pytakt.interpolator module

This module defines classes for piecewise linear or cubic interpolation.

class Point(t, value, slope=1)

Bases: object

This class represents the control points on which the interpolation is based. Each control point has information about time, value, and slope. In this module’s interpolation method, the interpolated line/curve always passes through the control points.

Constructor

Parameters:

  • t (int, float or None) – The time at the control point, where None means that the time of this control point is determined by dividing equally between the non-None times of the nearby control points.

  • value (int or float) – The value at the control point.

  • slope (int, float, None, or 2-tuple) – The slope at the control point, relative to the polyline case. Thus, if all slopes are 1, interpolation is done along a polyline (default). If at least one of the slopes at the start and end of an interval span is a real number other than 1, the span is interpolated by a cubic curve. If slope is the string ‘free’, the slope is automatically calculated from the information of the previous and next control points to create a smooth connection. The slope can also be a 2-tuple, in which case the left and right slope values are specified separately. If the left slope is None, it means that the values will be changed in a staircase fashion without interpolation. slope=None is equivalent to slope=(None, 1).


class Interpolator(points)

Bases: object

A class representing an object for interpolating values. Given a list of control points, once this object f is created, it can be called like f(time) to get the interpolated values. Before the time of the first control point, f(time) is the value of the first control point, and after the time of the last control point, it is the value of the last control point.

Constructor

Parameters:

points (list of Point, etc.) –

List of control points (must contain at least 1 point). The control points must be ordered by time. It is possible to specify two control points at the same time, which can be used for sawtooth-like changes. Each control point can be a Point instance or the following shorthand forms.

  • value – equivalent to Point(None, value).

  • (t, value) – equivalent to Point(t, value).

  • [value, slope] – equivalent to Point(None, value, slope).

  • (t, value, slope) – equivalent to Point(t, value, slope).

If None is specified for the time of the first control point, it is assumed to be 0. None cannot be specified for the time of the last control point. Only control points other than the first and last can use ‘free’ for the slope attribute.

Examples

Interpolator([0, (480, 100)])

Represents a function that linearly interpolates such that the value is 0 at time 0 and 100 at time 480.

Interpolator([0, 100, (960, 50)])

Represents a function that varies along a polyline such that the value is 0 at time 0, 100 at time 480, and 50 at time 960.

Interpolator([0, [100, None], (960, 50, None)])

Represents a function that steps from 0 to 100 at time 480, and from 100 to 50 at time 960.

Interpolator([0, [100, 'free'], (960, 50)])

Represents a piecewise cubic curve that varies smoothly from 0 at time 0, to 100 at time 480, to 50 at time 960.

Interpolator([(0, 100, 3.0), (480, 0, 0.0)])

Represents a cubic curve (in this case a curve similar to an exponential decay) such that at time 0 the value is 100 and the slope is 3 times that of the line connecting the two points, and at time 480 the value is 0 and the slope is 0.

Interpolator([(0, 100, 0), (240, 0, 0) (480, 100, 0)])

Represents a piecewise cubic curve that varies smoothly like the cosine function, 100 -> 0 -> 100.


maxtime() → Union[int, float, Fraction]

Returns the time of the last control point.

iterator(tstep, ystep=-1) → Iterator[Tuple[Union[int, float, Fraction], float]]

Generator function that yields time/value pairs (t, value) sequentially along an interpolated line or curve. Times range from the time of the first control point to the time of the last control point.

Parameters:

  • tstep (ticks) – Specifies the time step value. The pairs are output sequentially with this time interval starting from the time at which each control point exists. The pair at the time of the control point is always output.

  • ystep (int or float, optional) – If specified, output is omitted if the absolute value of the difference between the current value and the previous value is less than or equal to ystep. (But the pair will always be output at the time when a control point exists.)