Barrier

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

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.

double ipc::barrier_first_derivative(
    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_second_derivative(
    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.

Barrier Force Magnitude

double ipc::barrier_force_magnitude(const double distance_squared,
    const Barrier& barrier, const double dhat,
    const double barrier_stiffness, const double dmin = 0)

Compute the magnitude of the force due to a barrier.

Parameters:
const double distance_squared

The squared distance between elements.

const Barrier &barrier

The barrier function.

const double dhat

The activation distance of the barrier.

const double barrier_stiffness

The stiffness of the barrier.

const double dmin = 0

The minimum distance offset to the barrier.

Returns:

The magnitude of the force.

VectorMax12d ipc::barrier_force_magnitude_gradient(
    const double distance_squared,
    const VectorMax12d& distance_squared_gradient,
    const Barrier& barrier, const double dhat,
    const double barrier_stiffness, const double dmin = 0)

Compute the gradient of the magnitude of the force due to a barrier.

Parameters:
const double distance_squared

The squared distance between elements.

const VectorMax12d &distance_squared_gradient

The gradient of the squared distance.

const Barrier &barrier

The barrier function.

const double dhat

The activation distance of the barrier.

const double barrier_stiffness

The stiffness of the barrier.

const double dmin = 0

The minimum distance offset to the barrier.

Returns:

The gradient of the force.

Adaptive Barrier Stiffness

double ipc::initial_barrier_stiffness(const double bbox_diagonal,
    const Barrier& barrier, 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 Barrier &barrier

[in] Barrier function.

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.

Barrier Class

class Barrier

Inheritence diagram for ipc::Barrier:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "2" [label="ipc::ClampedLogBarrier" tooltip="ipc::ClampedLogBarrier"] "3" [label="ipc::NormalizedClampedLogBarrier" tooltip="ipc::NormalizedClampedLogBarrier"] "1" [label="ipc::Barrier" tooltip="ipc::Barrier" fillcolor="#BFBFBF"] "2" -> "1" [dir=forward tooltip="public-inheritance"] "3" -> "2" [dir=forward tooltip="public-inheritance"] }

Base class for barrier functions.

Subclassed by ipc::ClampedLogBarrier

Public Functions

Barrier() = default
virtual ~Barrier() = default
virtual double operator()(
    const double d, const double dhat) const = 0

Evaluate the barrier function.

Parameters:
const double d

Distance.

const double dhat

Activation distance of the barrier.

Returns:

The value of the barrier function at d.

virtual double first_derivative(
    const double d, const double dhat) const = 0

Evaluate the first derivative of the barrier function wrt d.

Parameters:
const double d

Distance.

const double dhat

Activation distance of the barrier.

Returns:

The value of the first derivative of the barrier function at d.

virtual double second_derivative(
    const double d, const double dhat) const = 0

Evaluate the second derivative of the barrier function wrt d.

Parameters:
const double d

Distance.

const double dhat

Activation distance of the barrier.

Returns:

The value of the second derivative of the barrier function at d.

virtual double units(const double dhat) const = 0

Get the units of the barrier function.

Parameters:
const double dhat

The activation distance of the barrier.

Returns:

Clamped Log Barrier

class ClampedLogBarrier : public ipc::Barrier

Inheritence diagram for ipc::ClampedLogBarrier:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "1" [label="ipc::ClampedLogBarrier" tooltip="ipc::ClampedLogBarrier" fillcolor="#BFBFBF"] "3" [label="ipc::NormalizedClampedLogBarrier" tooltip="ipc::NormalizedClampedLogBarrier"] "2" [label="ipc::Barrier" tooltip="ipc::Barrier"] "1" -> "2" [dir=forward tooltip="public-inheritance"] "3" -> "1" [dir=forward tooltip="public-inheritance"] }

Collaboration diagram for ipc::ClampedLogBarrier:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "1" [label="ipc::ClampedLogBarrier" tooltip="ipc::ClampedLogBarrier" fillcolor="#BFBFBF"] "2" [label="ipc::Barrier" tooltip="ipc::Barrier"] "1" -> "2" [dir=forward tooltip="public-inheritance"] }

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

Subclassed by ipc::NormalizedClampedLogBarrier

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.

Normalized Clamped Log Barrier

class NormalizedClampedLogBarrier : public ipc::ClampedLogBarrier

Inheritence diagram for ipc::NormalizedClampedLogBarrier:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "2" [label="ipc::ClampedLogBarrier" tooltip="ipc::ClampedLogBarrier"] "1" [label="ipc::NormalizedClampedLogBarrier" tooltip="ipc::NormalizedClampedLogBarrier" fillcolor="#BFBFBF"] "3" [label="ipc::Barrier" tooltip="ipc::Barrier"] "2" -> "3" [dir=forward tooltip="public-inheritance"] "1" -> "2" [dir=forward tooltip="public-inheritance"] }

Collaboration diagram for ipc::NormalizedClampedLogBarrier:

digraph { graph [bgcolor="#00000000"] node [shape=rectangle style=filled fillcolor="#FFFFFF" font=Helvetica padding=2] edge [color="#1414CE"] "2" [label="ipc::ClampedLogBarrier" tooltip="ipc::ClampedLogBarrier"] "1" [label="ipc::NormalizedClampedLogBarrier" tooltip="ipc::NormalizedClampedLogBarrier" fillcolor="#BFBFBF"] "3" [label="ipc::Barrier" tooltip="ipc::Barrier"] "2" -> "3" [dir=forward tooltip="public-inheritance"] "1" -> "2" [dir=forward tooltip="public-inheritance"] }

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

Public Functions

NormalizedClampedLogBarrier() = 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.

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

Parameters:
const double d

The distance.

const double dhat

Activation distance of the barrier.

Returns:

The value of the barrier function at d.

inline virtual 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 virtual 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 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.

Last update: Dec 12, 2024