Continuous Collision Detection

bool ipc::is_step_collision_free(const CollisionMesh& mesh,
    const Eigen::MatrixXd& vertices_t0,
    const Eigen::MatrixXd& vertices_t1,
    const double min_distance = 0.0,
    const std::shared_ptr<BroadPhase> broad_phase
    = make_default_broad_phase(),
    const NarrowPhaseCCD& narrow_phase_ccd
    = DEFAULT_NARROW_PHASE_CCD);

Determine if the step is collision free.

Note

Assumes the trajectory is linear.

Parameters:
const CollisionMesh &mesh

The collision mesh.

const Eigen::MatrixXd &vertices_t0

Surface vertex vertices at start as rows of a matrix.

const Eigen::MatrixXd &vertices_t1

Surface vertex vertices at end as rows of a matrix.

const double min_distance = 0.0

The minimum distance allowable between any two elements.

broad_phase_method

The broad phase method to use.

const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD

The narrow phase CCD algorithm to use.

Returns:

True if any collisions occur.

double ipc::compute_collision_free_stepsize(
    const CollisionMesh& mesh, const Eigen::MatrixXd& vertices_t0,
    const Eigen::MatrixXd& vertices_t1,
    const double min_distance = 0.0,
    const std::shared_ptr<BroadPhase> broad_phase
    = make_default_broad_phase(),
    const NarrowPhaseCCD& narrow_phase_ccd
    = DEFAULT_NARROW_PHASE_CCD);

Computes a maximal step size that is collision free.

Note

Assumes the trajectory is linear.

Parameters:
const CollisionMesh &mesh

The collision mesh.

const Eigen::MatrixXd &vertices_t0

Vertex vertices at start as rows of a matrix. Assumes vertices_t0 is intersection free.

const Eigen::MatrixXd &vertices_t1

Surface vertex vertices at end as rows of a matrix.

const double min_distance = 0.0

The minimum distance allowable between any two elements.

broad_phase_method

The broad phase method to use.

const NarrowPhaseCCD &narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD

The narrow phase CCD algorithm to use.

Returns:

A step-size \(\in [0, 1]\) that is collision free. A value of 1.0 if a full step and 0.0 is no step.

Narrow Phase CCD

class NarrowPhaseCCD;

Inheritence diagram for ipc::NarrowPhaseCCD:

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

Subclassed by ipc::AdditiveCCD, ipc::TightInclusionCCD

Public Functions

NarrowPhaseCCD() = default;
virtual ~NarrowPhaseCCD() = default;
virtual bool point_point_ccd(const VectorMax3d& p0_t0,
    const VectorMax3d& p1_t0, const VectorMax3d& p0_t1,
    const VectorMax3d& p1_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const
    = 0;
virtual bool point_edge_ccd(const VectorMax3d& p_t0,
    const VectorMax3d& e0_t0, const VectorMax3d& e1_t0,
    const VectorMax3d& p_t1, const VectorMax3d& e0_t1,
    const VectorMax3d& e1_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const
    = 0;
virtual bool point_triangle_ccd(const Eigen::Vector3d& p_t0,
    const Eigen::Vector3d& t0_t0, const Eigen::Vector3d& t1_t0,
    const Eigen::Vector3d& t2_t0, const Eigen::Vector3d& p_t1,
    const Eigen::Vector3d& t0_t1, const Eigen::Vector3d& t1_t1,
    const Eigen::Vector3d& t2_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const
    = 0;
virtual bool edge_edge_ccd(const Eigen::Vector3d& ea0_t0,
    const Eigen::Vector3d& ea1_t0, const Eigen::Vector3d& eb0_t0,
    const Eigen::Vector3d& eb1_t0, const Eigen::Vector3d& ea0_t1,
    const Eigen::Vector3d& ea1_t1, const Eigen::Vector3d& eb0_t1,
    const Eigen::Vector3d& eb1_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const
    = 0;

Tight Inclusion CCD

class TightInclusionCCD : public ipc::NarrowPhaseCCD;

Inheritence diagram for ipc::TightInclusionCCD:

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

Collaboration diagram for ipc::TightInclusionCCD:

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

Public Functions

TightInclusionCCD(const double tolerance = DEFAULT_TOLERANCE,
    const long max_iterations = DEFAULT_MAX_ITERATIONS,
    const double conservative_rescaling
    = DEFAULT_CONSERVATIVE_RESCALING);

Construct a new AdditiveCCD object.

