Continuous Collision Detection¶

ipctk.is_step_collision_free(mesh: ipctk.CollisionMesh, vertices_t0: numpy.ndarray[numpy.float64[m, n]], vertices_t1: numpy.ndarray[numpy.float64[m, n]], min_distance: float = 0.0, broad_phase_method: ipctk.BroadPhaseMethod = <BroadPhaseMethod.HASH_GRID: 1>, narrow_phase_ccd: ipctk.NarrowPhaseCCD = <ipctk.TightInclusionCCD object at 0x7fb2f5a25bf0>) → bool¶

Determine if the step is collision free.

Note

Assumes the trajectory is linear.

Parameters:¶

mesh: The collision mesh.
vertices_t0: Surface vertex vertices at start as rows of a matrix.
vertices_t1: Surface vertex vertices at end as rows of a matrix.
min_distance: The minimum distance allowable between any two elements.
broad_phase_method: The broad phase method to use.
narrow_phase_ccd: The narrow phase CCD algorithm to use.

Returns:¶

True if <b>any</b> collisions occur.

ipctk.compute_collision_free_stepsize(mesh: ipctk.CollisionMesh, vertices_t0: numpy.ndarray[numpy.float64[m, n]], vertices_t1: numpy.ndarray[numpy.float64[m, n]], min_distance: float = 0.0, broad_phase_method: ipctk.BroadPhaseMethod = <BroadPhaseMethod.HASH_GRID: 1>, narrow_phase_ccd: ipctk.NarrowPhaseCCD = <ipctk.TightInclusionCCD object at 0x7fb301a6ddb0>) → float¶

Computes a maximal step size that is collision free.

Note

Assumes the trajectory is linear.

Parameters:¶

mesh: The collision mesh.
vertices_t0: Vertex vertices at start as rows of a matrix. Assumes vertices_t0 is intersection free.
vertices_t1: Surface vertex vertices at end as rows of a matrix.
min_distance: The minimum distance allowable between any two elements.
broad_phase_method: The broad phase method to use.
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 ipctk.NarrowPhaseCCD¶

Bases: pybind11_object

Public Methods:

`__init__`(args, *kwargs)
`point_point_ccd`(self, p0_t0, p1_t0, p0_t1, p1_t1)
`point_edge_ccd`(self, p_t0, e0_t0, e1_t0, ...)
`point_triangle_ccd`(self, p_t0, t0_t0, t1_t0, ...)
`edge_edge_ccd`(self, ea0_t0, ea1_t0, eb0_t0, ...)

Inherited from pybind11_object

__annotations__ = {}¶

__init__(*args, **kwargs)¶

__module__ = 'ipctk'¶

edge_edge_ccd(self, ea0_t0: numpy.ndarray[numpy.float64[3, 1]], ea1_t0: numpy.ndarray[numpy.float64[3, 1]], eb0_t0: numpy.ndarray[numpy.float64[3, 1]], eb1_t0: numpy.ndarray[numpy.float64[3, 1]], ea0_t1: numpy.ndarray[numpy.float64[3, 1]], ea1_t1: numpy.ndarray[numpy.float64[3, 1]], eb0_t1: numpy.ndarray[numpy.float64[3, 1]], eb1_t1: numpy.ndarray[numpy.float64[3, 1]], min_distance: float = 0.0, tmax: float = 1.0) → tuple[bool, float]¶

point_edge_ccd(self, p_t0: numpy.ndarray[numpy.float64[m, 1]], e0_t0: numpy.ndarray[numpy.float64[m, 1]], e1_t0: numpy.ndarray[numpy.float64[m, 1]], p_t1: numpy.ndarray[numpy.float64[m, 1]], e0_t1: numpy.ndarray[numpy.float64[m, 1]], e1_t1: numpy.ndarray[numpy.float64[m, 1]], min_distance: float = 0.0, tmax: float = 1.0) → tuple[bool, float]¶

point_point_ccd(self, p0_t0: numpy.ndarray[numpy.float64[m, 1]], p1_t0: numpy.ndarray[numpy.float64[m, 1]], p0_t1: numpy.ndarray[numpy.float64[m, 1]], p1_t1: numpy.ndarray[numpy.float64[m, 1]], min_distance: float = 0.0, tmax: float = 1.0) → tuple[bool, float]¶

