== Create a Prolate Spheroidal Mesh and Convert to Cartesian Coordinates ==
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[[TableOfContents(3)]]

=== 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 [:Continuity/Documentation/Help/ReadPythonScript:File→Scripts→Read Script→Python script]
=== Start Continuity ===
 * Launch the Continuity Client
 * On the [:Continuity/Documentation/Help/HelpAboutContinuity:About Continuity startup screen]
  * leave the '''mesh''' checkbox checked under {{{Use Modules:}}}
 * Click '''OK''' to bring up the main window
=== Create coordinates and basis functions ===
 * [:Continuity/Documentation/Help/MeshEditCoordinates:Mesh→Edit→Coordinates...]
  * Select '''prolate spheriodal''' in the {{{Global Coordinates:}}} pop-up menu
  * Enter '''3.75''' in the {{{Focus Position}}} field
  * Click '''OK''' to submit {{{Coordinate Form}}}
 * [:Continuity/Documentation/Help/MeshEditBasis:Mesh→Edit→Basis...]
  * Choose '''Hermite Basis Function→3D→Linear-Cubic-Cubic'''
  * Click '''Add Linear-Cubic-Cubic'''
  * Choose '''Hermite Basis Function→3D→Cubic-Cubic-Cubic'''
  * Click '''Add 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 ===
 * [:Continuity/Documentation/Help/MeshEditNodes:Mesh→Edit→Nodes...]
  * Click '''Import/Export/Graph''' button to open [:Continuity/Documentation/Help/TableManager:Continuity Table Manager]
   * [:Continuity/Documentation/Help/TableManager#FileMenu:Continuity Table Manager→File→Open...]
    * Select tab-delimited nodes file ( attachment:nodes.xls )
    * [:Continuity/Documentation/Help/TableManager#FileMenu:Continuity Table Manager→File→Close and update form]
  * 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}}}
 * [:Continuity/Documentation/Help/MeshEditElements:Mesh→Edit→Elements...]
  * Click '''Import/Export''' button to open [:Continuity/Documentation/Help/TableManager:Continuity Table Manager]
   * [:Continuity/Documentation/Help/TableManager#FileMenu:Continuity Table Manager→File→Open...]
    * Select tab-delimited elements file [( attachment:elems.xls )
    * [:Continuity/Documentation/Help/TableManager#FileMenu:Continuity Table Manager→File→Close and update form]
  * You should now have only one element in the list
  * Click '''OK''' to submit {{{Element Form}}}
=== Calculate and render mesh ===
 * [:Continuity/Documentation/Help/MeshRenderElements:Mesh→Render→Elements...]
  * Click '''lines''' radio button
  * Click '''Render''' to display mesh
  * The mesh should now look similar to the first screenshot
=== Refine mesh circumferentially into four elements ===
 * [:Continuity/Documentation/Help/MeshRefine:Mesh→Refine...]
  * 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 ===
 * [:Continuity/Documentation/Help/MeshEditNodes:Mesh→Edit→Nodes...]
  * 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}}}
 * [:Continuity/Documentation/Help/FileSend:File→Send]
  * If the Dimensions Form appears, simply click '''Apply Marked Recommendations''' and then '''OK'''
 * [:Continuity/Documentation/Help/MeshCalculateMesh:Mesh→Calculate Mesh...]
 * [:Continuity/Documentation/Help/MeshRenderElements:Mesh→Render→Elements...]
  * Click '''lines''' radio button
  * Click '''Render''' to display mesh surface
 * [:Continuity/Documentation/Help/ViewShowOpenMesh:View→Show Open Mesh...]
  * 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 ===
 * [:Continuity/Documentation/Help/MeshConvertNodesToCartesian:Mesh→Convert nodes to Cartesian...]
  * Leave the {{{update nodes}}} and {{{update coordinates}}} checkboxes checked
  * Click '''OK'''
 * [:Continuity/Documentation/Help/FileReset:File→Reset...]
  * Select the '''Save, reset, and reload''' radio button on the bottom
  * Click '''OK'''
 * [:Continuity/Documentation/Help/MeshRenderElements:Mesh→Render→Elements...]
  * Click '''lines''' radio button
  * Click '''Render''' to display mesh surface
 * [:Continuity/Documentation/Help/ViewShowOpenMesh: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 '''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: attachment:mesh7.cont6 (As this is the final model, rendering elements will produce the mesh like the last screenshot)