segmentedFunction

Creates a new piecewise linear function.

Syntax

This function uses the syntax depicted in the following diagram:

In order to simplify code generation, a trailing comma is allowed.

Parameters

The first parameter is a pair of floating-point values (s₀, y₀).
The remaining parameters are triples of floating-point values (x_i, y_i, s_i) sorted by x_i.

Description

This function creates a new piecewise linear function. Each parameter (pair or triple) represents one segment of the function. The segments are defined by splitting points x₁, x₂,.. x_n, values at the splitting point y₀, y₁,.. y_n and slopes of the segments s₀, s₁,.. s_n:

The segments of the function are:

Segment number	Definition interval	Function value at `t`
0	`(-∞, x₁)`	`y₀ + s₀ (t - x₁)`
`i=1,2,.. n-1`	`[x_i, x_i+1)`	`y_i + s_i (t - x_i)`
`n`	`[x_n, ∞)`	`y_n + s_n (t - x_n)`

The function is always defined on (-∞, ∞), however it does not have to be continuous (in the example above the function is discontinuous at x₁ and x₃.

If only a single pair (s₀, y₀) is specified, then s₀ must be 0 and the result is constant function that has value y₀ everywhere.

Example


function = segmentedFunction((-1, 5), (10, 0, 0), (15, 5, 3));

The code above creates function with the following graph:

Requirements

The segments must be sorted in ascending order by x_i.
Two segments with the same value x_i are not allowed.

Notes

The only way to evaluate a segmented function at given point is to use one of the functions startEval, endEval, lengthEval and sizeEval.