Distance¶

Distance Type¶

class ipctk.PointEdgeDistanceType¶

Bases: pybind11_object

Members:

P_E0 : point is closest to edge vertex zero

P_E1 : point is closest to edge vertex one

P_E : point is closest to the interior of the edge

AUTO : automatically determine the closest point

AUTO = <PointEdgeDistanceType.AUTO: 3>¶

P_E = <PointEdgeDistanceType.P_E: 2>¶

P_E0 = <PointEdgeDistanceType.P_E0: 0>¶

P_E1 = <PointEdgeDistanceType.P_E1: 1>¶

__annotations__ = {}¶

__eq__(self, other: object) → bool¶

__getstate__(self) → int¶

__hash__(self) → int¶

__index__(self) → int¶

__init__(self, value: int)¶

__int__(self) → int¶

__members__ = {'AUTO': <PointEdgeDistanceType.AUTO: 3>, 'P_E': <PointEdgeDistanceType.P_E: 2>, 'P_E0': <PointEdgeDistanceType.P_E0: 0>, 'P_E1': <PointEdgeDistanceType.P_E1: 1>}¶

__module__ = 'ipctk'¶

__ne__(self, other: object) → bool¶

__repr__(self) → str¶

__setstate__(self, state: int) → None¶

__str__(self) → str¶

property name : str¶

property value : int¶

class ipctk.EdgeEdgeDistanceType¶

Bases: pybind11_object

Members:

EA0_EB0 : edges are closest at vertex 0 of edge A and 0 of edge B

EA0_EB1 : edges are closest at vertex 0 of edge A and 1 of edge B

EA1_EB0 : edges are closest at vertex 1 of edge A and 0 of edge B

EA1_EB1 : edges are closest at vertex 1 of edge A and 1 of edge B

EA_EB0 : edges are closest at the interior of edge A and vertex 0 of edge B

EA_EB1 : edges are closest at the interior of edge A and vertex 1 of edge B

EA0_EB : edges are closest at vertex 0 of edge A and the interior of edge B

EA1_EB : edges are closest at vertex 1 of edge A and the interior of edge B

EA_EB : edges are closest at an interior point of edge A and B

AUTO : automatically determine the closest point

AUTO = <EdgeEdgeDistanceType.AUTO: 9>¶

EA0_EB = <EdgeEdgeDistanceType.EA0_EB: 6>¶

EA0_EB0 = <EdgeEdgeDistanceType.EA0_EB0: 0>¶

EA0_EB1 = <EdgeEdgeDistanceType.EA0_EB1: 1>¶

EA1_EB = <EdgeEdgeDistanceType.EA1_EB: 7>¶

EA1_EB0 = <EdgeEdgeDistanceType.EA1_EB0: 2>¶

EA1_EB1 = <EdgeEdgeDistanceType.EA1_EB1: 3>¶

EA_EB = <EdgeEdgeDistanceType.EA_EB: 8>¶

EA_EB0 = <EdgeEdgeDistanceType.EA_EB0: 4>¶

EA_EB1 = <EdgeEdgeDistanceType.EA_EB1: 5>¶

__annotations__ = {}¶

__eq__(self, other: object) → bool¶

__getstate__(self) → int¶

__hash__(self) → int¶

__index__(self) → int¶

__init__(self, value: int)¶

__int__(self) → int¶

__members__ = {'AUTO': <EdgeEdgeDistanceType.AUTO: 9>, 'EA0_EB': <EdgeEdgeDistanceType.EA0_EB: 6>, 'EA0_EB0': <EdgeEdgeDistanceType.EA0_EB0: 0>, 'EA0_EB1': <EdgeEdgeDistanceType.EA0_EB1: 1>, 'EA1_EB': <EdgeEdgeDistanceType.EA1_EB: 7>, 'EA1_EB0': <EdgeEdgeDistanceType.EA1_EB0: 2>, 'EA1_EB1': <EdgeEdgeDistanceType.EA1_EB1: 3>, 'EA_EB': <EdgeEdgeDistanceType.EA_EB: 8>, 'EA_EB0': <EdgeEdgeDistanceType.EA_EB0: 4>, 'EA_EB1': <EdgeEdgeDistanceType.EA_EB1: 5>}¶

