# Create a Prolate Spheroidal Mesh and Convert to Cartesian Coordinates

### Description

• In this example, a 3-D ellipsoidal mesh is created in prolate spheroidal coordinates using one trilinear Lagrange element. It is then converted to a 4-element cubic Hermite mesh in Cartesian coordinates.
• The nodal coordinates and element connectivities are read from tab-delimited spreadsheets.
• The steps below are saved in a script that can be found in the examples directory on your Continuity client .../continuity/pcty/examples/mesh04/convertToCartesianUnit.py which can be executed automatically with File→Scripts→Read Script→Python script

### Start Continuity

• Launch the Continuity Client
• leave the mesh checkbox checked under Use Modules:

• Click OK to bring up the main window

### Create coordinates and basis functions

• Select prolate spheriodal in the Global Coordinates: pop-up menu

• Enter 3.75 in the Focus Position field

• Click OK to submit Coordinate Form

• Choose Hermite Basis Function→3D→Linear-Cubic-Cubic

• Choose Hermite Basis Function→3D→Cubic-Cubic-Cubic

• Verify that the list of basis functions now contains:
• Linear-Cubic-Cubic Hermite 3*3*3
• Linear-Cubic Hermite 3*3
• Cubic-Cubic Hermite 3*3
• Cubic-Linear Hermite 3*3
• Cubic-Cubic-Cubic Hermite 3*3*3
• Click OK to submit Basis Form

### Read prolate spheroidal nodal coordinates and element

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

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

• Under Coordinate 1, Coordinate 2, and Coordinate 3, verify that the basis function for each coordinate is Linear-Cubic-Cubic Hermite. If it is Cubic-Cubic-Cubic Hermite or anything else, make sure to change it to Linear-Cubic-Cubic Hermite.

• In the Node Form under Dervatives with respect to, select the Angle Changes radio button

• You should now have nodes numbered 1-4
• Click OK to submit Node Form

• Click Import/Export button to open Continuity Table Manager

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

• You should now have only one element in the list
• Click OK to submit Element Form

### Calculate and render mesh

• Click Render to display mesh

• The mesh should now look similar to the first screenshot

### Refine mesh circumferentially into four elements

• Enter 4 for xi1, 1 for xi2, and 1 for xi3 under New Element per old element in

• Select the Local coordinates radio button under New nodal derivatives with respect to:

• Click OK to submit

### Change basis functions to cubic Hermite and render mesh

• Select Cubic-Cubic-Cubic under Coordinate 1, Coordinate 2, and Coordinate 3

• All derivatives for all three coordinates should now be enabled
• Click OK to submit Node Form

• If the Dimensions Form appears, simply click Apply Marked Recommendations and then OK

• Click Render to display mesh surface

• Click on elements lines2 in the list on the left

• Click on the Colors tab

• Change the R,G,B color field to 1.0, 0.0, 0.0 to change the color to the brightest red and hit Enter

• Click on elements lines1 in the list on the left

• Check and uncheck the Visibility checkbox a couple times to compare the two different renderings

• Close the window by clicking the X button

• The mesh should now look similar to the second screenshot

### Convert coordinates to rectangular Cartesian

• Leave the update nodes and update coordinates checkboxes checked

• Click OK

• Select the Save, reset, and reload radio button on the bottom

• Click OK

• Click Render to display mesh surface

• Click on elements lines3 in the list on the left

• Click on the Colors tab

• Change the R,G,B color field to 0,0,0 to change the color to black and hit Enter

• Click on elements lines2 in the list on the left

• Check and uncheck the Visibility checkbox a couple times to compare the two different renderings

• Close the window by clicking the X button

• The mesh should now look similar to the third screenshot

### Pre-built model

This cont6 file contains all data and parameters for this problem: mesh7.cont6 (As this is the final model, rendering elements will produce the mesh like the last screenshot)