

void shape_derivative(const NormalCollision& collision,
    const std::array<long, 4>& vertex_ids,
    const VectorMax12d& rest_positions,
    const VectorMax12d& positions,
    std::vector<Eigen::Triplet<double>>& out) const;¶

Compute the shape derivative of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

[in] The collision.

const std::array<long, 4> &vertex_ids¶

[in] The collision stencil’s vertex ids.

const VectorMax12d &rest_positions¶

[in] The collision stencil’s rest positions.

const VectorMax12d &positions¶

[in] The collision stencil’s positions.

std::vector<Eigen::Triplet<double>> &out¶

[inout] Store the triplets of the shape derivative here.

virtual double force_magnitude(const double distance_squared,
    const double dmin, const double barrier_stiffness) const
    = 0;¶

Compute the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The barrier stiffness.

Returns:¶

The force magnitude.

virtual VectorMax12d force_magnitude_gradient(
    const double distance_squared,
    const VectorMax12d& distance_squared_gradient,
    const double dmin, const double barrier_stiffness) const
    = 0;¶

Compute the gradient of the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const VectorMax12d &distance_squared_gradient¶

The gradient of the squared distance.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

Returns:¶

The gradient of the force.

Protected Functions¶

virtual double operator()(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the unmollified distance-based potential for a collisions.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The unmollified distance-based potential.

virtual double gradient(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the gradient of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the unmollified distance-based potential.

virtual double hessian(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the hessian of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the unmollified distance-based potential.

Private Types¶

using Super = Potential<NormalCollisions>;¶

Barrier Potential¶

class BarrierPotential : public ipc::NormalPotential;¶

Inheritence diagram for ipc::BarrierPotential:

Collaboration diagram for ipc::BarrierPotential:

The barrier collision potential.

Public Functions¶

explicit BarrierPotential(
    const double dhat, const bool use_physical_barrier = false);¶

Construct a barrier potential.

Parameters:¶

const double dhat¶

The activation distance of the barrier.

BarrierPotential(const std::shared_ptr<Barrier> barrier,
    const double dhat, const bool use_physical_barrier = false);¶

Construct a barrier potential.

Parameters:¶

const std::shared_ptr<Barrier> barrier¶

The barrier function.

const double dhat¶

The activation distance of the barrier.

inline double dhat() const;¶

Get the activation distance of the barrier.

inline void set_dhat(const double dhat);¶

Set the activation distance of the barrier.

Parameters:¶

const double dhat¶

The activation distance of the barrier.

inline const Barrier& barrier() const;¶

Get the barrier function used to compute the potential.

inline void set_barrier(const std::shared_ptr<Barrier> barrier);¶

Set the barrier function used to compute the potential.

Parameters:¶

const std::shared_ptr<Barrier> barrier¶

The barrier function used to compute the potential.

virtual double force_magnitude(const double distance_squared,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The barrier stiffness.

Returns:¶

The force magnitude.

virtual VectorMax12d force_magnitude_gradient(
    const double distance_squared,
    const VectorMax12d& distance_squared_gradient,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the gradient of the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const VectorMax12d &distance_squared_gradient¶

The gradient of the squared distance.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

Returns:¶

The gradient of the force.

inline bool use_physical_barrier() const;¶

Get whether to use the physical barrier.

Note

When using the convergent formulation we want the barrier to have units of Pa⋅m, so κ gets units of Pa and the barrier function should have units of m. See notebooks/physical_barrier.ipynb for more details.

inline void set_use_physical_barrier(bool use_physical_barrier);¶

Set use physical barrier flag.

Note

When using the convergent formulation we want the barrier to have units of Pa⋅m, so κ gets units of Pa and the barrier function should have units of m. See notebooks/physical_barrier.ipynb for more details.

Parameters:¶

bool use_physical_barrier¶

Whether to use the physical barrier.

VectorMax12d gradient(const NormalCollision& collision,
    const VectorMax12d& positions) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

virtual double gradient(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the gradient of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the unmollified distance-based potential.

MatrixMax12d hessian(const NormalCollision& collision,
    const VectorMax12d& positions,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const override;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The hessian of the potential.

virtual double hessian(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the hessian of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the unmollified distance-based potential.

