NormalPotential¶

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

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,
    Eigen::ConstRef<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.

Eigen::ConstRef<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,
    Eigen::ConstRef<VectorMax12d> positions) const override;¶

Compute the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> positions¶

The collision stencil’s positions.

Returns:¶

The potential.

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

Compute the gradient of the potential for a single collision.

Parameters:¶

const NormalCollision &collision¶

The collision.

Eigen::ConstRef<VectorMax12d> positions¶

The collision stencil’s positions.

Returns:¶

The gradient of the potential.

MatrixMax12d hessian(const NormalCollision& collision,
    Eigen::ConstRef<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.

Eigen::ConstRef<VectorMax12d> positions¶

The collision stencil’s positions.

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.

void shape_derivative(const NormalCollision& collision,
    const std::array<index_t, 4>& vertex_ids,
    Eigen::ConstRef<VectorMax12d> rest_positions,
    Eigen::ConstRef<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<index_t, 4> &vertex_ids¶

[in] The collision stencil’s vertex ids.

Eigen::ConstRef<VectorMax12d> rest_positions¶

[in] The collision stencil’s rest positions.

Eigen::ConstRef<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,
    Eigen::ConstRef<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.

Eigen::ConstRef<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>;¶