__module__ = 'ipctk'¶

__ne__(self, other: object) → bool¶

__repr__(self) → str¶

__setstate__(self, state: int) → None¶

__str__(self) → str¶

property name : str¶

property value : int¶

class ipctk.PointTriangleDistanceType¶

Bases: pybind11_object

Members:

P_T0 : point is closest to triangle vertex zero

P_T1 : point is closest to triangle vertex one

P_T2 : point is closest to triangle vertex two

P_E0 : point is closest to triangle edge zero (vertex zero to one)

P_E1 : point is closest to triangle edge one (vertex one to two)

P_E2 : point is closest to triangle edge two (vertex two to zero)

P_T : point is closest to the interior of the triangle

AUTO : automatically determine the closest point

AUTO = <PointTriangleDistanceType.AUTO: 7>¶

P_E0 = <PointTriangleDistanceType.P_E0: 3>¶

P_E1 = <PointTriangleDistanceType.P_E1: 4>¶

P_E2 = <PointTriangleDistanceType.P_E2: 5>¶

P_T = <PointTriangleDistanceType.P_T: 6>¶

P_T0 = <PointTriangleDistanceType.P_T0: 0>¶

P_T1 = <PointTriangleDistanceType.P_T1: 1>¶

P_T2 = <PointTriangleDistanceType.P_T2: 2>¶

__annotations__ = {}¶

__eq__(self, other: object) → bool¶

__getstate__(self) → int¶

__hash__(self) → int¶

__index__(self) → int¶

__init__(self, value: int)¶

__int__(self) → int¶

__members__ = {'AUTO': <PointTriangleDistanceType.AUTO: 7>, 'P_E0': <PointTriangleDistanceType.P_E0: 3>, 'P_E1': <PointTriangleDistanceType.P_E1: 4>, 'P_E2': <PointTriangleDistanceType.P_E2: 5>, 'P_T': <PointTriangleDistanceType.P_T: 6>, 'P_T0': <PointTriangleDistanceType.P_T0: 0>, 'P_T1': <PointTriangleDistanceType.P_T1: 1>, 'P_T2': <PointTriangleDistanceType.P_T2: 2>}¶

__module__ = 'ipctk'¶

__ne__(self, other: object) → bool¶

__repr__(self) → str¶

__setstate__(self, state: int) → None¶

__str__(self) → str¶

property name : str¶

property value : int¶

ipctk.point_edge_distance_type(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]]) → ipctk.PointEdgeDistanceType¶

Determine the closest pair between a point and edge.

Parameters:¶

p: numpy.ndarray[numpy.float64[m, 1]]¶: The point.
e0: numpy.ndarray[numpy.float64[m, 1]]¶: The first vertex of the edge.
e1: numpy.ndarray[numpy.float64[m, 1]]¶: The second vertex of the edge.

Returns:¶

The distance type of the point-edge pair.

ipctk.edge_edge_distance_type(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → ipctk.EdgeEdgeDistanceType¶

Determine the closest pair between two edges.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the first edge.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the first edge.
eb0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the second edge.
eb1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the second edge.

Returns:¶

The distance type of the edge-edge pair.

ipctk.point_triangle_distance_type(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]]) → ipctk.PointTriangleDistanceType¶

Determine the closest pair between a point and triangle.

Parameters:¶

p: numpy.ndarray[numpy.float64[3, 1]]¶: The point.
t0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the triangle.
t1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the triangle.
t2: numpy.ndarray[numpy.float64[3, 1]]¶: The third vertex of the triangle.

Returns:¶

The distance type of the point-triangle pair.

Edge-Edge¶

ipctk.edge_edge_distance(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.EdgeEdgeDistanceType = <EdgeEdgeDistanceType.AUTO: 9>) → float¶

Compute the distance between a two lines segments in 3D.

