bentcableAR (version 0.3.0)

fullcable.t: Evaluate Bent Cable Function

Description

The bent-cable response is evaluated at a provided design point t.

Usage

fullcable.t(t, b0, b1, b2, tau, gamma)

Arguments

t

A design point at which the bent cable is to be evaluated.

b0

Intercept.

b1

Incoming slope.

b2

Coefficient of the basic bent cable.

tau

Centre of the quadratic bend (transition).

gamma

Non-negative half-width of the quadratic bend.

Details

All arguments must be numeric, and at most one can be a vector.

The full bent cable has the form $f(t) = b_0 + b_1 t + b_2 q(t)$, where $q(t)$ is the basic bent cable function with intercept and slope 0 and outgoing slope 1: $$q(t)=\frac{(t-\tau+\gamma)^2}{4\gamma} I{|t-\tau|\leq\gamma} + (t-\tau) I{t>\tau+\gamma}$$ for $\gamma\geq 0$.

References

See the bentcableAR package references.

Examples

# basic broken stick, kink at 0:
	plot( seq(-10,10), fullcable.t(seq(-10,10),0,0,1,0,0) )
	
	# full bent cable, bend centred at 0 with half-width 3:
	plot( seq(-10,10), fullcable.t(seq(-10,10),1,.1,-.5,0,3) )