Parameters:
const double conservative_rescaling = DEFAULT_CONSERVATIVE_RESCALING

The conservative rescaling of the time of impact.

virtual bool point_point_ccd(const VectorMax3d& p0_t0,
    const VectorMax3d& p1_t0, const VectorMax3d& p0_t1,
    const VectorMax3d& p1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between two points using continuous collision detection.

Parameters:
const VectorMax3d &p0_t0

[in] The initial position of the first point.

const VectorMax3d &p1_t0

[in] The initial position of the second point.

const VectorMax3d &p0_t1

[in] The final position of the first point.

const VectorMax3d &p1_t1

[in] The final position of the second point.

double &toi

[out] The time of impact between the two points.

const double min_distance = 0.0

[in] The minimum distance between the points.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

virtual bool point_edge_ccd(const VectorMax3d& p_t0,
    const VectorMax3d& e0_t0, const VectorMax3d& e1_t0,
    const VectorMax3d& p_t1, const VectorMax3d& e0_t1,
    const VectorMax3d& e1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between a point and an edge using continuous collision detection.

Parameters:
const VectorMax3d &p_t0

[in] The initial position of the point.

const VectorMax3d &e0_t0

[in] The initial position of the first endpoint of the edge.

const VectorMax3d &e1_t0

[in] The initial position of the second endpoint of the edge.

const VectorMax3d &p_t1

[in] The final position of the point.

const VectorMax3d &e0_t1

[in] The final position of the first endpoint of the edge.

const VectorMax3d &e1_t1

[in] The final position of the second endpoint of the edge.

double &toi

[out] The time of impact between the point and the edge.

const double min_distance = 0.0

[in] The minimum distance between the objects.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

virtual bool edge_edge_ccd(const Eigen::Vector3d& ea0_t0,
    const Eigen::Vector3d& ea1_t0, const Eigen::Vector3d& eb0_t0,
    const Eigen::Vector3d& eb1_t0, const Eigen::Vector3d& ea0_t1,
    const Eigen::Vector3d& ea1_t1, const Eigen::Vector3d& eb0_t1,
    const Eigen::Vector3d& eb1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between two edges in 3D using continuous collision detection.

Parameters:
const Eigen::Vector3d &ea0_t0

[in] The initial position of the first endpoint of the first edge.

const Eigen::Vector3d &ea1_t0

[in] The initial position of the second endpoint of the first edge.

const Eigen::Vector3d &eb0_t0

[in] The initial position of the first endpoint of the second edge.

const Eigen::Vector3d &eb1_t0

[in] The initial position of the second endpoint of the second edge.

const Eigen::Vector3d &ea0_t1

[in] The final position of the first endpoint of the first edge.

const Eigen::Vector3d &ea1_t1

[in] The final position of the second endpoint of the first edge.

const Eigen::Vector3d &eb0_t1

[in] The final position of the first endpoint of the second edge.

const Eigen::Vector3d &eb1_t1

[in] The final position of the second endpoint of the second edge.

double &toi

[out] The time of impact between the two edges.

const double min_distance = 0.0

[in] The minimum distance between the objects.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

virtual bool point_triangle_ccd(const Eigen::Vector3d& p_t0,
    const Eigen::Vector3d& t0_t0, const Eigen::Vector3d& t1_t0,
    const Eigen::Vector3d& t2_t0, const Eigen::Vector3d& p_t1,
    const Eigen::Vector3d& t0_t1, const Eigen::Vector3d& t1_t1,
    const Eigen::Vector3d& t2_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between a point and a triangle in 3D using continuous collision detection.

