$\newcommand{\deriv}[2][]{\dfrac{\partial #1}{\partial #2}} \newcommand{\tderiv}[2][]{\tfrac{\partial #1}{\partial #2}} \newcommand{\fderiv}[2][]{\dfrac{d #1}{d #2}} \newcommand{\derivII}[3][]{\dfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\tderivII}[3][]{\tfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\derivIII}[4][]{\dfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\tderivIII}[4][]{\tfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\derivIV}[5][]{\dfrac{\partial^4 #1}{\partial #2 \partial #3 \partial #4 \partial #5}} \newcommand{\half}{\tfrac{1}{2}} % Macro for 1/2 \newcommand{\ud}{\mathrm{d}} \newcommand{\op}{\circ} \newcommand{\dq}{\dot{q}} \newcommand{\ddq}{\ddot{q}} \newcommand{\dt}{\Delta t}$

Spline – Spline Objects

class trep.Spline(points)

Parameters:points – A list of points defining the spline. See details.

The Spline class implements 1D spline interpolation between a set of points. Spline provides methods to evaluate points on the spline curve as well as its first and second derivatives. It can be used by new types of forces, potentials, and constraints to implement calculations.

The spline is defined by the list points. Each entry in points is a list of 2-4 numbers. The first two numbers are the x and y values of the points. The remaining two numbers, if provided and not None, are the first and second derivatives of the curve at that point. Any derivatives not provided are determined by the resulting interpolation.

For N points, The spline will comprise N-1 polynomials of order 3-5, depending on how many derivatives were specified. Spline will choose the lowest order polynomials possible while still being able to satisfy the specified values. Specifying derivatives directly is much more effective than placing several points infinitesimally close to force the curve into a particular shape.

Spline Objects

Spline.x_points

Return type:numpy.ndarray

List of the x points that define this spline.

(read-only)

Spline.y_points

Return type:numpy.ndarray

List of the y points that define this spline.

(read-only)

Spline.coefficients

Return type:numpy.ndarray

The coefficients of the interpolating polynomials.

(read-only)

Spline.copy()

Return type:Spline

Create a new copy of this Spline.

Spline.y(x)

Return type:Float

Evaluate the spline at x.

Spline.dy(x)

Return type:Float

Evaluate the derivative of the spline at x.

Spline.ddy(x)

Return type:Float

Evaluate the second derivative of the spline at x.