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 0x7fbabfd2f970>) → 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 0x7fbabfd2faf0>) → 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.

Individual CCD Functions¶

Generic Interface¶

Tight Inclusion CCD¶

ipctk.tight_inclusion.edge_edge_ccd(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, tmax: float = 1, tolerance: float = 1e-06, max_iterations: int = 10000000, filter: numpy.ndarray[numpy.float64[3, 1]] = array([-1., -1., -1.]), no_zero_toi: bool = False, ccd_method: ipctk.tight_inclusion.CCDRootFindingMethod = <CCDRootFindingMethod.BREADTH_FIRST_SEARCH: 1>) → tuple[bool, float, float]¶

Determine the earliest time of impact between two edges (optionally with a minimum separation).

Parameters:¶

ea0_t0: Starting position of the first vertex of the first edge.
ea1_t0: Start position of the second vertex of the first edge.
eb0_t0: Start position of the first vertex of the second edge.
eb1_t0: Start position of the second vertex of the second edge.
ea0_t1: End position of the first vertex of the first edge.
ea1_t1: End position of the second vertex of the first edge.
eb0_t1: End position of the first vertex of the second edge.
eb1_t1: End position of the second vertex of the second edge.
min_distance: Minimum separation distance (default: 0).
tmax: Upper bound of the time interval [0,tmax] to be checked (0<=tmax<=1).
tolerance: Solver tolerance (default: 1e-6).
max_iterations: Maximum number of solver iterations (default: 1e7). If negative, solver will run until convergence.
filter: Filters calculated using get_numerical_error (default: (-1,-1,-1)). Use (-1,-1,-1) if checking a single query.
no_zero_toi: Refine further if a zero TOI is produced (assuming not initially in contact).
ccd_method: Root finding method (default: BREADTH_FIRST_SEARCH).

Returns:¶

True if there is a collision, false otherwise, the earliest time of collision if collision happens (infinity if no collision occurs), and if max_iterations < 0, the solver precision otherwise the input tolerance.

Return type:¶

Tuple of

ipctk.tight_inclusion.point_triangle_ccd(v_t0: numpy.ndarray[numpy.float64[3, 1]], f0_t0: numpy.ndarray[numpy.float64[3, 1]], f1_t0: numpy.ndarray[numpy.float64[3, 1]], f2_t0: numpy.ndarray[numpy.float64[3, 1]], v_t1: numpy.ndarray[numpy.float64[3, 1]], f0_t1: numpy.ndarray[numpy.float64[3, 1]], f1_t1: numpy.ndarray[numpy.float64[3, 1]], f2_t1: numpy.ndarray[numpy.float64[3, 1]], min_distance: float = 0, tmax: float = 1, tolerance: float = 1e-06, max_iterations: int = 10000000, filter: numpy.ndarray[numpy.float64[3, 1]] = array([-1., -1., -1.]), no_zero_toi: bool = False, ccd_method: ipctk.tight_inclusion.CCDRootFindingMethod = <CCDRootFindingMethod.BREADTH_FIRST_SEARCH: 1>) → tuple[bool, float, float]¶

Determine the earliest time of impact between a point and triangle (optionally with a minimum separation).

Parameters:¶

v_t0: Starting position of the vertex.
f0_t0: Starting position of the first vertex of the face.
f1_t0: Starting position of the second vertex of the face.
f2_t0: Starting position of the third vertex of the face.
v_t1: Ending position of the vertex.
f0_t1: Ending position of the first vertex of the face.
f1_t1: Ending position of the second vertex of the face.
f2_t1: Ending position of the third vertex of the face.
min_distance: Minimum separation distance (default: 0).
tmax: Upper bound of the time interval [0,tmax] to be checked (0<=tmax<=1).
tolerance: Solver tolerance (default: 1e-6).
max_iterations: Maximum number of solver iterations (default: 1e7). If negative, solver will run until convergence.
filter: Filters calculated using get_numerical_error (default: (-1,-1,-1)). Use (-1,-1,-1) if checking a single query.
no_zero_toi: Refine further if a zero TOI is produced (assuming not initially in contact).
ccd_method: Root finding method (default: BREADTH_FIRST_SEARCH).

Returns:¶

Return type:¶

Tuple of

ipctk.tight_inclusion.compute_ccd_filters(min_corner: numpy.ndarray[numpy.float64[3, 1]], max_corner: numpy.ndarray[numpy.float64[3, 1]], is_vertex_face: bool, using_minimum_separation: bool) → numpy.ndarray[numpy.float64[3, 1]]¶

Compute the numerical error filters for the input to the CCD solver.

Before you run the simulation, you need to conservatively estimate the axis-aligned bounding box in which the meshes will be located during the whole simulation process.

Parameters:¶

min_corner: numpy.ndarray[numpy.float64[3, 1]]¶: Minimum corner of the axis-aligned bounding box of the simulation scene.
max_corner: numpy.ndarray[numpy.float64[3, 1]]¶: Maximum corner of the axis-aligned bounding box of the simulation scene.
is_vertex_face: bool¶: True if checking vertex-face collision, false if checking edge-edge collision.
using_minimum_separation: bool¶: True if using minimum separation CCD, false otherwise.

Returns:¶

The numerical error filters for the input parameters.

Additive CCD¶

Generic Interface¶

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

Generic Interface¶

ipctk.conservative_piecewise_linear_ccd(distance: collections.abc.Callable[[float], float], max_distance_from_linear: collections.abc.Callable[[float, float], float], linear_ccd: collections.abc.Callable[[float, float, float, bool, float], bool], tmax: float = 1.0, min_distance: float = 0, conservative_rescaling: float = 0.8) → tuple[bool, float]¶

Perform conservative piecewise linear CCD of a nonlinear trajectories.

Parameters:¶

distance: collections.abc.Callable[[float], float]¶: Return the distance for a given time in [0, 1].
max_distance_from_linear: collections.abc.Callable[[float, float], float]¶: Return the maximum distance from the linearized trajectory for a given time interval.
linear_ccd: collections.abc.Callable[[float, float, float, bool, float], bool]¶: Perform linear CCD on a given time interval.
tmax: float = 1.0¶: Maximum time to check for collision.
min_distance: float = 0¶: Minimum separation distance between the objects.
conservative_rescaling: float = 0.8¶: Conservative rescaling of the time of impact.

Returns:¶

Output time of impact.

Return type:¶

Tuple of

Last update: Sep 10, 2024