Potentials¶

Normal Potentials¶

class ipctk.NormalPotential¶

Bases: pybind11_object

Public Methods:

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
shape_derivative(*args, **kwargs)	Overloaded function.
force_magnitude(self, distance_squared, ...)	Compute the force magnitude for a collision.
force_magnitude_gradient(self, ...)	Compute the gradient of the force magnitude for a collision.

Inherited from pybind11_object

---

__annotations__ = {}¶

__call__(*args, **kwargs)¶

Overloaded function.

1. __call__(self: ipctk.NormalPotential, collisions: ipctk.NormalCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]]) -> float

   Compute the potential for a set of collisions.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. X: Degrees of freedom of the collision mesh (e.g., vertices or velocities).

   Returns:

   The potential for a set of collisions.

2. __call__(self: ipctk.NormalPotential, collision: ipctk.NormalCollision, x: numpy.ndarray[numpy.float64[m, 1]]) -> float

   Compute the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The potential.

__init__(*args, **kwargs)¶

__module__ = 'ipctk'¶

force_magnitude(self, distance_squared: float, dmin: float, barrier_stiffness: float) → float¶

Compute the force magnitude for a collision.

Parameters:¶

distance_squared: float¶

The squared distance between elements.

dmin: float¶

The minimum distance offset to the barrier.

barrier_stiffness: float¶

The barrier stiffness.

Returns:¶

The force magnitude.

force_magnitude_gradient(self, distance_squared: float, distance_squared_gradient: numpy.ndarray[numpy.float64[m, 1]], dmin: float, barrier_stiffness: float) → numpy.ndarray[numpy.float64[m, 1]]¶

Compute the gradient of the force magnitude for a collision.

Parameters:¶

distance_squared: float¶

The squared distance between elements.

distance_squared_gradient: numpy.ndarray[numpy.float64[m, 1]]¶

The gradient of the squared distance.

dmin: float¶

The minimum distance offset to the barrier.

barrier_stiffness: float¶

The stiffness of the barrier.

Returns:¶

The gradient of the force.

gradient(*args, **kwargs)¶

Overloaded function.

1. gradient(self: ipctk.NormalPotential, collisions: ipctk.NormalCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]]) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the gradient of the potential.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. 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|.

2. gradient(self: ipctk.NormalPotential, collision: ipctk.NormalCollision, x: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the gradient of the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The gradient of the potential.

hessian(*args, **kwargs)¶

Overloaded function.

1. hessian(self: ipctk.NormalPotential, collisions: ipctk.NormalCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]], project_hessian_to_psd: ipctk.PSDProjectionMethod = <PSDProjectionMethod.NONE: 0>) -> scipy.sparse.csc_matrix[numpy.float64]

   Compute the hessian of the potential.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. X: Degrees of freedom of the collision mesh (e.g., vertices or velocities). project_hessian_to_psd: 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|.

2. hessian(self: ipctk.NormalPotential, collision: ipctk.NormalCollision, x: numpy.ndarray[numpy.float64[m, 1]], project_hessian_to_psd: ipctk.PSDProjectionMethod = <PSDProjectionMethod.NONE: 0>) -> numpy.ndarray[numpy.float64[m, n]]

   Compute the hessian of the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The hessian of the potential.

shape_derivative(*args, **kwargs)¶

Overloaded function.

1. shape_derivative(self: ipctk.NormalPotential, collisions: ipctk.NormalCollisions, mesh: ipc::CollisionMesh, vertices: numpy.ndarray[numpy.float64[m, n]]) -> scipy.sparse.csc_matrix[numpy.float64]

   Compute the shape derivative of the potential.

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

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. vertices: Vertices of the collision mesh.

   Returns:

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

2. shape_derivative(self: ipctk.NormalPotential, collision: ipctk.NormalCollision, vertex_ids: Annotated[list[int], FixedSize(4)], rest_positions: numpy.ndarray[numpy.float64[m, 1]], positions: numpy.ndarray[numpy.float64[m, 1]]) -> list[Eigen::Triplet<double, int>]

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

   Parameters:

   collision: The collision. vertex_ids: The collision stencil’s vertex ids. rest_positions: The collision stencil’s rest positions. positions: The collision stencil’s positions. ,out]: out Store the triplets of the shape derivative here.