Note

The distance is actually squared distance.

Parameters:¶

ea0: The first vertex of the first edge.
ea1: The second vertex of the first edge.
eb0: The first vertex of the second edge.
eb1: The second vertex of the second edge.
dtype: The point edge distance type to compute.

Returns:¶

The distance between the two edges.

ipctk.edge_edge_distance_gradient(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.EdgeEdgeDistanceType = <EdgeEdgeDistanceType.AUTO: 9>) → numpy.ndarray[numpy.float64[12, 1]]¶

Compute the gradient of the distance between a two lines segments.

Note

The distance is actually squared distance.

Parameters:¶

ea0: The first vertex of the first edge.
ea1: The second vertex of the first edge.
eb0: The first vertex of the second edge.
eb1: The second vertex of the second edge.
dtype: The point edge distance type to compute.

Returns:¶

The gradient of the distance wrt ea0, ea1, eb0, and eb1.

ipctk.edge_edge_distance_hessian(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.EdgeEdgeDistanceType = <EdgeEdgeDistanceType.AUTO: 9>) → numpy.ndarray[numpy.float64[12, 12]]¶

Compute the hessian of the distance between a two lines segments.

Note

The distance is actually squared distance.

Parameters:¶

ea0: The first vertex of the first edge.
ea1: The second vertex of the first edge.
eb0: The first vertex of the second edge.
eb1: The second vertex of the second edge.
dtype: The point edge distance type to compute.

Returns:¶

The hessian of the distance wrt ea0, ea1, eb0, and eb1.

Edge-Edge Mollifier¶

ipctk.edge_edge_mollifier_threshold(ea0_rest: numpy.ndarray[numpy.float64[3, 1]], ea1_rest: numpy.ndarray[numpy.float64[3, 1]], eb0_rest: numpy.ndarray[numpy.float64[3, 1]], eb1_rest: numpy.ndarray[numpy.float64[3, 1]]) → float¶

Compute the threshold of the mollifier edge-edge distance.

This values is computed based on the edges at rest length.

Parameters:¶

ea0_rest: numpy.ndarray[numpy.float64[3, 1]]¶: The rest position of the first vertex of the first edge.
ea1_rest: numpy.ndarray[numpy.float64[3, 1]]¶: The rest position of the second vertex of the first edge.
eb0_rest: numpy.ndarray[numpy.float64[3, 1]]¶: The rest position of the first vertex of the second edge.
eb1_rest: numpy.ndarray[numpy.float64[3, 1]]¶: The rest position of the second vertex of the second edge.

Returns:¶

Threshold for edge-edge mollification.

ipctk.edge_edge_cross_squarednorm(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → float¶

Compute the squared norm of the edge-edge cross product.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the first edge.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the first edge.
eb0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the second edge.
eb1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the second edge.

Returns:¶

The squared norm of the edge-edge cross product.

ipctk.edge_edge_cross_squarednorm_gradient(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → numpy.ndarray[numpy.float64[12, 1]]¶

Compute the gradient of the squared norm of the edge cross product.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the first edge.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the first edge.
eb0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the second edge.
eb1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the second edge.

Returns:¶

The gradient of the squared norm of the edge cross product wrt ea0, ea1, eb0, and eb1.

ipctk.edge_edge_cross_squarednorm_hessian(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → numpy.ndarray[numpy.float64[12, 12]]¶

Compute the hessian of the squared norm of the edge cross product.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the first edge.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the first edge.
eb0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the second edge.
eb1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the second edge.

Returns:¶

The hessian of the squared norm of the edge cross product wrt ea0, ea1, eb0, and eb1.

ipctk.edge_edge_mollifier(*args, **kwargs)¶

Overloaded function.

edge_edge_mollifier(x: float, eps_x: float) -> float

Mollifier function for edge-edge distance.

Parameters:
x: Squared norm of the edge-edge cross product. eps_x: Mollifier activation threshold.

