How to Acquire Sinewave Spheres via Excel

Three Parts:The TutorialExplanatory Charts, Diagrams, PhotosHelpful Guidance

Learn to make images like the one below as you acquire from the following steps the knowledge of sinewave spheres.


  • Become familiar with the basic image to be created:

Part 1
The Tutorial

  1. 1
    Open a new Excel workbook and create 3 worksheets (except Chart if you are using Chart Wizard): Data, Chart and Saves.
  2. 2
    Set Your Preferences: Open Preferences in the Excel menu and follow the directions below for each tab/icon.
    • In General, set R1C1 to Off and select Show the 10 Most Recent Documents .
    • In Edit, set all the first options to checked except Automatically Convert Date System . Set Display number of decimal places to blank (as integers are preferred). Preserve the display of dates and set 30 for 21st century cutoff.
    • In View, click on show Formula Bar and Status Bar and hover for comments of all Objects . Check Show gridlines and set all boxes below that to auto or checked.
    • In Chart, allow show chart names and set data markers on hover and leave the rest unchecked for now.
    • In Calculation, Make sure Automatically and calculate before save is checked. Set max change to .000,000,000,000,01 without commas as goal-seeking is done a lot. Check save external link values and use 1904 system
    • In Error checking, check all the options.
    • In Save, select save preview picture with new files and Save Autorecover after 5 minutes
    • In Ribbon, keep all of them checked except Hide group titles and Developer .
  3. 3
    It helps placing the cursor at cell A14 and doing Freeze Panes. Edit Go To cell range A1:E5765 and Format Cells Number Number Decimal Places 4, Font Size 9 or 10, Fill (from the color wheel) a nice fuchsia and make the Border Dark Blue bold Outline.
  4. 4
    Enter the Defined Variable Names and some initial values:
    • In A1, enter a;
    • In A2, enter b;
    • In A3, enter c_;
    • Select cell range A1:B3 and Insert Names Create in Left Column; select cell range B1:B3 and Format Fill yellow (for input);
    • In B1, enter 18; f(or the complete sphere, the value = 100)
    • In B2, enter .8; f(or the complete sphere, the value = .5)
    • In B3, enter .6; f(or the complete sphere, the value = .5)
    • In cell D1, enter Change;
    • In cell E1, Enter Stretch_y;
    • Select cell range D1:E2 and Insert Names Create in Top Row;
    • Select cell range D1:D2 and Format Cell Fill White or None.
    • Input "=Stretch_y" w/o quotes into cell D2;
    • Input 6 into cell E2 and Format Cells Fill yellow.
  5. 5
    Input Column Headers:
    • A5: t: 0 to 2π
    • B5: z
    • C4 Charting ... D4: Charting
    • C5: x: No z
    • D5: y: With z
    • E5: Adj_y
    • Edit Go To cell range B6:B5765 and Insert Name Define name z to range $B$6:$B$5765;
    • Edit Go To cell range E6:E5765 and Insert Name Define name Adj_y to range $E$6:$E$5765.
  6. 6
    Enter series or formulas in columns:
    • Edit Go To Cell range A6:A1445 and input 0 into A6 and "=2*PI()" into A1445 and do Edit Fill Series Trend OK. Copy this data section three more times until cell A5765 has 2pi in it.
    • z: Edit Go To cell range B6:B5765 and enter into B6 w/o quotes the formula, "=c_*COS(a*A6)" and Edit Fill Down.
    • x: No z: Edit Go To cell range C6:C5765 and enter into C6 w/o quotes the formula, "=(((b^2-c_^2*COS(a*A6)*COS(a*A6))^0.5*COS(A6)))" and Edit Fill Down.
    • y: With z: Edit Go To cell range D6:D5765 and enter into D6 w/o quotes the formula, "=(Stretch_y*(((b^2-c_^2*COS(a*A6)*COS(a*A6))^0.5*SIN(A6))+z)+Adj_y)" and Edit Fill Down.
    • Adj_y: Edit Go To Cell range E6:E1445 and input 2.9473;
    • Select cell E1446 and input w/o quotes the formula "=Change+E1445". Edit Go To cell range E1447:E2885 and input into E1447 "=E1446" and Edit Fill Down.
    • Select cell E2886 and input w/o quotes the formula "=Change+E2885". Edit Go To cell range E2887:E4325 and input into E2887 "=E2886" and Edit Fill Down.
    • Select cell E4326 and input w/o quotes the formula "=Change+E4325". Edit Go To cell range E4327:E5765 and input into E4327 "=E4326" and Edit Fill Down. Fix the bottom border line.