point_triangle_ccd(self, p_t0: numpy.ndarray[numpy.float64[3, 1]], t0_t0: numpy.ndarray[numpy.float64[3, 1]], t1_t0: numpy.ndarray[numpy.float64[3, 1]], t2_t0: numpy.ndarray[numpy.float64[3, 1]], p_t1: numpy.ndarray[numpy.float64[3, 1]], t0_t1: numpy.ndarray[numpy.float64[3, 1]], t1_t1: numpy.ndarray[numpy.float64[3, 1]], t2_t1: numpy.ndarray[numpy.float64[3, 1]], min_distance: float = 0.0, tmax: float = 1.0) → tuple[bool, float]¶

Tight Inclusion CCD¶

class ipctk.TightInclusionCCD¶

Bases: NarrowPhaseCCD

Public Data Attributes:

`DEFAULT_TOLERANCE`
`DEFAULT_MAX_ITERATIONS`
`DEFAULT_CONSERVATIVE_RESCALING`
`SMALL_TOI`
`tolerance`	Solver tolerance.
`max_iterations`	Maximum number of iterations.
`conservative_rescaling`	Conservative rescaling of the time of impact.

Public Methods:

`__init__`(self[, tolerance, max_iterations, ...])	Construct a new AdditiveCCD object.

Inherited from NarrowPhaseCCD

`__init__`(args, *kwargs)
`point_point_ccd`(self, p0_t0, p1_t0, p0_t1, p1_t1)
`point_edge_ccd`(self, p_t0, e0_t0, e1_t0, ...)
`point_triangle_ccd`(self, p_t0, t0_t0, t1_t0, ...)
`edge_edge_ccd`(self, ea0_t0, ea1_t0, eb0_t0, ...)

Inherited from pybind11_object

DEFAULT_CONSERVATIVE_RESCALING = 0.8¶

DEFAULT_MAX_ITERATIONS = 10000000¶

DEFAULT_TOLERANCE = 1e-06¶

SMALL_TOI = 1e-06¶

__annotations__ = {}¶

__init__(self, tolerance: float = 1e-06, max_iterations: int = 10000000, conservative_rescaling: float = 0.8)¶

Construct a new AdditiveCCD object.

Parameters:¶

conservative_rescaling: float = 0.8¶: The conservative rescaling of the time of impact.

__module__ = 'ipctk'¶

property conservative_rescaling : float¶: Conservative rescaling of the time of impact.

property max_iterations : int¶: Maximum number of iterations.

property tolerance : float¶: Solver tolerance.

Additive CCD¶

class ipctk.AdditiveCCD¶

Bases: NarrowPhaseCCD

Public Data Attributes:

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

Public Methods:

`__init__`(self[, max_iterations, ...])	Construct a new AdditiveCCD object.

Inherited from NarrowPhaseCCD

`__init__`(args, *kwargs)
`point_point_ccd`(self, p0_t0, p1_t0, p0_t1, p1_t1)
`point_edge_ccd`(self, p_t0, e0_t0, e1_t0, ...)
`point_triangle_ccd`(self, p_t0, t0_t0, t1_t0, ...)
`edge_edge_ccd`(self, ea0_t0, ea1_t0, eb0_t0, ...)

Inherited from pybind11_object

DEFAULT_CONSERVATIVE_RESCALING = 0.9¶

__annotations__ = {}¶

__init__(self, max_iterations: float = 10000000, conservative_rescaling: float = 0.9)¶

Construct a new AdditiveCCD object.

Parameters:¶

conservative_rescaling: float = 0.9¶: The conservative rescaling of the time of impact.

__module__ = 'ipctk'¶

property conservative_rescaling : float¶: The conservative rescaling value used to avoid taking steps exactly to impact.

