ClampedLogSqBarrier¶

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

Inheritance diagram for ipc::ClampedLogSqBarrier:

Collaboration diagram for ipc::ClampedLogSqBarrier:

Clamped log barrier with a quadratic log term from [Huang et al. 2024].

Public Functions¶

ClampedLogSqBarrier() = default;¶

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

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

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

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.

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

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.

\[ b''(d) = 2 \left(\ln^2\left(\frac{d}{\hat{d}}\right) - \left( \ln\left(\frac{d}{\hat{d}}\right) - 1\right) \frac{(\hat{d} - d)^2}{d^2} - 4 \ln\left(\frac{d}{\hat{d}}\right) \frac{\hat{d} - d}{d}\right) \]

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.