Protected Functions¶

virtual double operator()(const double distance_squared,
    const double dmin = 0) const override;¶

Compute the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The barrier potential.

virtual double gradient(const double distance_squared,
    const double dmin = 0) const override;

Compute the gradient of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the barrier potential.

virtual double hessian(const double distance_squared,
    const double dmin = 0) const override;

Compute the hessian of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the barrier potential.

Protected Attributes¶

std::shared_ptr<Barrier> m_barrier
    = std::make_shared<ClampedLogBarrier>();¶

The barrier function used to compute the potential.

double m_dhat;¶

The activation distance of the barrier.

bool m_use_physical_barrier = false;¶

Whether to use the physical barrier.

Note

When using the convergent formulation we want the barrier to have units of Pa⋅m, so κ gets units of Pa and the barrier function should have units of m. See notebooks/physical_barrier.ipynb for more details.

Private Types¶

using Super = NormalPotential;¶

Normal Adhesion Potential¶

class NormalAdhesionPotential : public ipc::NormalPotential;¶

Inheritence diagram for ipc::NormalAdhesionPotential:

Collaboration diagram for ipc::NormalAdhesionPotential:

The normal adhesion potential.

Public Functions¶

NormalAdhesionPotential(const double _dhat_p, const double _dhat_a,
    const double _Y, const double _eps_c);¶

virtual double force_magnitude(const double distance_squared,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The barrier stiffness.

Returns:¶

The force magnitude.

virtual VectorMax12d force_magnitude_gradient(
    const double distance_squared,
    const VectorMax12d& distance_squared_gradient,
    const double dmin,
    const double barrier_stiffness) const override;¶

Compute the gradient of the force magnitude for a collision.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const VectorMax12d &distance_squared_gradient¶

The gradient of the squared distance.

const double dmin¶

The minimum distance offset to the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

Returns:¶

The gradient of the force.

VectorMax12d gradient(const NormalCollision& collision,
    const VectorMax12d& positions) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

virtual double gradient(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the gradient of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the unmollified distance-based potential.

MatrixMax12d hessian(const NormalCollision& collision,
    const VectorMax12d& positions,
    const PSDProjectionMethod project_hessian_to_psd
    = PSDProjectionMethod::NONE) const override;¶

Compute the hessian of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The hessian of the potential.

virtual double hessian(
    const double distance_squared, const double dmin = 0) const
    = 0;¶

Compute the hessian of the unmollified distance-based potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the unmollified distance-based potential.

Public Members¶

double dhat_p;¶

The distance of largest adhesion force ( \(\hat{d}_p\)) ( \(0 < \hat{d}_p < \hat{d}_a\)).

double dhat_a;¶

The adhesion activation distance ( \(\hat{d}_a\)).

double Y;¶

The Young’s modulus ( \(Y\)).

double eps_c;¶

The critical strain ( \(\varepsilon_c\)).

Protected Functions¶

virtual double operator()(const double distance_squared,
    const double dmin = 0) const override;¶

Compute the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The barrier potential.

virtual double gradient(const double distance_squared,
    const double dmin = 0) const override;

Compute the gradient of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The gradient of the barrier potential.

virtual double hessian(const double distance_squared,
    const double dmin = 0) const override;

Compute the hessian of the barrier potential for a collision.

Parameters:¶

const double distance_squared¶

The distance (squared) between the two objects.

const double dmin = 0¶

The minimum distance (unsquared) between the two objects.

Returns:¶

The hessian of the barrier potential.

Private Types¶

using Super = NormalPotential;¶

Private Functions¶

std::array<double, 3> normal_adhesion_potential_args(
    const double dmin) const;¶

Tangential Potentials¶

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

Inheritence diagram for ipc::TangentialPotential:

Collaboration diagram for ipc::TangentialPotential:

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,
    const Eigen::MatrixXd& rest_positions,
    const Eigen::MatrixXd& lagged_displacements,
    const 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.

const Eigen::MatrixXd &rest_positions¶

Rest positions of the vertices (rowwise).

const Eigen::MatrixXd &lagged_displacements¶

Previous displacements of the vertices (rowwise).

const 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,
    const Eigen::MatrixXd& rest_positions,
    const Eigen::MatrixXd& lagged_displacements,
    const 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.

const Eigen::MatrixXd &rest_positions¶

Rest positions of the vertices (rowwise).

const Eigen::MatrixXd &lagged_displacements¶

Previous displacements of the vertices (rowwise).

const 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,
    const VectorMax12d& velocities) const override;¶

Compute the potential for a single collision.