Inexact CCD¶

Note

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

ipctk.inexact_point_edge_ccd_2D(p_t0: numpy.ndarray[numpy.float64[2, 1]], e0_t0: numpy.ndarray[numpy.float64[2, 1]], e1_t0: numpy.ndarray[numpy.float64[2, 1]], p_t1: numpy.ndarray[numpy.float64[2, 1]], e0_t1: numpy.ndarray[numpy.float64[2, 1]], e1_t1: numpy.ndarray[numpy.float64[2, 1]], conservative_rescaling: float) → tuple[bool, float]¶

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

Parameters:¶

p_t0: numpy.ndarray[numpy.float64[2, 1]]¶: Initial position of the point
e0_t0: numpy.ndarray[numpy.float64[2, 1]]¶: Initial position of the first endpoint of the edge
e1_t0: numpy.ndarray[numpy.float64[2, 1]]¶: Initial position of the second endpoint of the edge
p_t1: numpy.ndarray[numpy.float64[2, 1]]¶: Final position of the point
e0_t1: numpy.ndarray[numpy.float64[2, 1]]¶: Final position of the first endpoint of the edge
e1_t1: numpy.ndarray[numpy.float64[2, 1]]¶: Final position of the second endpoint of the edge
conservative_rescaling: float¶: Conservative rescaling of the time of impact

Returns:¶

True if a collision was detected, false otherwise. Output time of impact

Return type:¶

Tuple of

Nonlinear CCD¶

class ipctk.NonlinearTrajectory¶

Bases: pybind11_object

Public Methods:

`__init__`(self)
`__call__`(self, t)	Compute the point's position at time t
`max_distance_from_linear`(self, t0, t1)	Compute the maximum distance from the nonlinear trajectory to a linearized trajectory

Inherited from pybind11_object

__annotations__ = {}¶

__call__(self, t: float) → numpy.ndarray[numpy.float64[m, 1]]¶: Compute the point’s position at time t

__init__(self)¶

__module__ = 'ipctk'¶

max_distance_from_linear(self, t0: float, t1: float) → float¶

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

Parameters:¶

t0: float¶: Start time of the trajectory
t1: float¶: End time of the trajectory

class ipctk.IntervalNonlinearTrajectory¶

Bases: NonlinearTrajectory

Public Methods:

`__init__`(self)
`__call__`(args, *kwargs)	Overloaded function.
`max_distance_from_linear`(self, t0, t1)	Compute the maximum distance from the nonlinear trajectory to a linearized trajectory

Inherited from NonlinearTrajectory

`__init__`(self)
`__call__`(self, t)	Compute the point's position at time t
`max_distance_from_linear`(self, t0, t1)	Compute the maximum distance from the nonlinear trajectory to a linearized trajectory

Inherited from pybind11_object

__annotations__ = {}¶

__call__(*args, **kwargs)¶

Overloaded function.

__call__(self: ipctk.IntervalNonlinearTrajectory, t: float) -> numpy.ndarray[numpy.float64[m, 1]]

Compute the point’s position at time t

__call__(self: ipctk.IntervalNonlinearTrajectory, t: filib::Interval) -> numpy.ndarray[filib::Interval[m, 1]]

Compute the point’s position over a time interval t

__init__(self)¶

__module__ = 'ipctk'¶

max_distance_from_linear(self, t0: float, t1: float) → float¶

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:¶

t0: float¶: Start time of the trajectory
t1: float¶: End time of the trajectory

ipctk.point_point_nonlinear_ccd(p0: ipctk.NonlinearTrajectory, p1: ipctk.NonlinearTrajectory, tmax: float = 1.0, min_distance: float = 0, tolerance: float = 1e-06, max_iterations: int = 10000000, conservative_rescaling: float = 0.8) → tuple[bool, float]¶

Perform nonlinear CCD between two points moving along nonlinear trajectories.

Parameters:¶

p0: ipctk.NonlinearTrajectory¶: First point’s trajectory
p1: ipctk.NonlinearTrajectory¶: Second point’s trajectory
tmax: float = 1.0¶: Maximum time to check for collision
min_distance: float = 0¶: Minimum separation distance between the two points
tolerance: float = 1e-06¶: Tolerance for the linear CCD algorithm
max_iterations: int = 10000000¶: Maximum number of iterations for the linear CCD algorithm
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact

Returns:¶

True if the two points collide, false otherwise. Output time of impact

Return type:¶

Tuple of

ipctk.point_edge_nonlinear_ccd(p: ipctk.NonlinearTrajectory, e0: ipctk.NonlinearTrajectory, e1: ipctk.NonlinearTrajectory, tmax: float = 1.0, min_distance: float = 0, tolerance: float = 1e-06, max_iterations: int = 10000000, conservative_rescaling: float = 0.8) → tuple[bool, float]¶

