Two-Stage Barrier¶

template <typename T = double>
class TwoStageBarrier : public ipc::BarrierBase<double>;¶

Inheritance diagram for ipc::TwoStageBarrier:

Collaboration diagram for ipc::TwoStageBarrier:

2-Stage activation function from [Chen et al. 2025].

Public Functions¶

TwoStageBarrier() = default;¶

virtual T operator()(const T d, const T dhat) const override;¶

Two-stage activation barrier.

\[\begin{split} b(d) = \begin{cases} \infty & d \le 0\\ -\frac{\hat{d}^2}{4} \left(\ln\left(\frac{2d}{\hat{d}}\right) - \tfrac{1}{2}\right) & d < \frac{\hat{d}}{2}\\ \tfrac{1}{2} (\hat{d} - d)^2 & d < \hat{d}\\ 0 & d \ge \hat{d} \end{cases} \end{split}\]

Parameters:¶

const T d¶

The distance.

const T dhat¶

Activation distance of the barrier.

Returns:¶

The value of the barrier function at d.

virtual T first_derivative(const T d, const T dhat) const override;¶

Derivative of the barrier function.

\[\begin{split} b'(d) = \begin{cases} 0 & d \le 0\\ -\frac{\hat{d}^2}{4d} & d < \frac{\hat{d}}{2}\\ d - \hat{d} & d < \hat{d}\\ 0 & d \ge \hat{d} \end{cases} \end{split}\]

Parameters:¶

const T d¶

The distance.

const T dhat¶

Activation distance of the barrier.

Returns:¶

The derivative of the barrier wrt d.

virtual T second_derivative(const T d, const T dhat) const override;¶

Second derivative of the barrier function.

\[\begin{split} b''(d) = \begin{cases} 0 & d \le 0\\ \frac{\hat{d}^2}{4d^2} & d < \frac{\hat{d}}{2}\\ 1 & d < \hat{d}\\ 0 & d \ge \hat{d} \end{cases} \end{split}\]

Parameters:¶

const T d¶

The distance.

const T dhat¶

Activation distance of the barrier.

Returns:¶

The second derivative of the barrier wrt d.

inline virtual T units(const T dhat) const override;¶

Get the units of the barrier function.

Parameters:¶

const T dhat¶

The activation distance of the barrier.

Returns:¶

The units of the barrier function.