Potentials¶

Generic Potential¶

template <class TCollisions> class 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¶

Distance-based Potential¶

class DistanceBasedPotential : public ipc::Potential<Collisions>¶

Inheritence diagram for ipc::DistanceBasedPotential:

Collaboration diagram for ipc::DistanceBasedPotential:

Base class for distance-based potentials.

Subclassed by ipc::BarrierPotential

Public Functions

DistanceBasedPotential() = default¶

virtual ~DistanceBasedPotential() = default¶

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

Compute the shape derivative of the potential.

Parameters:¶

const Collisions &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 Collision& collision,
    const VectorMax12d& positions) const override¶

Compute the potential for a single collision.

Parameters:¶

const Collision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The potential.

VectorMax12d gradient(const Collision& collision,
    const VectorMax12d& positions) const override¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const Collision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const Collision& 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 Collision &collision¶

The collision.

const VectorMax12d &positions¶

The collision stencil’s positions.

Returns:¶

The hessian of the potential.

void shape_derivative(const Collision& 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 Collision &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.

Protected Functions

virtual double distance_based_potential(
    const double distance_sqr, const double dmin = 0) const = 0¶

Compute the unmollified distance-based potential for a collisions.

Parameters:¶

const double distance_sqr¶

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 distance_based_potential_gradient(
    const double distance_sqr, const double dmin = 0) const = 0¶

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

Parameters:¶

const double distance_sqr¶

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 distance_based_potential_hessian(
    const double distance_sqr, const double dmin = 0) const = 0¶

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

Parameters:¶

const double distance_sqr¶

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<Collisions>¶

Barrier Potential¶

class BarrierPotential : public ipc::DistanceBasedPotential¶

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 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.

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.

Protected Functions

virtual double distance_based_potential(const double distance_sqr,
    const double dmin = 0) const override¶

Compute the barrier potential for a collision.

Parameters:¶

const double distance_sqr¶

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 distance_based_potential_gradient(
    const double distance_sqr,
    const double dmin = 0) const override¶

Compute the gradient of the barrier potential for a collision.

Parameters:¶

const double distance_sqr¶

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 distance_based_potential_hessian(
    const double distance_sqr,
    const double dmin = 0) const override¶

Compute the hessian of the barrier potential for a collision.

Parameters:¶

const double distance_sqr¶

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.

Friction Potential¶

class FrictionPotential : public ipc::Potential<FrictionCollisions>¶

Inheritence diagram for ipc::FrictionPotential:

Collaboration diagram for ipc::FrictionPotential:

The friction dissipative potential.

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

explicit FrictionPotential(const double epsv)¶

Construct a friction potential.

Parameters:¶

const double epsv¶

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

inline double epsv() const¶

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

inline void set_epsv(const double epsv)¶

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

Parameters:¶

const double epsv¶

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

Eigen::VectorXd force(const FrictionCollisions& collisions,
    const CollisionMesh& mesh,
    const Eigen::MatrixXd& rest_positions,
    const Eigen::MatrixXd& lagged_displacements,
    const Eigen::MatrixXd& velocities,
    const BarrierPotential& barrier_potential,
    const double barrier_stiffness, const double dmin = 0,
    const bool no_mu = false) const¶

Compute the friction force from the given velocities.

Parameters:¶

const FrictionCollisions &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 BarrierPotential &barrier_potential¶

Barrier potential (used for normal force magnitude).

const double barrier_stiffness¶

Barrier 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 FrictionCollisions& collisions, const CollisionMesh& mesh,
    const Eigen::MatrixXd& rest_positions,
    const Eigen::MatrixXd& lagged_displacements,
    const Eigen::MatrixXd& velocities,
    const BarrierPotential& barrier_potential,
    const double barrier_stiffness, const DiffWRT wrt,
    const double dmin = 0) const¶

Compute the Jacobian of the friction force wrt the velocities.

Parameters:¶

const FrictionCollisions &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 BarrierPotential &barrier_potential¶

Barrier potential (used for normal force magnitude).

const double barrier_stiffness¶

Barrier 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 FrictionCollision& collision,
    const VectorMax12d& velocities) const override¶

Compute the potential for a single collision.

Parameters:¶

const FrictionCollision &collision¶

The collision

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The potential.

VectorMax12d gradient(const FrictionCollision& collision,
    const VectorMax12d& velocities) const override¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const FrictionCollision &collision¶

The collision

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const FrictionCollision& 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 FrictionCollision &collision¶

The collision

const VectorMax12d &velocities¶

The collision stencil’s velocities.

Returns:¶

The hessian of the potential.

VectorMax12d force(const FrictionCollision& collision,
    const VectorMax12d& rest_positions,
    const VectorMax12d& lagged_displacements,
    const VectorMax12d& velocities,
    const BarrierPotential& barrier_potential,
    const double barrier_stiffness, const double dmin = 0,
    const bool no_mu = false) const¶

Compute the friction force.

Parameters:¶

const FrictionCollision &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 BarrierPotential &barrier_potential¶

Barrier potential (used for normal force magnitude).

const double barrier_stiffness¶

Barrier 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 FrictionCollision& collision,
    const VectorMax12d& rest_positions,
    const VectorMax12d& lagged_displacements,
    const VectorMax12d& velocities,
    const BarrierPotential& barrier_potential,
    const double barrier_stiffness, const DiffWRT wrt,
    const double dmin = 0) const¶

Compute the friction force Jacobian.

Parameters:¶

const FrictionCollision &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 BarrierPotential &barrier_potential¶

Barrier potential (used for normal force magnitude).

const double barrier_stiffness¶

Barrier 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|.

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|.

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 Attributes

double m_epsv¶

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

Private Types

using Super = Potential¶