Barrier¶

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

Function that grows to infinity as x 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_gradient(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_hessian(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.

Adaptive Barrier Stiffness¶

double ipc::initial_barrier_stiffness(const double bbox_diagonal,
    const double dhat, const double average_mass,
    const Eigen::VectorXd& grad_energy,
    const 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 double dhat¶

[in] Activation distance of the barrier.

const double average_mass¶

[in] Average mass of all bodies.

const Eigen::VectorXd &grad_energy¶

[in] Gradient of the elasticity energy function.

const 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.