ClampedLogBarrier¶

class ClampedLogBarrier : public ipc::Barrier;¶

Inheritance diagram for ipc::ClampedLogBarrier:

Collaboration diagram for ipc::ClampedLogBarrier:

Smoothly clamped log barrier functions from [Li et al. 2020].

Public Functions¶

ClampedLogBarrier() = default;¶

inline virtual double operator()(
    const double d, const double dhat) const override;¶

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.

inline virtual double first_derivative(
    const double d, const double dhat) const override;¶

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.

inline virtual double second_derivative(
    const double d, const double dhat) const override;¶

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.

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

Get the units of the barrier function.

Parameters:¶

const double dhat¶

The activation distance of the barrier.

Returns:¶

The units of the barrier function.