STEP5

Given a specific x value, the Step5 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

Step5 ( 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 Step5 function begins.

y 0

The value of the Step5 function desired at x 0 .

x 1

The x value at which the Step5 function ends.

y 1
The value of the Step5 function desired at x 1

Definition

(1)
step5  = { y 0 ,   if  x x 0 y 0 + Δ y x ˜ 3 ( 10 15 x ˜ + 6 x ˜ 2 ) ,  if x 0 < x < x 1 y 1 ,    if  x x 1 where, Δ y = ( y 1 y 0 ) x ˜ = ( x x 0 ) ( x 1 x 0 )

Example

<Motion_Joint
     id                  = "104003"
     type                = "EXPRESSION"
     val_type            = "D"
     expr                = "STEP5(TIME,0,0,0.01,-50)"
     joint_id            = "104008"
     joint_type          = "T"
/>