1D Cubic Line Fit

Description

• These step-by-step instructions will guide you through data fitting by using one-dimensional Hermite basis function.
• This fitting concept is to initiate the line element and then choose the proper basis function to fit the initial element and the data.

• An automated script that runs this tutorial is included in the Continuity installation: examples\data07\fitting1dCircle.py. To run it, click File→Scripts→Read script…

Start Continuity

• Launch the Continuity Client

• On the About Continuity startup screen

  • check the fitting box under Use Modules:

• Click OK to bring up the main window

Setting up the geometry

• Mesh→Edit→Coordinates…

  • Select rectangular cartesian in the Global Coordinates: pop-up menu

  • Click OK to submit Coordinate Form

• Mesh→Edit→Basis…

  • Choose Hermite Basis Function→1D→Cubic

  • Click Add

  • Verify that the list of basis functions now contains:
    • Cubic Hermite 3

  • Click OK to submit Basis Form

• Mesh→Edit→Nodes…

  • Click Import/Export/Graph button to open Continuity Table Manager

    • Continuity Table Manager→File→Open…

      • Select tab-delimited nodes file ( nodes.xls )

      • Continuity Table Manager→File→Close and update form

  • You should now have nodes numbered 1-4

  • Click on the Field Vector 1 tab

  • Select Cubic under Field Variable 1

  • Click OK to submit Node Form

• Mesh→Edit→Elements…

  • Click Import/Export button to open Continuity Table Manager

    • Continuity Table Manager→File→Open…

      • Select tab-delimited elements file ( elems.xls )

      • Continuity Table Manager→File→Close and update form

  • You should now have 4 elements in the list

  • Click OK to submit Element Form

• Mesh→Render→Elements…

  • Click the lines radio button

  • Click Render

  • The mesh should now look similar to the first screenshot

Setting up the data

• If the Fitting menu is not loaded, select File→Load Continuity Modules…

  • Select fitting and click OK

  • The menu bar should now show the Fitting command

• Fitting→Edit→Data…

  • Click Import/Export/Graph button to open Continuity Table Manager

    • Continuity Table Manager→File→Open…

      • Select tab-delimited data file ( data.xls )

      • Continuity Table Manager→File→Close and update form

  • You should now have Data numbered 1-64

  • Click OK to submit Data Form

• Fitting→Edit→Fit Weights…

  • For all three coordinates, fill in the values according to the table below (use these as a starting guide)

    s(1)	s(1)s(1)	s(2)	s(1)(2)	s(2)(2)	s(3)	s(1)s(3)	s(2)s(3)	s(3)s(3)
    0.01	0.01	0.01	0.01	0.02	0.0	0.0	0.0	0.0

     

  • Click OK to submit Fit Weights Form

• File→Send

  • If the Dimensions Helper comes up, click Accept marked recommendations and click OK

• Mesh→Calculate Mesh…

• Fitting→Render→RawData…

  • Make sure all appears in the Data Points text box

  • Click OK to submit Render Data Form

• View→Show Open Mesh…

  • Select datapoints2 from the list on the left, click on the Properties tab, and set the Size field to 0.015. Then hit Enter

• At this point, it’s a good idea to save the problem.

Perform fit

• Fitting→Fit Data

  • In the Cooridinates tab, select coord_1, coord_2, coord_3 for the three coordinates

  • In the Xi Projections tab, set the Ignore points with distance > field to 1.0.

  • Click the Fit button on the bottom

  • Close the window by clicking the X button

• File→Send

• Mesh→Calculate Mesh…

• Mesh→Render→Elements…

  • Click the lines radio button

  • Click Render

• View→Show Open Mesh…

  • Click on elements lines3 in the list on the left

  • Click on the Colors tab

  • Change the R,G,B color field to 1, 0, 0 to change the color to the brightest red and then hit Enter

  • The mesh should now look similar to the second screenshot

Pre-built model

This cont6 file contains all data and parameters for this problem: fit1.cont6