Parameters:
const Eigen::Vector3d &p_t0

[in] The initial position of the point.

const Eigen::Vector3d &t0_t0

[in] The initial position of the first vertex of the triangle.

const Eigen::Vector3d &t1_t0

[in] The initial position of the second vertex of the triangle.

const Eigen::Vector3d &t2_t0

[in] The initial position of the third vertex of the triangle.

const Eigen::Vector3d &p_t1

[in] The final position of the point.

const Eigen::Vector3d &t0_t1

[in] The final position of the first vertex of the triangle.

const Eigen::Vector3d &t1_t1

[in] The final position of the second vertex of the triangle.

const Eigen::Vector3d &t2_t1

[in] The final position of the third vertex of the triangle.

double &toi

[out] The time of impact between the point and the triangle.

const double min_distance = 0.0

[in] The minimum distance between the objects.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

Public Members

double tolerance;

Solver tolerance.

long max_iterations;

Maximum number of iterations.

double conservative_rescaling;

Conservative rescaling of the time of impact.

Public Static Attributes

static constexpr double DEFAULT_TOLERANCE = 1e-6;

The default tolerance used with Tight-Inclusion CCD.

static constexpr long DEFAULT_MAX_ITERATIONS = 10'000'000l;

The default maximum number of iterations used with Tight-Inclusion CCD.

static constexpr double DEFAULT_CONSERVATIVE_RESCALING = 0.8;

The default conservative rescaling value used to avoid taking steps exactly to impact.

static constexpr double SMALL_TOI = 1e-6;

Tolerance for small time of impact which triggers rerunning CCD without a minimum separation.

Private Functions

bool point_point_ccd_3D(const Eigen::Vector3d& p0_t0,
    const Eigen::Vector3d& p1_t0, const Eigen::Vector3d& p0_t1,
    const Eigen::Vector3d& p1_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const;

Computes the time of impact between two points in 3D using continuous collision detection.

Parameters:
const Eigen::Vector3d &p0_t0

[in] The initial position of the first point.

const Eigen::Vector3d &p1_t0

[in] The initial position of the second point.

const Eigen::Vector3d &p0_t1

[in] The final position of the first point.

const Eigen::Vector3d &p1_t1

[in] The final position of the second point.

double &toi

[out] The time of impact between the two points.

const double min_distance = 0.0

[in] The minimum distance between the objects.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

bool point_edge_ccd_3D(const Eigen::Vector3d& p_t0,
    const Eigen::Vector3d& e0_t0, const Eigen::Vector3d& e1_t0,
    const Eigen::Vector3d& p_t1, const Eigen::Vector3d& e0_t1,
    const Eigen::Vector3d& e1_t1, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const;

Computes the time of impact between a point and an edge in 3D using continuous collision detection.

Parameters:
const Eigen::Vector3d &p_t0

[in] The initial position of the point.

const Eigen::Vector3d &e0_t0

[in] The initial position of the first endpoint of the edge.

const Eigen::Vector3d &e1_t0

[in] The initial position of the second endpoint of the edge.

const Eigen::Vector3d &p_t1

[in] The final position of the point.

const Eigen::Vector3d &e0_t1

[in] The final position of the first endpoint of the edge.

const Eigen::Vector3d &e1_t1

[in] The final position of the second endpoint of the edge.

double &toi

[out] The time of impact between the point and the edge.

const double min_distance = 0.0

[in] The minimum distance between the objects.

const double tmax = 1.0

[in] The maximum time to check for collisions.

Returns:

True if a collision was detected, false otherwise.

Private Static Functions

static bool ccd_strategy(
    const std::function<bool(double, bool, double&)>& ccd,
    const double min_distance, const double initial_distance,
    const double conservative_rescaling, double& toi);

Perform the CCD strategy outlined by Li et al.

[2020].

