In a few months they will start to build the largest tower in The Netherlands (with 262 meters not a stunning accomplishment on a global scale, but impressive for our little otherwise mostly flat country). This will be very near my home, so I think it will be a nice project to take a snapshot every week of its progress, so that once it's finished I can create a little documentary of the construction.

I'm trying to find out the proper position to take this weekly picture, to ensure that the complete tower will fit in the picture precisely when it's finished, so that I don't have to move back after a while and can remain in the right spot for the duration of the project, and I'm close enough to not waste much pixels.

My camera has a certain viewport, so plain old Pythagoras won't be sufficient; so I'm trying to figure out what the best position will be, and how I can determine this using nothing more than math, some experimentation and educated guesswork. I'm relatively lazy, so it has to be a simple practical method that doesn't take ages or enormous amounts of effort. Also, it has to be a verifiable method so I don't end up moving the position halfway through the project; they're only going to build this tower once.

The position of the tower will be:

View Larger Map

Ideas? I'll throw in a signed copy of my enterprise php book for the most creative or pragmatic approach, or an amazon gift certificate for those not into PHP.

Bonuspoints if you point out the spot on the map, taking into account buildings or other structures

More details (if relevant):

• The camera will be this Canon Ixus 95
• I am able to use a tripod
• Most roads near the construction site are at the same level as the start of the tower (to my knowledge, anyway)
• The A2 highway north of the tower has elevated soundproof walls, so anything on the other side of the A2 is not an option.
• Details on the tower are here.

Have fun!

Update: I might actually use my Canon 450D for this project. Based on this blogpost, the construction company has contacted me that they are interested in the project and would like to cooperate.

Ok, this post has no use whatsoever, but I need to get this out of my system. I was in an incredibly dull meeting the other day, and at one point, I had on my sheet of notes 3 randomly placed dots:

 
.
 
             .
   .
 

For some reason, I don't know why, I started to wonder if there would be one or more circles that have an outline that touches these 3 dots. Yes I am a nerd (just imagine how boring the meeting was).

To put this puzzle in other words: is there, for any given set of 3 points, a 4th point that has an equal distance to the first 3 points?

My preliminary conclusion is that for each three points, there is exactly 1 circle that has a matching outline, unless the 3 points are positioned exactly in one line. I lack the mathematical background however to prove/disprove this in theory. I discussed this with a fellow nerd and he also concluded that there should be exactly 1 circle for each set of 3 points (as long as they are not in a straight line).

Now I'm curious. Am I right in the 'exactly 1 circle' assumption? If so, what would be the optimal way of determining the center of the circle? In other words, how would you implement:

 
/**
 * Determine the center point of a circle whose outline strikes 3 given points.
 * @param Point $a
 * @param Point $b
 * @param Point $c
 * @return Point The center point of the circle outlining point $a, $b and $c
 */
function centerpoint($a, $b, $c)
{
  ....
  return new Point($x, $y);
}
 

On to something else. The rumours of the Zend Framework are spreading quickly. I haven't been contacted by Zend so it's not going to be Zend ATK. I'm wondering what it is though. Whether it's anything like a business framework, or more of an IDE kind of thing, or just a set of classes providing some API.

Finally an update on ATK: we're wrapping up RC1 of ATK 5.3. It should be out real soon now.