Returns:
The mollifier coefficient to premultiply the edge-edge distance.
edge_edge_mollifier(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], eps_x: float) -> float

Compute a mollifier for the edge-edge distance.

This helps smooth the non-smoothness at close to parallel edges.

Parameters:
ea0: The first vertex of the first edge. ea1: The second vertex of the first edge. eb0: The first vertex of the second edge. eb1: The second vertex of the second edge. eps_x: Mollifier activation threshold.

Returns:
The mollifier coefficient to premultiply the edge-edge distance.

ipctk.edge_edge_mollifier_gradient(*args, **kwargs)¶

Overloaded function.

edge_edge_mollifier_gradient(x: float, eps_x: float) -> float

The gradient of the mollifier function for edge-edge distance.

Parameters:
x: Squared norm of the edge-edge cross product. eps_x: Mollifier activation threshold.

Returns:
The gradient of the mollifier function for edge-edge distance wrt x.
edge_edge_mollifier_gradient(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], eps_x: float) -> numpy.ndarray[numpy.float64[12, 1]]

Compute the gradient of the mollifier for the edge-edge distance.

Parameters:
ea0: The first vertex of the first edge. ea1: The second vertex of the first edge. eb0: The first vertex of the second edge. eb1: The second vertex of the second edge. eps_x: Mollifier activation threshold.

Returns:
The gradient of the mollifier.

ipctk.edge_edge_mollifier_hessian(*args, **kwargs)¶

Overloaded function.

edge_edge_mollifier_hessian(x: float, eps_x: float) -> float

The hessian of the mollifier function for edge-edge distance.

Parameters:
x: Squared norm of the edge-edge cross product. eps_x: Mollifier activation threshold.

Returns:
The hessian of the mollifier function for edge-edge distance wrt x.
edge_edge_mollifier_hessian(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]], eps_x: float) -> numpy.ndarray[numpy.float64[12, 12]]

Compute the hessian of the mollifier for the edge-edge distance.

Parameters:
ea0: The first vertex of the first edge. ea1: The second vertex of the first edge. eb0: The first vertex of the second edge. eb1: The second vertex of the second edge. eps_x: Mollifier activation threshold.

Returns:
The hessian of the mollifier.

Line-Line¶

ipctk.line_line_distance(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → float¶

Compute the distance between a two infinite lines in 3D.

Note

The distance is actually squared distance.

Warning

If the lines are parallel this function returns a distance of zero.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the first line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the first line.
ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the second line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the second line.

Returns:¶

The distance between the two lines.

ipctk.line_line_distance_gradient(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → numpy.ndarray[numpy.float64[12, 1]]¶

Compute the gradient of the distance between a two lines in 3D.

Note

The distance is actually squared distance.

Warning

If the lines are parallel this function returns a distance of zero.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the first line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the first line.
ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the second line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the second line.

Returns:¶

The gradient of the distance wrt ea0, ea1, eb0, and eb1.

ipctk.line_line_distance_hessian(ea0: numpy.ndarray[numpy.float64[3, 1]], ea1: numpy.ndarray[numpy.float64[3, 1]], eb0: numpy.ndarray[numpy.float64[3, 1]], eb1: numpy.ndarray[numpy.float64[3, 1]]) → numpy.ndarray[numpy.float64[12, 12]]¶

Compute the hessian of the distance between a two lines in 3D.

Note

The distance is actually squared distance.

Warning

If the lines are parallel this function returns a distance of zero.

Parameters:¶

ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the first line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the first line.
ea0: numpy.ndarray[numpy.float64[3, 1]]¶: The first vertex of the edge defining the second line.
ea1: numpy.ndarray[numpy.float64[3, 1]]¶: The second vertex of the edge defining the second line.

Returns:¶

The hessian of the distance wrt ea0, ea1, eb0, and eb1.

Point-Edge¶

ipctk.point_edge_distance(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]], dtype: ipctk.PointEdgeDistanceType = <PointEdgeDistanceType.AUTO: 3>) → float¶

Compute the distance between a point and edge in 2D or 3D.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
e0: The first vertex of the edge.
e1: The second vertex of the edge.
dtype: The point edge distance type to compute.