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

Parameters:¶

p: ipctk.NonlinearTrajectory¶: Point’s trajectory
e0: ipctk.NonlinearTrajectory¶: Edge’s first endpoint’s trajectory
e1: ipctk.NonlinearTrajectory¶: Edge’s second endpoint’s trajectory
tmax: float = 1.0¶: Maximum time to check for collision
min_distance: float = 0¶: Minimum separation distance between the point and the edge
tolerance: float = 1e-06¶: Tolerance for the linear CCD algorithm
max_iterations: int = 10000000¶: Maximum number of iterations for the linear CCD algorithm
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact

Returns:¶

True if the point and edge collide, false otherwise. Output time of impact

Return type:¶

Tuple of

ipctk.edge_edge_nonlinear_ccd(ea0: ipctk.NonlinearTrajectory, ea1: ipctk.NonlinearTrajectory, eb0: ipctk.NonlinearTrajectory, eb1: ipctk.NonlinearTrajectory, tmax: float = 1.0, min_distance: float = 0, tolerance: float = 1e-06, max_iterations: int = 10000000, conservative_rescaling: float = 0.8) → tuple[bool, float]¶

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

Parameters:¶

ea0: ipctk.NonlinearTrajectory¶: First edge’s first endpoint’s trajectory
ea1: ipctk.NonlinearTrajectory¶: First edge’s second endpoint’s trajectory
eb0: ipctk.NonlinearTrajectory¶: Second edge’s first endpoint’s trajectory
eb1: ipctk.NonlinearTrajectory¶: Second edge’s second endpoint’s trajectory
tmax: float = 1.0¶: Maximum time to check for collision
min_distance: float = 0¶: Minimum separation distance between the two edges
tolerance: float = 1e-06¶: Tolerance for the linear CCD algorithm
max_iterations: int = 10000000¶: Maximum number of iterations for the linear CCD algorithm
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact

Returns:¶

True if the two edges collide, false otherwise. Output time of impact

Return type:¶

Tuple of

ipctk.point_triangle_nonlinear_ccd(p: ipctk.NonlinearTrajectory, t0: ipctk.NonlinearTrajectory, t1: ipctk.NonlinearTrajectory, t2: ipctk.NonlinearTrajectory, tmax: float = 1.0, min_distance: float = 0, tolerance: float = 1e-06, max_iterations: int = 10000000, conservative_rescaling: float = 0.8) → tuple[bool, float]¶

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

Parameters:¶

p: ipctk.NonlinearTrajectory¶: Point’s trajectory
t0: ipctk.NonlinearTrajectory¶: Triangle’s first vertex’s trajectory
t1: ipctk.NonlinearTrajectory¶: Triangle’s second vertex’s trajectory
t2: ipctk.NonlinearTrajectory¶: Triangle’s third vertex’s trajectory
tmax: float = 1.0¶: Maximum time to check for collision
min_distance: float = 0¶: Minimum separation distance between the two edges
tolerance: float = 1e-06¶: Tolerance for the linear CCD algorithm
max_iterations: int = 10000000¶: Maximum number of iterations for the linear CCD algorithm
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact

Returns:¶

True if the point and triangle collide, false otherwise. Output time of impact

Return type:¶

Tuple of

Miscellaneous¶

ipctk.point_static_plane_ccd(p_t0: numpy.ndarray[numpy.float64[m, 1]], p_t1: numpy.ndarray[numpy.float64[m, 1]], plane_origin: numpy.ndarray[numpy.float64[m, 1]], plane_normal: numpy.ndarray[numpy.float64[m, 1]], conservative_rescaling: float = 0.8) → tuple[bool, float]¶

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

Parameters:¶

p_t0: numpy.ndarray[numpy.float64[m, 1]]¶: The initial position of the point.
p_t1: numpy.ndarray[numpy.float64[m, 1]]¶: The final position of the point.
plane_origin: numpy.ndarray[numpy.float64[m, 1]]¶: The origin of the plane.
plane_normal: numpy.ndarray[numpy.float64[m, 1]]¶: The normal of the plane.
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact.

Returns:¶

True if a collision was detected, false otherwise. Output time of impact

Return type:¶

Tuple of

Last update: Jan 21, 2025