Parameters:¶

const TangentialCollision &collision¶

The collision

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The potential.

VectorMax12d gradient(const TangentialCollision& collision,
    const VectorMax12d& velocities) const override;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TangentialCollision &collision¶

The collision

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const TangentialCollision& collision,
    const 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

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The hessian of the potential.

VectorMax12d force(const TangentialCollision& collision,
    const VectorMax12d& rest_positions,
    const VectorMax12d& lagged_displacements,
    const 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

const VectorMax12d &rest_positions¶

Rest positions of the vertices (rowwise).

const VectorMax12d &lagged_displacements¶

Previous displacements of the vertices (rowwise).

const 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,
    const VectorMax12d& rest_positions,
    const VectorMax12d& lagged_displacements,
    const 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

const VectorMax12d &rest_positions¶

Rest positions of the vertices (rowwise).

const VectorMax12d &lagged_displacements¶

Previous displacements of the vertices (rowwise).

const 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, const Eigen::MatrixXd& X) const;¶

Compute the gradient of the potential.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

const 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, const VectorMax12d& x) const
    = 0;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

const 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, const 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.

const 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,
    const 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.

const VectorMax12d &x¶

The collision stencil’s degrees of freedom.

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;¶

Friction Potential¶

class FrictionPotential : public ipc::TangentialPotential;¶

Inheritence diagram for ipc::FrictionPotential:

Collaboration diagram for ipc::FrictionPotential:

The friction dissipative potential.

Public Functions¶

explicit FrictionPotential(const double eps_v);¶

Construct a friction potential.

Parameters:¶

const double eps_v¶

The smooth friction mollifier parameter \(\epsilon_v\).

inline double eps_v() const;¶

Get the smooth friction mollifier parameter \(\epsilon_v\).

inline void set_eps_v(const double eps_v);¶

Set the smooth friction mollifier parameter \(\epsilon_v\).

Parameters:¶

const double eps_v¶

The smooth friction mollifier parameter \(\epsilon_v\).

Protected Functions¶

virtual double f0(const double x) const override;¶

virtual double f1_over_x(const double x) const override;¶

virtual double f2_x_minus_f1_over_x3(const double x) const override;¶

inline virtual bool is_dynamic(const double speed) const override;¶

Protected Attributes¶

double m_eps_v;¶

The smooth friction mollifier parameter \(\epsilon_v\).

Private Types¶

using Super = TangentialPotential;¶

Tangential Adhesion Potential¶

class TangentialAdhesionPotential : public ipc::TangentialPotential;¶

Inheritence diagram for ipc::TangentialAdhesionPotential:

Collaboration diagram for ipc::TangentialAdhesionPotential:

The tangential adhesion potential.

Public Functions¶

explicit TangentialAdhesionPotential(const double eps_a);¶

Construct a tangential adhesion potential.

Parameters:¶

const double eps_a¶

The tangential adhesion mollifier parameter \(\epsilon_a\).

inline double eps_a() const;¶

Get the tangential adhesion mollifier parameter \(\epsilon_a\).

inline void set_eps_a(const double eps_a);¶

Set the tangential adhesion mollifier parameter \(\epsilon_v\).

Parameters:¶

const double eps_a¶

The tangential adhesion mollifier parameter \(\epsilon_v\).

Protected Functions¶

virtual double f0(const double x) const override;¶

virtual double f1_over_x(const double x) const override;¶

virtual double f2_x_minus_f1_over_x3(const double x) const override;¶

inline virtual bool is_dynamic(const double speed) const override;¶

Protected Attributes¶

double m_eps_a;¶

The tangential adhesion mollifier parameter \(\epsilon_a\).

Private Types¶

using Super = TangentialPotential;¶