tactics2d.interpolator

Interpolator module.

BSpline

This class implements a B-spline curve interpolator.

get_curve(control_points, knot_vectors=None, degree=0, n_interpolation=100) staticmethod

Get the interpolation points of a b-spline curve.

Parameters:

• control_points (ndarray) –

  The control points of the curve. Usually denoted as \(P_0, P_1, \dots, P_n\) in literature. The shape is \((n + 1, 2)\).

• knot_vectors (ndarray, default: None ) –

  The knots of the curve. Usually denoted as \(u_0, u_1, \dots, u_t\) in literature. The shape is \((t + 1, )\). Defaults to None.

• degree (int, default: 0 ) –

  The degree of the B-spline curve. Usually denoted as p in the literature. Defaults to 0.

• n_interpolation (int, default: 100 ) –

  The number of interpolation points. Defaults to 100.

Returns:

• curve_points ( ndarray ) –

  The interpolation points of the curve. The shape is (n_interpolation, 2).

Bezier

This class implements a Bezier curve interpolator.

get_curve(control_points, n_interpolation, order=None) staticmethod

Parameters:

• control_points (ndarray) –

  The control points of the curve. The shape is (order + 1, 2).

• n_interpolation (int) –

  The number of interpolations.

• order (int, default: None ) –

  The order of the Bezier curve. If not provided, it will be set to the number of control points minus one.

Returns:

• curve_points ( ndarray ) –

  The interpolated points of the curve. The shape is (n_interpolation, 2).

CubicSpline

This class implement a cubic spline interpolator.

Attributes:

• boundary_type (int) –

  Boundary condition type. The cubic spline interpolator offers three distinct boundary condition options: Natural (1), Clamped (2), and NotAKnot (3). By default, the not-a-knot boundary condition is applied, serving as a wise choice when specific boundary condition information is unavailable.

BoundaryType

Bases: Enum

The boundary condition type of the cubic spline interpolator.

Attributes:

• Natural (int) –

  Natural boundary condition. The second derivative of the curve at the first and the last control points is set to 0.

• Clamped (int) –

  Clamped boundary condition. The first derivative of the curve at the first and the last control points is set to the given values.

• NotAKnot (int) –

  Not-a-knot boundary condition. The first and the second cubic functions are connected at the second and the third control points, and the last and the second-to-last cubic functions are connected at the last and the second-to-last control points.

get_curve(control_points, first_derivatives=(0, 0), n_interpolation=100, boundary_type=BoundaryType.NotAKnot) staticmethod

Get the interpolation points of a cubic spline curve.

Parameters:

• control_points (ndarray) –

  The control points of the curve. The shape is (n + 1, 2).

• first_derivatives (tuple, default: (0, 0) ) –

  The first derivatives (f'(x₀), f'(xₙ)) at the first and last control points. Only used for Clamped boundary condition. Defaults to (0, 0).

• n_interpolation (int, default: 100 ) –

  The number of interpolations between every two control points. Defaults to 100.

• boundary_type (Union[int, BoundaryType], default: NotAKnot ) –

  The boundary condition type. It can be an integer value from 1 to 3 or a BoundaryType enum value. Defaults to NotAKnot.

Returns:

• curve_points ( ndarray ) –

  The interpolation points of the curve. The shape is (n_interpolation * n + 1, 2).

Dubins

This class implements a Dubins curve interpolator.

The curve comprises a sequence of three segments: RSR, RSL, LSL, LSR, RLR, and LRL. R stands for the right turn, L for the left turn, and S for the straight line. A Dubins path planner operates within the constraints of forward actions exclusively.

Attributes:

• radius (float) –

  The minimum turning radius.

__init__(radius)

Initialize the Dubins curve interpolator.

Parameters:

• radius (float) –

  The minimum turning radius.

Raises:

• ValueError –

  The minimum turning radius must be positive.

get_all_path(start_point, start_heading, end_point, end_heading)

This function returns all the Dubins paths connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The heading of the start point. The unit is radian.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The heading of the end point. The unit is radian.

Returns:

• paths ( list ) –

  A list of Dubins paths.

get_curve(start_point, start_heading, end_point, end_heading, step_size=0.1)

Get the shortest Dubins curve connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The heading of the start point. The unit is radian.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The heading of the end point. The unit is radian.

• step_size (float, default: 0.1 ) –

  The step size of the curve. Defaults to 0.1.

