Time for another self-serving, shameless plug for my free book.
After about 15 years and a two foot tall stack of draft printouts, want to let others know about it.
"Interpolation and Curves for Graphics" - A Study of Piecewise Polynomial Interpolation Fundamentals And Curve Reference
This is *both* a study of the fundamentals for a beginner and an advanced reference of all common piecewise interpolation types with sample curves to demonstrate the behaviors. It also has a few things that I think derive from new ways of looking at various aspects of the math.
When I wanted to learn about Piecewise Polynomial Interpolation for the laser light show system I built, I couldn't find a book suitable for me. After much reading and searching on the net a number of years ago, I had many notes, so I put them in order and it turned into the book I originally needed. Comments are always welcome via my site, but I probably won't be writing much in the way of additional revisions (time to ship it).
> Time for another self-serving, shameless plug for my free book.
First of all, kudos for taking the time to write this book. Really nice stuff.
Two things about the book:
- Is it possible to add a reference to the Weiestrass approximation theorem? It would be a nice way to demonstrate how important polynomial interpolation is.
- It doesn't appear that your book isn't prepared with LaTeX. Is this true, and is there a reason for that?
On Saturday, October 27, 2012 5:28:57 AM UTC-5, Rui Maciel wrote:
> Noskosteve wrote: > Time for another self-serving, shameless plug for my free book.
First of all, kudos for taking the time to write this book. Really nice stuff. Two things about the book: - Is it possible to add a reference to the Weiestrass approximation theorem? It would be a nice way to demonstrate how important polynomial interpolation is. - It doesn't appear that your book isn't prepared with LaTeX. Is this true, and is there a reason for that? Rui Maciel
It's a good thing I decided to do another plug. I get over here infrequently.
0 - Thank you. It was a labor of love. Many authors wind up writing the book the initially needed. I'd appreciate any specific comments you may have.
1 - I haven't a clue what the Weiestrass approximation theorem is. As I state in my explanations, I simply wanted to produce the book I needed to get to where I wanted to get, and I figured others would have the same need and a few have written to let me know they did. My method comes from a career in Engineering. Namely that it (the circle arc) looks very good it is therefore suitable. THe quest for a real circle is admirable, but frequently unnecessary.
2 - I was a Macintosh type in the 80's. (now I'm “ambidextrous”) I had Word and Excel. I also had a version of Microsoft's Quick Basic (1.0) that needed an early version of the operating system (6) that was never advanced past that. I used Excel to study, and produce, the books Function curves. I used Quick Basic to study and draw all the Interpolated "curves". I used Word(vers 4 & 5) to build the book.
I had to do some not obvious gymnastics to get it on the web since Windows Word was unable to reproduce the graphics created with Mac’s Quick Basic. The book came from a Mac, through floppies, to a Win NT laptop to be emailed to a modern Mac for final conversion to PDFs. Quite a journey.
> On Saturday, October 27, 2012 5:28:57 AM UTC-5, Rui Maciel wrote: > > Noskosteve wrote: > > Time for another self-serving, shameless plug ...
> First of all, kudos ...
> Is it possible to add a reference to the Weiestrass approximation theorem?
Hi again, Rui,
A quick Wiki on Weiestrass shows me that what I saw can be reduced to a theorem. Again, I was concerned with PPI (Piecewise Poli...) fundamentals.
My limited discussion of circle approximation techniques or analysis was only a secondary thing. It was *only* done that way (just touched on) because drawing the almighty circle always pops up on c.g.a and in the literature. It is one of those never-ending quests, like the "Can I draw XXX with A YYY curve engine? and the like". I did my best to cover a number of similar frequently asked questions in my book as well.
Perhaps, just perhaps, my Curve Type-Morphing techniques will be useful in the future in some yet unknown application (like Boolean concepts were carried into computers today)
Finally, there are a number of things I wanted to add (seen in RED in the Appendix) that current priorities, sadly, are preventing me from adding. I have a couple of additional curve types that I found interesting as well as that Quadratic circle approximation.
These would also take the same gymnastics to get them into the book and those old Macs are sitting in the basement not having been turned on since the last furniture rearrangement 4-5 years ago - and the NT laptop has an intermittent Network card - Arrrg! – and a really old browser that may not be able to get to Yahoo to email -- and I never figured out how to get the latest Mac to do P2P with the NT, nor the old Macs. Come to think of it, I actually had another step - Mac, floppy-net to the NT then ethernet to my PC to email to recent Mac then to PDF and upload to site!
I'd also have to re-learn how to program the curves into my Quick Basic Curve demo program to draw the curves. (;-)