NormalizedBarrier¶

template <typename BarrierT>
class NormalizedBarrier : public BarrierT;¶

Inheritance diagram for ipc::NormalizedBarrier:

Collaboration diagram for ipc::NormalizedBarrier:

Normalized barrier function from [Li et al. 2023].

Public Functions¶

NormalizedBarrier() = default;¶

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

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

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

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The value of the barrier function at d.

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

Derivative of the barrier function.

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

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The derivative of the barrier wrt d.

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

Second derivative of the barrier function.

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

Parameters:¶

const double d¶

The distance.

const double dhat¶

Activation distance of the barrier.

Returns:¶

The second derivative of the barrier wrt d.

inline 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.