Returns:

• shortest_path ( DubinsPath ) –

  The shortest Dubins path connecting two points.

get_path(start_point, start_heading, end_point, end_heading)

This function returns the shortest Dubins path connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The heading of the start point. The unit is radian.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The heading of the end point. The unit is radian.

Returns:

• shortest_path ( DubinsPath ) –

  The shortest Dubins path.

ParamPoly3

This class implements a parametric cubic polynomial curve interpolation.

fit(pts) staticmethod

Fit a paramPoly3 curve to a polyline segment.

Transforms the segment to a local frame (origin at start, x-axis along initial heading), then fits cubic polynomials U(p) and V(p) where p is the normalised arc-length parameter in [0, 1].

Parameters:

• pts (ndarray) –

  Polyline points in world coordinates. Shape (N, 2).

Returns:

• tuple | None –

  tuple | None: A tuple of (x, y, hdg, length, aU, bU, cU, dU, aV, bV, cV, dV). Returns None if the segment is degenerate.

Example

import numpy as np from tactics2d.interpolator.param_poly3 import ParamPoly3 pts = np.array([[0., 0.], [10., 1.], [20., 0.]]) result = ParamPoly3.fit(pts) x, y, hdg, length, aU, bU, cU, dU, aV, bV, cV, dV = result length > 0 True

get_curve(length, start_point, heading, aU, bU, cU, dU, aV, bV, cV, dV, p_range_type='normalized') staticmethod

Get the points on a paramPoly3 curve defined in the OpenDRIVE standard.

Parameters:

• length (float) –

  The arc length of the curve segment.

• start_point (tuple) –

  The (x, y) world coordinates of the curve start.

• heading (float) –

  The heading angle at the start point in radians.

• aU (float) –

  Constant coefficient of the U polynomial.

• bU (float) –

  Linear coefficient of the U polynomial.

• cU (float) –

  Quadratic coefficient of the U polynomial.

• dU (float) –

  Cubic coefficient of the U polynomial.

• aV (float) –

  Constant coefficient of the V polynomial.

• bV (float) –

  Linear coefficient of the V polynomial.

• cV (float) –

  Quadratic coefficient of the V polynomial.

• dV (float) –

  Cubic coefficient of the V polynomial.

• p_range_type (str, default: 'normalized' ) –

  Parameter range type as specified in OpenDRIVE. "normalized" maps p in [0, 1]; "arcLength" maps p in [0, length]. Defaults to "normalized".

Returns:

• ndarray –

  np.ndarray: World-coordinate points on the curve. Shape is (n, 2).

ReedsShepp

This class implements a Reeds-Shepp curve interpolator.

Reference

Reeds, James, and Lawrence Shepp. "Optimal paths for a car that goes both forwards and backwards." Pacific journal of mathematics 145.2 (1990): 367-393.

Attributes:

• radius (float) –

  The minimum turning radius of the vehicle.

get_all_path(start_point, start_heading, end_point, end_heading)

Get all the Reeds-Shepp paths connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The start heading of the curve.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The end heading of the curve.

Returns:

• paths ( list ) –

  A list of Reeds-Shepp paths.

get_curve(start_point, start_heading, end_point, end_heading, step_size=0.01)

Get the shortest Reeds-Shepp curve connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The start heading of the curve.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The end heading of the curve.

Returns:

• shortest_path ( ReedsSheppPath ) –

  The shortest Reeds-Shepp curve connecting two points.

get_path(start_point, start_heading, end_point, end_heading)

Get the shortest Reeds-Shepp path connecting two points.

Parameters:

• start_point (ndarray) –

  The start point of the curve. The shape is (2,).

• start_heading (float) –

  The start heading of the curve.

• end_point (ndarray) –

  The end point of the curve. The shape is (2,).

• end_heading (float) –

  The end heading of the curve.

Returns:

• shortest_path ( ReedsSheppPath ) –

  The shortest Reeds-Shepp path connecting two points.

Spiral

This class implements a spiral interpolation.

get_curve(length, start_point, heading, start_curvature, gamma, n_interpolation=100) staticmethod

This function gets the points on a spiral curve line.

Parameters:

• length (float) –

  The length of the spiral.

• start_point (ndarray) –

  The start point of the spiral. The shape is (2,).

• heading (float) –

  The heading of the start point. The unit is radian.

• start_curvature (float) –

  The curvature of the start point.

• gamma (float) –

  The rate of change of curvature

• n_interpolation (int, default: 100 ) –

  The number of interpolation points. Defaults to 100.

Returns:

• ndarray –

  np.ndarray: The points on the spiral curve line. The shape is (n_interpolation, 2).