Chapter One: Surface Story (pdf 13MB)

This is my start of an exposition on surfaces using Mathematica code. Click on the title above for the .pdf 13MB file. This story covers naive implicit surfaces and rational parametric surfaces in real 3 space. By naive implicit surfaces I mean surfaces given by a single polynomial equation in 3 real variables with integer or Mathematica machine number coefficients. Most of the algorithms are numerical.

In addition to the .pdf text I have several other files. The global functions used are in the file GlobalFunctionsS.nb (nb. file) This file contains also most of the functions for Plane curves and Space Curves under suffixes 2D 3D and MD. New files may have suffixes S,NS or RS for general surface functions, naive surface functions or rational surface functions respectively. Here is the index to surface Global Functions (pdf) A warning is that several of the old functions have new code.

In addition for Mathematica users, are my appendices for Section 1.9 Appendix A (.nb file), Appendix B (.nb file) and Appendix C (.nb file). These are made to be executed, not so much to be read, and are given separately.

Note from author: Originally this was to be called the Surface Book. However that name is a trademark owned by Microsoft. Worse, any search engine will give hundreds of links to the Microsoft product if you search for Surface Book. So this is instead my Surface Story. If you want to get back to this page through a search engine I suggest you search for Barry Dayton Surface Story.

Table of Contents
Chapter 1

Preview of revised Section 7 on quadric surfaces, April 2022. In a future version of this book Chapter 1 section 7 will be revised and enlarged and moved to Chapter 2 section 3. Here is a preview of this new section (PDF) Some material that will appear in Sections 1 and 2 of Chapter 2 may be missing but probably not critical. A preliminary GlobalFunctionsSC2.nb contains any new functions used as well as all old functions.