Barrier Potential¶

class ipctk.BarrierPotential¶

Bases: NormalPotential

Public Data Attributes:

dhat	Barrier activation distance.
barrier	Barrier function used to compute the potential.

Public Methods:

__init__(*args, **kwargs)

Overloaded function.

Inherited from NormalPotential

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
shape_derivative(*args, **kwargs)	Overloaded function.
force_magnitude(self, distance_squared, ...)	Compute the force magnitude for a collision.
force_magnitude_gradient(self, ...)	Compute the gradient of the force magnitude for a collision.

Inherited from pybind11_object

---

__annotations__ = {}¶

__init__(*args, **kwargs)¶

Overloaded function.

1. __init__(self: ipctk.BarrierPotential, dhat: float, use_physical_barrier: bool = False) -> None

   Construct a barrier potential.

   Parameters:

   dhat: The activation distance of the barrier.

2. __init__(self: ipctk.BarrierPotential, barrier: ipctk.Barrier, dhat: float, use_physical_barrier: bool = False) -> None

   Construct a barrier potential.

   Parameters:

   barrier: The barrier function. dhat: The activation distance of the barrier.

__module__ = 'ipctk'¶

property barrier : ipctk.Barrier¶

Barrier function used to compute the potential.

property dhat : float¶

Barrier activation distance.

Normal Adhesion Potential¶

class ipctk.NormalAdhesionPotential¶

Bases: NormalPotential

Public Data Attributes:

dhat_p	The distance of largest adhesion force (\(\hat{d}_{p}\)) (\(0 < \hat{d}_{p} < \hat{d}_{a}\)).
dhat_a	The adhesion activation distance (\(\hat{d}_{a}\).
Y	The Young's modulus (\(Y\))).
eps_c	The critical strain (\(\varepsilon_{c}\))).

Public Methods:

__init__(self, dhat_p, dhat_a, Y, eps_c)

Inherited from NormalPotential

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
shape_derivative(*args, **kwargs)	Overloaded function.
force_magnitude(self, distance_squared, ...)	Compute the force magnitude for a collision.
force_magnitude_gradient(self, ...)	Compute the gradient of the force magnitude for a collision.

Inherited from pybind11_object

---

property Y : float¶

The Young’s modulus (\(Y\))).

__annotations__ = {}¶

__init__(self, dhat_p: float, dhat_a: float, Y: float, eps_c: float)¶

__module__ = 'ipctk'¶

property dhat_a : float¶

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

property dhat_p : float¶

The distance of largest adhesion force (\(\hat{d}_{p}\)) (\(0 < \hat{d}_{p} < \hat{d}_{a}\)).

property eps_c : float¶

The critical strain (\(\varepsilon_{c}\))).

Tangential Potentials¶

class ipctk.TangentialPotential¶

Bases: pybind11_object

Public Data Attributes:

REST_POSITIONS
LAGGED_DISPLACEMENTS
VELOCITIES

Public Methods:

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
force(*args, **kwargs)	Overloaded function.
force_jacobian(*args, **kwargs)	Overloaded function.

Inherited from pybind11_object

---

class DiffWRT¶

Bases: pybind11_object

Members:

REST_POSITIONS : Differentiate w.r.t. rest positions

LAGGED_DISPLACEMENTS : Differentiate w.r.t. lagged displacements

VELOCITIES : Differentiate w.r.t. current velocities

LAGGED_DISPLACEMENTS = <DiffWRT.LAGGED_DISPLACEMENTS: 1>¶

REST_POSITIONS = <DiffWRT.REST_POSITIONS: 0>¶

VELOCITIES = <DiffWRT.VELOCITIES: 2>¶

__annotations__ = {}¶

__eq__(self, other: object) → bool¶

__getstate__(self) → int¶

__hash__(self) → int¶

__index__(self) → int¶

__init__(self, value: int)¶

__int__(self) → int¶

__members__ = {'LAGGED_DISPLACEMENTS': <DiffWRT.LAGGED_DISPLACEMENTS: 1>, 'REST_POSITIONS': <DiffWRT.REST_POSITIONS: 0>, 'VELOCITIES': <DiffWRT.VELOCITIES: 2>}¶

__module__ = 'ipctk'¶

__ne__(self, other: object) → bool¶

__repr__(self) → str¶

__setstate__(self, state: int) → None¶

__str__(self) → str¶

property name : str¶

property value : int¶

LAGGED_DISPLACEMENTS = <DiffWRT.LAGGED_DISPLACEMENTS: 1>¶

REST_POSITIONS = <DiffWRT.REST_POSITIONS: 0>¶

VELOCITIES = <DiffWRT.VELOCITIES: 2>¶

__annotations__ = {}¶

__call__(*args, **kwargs)¶

Overloaded function.

