Spline

Class Name

Spline

Description

In mathematics, splines are often used for fitting and interpolating measured data. Reference_Spline defines a spline with two or three independent variables. In other words, the data can be a curve or a surface.

Attribute Summary

Name	Property	Modifiable by command?	Designable?
id	Int ()
label	Str ()
x	Double (count=0)	Yes	FD Only
y	Double (count=0)	Yes	FD Only
z	Double (count=0)		FD Only
linear_extrapolate	Bool (False)	Yes
file	String ()	Yes
block	String ()	Yes
function	Function ("SPLINE_READ")

Usage

MotionSolve provides four different ways for defining splines.

#1: Spline for X-Y data
Spline (x=list, y=list, optional_attributes)

#2: Spline for X-Y-Z data
Spline (x=list, y=list, optional_attributes)

#3: Spline data read from a file by a compiled user subroutine
Spline (file=string, function=userString, routine=string, optional_attributes)

#4: Spline data read from a file by a Python function
Spline (file=string, function=userString, routine=functionPointer, optional_attributes)

Attributes

Spline for X-Y data

x

List of numeric values.

Specifies the list of the X values of the spline.

The x attribute is mandatory.

Requirements: len (x) ≥ 4

y

List of numeric values

Specifies the list of the Y values of the spline.

The y attribute is mandatory.

Requirements:

len (y) ≥ 4
len (x) = len (y)

Spline for X-Y-Z data

x

List of numeric values.

Specifies the list of the X values of the spline.

The x attribute is mandatory.

Requirements: len (x) ≥ 4.

z

List of numeric values.

Specifies the list of the Z values of the spline.

The z attribute is optional.

y

List of numeric values.

Specifies the list of the Y values of the spline.

The y attribute is mandatory.

Requirements when Z is specified:

y is a matrix of dimensions (M,N) specified as a two-dimensional list.
M is the number of z values.
N is the number of x values.
Each row corresponds to one value of z.

Requirements when Z is not specified:

y is a matrix of dimensions (1,N) specified as a one-dimensional list.
N is the number of x values.
There must be at least four numbers in each row.
All rows must have the same length.

Spline data read from a file by a compiled user subroutine

file

String

Specifies the path and name of the file containing the spline data. Use only when the data is contained in an external file.

The file attribute is mandatory.

function

String

The list of parameters that are passed from the data file to the user-defined subroutine.

The function attribute is mandatory.

routine

String

Specifies an alternative name for the user subroutine. The name consists of two pieces of information, separated by "::". The first is the pathname to the shared library containing the function that computes the response of the user-defined Surface. The second is the name of the function in the shared library that does the computation.

An example is: routine="/staff/Altair/engine.dll::mySplineRead"

"/staff/Altair/ engine.dll is the DLL
"mySplineRead" is the function within this DLL that performs the calculations

The attribute routine is optional.

When not specified, routine defaults to Spline_Read.

The attribute routine is optional.

block

String

Specifies the block name containing the spline data. A single file may contain several blocks of data.

This parameter is optional. Use only when the data is contained in an external file with many blocks of data.

The block attribute is optional.

Spline data read from a file by a Python function

file

String

Specifies the path and name of the file containing the spline data. Use only when the data is contained in an external file.

The file attribute is mandatory.

function

String

The list of parameters that are passed from the data file to the user-defined subroutine.

The function attribute is mandatory.

routine

Pointer to a callable function in Python.

An example is: routine=my_Spline_Read.

my_Spline_Read is a Python function or method that can be called from wherever the model resides.

The attribute routine is optional.

When not specified, routine defaults to Spline_Read.

block

String

Specifies the block name containing the spline data. A single file may contain several blocks of data.

This parameter is optional. Use only when the data is contained in an external file with many blocks of data.

The block attribute is optional.

Optional Attributes - Available to all description methods

id

Integer

Specifies the element identification number. This number must be unique among all the Spline objects in the model.

This attribute is optional. MotionSolve will automatically create an ID when one is not specified.

Range of values: id > 0.

label

String

Specifies the name of the Spline object.

This attribute is optional. When not specified, MotionSolve will create a label for you.

linear_extrapolate

Boolean

A logical flag that specifies how MotionSolve is to deal with the situation when the independent coordinate falls out of the range of data provided. Select either True or False.