Parameters:
const std::function<bool(double, bool, double&)> &ccd

[in] The continuous collision detection function.

const double min_distance

[in] The minimum distance between the objects.

const double initial_distance

[in] The initial distance between the objects.

const double conservative_rescaling

[in] The conservative rescaling of the time of impact.

double &toi

[out] Output time of impact.

Returns:

True if a collision was detected, false otherwise.

Additive CCD

class AdditiveCCD : public ipc::NarrowPhaseCCD;

Inheritence diagram for ipc::AdditiveCCD:

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

Collaboration diagram for ipc::AdditiveCCD:

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

Additive Continuous Collision Detection (CCD) from [Li et al. 2021].

Public Functions

AdditiveCCD(const long max_iterations = UNLIMITTED_ITERATIONS,
    const double conservative_rescaling
    = DEFAULT_CONSERVATIVE_RESCALING);

Construct a new AdditiveCCD object.

Parameters:
const double conservative_rescaling = DEFAULT_CONSERVATIVE_RESCALING

The conservative rescaling of the time of impact.

virtual bool point_point_ccd(const VectorMax3d& p0_t0,
    const VectorMax3d& p1_t0, const VectorMax3d& p0_t1,
    const VectorMax3d& p1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between two points using continuous collision detection.

Parameters:
const VectorMax3d &p0_t0

The initial position of the first point.

const VectorMax3d &p1_t0

The initial position of the second point.

const VectorMax3d &p0_t1

The final position of the first point.

const VectorMax3d &p1_t1

The final position of the second point.

double &toi

[out] The time of impact between the two points.

const double min_distance = 0.0

The minimum distance between two objects.

const double tmax = 1.0

The maximum time to check for collisions.

conservative_rescaling

The conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

virtual bool point_edge_ccd(const VectorMax3d& p_t0,
    const VectorMax3d& e0_t0, const VectorMax3d& e1_t0,
    const VectorMax3d& p_t1, const VectorMax3d& e0_t1,
    const VectorMax3d& e1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between a point and an edge using continuous collision detection.

Parameters:
const VectorMax3d &p_t0

The initial position of the point.

const VectorMax3d &e0_t0

The initial position of the first endpoint of the edge.

const VectorMax3d &e1_t0

The initial position of the second endpoint of the edge.

const VectorMax3d &p_t1

The final position of the point.

const VectorMax3d &e0_t1

The final position of the first endpoint of the edge.

const VectorMax3d &e1_t1

The final position of the second endpoint of the edge.

double &toi

[out] The time of impact between the point and the edge.

const double min_distance = 0.0

The minimum distance between two objects.

const double tmax = 1.0

The maximum time to check for collisions.

conservative_rescaling

The conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

virtual bool point_triangle_ccd(const Eigen::Vector3d& p_t0,
    const Eigen::Vector3d& t0_t0, const Eigen::Vector3d& t1_t0,
    const Eigen::Vector3d& t2_t0, const Eigen::Vector3d& p_t1,
    const Eigen::Vector3d& t0_t1, const Eigen::Vector3d& t1_t1,
    const Eigen::Vector3d& t2_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between a point and a triangle using continuous collision detection.

Parameters:
const Eigen::Vector3d &p_t0

The initial position of the point.

const Eigen::Vector3d &t0_t0

The initial position of the first vertex of the triangle.

const Eigen::Vector3d &t1_t0

The initial position of the second vertex of the triangle.

const Eigen::Vector3d &t2_t0

The initial position of the third vertex of the triangle.

const Eigen::Vector3d &p_t1

The final position of the point.

const Eigen::Vector3d &t0_t1

The final position of the first vertex of the triangle.

const Eigen::Vector3d &t1_t1

The final position of the second vertex of the triangle.

const Eigen::Vector3d &t2_t1

The final position of the third vertex of the triangle.

double &toi

[out] The time of impact between the point and the triangle.

const double min_distance = 0.0

The minimum distance between two objects.

const double tmax = 1.0

The maximum time to check for collisions.

conservative_rescaling

The conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

virtual bool edge_edge_ccd(const Eigen::Vector3d& ea0_t0,
    const Eigen::Vector3d& ea1_t0, const Eigen::Vector3d& eb0_t0,
    const Eigen::Vector3d& eb1_t0, const Eigen::Vector3d& ea0_t1,
    const Eigen::Vector3d& ea1_t1, const Eigen::Vector3d& eb0_t1,
    const Eigen::Vector3d& eb1_t1, double& toi,
    const double min_distance = 0.0,
    const double tmax = 1.0) const override;

Computes the time of impact between two edges using continuous collision detection.