Returns:¶

The distance between the point and edge.

ipctk.point_edge_distance_gradient(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]], dtype: ipctk.PointEdgeDistanceType = <PointEdgeDistanceType.AUTO: 3>) → numpy.ndarray[numpy.float64[m, 1]]¶

Compute the gradient of the distance between a point and edge.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
e0: The first vertex of the edge.
e1: The second vertex of the edge.
dtype: The point edge distance type to compute.

Returns:¶

grad The gradient of the distance wrt p, e0, and e1.

ipctk.point_edge_distance_hessian(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]], dtype: ipctk.PointEdgeDistanceType = <PointEdgeDistanceType.AUTO: 3>) → numpy.ndarray[numpy.float64[m, n]]¶

Compute the hessian of the distance between a point and edge.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
e0: The first vertex of the edge.
e1: The second vertex of the edge.
dtype: The point edge distance type to compute.

Returns:¶

hess The hessian of the distance wrt p, e0, and e1.

Point-Line¶

ipctk.point_line_distance(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]]) → float¶

Compute the distance between a point and line in 2D or 3D.

Note

The distance is actually squared distance.

Parameters:¶

p: numpy.ndarray[numpy.float64[m, 1]]¶: The point.
e0: numpy.ndarray[numpy.float64[m, 1]]¶: The first vertex of the edge defining the line.
e1: numpy.ndarray[numpy.float64[m, 1]]¶: The second vertex of the edge defining the line.

Returns:¶

The distance between the point and line.

ipctk.point_line_distance_gradient(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]¶

Compute the gradient of the distance between a point and line.

Note

The distance is actually squared distance.

Parameters:¶

p: numpy.ndarray[numpy.float64[m, 1]]¶: The point.
e0: numpy.ndarray[numpy.float64[m, 1]]¶: The first vertex of the edge defining the line.
e1: numpy.ndarray[numpy.float64[m, 1]]¶: The second vertex of the edge defining the line.

Returns:¶

The gradient of the distance wrt p, e0, and e1.

ipctk.point_line_distance_hessian(p: numpy.ndarray[numpy.float64[m, 1]], e0: numpy.ndarray[numpy.float64[m, 1]], e1: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, n]]¶

Compute the hessian of the distance between a point and line.

Note

The distance is actually squared distance.

Parameters:¶

p: numpy.ndarray[numpy.float64[m, 1]]¶: The point.
e0: numpy.ndarray[numpy.float64[m, 1]]¶: The first vertex of the edge defining the line.
e1: numpy.ndarray[numpy.float64[m, 1]]¶: The second vertex of the edge defining the line.

Returns:¶

The hessian of the distance wrt p, e0, and e1.

Point-Plane¶

ipctk.point_plane_distance(*args, **kwargs)¶

Overloaded function.

point_plane_distance(p: numpy.ndarray[numpy.float64[3, 1]], origin: numpy.ndarray[numpy.float64[3, 1]], normal: numpy.ndarray[numpy.float64[3, 1]]) -> float

Compute the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. origin: The origin of the plane. normal: The normal of the plane.

Returns:
The distance between the point and plane.
point_plane_distance(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]]) -> float

Compute the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. t0: The first vertex of the triangle. t1: The second vertex of the triangle. t2: The third vertex of the triangle.

Returns:
The distance between the point and plane.

ipctk.point_plane_distance_gradient(*args, **kwargs)¶

Overloaded function.

point_plane_distance_gradient(p: numpy.ndarray[numpy.float64[3, 1]], origin: numpy.ndarray[numpy.float64[3, 1]], normal: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[3, 1]]

Compute the gradient of the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. origin: The origin of the plane. normal: The normal of the plane.

Returns:
The gradient of the distance wrt p.
point_plane_distance_gradient(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[12, 1]]

Compute the gradient of the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. t0: The first vertex of the triangle. t1: The second vertex of the triangle. t2: The third vertex of the triangle.

