I briefly considered delaying this post until tomorrow, March 25. On that day, in the year 3019 of the 3rd age, The One Ring fell into Mount Doom and Sauron fell into ruin. Some people celebrate March 25 as “Tolkien Reading Day”.
I think I’ll do mathematics instead, tomorrow… but maybe I should start talking to a friend about watching all of “Lord of the Rings” again in one day… after all, it’s been a year since we last did it.
For a change, I have absolutely no external obligations today… how much mathematics can I get done today? It occurs to me that the major limitation will be cats crying and trying to sleep in my computer chair. The black cat will come here around 5 PM, and I find it hard to resist him. The white cat has been trying to sleep here for the past hour… every time I get up, he jumps into the chair. (There’s no sun this morning, so his usual sunny corner window isn’t.)
As for the past week…
I’ve made some progress on the sampled sign wave… I can compute the effect of shifting the sampling interval… the only problem is I need to reverse the vector which specifies the effect. This seems odd… I’ll keep fussing with it.
Last Monday’s post, as you can see, was a very simple truss. This Monday’s post will be only a little more complicated… but it will be another example of solving a truss.
My alter ego the undergraduate is having a blast with trusses. Oh, I should not have complained about his not doing electric circuits – he deserves credit for putting out all the group theory posts.
I have often said that one of the great benefits to me of this blog is that I get to finish things. Well, the finishing that went into the 1st truss post has left me able to polish off new problems very easily. And they’re fun!
I daresay that is what makes me a useful applied mathematician at work: I enjoy getting answers to specific problems.
Anyway, my undergraduate really really wants to do some more truss problems today.
Another alter ego, Mr. Belvedere – the nanny who cleans up after the kid – has decided that the book “Multiple View Geometry in Computer Vision” (by Hartley and Zisserman) is not as immediately useful as I had hoped. Although it has many so-called “examples”, most of them are not what I would consider to be examples.
Quite a few of them are “corollaries”… using the more general algebraic results in the book to work out somewhat more specific algebraic results. Collectively, the book has a lot of applied mathematics, and I’m still delighted in that. If all I wanted was equations, I’d be in heaven.
Other so-called examples are more like teasers – look what we can do! – typified by the following figure from the book.
Yes, that’s a wonderful picture. It confirms that the mathematics in this chapter can be used to do just what I expected. I like to know what I can do with the reading material.
The only problem is… the book shows absolutely nothing of the actual mathematics for this pair of images. In order to work it out, I’m going to have to put coordinates on the left–side image… get equations for lines running through the tops and bottoms of the windows… probably find the location of the “vanishing point”… and then figure out what transformation will get me the right–side image. The book does none of that… and doesn’t even provide the final transformation. Oh, and just how do we transform the pixels themselves?
In other words, this should have been called exercise 2.12 or even problem 2.12, not example 2.12.
Now, it’s not a bad thing that this is, in fact, an exercise instead of an example – but it exemplifies that the book has very few examples per se. And I have no doubt that the math in the book is adequate to do this problem… but the devil is in the details, and I expected an example to illustrate the details.
Guess what? I’ve ordered another book.
And with that, I’m off to math.