Parameters:
const Eigen::Vector3d &ea0_t0

The initial position of the first endpoint of the first edge.

const Eigen::Vector3d &ea1_t0

The initial position of the second endpoint of the first edge.

const Eigen::Vector3d &eb0_t0

The initial position of the first endpoint of the second edge.

const Eigen::Vector3d &eb1_t0

The initial position of the second endpoint of the second edge.

const Eigen::Vector3d &ea0_t1

The final position of the first endpoint of the first edge.

const Eigen::Vector3d &ea1_t1

The final position of the second endpoint of the first edge.

const Eigen::Vector3d &eb0_t1

The final position of the first endpoint of the second edge.

const Eigen::Vector3d &eb1_t1

The final position of the second endpoint of the second edge.

double &toi

[out] The time of impact between the two edges.

const double min_distance = 0.0

The minimum distance between two objects.

const double tmax = 1.0

The maximum time to check for collisions.

conservative_rescaling

The conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

Public Members

long max_iterations;

Maximum number of iterations.

double conservative_rescaling;

The conservative rescaling value used to avoid taking steps exactly to impact.

Public Static Attributes

static constexpr long DEFAULT_MAX_ITERATIONS = 10'000'000l;

The default maximum number of iterations used with Tight-Inclusion CCD.

static constexpr long UNLIMITTED_ITERATIONS = -1;

Unlimitted number of iterations.

static constexpr double DEFAULT_CONSERVATIVE_RESCALING = 0.9;

The default conservative rescaling value used to avoid taking steps exactly to impact.

Value choosen to based on [Li et al. 2021].

Private Functions

bool additive_ccd(VectorMax12d x, const VectorMax12d& dx,
    const std::function<double(const VectorMax12d&)>&
        distance_squared,
    const double max_disp_mag, double& toi,
    const double min_distance = 0.0, const double tmax = 1.0) const;

Computes the time of impact between two objects using additive continuous collision detection.

Parameters:
const std::function<double(const VectorMax12d&)> &distance_squared

A function that computes the squared distance between the two objects at a given time.

double &toi

[out] The time of impact between the two objects.

const double min_distance = 0.0

The minimum distance between the objects.

const double tmax = 1.0

The maximum time to check for collisions.

conservative_rescaling

The amount to rescale the objects by to ensure conservative advancement.

Returns:

True if a collision was detected, false otherwise.

Inexact CCD

Note

This method is disabled by default. To enable it, set the IPC_TOOLKIT_WITH_INEXACT_CCD CMake option to ON.

bool ipc::inexact_point_edge_ccd_2D(const Eigen::Vector2d& p_t0,
    const Eigen::Vector2d& e0_t0, const Eigen::Vector2d& e1_t0,
    const Eigen::Vector2d& p_t1, const Eigen::Vector2d& e0_t1,
    const Eigen::Vector2d& e1_t1, double& toi,
    const double conservative_rescaling);

Inexact continuous collision detection between a point and an edge in 2D.

Parameters:
const Eigen::Vector2d &p_t0

[in] The initial position of the point.

const Eigen::Vector2d &e0_t0

[in] The initial position of the first endpoint of the edge.

const Eigen::Vector2d &e1_t0

[in] The initial position of the second endpoint of the edge.

const Eigen::Vector2d &p_t1

[in] The final position of the point.

const Eigen::Vector2d &e0_t1

[in] The final position of the first endpoint of the edge.

const Eigen::Vector2d &e1_t1

[in] The final position of the second endpoint of the edge.

double &toi

[out] Output time of impact.

const double conservative_rescaling

[in] The conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

Nonlinear CCD

class NonlinearTrajectory;

Inheritence diagram for ipc::NonlinearTrajectory:

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

A nonlinear trajectory is a function that maps time to a point in space.

