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,
    Eigen::ConstRef<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.

Eigen::ConstRef<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,
    Eigen::ConstRef<Eigen::MatrixXd> X) const;¶

Compute the gradient of the potential.

Parameters:¶

const TCollisions &collisions¶

The set of collisions.

const CollisionMesh &mesh¶

The collision mesh.

Eigen::ConstRef<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, Eigen::ConstRef<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.

Eigen::ConstRef<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,
    Eigen::ConstRef<VectorMaxNd> x) const
    = 0;¶

Compute the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

Eigen::ConstRef<VectorMaxNd> x¶

The collision stencil’s degrees of freedom.

Returns:¶

The potential.

virtual VectorMaxNd gradient(const TCollision& collision,
    Eigen::ConstRef<VectorMaxNd> x) const
    = 0;¶

Compute the gradient of the potential for a single collision.

Parameters:¶

const TCollision &collision¶

The collision.

Eigen::ConstRef<VectorMaxNd> x¶

The collision stencil’s degrees of freedom.

Returns:¶

The gradient of the potential.

virtual MatrixMaxNd hessian(const TCollision& collision,
    Eigen::ConstRef<VectorMaxNd> 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.

Eigen::ConstRef<VectorMaxNd> x¶

The collision stencil’s degrees of freedom.

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.

Protected Types¶

using TCollision = typename TCollisions::value_type;¶

using VectorMaxNd = Vector<double, Eigen::Dynamic, STENCIL_NDOF>;¶

using MatrixMaxNd = MatrixMax<double, STENCIL_NDOF, STENCIL_NDOF>;¶

Protected Static Attributes¶

static constexpr int STENCIL_NDOF = 3 * TCollision::STENCIL_SIZE;¶

Maximum degrees of freedom per collision.