BSpline

python_motion_planning.curve_generation.bspline_curve.BSpline

Bases: Curve

Class for B-Spline curve generation.

Parameters:

Name	Type	Description	Default
step	float	Simulation or interpolation size	required
k	int	Degree of curve	required

Examples:

Python Console Session

>>> from python_motion_planning.curve_generation import BSpline
>>>     points = [(0, 0, 0), (10, 10, -90), (20, 5, 60)]
>>> generator = BSpline(step, k)
>>> generator.run(points)

approximation(points, param, knot)

Given a set of N data points, D0, D1, ..., Dn, a degree k, and a number H, where N > H > k >= 1, find a B-spline curve of degree k defined by H control points that satisfies the following conditions: 1. this curve contains the first and last data points; 2. this curve approximates the data polygon in the sense of least square

Parameters:

Name	Type	Description	Default
points	list[tuple]	path points	required
param	list[float]	The parameters of given points	required
knot	list[float]	The knot vector Returns: control_points (np.ndarray): The control points	required

baseFunction(i, k, t, knot)

Calculate base function using Cox-deBoor function.

Parameters:

Name	Type	Description	Default
i	int	The index of base function	required
k	int	The degree of curve	required
t	float	parameter	required
knot	list[float]	knot vector	required

Returns:

Name	Type	Description
Nik_t	float	The value of base function Nik(t)

generation(t, k, knot, control_pts)

Generate the B-spline curve.

Parameters:

Name	Type	Description	Default
t	ndarray	The parameter values	required
k	int	The degree of the B-spline curve	required
knot	list[float]	The knot vector	required
control_pts	ndarray	The control points	required

Returns:

Name	Type	Description
curve	ndarray	The B-spline curve

interpolation(points, param, knot)

Given a set of N data points, D0, D1, ..., Dn and a degree k, find a B-spline curve of degree k defined by N control points that passes all data points in the given order.

Parameters:

Name	Type	Description	Default
points	list[tuple]	path points	required
param	list[float]	The parameters of given points	required
knot	list[float]	The knot vector	required

Returns:

Name	Type	Description
control_points	ndarray	The control points

knotGeneration(param, n)

Generate knot vector.

Parameters:

Name	Type	Description	Default
param	list[float]	The parameters of given points	required
n	int	The number of data points Returns: knot (list[float]): The knot vector	required

paramSelection(points)

Calculate parameters using the uniform spaced or chrod length or centripetal method.

Parameters:

Name	Type	Description	Default
points	list[tuple]	path points Returns: Parameters (list[float]): The parameters of given points	required

run(points, display=True)

Running both generation and animation.

Parameters:

Name	Type	Description	Default
points	list[tuple]	path points	required