Subclassed by ipc::IntervalNonlinearTrajectory

Public Functions

virtual ~NonlinearTrajectory() = default;
virtual VectorMax3d operator()(const double t) const = 0;

Compute the point’s position at time t.

virtual double max_distance_from_linear(
    const double t0, const double t1) const
    = 0;

Compute the maximum distance from the nonlinear trajectory to a linearized trajectory.

Parameters:
const double t0

[in] Start time of the trajectory

const double t1

[in] End time of the trajectory

class IntervalNonlinearTrajectory
    : public virtual ipc::NonlinearTrajectory;

Inheritence diagram for ipc::IntervalNonlinearTrajectory:

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

Collaboration diagram for ipc::IntervalNonlinearTrajectory:

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

A nonlinear trajectory with an implementation of the max_distance_from_linear function using interval arithmetic.

Public Functions

virtual ~IntervalNonlinearTrajectory() = default;
virtual VectorMax3I operator()(const filib::Interval& t) const = 0;

Compute the point’s position over a time interval t.

virtual double max_distance_from_linear(
    const double t0, const double t1) const;

Compute the maximum distance from the nonlinear trajectory to a linearized trajectory.

Note

This uses interval arithmetic to compute the maximum distance. If you know a tighter bound on the maximum distance, it is recommended to override this function.

Parameters:
const double t0

[in] Start time of the trajectory

const double t1

[in] End time of the trajectory

bool ipc::point_point_nonlinear_ccd(const NonlinearTrajectory& p0,
    const NonlinearTrajectory& p1, double& toi,
    const double tmax = 1.0, const double min_distance = 0,
    const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE,
    const long max_iterations
    = TightInclusionCCD::DEFAULT_MAX_ITERATIONS,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Perform nonlinear CCD between two points moving along nonlinear trajectories.

Parameters:
const NonlinearTrajectory &p0

[in] First point’s trajectory

const NonlinearTrajectory &p1

[in] Second point’s trajectory

double &toi

[out] Output time of impact

const double tmax = 1.0

[in] Maximum time to check for collision

const double min_distance = 0

[in] Minimum separation distance between the two points

const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE

[in] Tolerance for the linear CCD algorithm

const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS

[in] Maximum number of iterations for the linear CCD algorithm

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact

Returns:

True if the two points collide, false otherwise.

bool ipc::point_edge_nonlinear_ccd(const NonlinearTrajectory& p,
    const NonlinearTrajectory& e0, const NonlinearTrajectory& e1,
    double& toi, const double tmax = 1.0,
    const double min_distance = 0,
    const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE,
    const long max_iterations
    = TightInclusionCCD::DEFAULT_MAX_ITERATIONS,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Perform nonlinear CCD between a point and a linear edge moving along nonlinear trajectories.

Parameters:
const NonlinearTrajectory &p

[in] Point’s trajectory

const NonlinearTrajectory &e0

[in] Edge’s first endpoint’s trajectory

const NonlinearTrajectory &e1

[in] Edge’s second endpoint’s trajectory

double &toi

[out] Output time of impact

const double tmax = 1.0

[in] Maximum time to check for collision

const double min_distance = 0

[in] Minimum separation distance between the point and the edge

const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE

[in] Tolerance for the linear CCD algorithm

const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS

[in] Maximum number of iterations for the linear CCD algorithm

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact

Returns:

True if the point and edge collide, false otherwise.

bool ipc::edge_edge_nonlinear_ccd(const NonlinearTrajectory& ea0,
    const NonlinearTrajectory& ea1, const NonlinearTrajectory& eb0,
    const NonlinearTrajectory& eb1, double& toi,
    const double tmax = 1.0, const double min_distance = 0,
    const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE,
    const long max_iterations
    = TightInclusionCCD::DEFAULT_MAX_ITERATIONS,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Perform nonlinear CCD between two linear edges moving along nonlinear trajectories.

