Barrier¶

Barrier functions and functionals.

Types¶

Functions¶

Function Details¶

double ipc::barrier(const double d, const double dhat);¶

Function that grows to infinity as d approaches 0 from the right.

\[ b(d) = -(d-\hat{d})^2\ln\left(\frac{d}{\hat{d}}\right) \]

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The value of the barrier function at d.

double ipc::barrier_first_derivative(
    const double d, const double dhat);¶

Derivative of the barrier function.

\[ b'(d) = (\hat{d}-d) \left( 2\ln\left( \frac{d}{\hat{d}} \right) - \frac{\hat{d}}{d} + 1\right) \]

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The derivative of the barrier wrt d.

double ipc::barrier_second_derivative(
    const double d, const double dhat);¶

Second derivative of the barrier function.

\[ b''(d) = \left( \frac{\hat{d}}{d} + 2 \right) \frac{\hat{d}}{d} - 2\ln\left( \frac{d}{\hat{d}} \right) - 3 \]

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The second derivative of the barrier wrt d.

Barrier Force Magnitude¶

double ipc::barrier_force_magnitude(const double distance_squared,
    const Barrier& barrier, const double dhat,
    const double barrier_stiffness, const double dmin = 0);¶

Compute the magnitude of the force due to a barrier.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

const Barrier &barrier¶

The barrier function.

const double dhat¶

The activation distance of the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

const double dmin = 0¶

The minimum distance offset to the barrier.

Returns:¶

The magnitude of the force.

VectorMax12d ipc::barrier_force_magnitude_gradient(
    const double distance_squared,
    Eigen::ConstRef<VectorMax12d> distance_squared_gradient,
    const Barrier& barrier, const double dhat,
    const double barrier_stiffness, const double dmin = 0);¶

Compute the gradient of the magnitude of the force due to a barrier.

Parameters:¶

const double distance_squared¶

The squared distance between elements.

Eigen::ConstRef<VectorMax12d> distance_squared_gradient¶

The gradient of the squared distance.

const Barrier &barrier¶

The barrier function.

const double dhat¶

The activation distance of the barrier.

const double barrier_stiffness¶

The stiffness of the barrier.

const double dmin = 0¶

The minimum distance offset to the barrier.

Returns:¶

The gradient of the force.

Adaptive Barrier Stiffness¶

double ipc::initial_barrier_stiffness(const double bbox_diagonal,
    const Barrier& barrier, const double dhat,
    const double average_mass,
    Eigen::ConstRef<Eigen::VectorXd> grad_energy,
    Eigen::ConstRef<Eigen::VectorXd> grad_barrier,
    double& max_barrier_stiffness,
    const double min_barrier_stiffness_scale = 1e11,
    const double dmin = 0);¶

Compute an inital barrier stiffness using the barrier potential gradient.

Parameters:¶

const double bbox_diagonal¶

[in] Length of the diagonal of the bounding box of the scene.

const Barrier &barrier¶

[in] Barrier function.

const double dhat¶

[in] Activation distance of the barrier.

const double average_mass¶

[in] Average mass of all bodies.

Eigen::ConstRef<Eigen::VectorXd> grad_energy¶

[in] Gradient of the elasticity energy function.

Eigen::ConstRef<Eigen::VectorXd> grad_barrier¶

[in] Gradient of the barrier potential.

double &max_barrier_stiffness¶

[out] Maximum stiffness of the barrier.

const double min_barrier_stiffness_scale = 1e11¶

[in] Scale used to premultiply the minimum barrier stiffness.

const double dmin = 0¶

[in] Minimum distance between elements.

Returns:¶

The initial barrier stiffness.

double ipc::update_barrier_stiffness(const double prev_min_distance,
    const double min_distance, const double max_barrier_stiffness,
    const double barrier_stiffness, const double bbox_diagonal,
    const double dhat_epsilon_scale = 1e-9, const double dmin = 0);¶

Update the barrier stiffness if the distance is decreasing and less than dhat_epsilon_scale * diag.

Parameters:¶

const double prev_min_distance¶

[in] Previous minimum distance between elements.

const double min_distance¶

[in] Current minimum distance between elements.

const double max_barrier_stiffness¶

[in] Maximum stiffness of the barrier.

const double barrier_stiffness¶

[in] Current barrier stiffness.

const double bbox_diagonal¶

[in] Length of the diagonal of the bounding box of the scene.

const double dhat_epsilon_scale = 1e-9¶

[in] Update if distance is less than this fraction of the diagonal.

const double dmin = 0¶

[in] Minimum distance between elements.

Returns:¶

The updated barrier stiffness.

Semi-Implicit Stiffness¶

template <typename StencilsT>
Eigen::VectorXd ipc::semi_implicit_stiffness(
    const CollisionMesh& mesh,
    Eigen::ConstRef<Eigen::MatrixXd> vertices,
    const StencilsT& collisions,
    Eigen::ConstRef<Eigen::VectorXd> vertex_masses,
    const Eigen::SparseMatrix<double>& hess, const double dmin);¶

Compute the semi-implicit stiffness’s for all collisions.

Note

See [Ando 2024] for details.

Parameters:¶

const CollisionMesh &mesh¶

Collision mesh.

Eigen::ConstRef<Eigen::MatrixXd> vertices¶

Vertex positions.

const StencilsT &collisions¶

Normal collisions or collision candidates.

Eigen::ConstRef<Eigen::VectorXd> vertex_masses¶

Lumped vertex masses.

const Eigen::SparseMatrix<double> &hess¶

Hessian of the elasticity energy function.

const double dmin¶

Minimum distance between elements.

Returns:¶

The semi-implicit stiffness’s.