1. __call__(self: ipctk.TangentialPotential, collisions: ipctk.TangentialCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]]) -> float

   Compute the potential for a set of collisions.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. X: Degrees of freedom of the collision mesh (e.g., vertices or velocities).

   Returns:

   The potential for a set of collisions.

2. __call__(self: ipctk.TangentialPotential, collision: ipctk.TangentialCollision, x: numpy.ndarray[numpy.float64[m, 1]]) -> float

   Compute the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The potential.

__init__(*args, **kwargs)¶

__module__ = 'ipctk'¶

force(*args, **kwargs)¶

Overloaded function.

1. force(self: ipctk.TangentialPotential, collisions: ipctk.TangentialCollisions, mesh: ipc::CollisionMesh, rest_positions: numpy.ndarray[numpy.float64[m, n]], lagged_displacements: numpy.ndarray[numpy.float64[m, n]], velocities: numpy.ndarray[numpy.float64[m, n]], normal_potential: ipctk.NormalPotential, normal_stiffness: float, dmin: float = 0, no_mu: bool = False) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the friction force from the given velocities.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. rest_positions: Rest positions of the vertices (rowwise). lagged_displacements: Previous displacements of the vertices (rowwise). velocities: Current displacements of the vertices (rowwise). normal_potential: Normal potential (used for normal force magnitude). normal_stiffness: Normal stiffness (used for normal force magnitude). dmin: Minimum distance (used for normal force magnitude). no_mu: whether to not multiply by mu

   Returns:

   The friction force.

2. force(self: ipctk.TangentialPotential, collision: ipctk.TangentialCollision, rest_positions: numpy.ndarray[numpy.float64[m, 1]], lagged_displacements: numpy.ndarray[numpy.float64[m, 1]], velocities: numpy.ndarray[numpy.float64[m, 1]], normal_potential: ipctk.NormalPotential, normal_stiffness: float, dmin: float = 0, no_mu: bool = False) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the friction force.

   Parameters:

   collision: The collision rest_positions: Rest positions of the vertices (rowwise). lagged_displacements: Previous displacements of the vertices (rowwise). velocities: Current displacements of the vertices (rowwise). normal_potential: Normal potential (used for normal force magnitude). normal_stiffness: Normal stiffness (used for normal force magnitude). dmin: Minimum distance (used for normal force magnitude). no_mu: Whether to not multiply by mu

   Returns:

   Friction force

force_jacobian(*args, **kwargs)¶

Overloaded function.

1. force_jacobian(self: ipctk.TangentialPotential, collisions: ipctk.TangentialCollisions, mesh: ipc::CollisionMesh, rest_positions: numpy.ndarray[numpy.float64[m, n]], lagged_displacements: numpy.ndarray[numpy.float64[m, n]], velocities: numpy.ndarray[numpy.float64[m, n]], normal_potential: ipctk.NormalPotential, normal_stiffness: float, wrt: ipctk.TangentialPotential.DiffWRT, dmin: float = 0) -> scipy.sparse.csc_matrix[numpy.float64]

   Compute the Jacobian of the friction force wrt the velocities.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. rest_positions: Rest positions of the vertices (rowwise). lagged_displacements: Previous displacements of the vertices (rowwise). velocities: Current displacements of the vertices (rowwise). normal_potential: Normal potential (used for normal force magnitude). normal_stiffness: Normal stiffness (used for normal force magnitude). wrt: The variable to take the derivative with respect to. dmin: Minimum distance (used for normal force magnitude).

   Returns:

   The Jacobian of the friction force wrt the velocities.