Parameters:
const NonlinearTrajectory &ea0

[in] First edge’s first endpoint’s trajectory

const NonlinearTrajectory &ea1

[in] First edge’s second endpoint’s trajectory

const NonlinearTrajectory &eb0

[in] Second edge’s first endpoint’s trajectory

const NonlinearTrajectory &eb1

[in] Second edge’s second endpoint’s trajectory

double &toi

[out] Output time of impact

const double tmax = 1.0

[in] Maximum time to check for collision

const double min_distance = 0

[in] Minimum separation distance between the two edges

const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE

[in] Tolerance for the linear CCD algorithm

const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS

[in] Maximum number of iterations for the linear CCD algorithm

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact

Returns:

True if the two edges collide, false otherwise.

bool ipc::point_triangle_nonlinear_ccd(const NonlinearTrajectory& p,
    const NonlinearTrajectory& t0, const NonlinearTrajectory& t1,
    const NonlinearTrajectory& t2, double& toi,
    const double tmax = 1.0, const double min_distance = 0,
    const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE,
    const long max_iterations
    = TightInclusionCCD::DEFAULT_MAX_ITERATIONS,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Perform nonlinear CCD between a point and a linear triangle moving along nonlinear trajectories.

Parameters:
const NonlinearTrajectory &p

[in] Point’s trajectory

const NonlinearTrajectory &t0

[in] Triangle’s first vertex’s trajectory

const NonlinearTrajectory &t1

[in] Triangle’s second vertex’s trajectory

const NonlinearTrajectory &t2

[in] Triangle’s third vertex’s trajectory

double &toi

[out] Output time of impact

const double tmax = 1.0

[in] Maximum time to check for collision

const double min_distance = 0

[in] Minimum separation distance between the two edges

const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE

[in] Tolerance for the linear CCD algorithm

const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS

[in] Maximum number of iterations for the linear CCD algorithm

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact

Returns:

True if the point and triangle collide, false otherwise.

Generic Interface

bool ipc::conservative_piecewise_linear_ccd(
    const std::function<double(const double)>& distance,
    const std::function<double(const double, const double)>&
        max_distance_from_linear,
    const std::function<bool(const double, const double,
        const double, const bool, double&)>& linear_ccd,
    double& toi, const double tmax = 1.0,
    const double min_distance = 0,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Perform conservative piecewise linear CCD of a nonlinear trajectories.

Parameters:
const std::function<double(const double)> &distance

[in] Return the distance for a given time in [0, 1].

const std::function<double(const double, const double)> &max_distance_from_linear

[in] Return the maximum distance from the linearized trajectory for a given time interval.

const std::function<bool(const double, const double, const double, const bool, double&)> &linear_ccd

[in] Perform linear CCD on a given time interval.

double &toi

[out] Output time of impact.

const double tmax = 1.0

[in] Maximum time to check for collision.

const double min_distance = 0

[in] Minimum separation distance between the objects.

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact.

Returns:

Miscellaneous

bool ipc::point_static_plane_ccd(const VectorMax3d& p_t0,
    const VectorMax3d& p_t1, const VectorMax3d& plane_origin,
    const VectorMax3d& plane_normal, double& toi,
    const double conservative_rescaling
    = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING);

Computes the time of impact between a point and a static plane in 3D using continuous collision detection.

Parameters:
const VectorMax3d &p_t0

[in] The initial position of the point.

const VectorMax3d &p_t1

[in] The final position of the point.

const VectorMax3d &plane_origin

[in] The origin of the plane.

const VectorMax3d &plane_normal

[in] The normal of the plane.

double &toi

[out] Output time of impact.

const double conservative_rescaling = TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING

[in] Conservative rescaling of the time of impact.

Returns:

True if a collision was detected, false otherwise.

Last update: Feb 18, 2025