True indicates that MotionSolve is to use linear extrapolation to estimate the spline value.
False indicates that MotionSolve should not extrapolate; instead it should return an error.

This attribute is optional. When not specified, MotionSolve will set linear_extrapolate = True.

Example

XML vs. Python syntax for the same model.

XML Syntax Python Syntax

XML Syntax	Python Syntax
`<Reference_Spline id = "301001" label = "SWA vs. Time" num_x = "11" 0.00E+00 1.09E+00 1.00E-01 6.88E+00 2.00E-01 2.52E+00 3.00E-01 3.02E+00 4.00E-01 3.30E+00 5.00E-01 3.23E+00 6.00E-01 -8.91E-02 7.00E-01 -4.20E+00 8.00E-01 -3.00E+00 9.00E-01 2.05E+00 1.00E+00 0.04E+00 </Reference_Spline>`	`time = [ 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1] swa = [1.09, 6.88, 2.52, 3.02, 3.30, 3.23,-.0891,-4.20, 3, 2.05, 0] spl1 = Spline (label="SWA vs. Time", x=time, y=swa)`
`<Reference_Spline id = "301001" num_x = "5" num_z = "3"> <!--x Y(zl) Y(z2) Y(z3)--> 0.00 0.00 0.00 0.00 0.25 0.50 0.70 0.90 0.50 0.00 0.00 0.00 0.75 0.50 0.70 0.90 1.00 0.00 0.00 0.00 <!--Z values--> 0.00 1.00 20.0 </Reference_Spline>`	`xval = [ 0, 0.25, 0.5, 0.75, 1] zval = [ 0.0, 1.0, 20.0 ] yval = [[0, 0.5, 0, 0.5, 0] [0, 0.7, 0, 0.7, 0] [0, 0.9, 0, 0.9, 0]]spl2 = Spline (label="jagged surface", x=xval, y=yval, z=zval)`
`<Reference_Spline id = "301001" usrsub_dll_name = "./wheel.so" file_name = "./wheel_1.dat" block_name = "wheel_angle" />`	`dll = "./wheel.dll" fnam = "./wheel_1 .dat" blk = "wheel angle" spl3 = Spline (label="SWA vs. Time", routine=dll, file=fnam, block=blk)`

<Reference_Spline
  id = "301001"
  label = "SWA vs. Time"
  num_x = "11"
   0.00E+00  1.09E+00
   1.00E-01  6.88E+00
   2.00E-01  2.52E+00
   3.00E-01  3.02E+00
   4.00E-01  3.30E+00
   5.00E-01  3.23E+00
   6.00E-01 -8.91E-02
   7.00E-01 -4.20E+00
   8.00E-01 -3.00E+00
   9.00E-01  2.05E+00
   1.00E+00  0.04E+00
</Reference_Spline>

time = [ 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, 1] 
swa = [1.09, 6.88, 2.52, 3.02, 3.30, 3.23,-.0891,-4.20, 3, 2.05, 0]
spl1 = Spline (label="SWA vs. Time", x=time, y=swa)

<Reference_Spline
 id = "301001"
 num_x = "5"
 num_z = "3">
<!--x Y(zl) Y(z2) Y(z3)-->
 0.00 0.00 0.00 0.00
 0.25 0.50 0.70 0.90
 0.50 0.00 0.00 0.00
 0.75 0.50 0.70 0.90
 1.00 0.00 0.00 0.00
 <!--Z values-->
     0.00 1.00 20.0
</Reference_Spline>

xval = [ 0, 0.25, 0.5, 0.75, 1] 
zval = [ 0.0, 1.0, 20.0 ]
yval = [[0, 0.5, 0, 0.5, 0]
        [0, 0.7, 0, 0.7, 0]
        [0, 0.9, 0, 0.9, 0]]spl2 = Spline (label="jagged surface", x=xval, y=yval, z=zval)

<Reference_Spline
 id              = "301001"
 usrsub_dll_name = "./wheel.so"
 file_name       = "./wheel_1.dat"
 block_name      = "wheel_angle"
/>

dll = "./wheel.dll" 
fnam = "./wheel_1 .dat"
blk = "wheel angle"
spl3 = Spline (label="SWA vs. Time", routine=dll, 
file=fnam, block=blk)

Comments

See Properties for an explanation about what properties are, why they are used, and how you can extend these.
For a more detailed explanation about Spline, see Reference: Spline.