In the article, the formulas for orthographic parallel projection of 3D bodies on computer screen are derived using secondary school vector algebra. The spreadsheet implementation is demonstrated in six applications that project bodies with increasing intricacy – a convex body (cube) with non-solved visibility, convex bodies (cube, chapel) with solved visibility, a coloured convex body (chapel) with solved visibility, and a coloured non-convex body (church) with solved visibility. The projections are revolvable in horizontal and vertical plane, and they are changeable in size. The examples show an unusual way of using spreadsheets as a 3D computer graphics tool. The applications can serve as a simple introduction to the general principles of computer graphics, to the graphics with spreadsheets, and as a tool for exercising stereoscopic vision. The presented approach is usable at visualising 3D scenes within some topics of secondary school curricula as solid geometry (angles and distances of lines and planes within simple bodies) or analytic geometry in space (angles and distances of lines and planes in E3), and even at university level within calculus at visualising graphs of z = f(x,y) functions. Examples are pictured.

Distribution License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

3DwithSpreadsheets2003.xls (524 kB)
Excel 2003 version

3DwithSpreadsheets2007.xlsm (216 kB)
Excel 2007 version