Part 2
Explanatory Charts, Diagrams, Photos

  • (dependent upon the tutorial data above)
  1. 1
    Create the Chart:
    • Select C4:D5 and make the font Italic. Select C6:D1445 and Format Fill Color Light Blue. This is the area of the bottommost single sphere of 4 spheres or cut spheres. Right now, with a,b and c_ set to 18, .8 and .6 respectively, we're doing cut sphere(s). Select cell range C6:D1445 and do Charts on the Ribbon (or Chart Wizard), All/Other, Scattered - Smoothed Line Scatter. Copy or Cut and Paste the chart which landed atop the data or to the side and paste in the Chart worksheet, where it should be pulled open to an approximate square at the lower left by hovering the cursor until it changes to the double-headed arrow and then grabbing the chart frame and pulling down and right. Select Chart Layout and get rid of Axes, Grid lines, and the Legend. Click in the Chart Area outside the Plot Area near the outer border and choose no line and no Fill. Do the same for the Plot Area. To do all the 4 spheres, select the cell range C6:D5765. In that case, the chart area will need to be a tall squeezed rectangle until the spheres appear round. You can Copy Picture atop the data to get an image like the one at the top of this article and use Grabber application if Copy Picture refuses to pick up the underlying data's image. Copy and Paste both data and a picture of your charts to the Saves worksheet.
    • Try setting a,b and c_ to 100, .5 and .5 respectively and make sure the line weight is set to 1.
  2. 2
    That's it, you're finished!

Part 3
Helpful Guidance

  1. 1
    Make use of helper articles when proceeding through this tutorial:


  • 01 Sinewave Sphere

  • 02 Sinwave Sphere

  • 03 2 Sinewave Spheres

  • 04 4 Sinewave Spheres

  • 06 4 Cut Sinewave Spheres

  • 08 4 thin sinewave spheres

  • 09 2 filled thin sinewave spheres

  • 11 Combo image


  • ERRORS: If there are errors or error values, either the sheet in incomplete and needs further input or Lookup Tables for critical variables or perhaps there's a mistake somewhere along the line. If the instructions have been completed and there are still errors, select the cell that has the error value that is furthest left and topmost first. Look for a typo in a formula or unmatched parentheses. Possibly, a Defined Name is wrong -- they need to be input into the formulas exactly as they were defined. Do Insert Name Define to check. If there is a #DIV/0! error, the example does not, so look for a variable that somehow did not get filled in with a value perhaps. At any rate, what to do is select the cell with the error, and after checking all those typical errors, do Tools Auditing Trace Precedents and/or Trace Error. If fixing all the topmost leftmost errors does not fix the rest of your errors on the worksheet, one may need to do it the hard way, from the bottom right upwards then leftwards; that is the slow but sure way to fix all errors.
  • Also, errors in the chart data will most likely plot as zeros. This may be acceptable or desirable even. However, if too many lines (or curves) are returning to 0, it may indicate a logical flaw in the data -- or too many tiny values and then perhaps rescaling the chart is needed by inspecting the horizontal and vertical axes and changing them to zero in on the problem. Hover over or click on a data marker on the series plot and then do a search in the proper column by value for that value, and identify its precedents.

Sources and Citations

  • The Garthwaite Curve shown was first created by Chris Garthwaite in May of 1994 and is based upon the Spherical Helix found on page 264 along with the Sine Wave on Sphere on page 266 sof "CRC Standard Curves and Surfaces" by David von Seggern, CRC, ANN ARBOR, 1993. ISBN 0-8493-0196-3
  • Google for more information.
  • The workbooks used for this article were " THE Garthwaite Curve"(with spaces),"Sinewave On Sphere p 266.xlsx". and "THE GW Curve Sinewave Sphere.xlsx".

Article Info

Categories: Microsoft Excel Imagery | Graphics