STEP

Given a specific x value, the Step function evaluates the y value of a function that smoothly transitions from ( x 0 , y 0 ) to ( x 1 , y 1 ) . This function has continuous first and second derivatives, but discontinuous third derivatives at the end points.

Format

Step ( x , x 0 , y 0 , x 1 , y 1 )

Arguments

x
The independent variable. For example, to specify time as the independent variable, specify x as TIME.
x 0
The x value at which the Step function begins.
y 0
The value of the Step function desired at x 0
x 1
The x value at which the Step function ends.
y 1
The value of the Step function desired at x 1 .

Definition

(1)
step  = { y 0 ,   if  x ≤ x 0 y 0 + Δ y x ˜ 2 ( 3 − 2 x ˜ ) ,  if x 0 < x < x 1 y 1 ,    if  x ≥ x 1 where, Δ y = ( y 1 − y 0 ) a n d x ˜ = ( x − x 0 ) ( x 1 − x 0 )

Example

<Motion_Joint
     id                  = "104003"
     type                = "EXPRESSION"
     val_type            = "D"
     expr                = "STEP(TIME,0,0,0.01,-50)"
     joint_id            = "104008"
     joint_type          = "T"
/>