2. force_jacobian(self: ipctk.TangentialPotential, collision: ipctk.TangentialCollision, rest_positions: numpy.ndarray[numpy.float64[m, 1]], lagged_displacements: numpy.ndarray[numpy.float64[m, 1]], velocities: numpy.ndarray[numpy.float64[m, 1]], normal_potential: ipctk.NormalPotential, normal_stiffness: float, wrt: ipctk.TangentialPotential.DiffWRT, dmin: float = 0) -> numpy.ndarray[numpy.float64[m, n]]

   Compute the friction force Jacobian.

   Parameters:

   collision: The collision rest_positions: Rest positions of the vertices (rowwise). lagged_displacements: Previous displacements of the vertices (rowwise). velocities: Current displacements of the vertices (rowwise). normal_potential: Normal potential (used for normal force magnitude). normal_stiffness: Normal stiffness (used for normal force magnitude). wrt: Variable to differentiate the friction force with respect to. dmin: Minimum distance (used for normal force magnitude).

   Returns:

   Friction force Jacobian

gradient(*args, **kwargs)¶

Overloaded function.

1. gradient(self: ipctk.TangentialPotential, collisions: ipctk.TangentialCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]]) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the gradient of the potential.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. 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|.

2. gradient(self: ipctk.TangentialPotential, collision: ipctk.TangentialCollision, x: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

   Compute the gradient of the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The gradient of the potential.

hessian(*args, **kwargs)¶

Overloaded function.

1. hessian(self: ipctk.TangentialPotential, collisions: ipctk.TangentialCollisions, mesh: ipc::CollisionMesh, X: numpy.ndarray[numpy.float64[m, n]], project_hessian_to_psd: ipctk.PSDProjectionMethod = <PSDProjectionMethod.NONE: 0>) -> scipy.sparse.csc_matrix[numpy.float64]

   Compute the hessian of the potential.

   Parameters:

   collisions: The set of collisions. mesh: The collision mesh. X: Degrees of freedom of the collision mesh (e.g., vertices or velocities). project_hessian_to_psd: 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|.

2. hessian(self: ipctk.TangentialPotential, collision: ipctk.TangentialCollision, x: numpy.ndarray[numpy.float64[m, 1]], project_hessian_to_psd: ipctk.PSDProjectionMethod = <PSDProjectionMethod.NONE: 0>) -> numpy.ndarray[numpy.float64[m, n]]

   Compute the hessian of the potential for a single collision.

   Parameters:

   collision: The collision. x: The collision stencil’s degrees of freedom.

   Returns:

   The hessian of the potential.

Friction Potential¶

class ipctk.FrictionPotential¶

Bases: TangentialPotential

Public Data Attributes:

eps_v

The smooth friction mollifier parameter \(\epsilon_{v}\).

Inherited from TangentialPotential

REST_POSITIONS
LAGGED_DISPLACEMENTS
VELOCITIES

Public Methods:

__init__(self, eps_v)

Construct a friction potential.

Inherited from TangentialPotential

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
force(*args, **kwargs)	Overloaded function.
force_jacobian(*args, **kwargs)	Overloaded function.

Inherited from pybind11_object

---

__annotations__ = {}¶

__init__(self, eps_v: float)¶

Construct a friction potential.

Parameters:¶

eps_v: float¶

The smooth friction mollifier parameter \(\\epsilon_{v}\).

__module__ = 'ipctk'¶

property eps_v : float¶

The smooth friction mollifier parameter \(\epsilon_{v}\).

Tangential Adhesion Potential¶

class ipctk.TangentialAdhesionPotential¶

Bases: TangentialPotential

Public Data Attributes:

eps_a

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

Inherited from TangentialPotential

REST_POSITIONS
LAGGED_DISPLACEMENTS
VELOCITIES

Public Methods:

__init__(self, eps_a)

Construct a tangential adhesion potential.

Inherited from TangentialPotential

__init__(*args, **kwargs)
__call__(*args, **kwargs)	Overloaded function.
gradient(*args, **kwargs)	Overloaded function.
hessian(*args, **kwargs)	Overloaded function.
force(*args, **kwargs)	Overloaded function.
force_jacobian(*args, **kwargs)	Overloaded function.

Inherited from pybind11_object

---

__annotations__ = {}¶

__init__(self, eps_a: float)¶

Construct a tangential adhesion potential.

Parameters:¶

eps_a: float¶

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

__module__ = 'ipctk'¶

property eps_a : float¶

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