Returns:
The gradient of the distance wrt p, t0, t1, and t2.

ipctk.point_plane_distance_hessian(*args, **kwargs)¶

Overloaded function.

point_plane_distance_hessian(p: numpy.ndarray[numpy.float64[3, 1]], origin: numpy.ndarray[numpy.float64[3, 1]], normal: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[3, 3]]

Compute the hessian of the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. origin: The origin of the plane. normal: The normal of the plane.

Returns:
The hessian of the distance wrt p.
point_plane_distance_hessian(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[12, 12]]

Compute the hessian of the distance between a point and a plane.

Note:
The distance is actually squared distance.

Parameters:
p: The point. t0: The first vertex of the triangle. t1: The second vertex of the triangle. t2: The third vertex of the triangle.

Returns:
The hessian of the distance wrt p, t0, t1, and t2.

Point-Point¶

ipctk.point_point_distance(p0: numpy.ndarray[numpy.float64[m, 1]], p1: numpy.ndarray[numpy.float64[m, 1]]) → float¶

Compute the distance between two points.

Note

The distance is actually squared distance.

Parameters:¶

p0: numpy.ndarray[numpy.float64[m, 1]]¶: The first point.
p1: numpy.ndarray[numpy.float64[m, 1]]¶: The second point.

Returns:¶

The distance between p0 and p1.

ipctk.point_point_distance_gradient(p0: numpy.ndarray[numpy.float64[m, 1]], p1: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]¶

Compute the gradient of the distance between two points.

Note

The distance is actually squared distance.

Parameters:¶

p0: numpy.ndarray[numpy.float64[m, 1]]¶: The first point.
p1: numpy.ndarray[numpy.float64[m, 1]]¶: The second point.

Returns:¶

The computed gradient.

ipctk.point_point_distance_hessian(p0: numpy.ndarray[numpy.float64[m, 1]], p1: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, n]]¶

Compute the hessian of the distance between two points.

Note

The distance is actually squared distance.

Parameters:¶

p0: numpy.ndarray[numpy.float64[m, 1]]¶: The first point.
p1: numpy.ndarray[numpy.float64[m, 1]]¶: The second point.

Returns:¶

The computed hessian.

Point-Triangle¶

ipctk.point_triangle_distance(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.PointTriangleDistanceType = <PointTriangleDistanceType.AUTO: 7>) → float¶

Compute the distance between a points and a triangle.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
t0: The first vertex of the triangle.
t1: The second vertex of the triangle.
t2: The third vertex of the triangle.
dtype: The point-triangle distance type to compute.

Returns:¶

The distance between the point and triangle.

ipctk.point_triangle_distance_gradient(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.PointTriangleDistanceType = <PointTriangleDistanceType.AUTO: 7>) → numpy.ndarray[numpy.float64[12, 1]]¶

Compute the gradient of the distance between a points and a triangle.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
t0: The first vertex of the triangle.
t1: The second vertex of the triangle.
t2: The third vertex of the triangle.
dtype: The point-triangle distance type to compute.

Returns:¶

The gradient of the distance wrt p, t0, t1, and t2.

ipctk.point_triangle_distance_hessian(p: numpy.ndarray[numpy.float64[3, 1]], t0: numpy.ndarray[numpy.float64[3, 1]], t1: numpy.ndarray[numpy.float64[3, 1]], t2: numpy.ndarray[numpy.float64[3, 1]], dtype: ipctk.PointTriangleDistanceType = <PointTriangleDistanceType.AUTO: 7>) → numpy.ndarray[numpy.float64[12, 12]]¶

Compute the hessian of the distance between a points and a triangle.

Note

The distance is actually squared distance.

Parameters:¶

p: The point.
t0: The first vertex of the triangle.
t1: The second vertex of the triangle.
t2: The third vertex of the triangle.
dtype: The point-triangle distance type to compute.

Returns:¶

The hessian of the distance wrt p, t0, t1, and t2.

Last update: Dec 12, 2024