Dynamic Graphical representations and Models

[ewist]

Ok, I'm a little lost so if this subject is off topic for this forum then I appoligize.

I am working on a modeling project that I'm trying to implement some code for and I don't even know where to start. I'm not that good of a coder nor am I that great at math but this project, in part, is to help me improve on both fronts. So let's get down to my questions.

I'd like to model some 2d environments that have varing and dynamic degrees of magnatude. I thought a lot about that first sentence and I still don't know if it makes sense so let me give some examples.

Topographical Maps, Thermal Maps, Weather Radar. All of these represent in 2d a given gradiant of magnatude at anyone point. Meaning, a Topo map shows how High an area is, a Thermal map shows how hot an area is and so on. By using colors or boundry lines we get an understanding of the lvl of magnatude a specific point or region holds.

What I want to do, I want to be able to make an "occurance" happen at a given point I wan its impact to start at a max. level and then tapper off occordingly over a given range until it reaches 0. then I want to be able to make another "occurance" happen with in the bounds of the previous influance of the first occurance and I want this to add to, in order of magnatude to the maping of lvls in the areas around the two points. From there I could presume to do this to infidome and be able to then caculate the order of magnatude at anyone point in the maped area.

Is this making any sense? In laymens terms I just want to figure out how something like a thermal map shows what its showing and duplicate it. Then I want to code an environment to be able to create these maps and these "occurances". Finaly, I want to be able to pick any point in the x,y and find out the magnitude of influance there is. I also want to be able to control how big of an occurance there is and how far out its range is and its tapper off rate.

basic example:

something occures at 10,10 of the magnatude of 10. At that point you could read 10. one unit away you would read 9, 2 points 8, and so on, until 10 units away you reach 0. Then let's say something else happens at 12,12 of mgnatude 3. overlapping that with the magnatude that exists at that point (8) you would get 11 at that point. at 11,11 you would get 2+9= 11 and at 13,13 you would get 2+7=9

what I need is some direction on where to go to start setting up these models and how to describe them. Eventualy I have to figure out how to translate this into C# code and generate graphical models and build a system for creating and anylizing the points.

Let me know if anyone can help or if you have ANY idea what I'm talking about.

 

[AKG]

I think I would start by having a huge 2-d array, n x n. Then, each element of the array, say the element ij (i'th row, j'th column) would correspond to a position on the screen, a colour, and a value. The value is calculuated by processing each event. So, if we have the element ij with initial value of 0 and we have an event of ij with magnitude 10, then the value for ij becomes initial_value + 10 - distance_between_ij_and_event. Then, choose a colour based on the value, and display it to the screen. Does this help at all?

 

[ewist]

Yes it does.

I don't know if what your saying is practical for the over all application but I think its a really good starting point!

I guess, I'm also looking for a pointer in the direction of an online resource related to this topic as well. I've talked to 3 mathatitions and they can't even tell me what field of math I should start barking up to find more info.

Let me play around with your array idea and see what I come up with, it sounds like the right direction, at least for testing.

 

[AKG]

Yeah, I don't know if it sounds practical, because you'll have a huge array and for an n x n array with E events, you'll have En² calculuations, which will probably get pretty big. Then again, maybe projects like this are supposed to be big, we don't really do programs that big in first year university... I don't know if there is a branch of mathematics you need to be looking into. It seems like just basic, simple arithmetic calculations, just a lot of them. What did you have in mind? What part did you want to apply some mathematics to?

 

[ewist]

Well, my thinking is that there would be some kind of fomulation that could occur when loading an event into this "array" and then a formulation that would occur when reading a given point to determine magantude.

So in the end you could just build your area, giving it x,y range and then load your events in and you could map it all out in what ever level of detail you want. So if you want to see a low level of detail of the map it takes less work but if you want to see a color change or gradiant line for each change you could do so, but you would have to caculate each point. What your saying only give me one resolution (the size of the array). I'd much rather see a way to build an area and then caculate the magatude for not just a single x,y cord but maybe a 5x5 area or a 10x10 area depending on what level of detail is needed to represent your data.

Also, let's take into consideration a weather radar map. I can't see a radar system reading EVERY single point in a cloud formation to created those dipictions of weather paterns over head. There has to be some formulation inthere that exstrapolated sample readings to generate the overall outline of the cloud formation.

I think I just added another requirement on top of what I said above but you got me thinking now...opps.

 

[AKG]

Maybe a few examples of what you'd like to be able to do (state clearly the input and output), and a clear, concise, point form presentation of your requirements.

 

[Alex Bocast]

One step further...

Your problem is much like one I am working on. Occurrences are randomly distributed over some arbitrarily large grid. The effect of each occurrence swells vertically in a short time as the effect and the effect of each occurrence spreads across the grid. The effect could be modeled as an exponential distribution: the further from the origin of the occurrence, the less the effect. The effects of each occurrence then decay away over time. The overall problem is to determine how dense these occurrences must be both temporally and spatially before they become a permanent feature of the view.

I do not know if there is a name for such a problem. The advice already posted is good. You need a traversal that spirals outward from each occurrence point to cover all the neighboring points; if you use a square grid, you'll need to compute the distance to each occurrence point using h2=a2+b2.

Remember though that this approach will work only if the combined effect of n occurrences is strictly linear and additive. If not linear and additive, you will need to work with a system of simultaneous equations, one equation for each point in your grid. Now, that could become computationally intensive!

Please share your results so I can learn from your attempt. If you would like, I will do the same. -- Alex

 

[rayjohn01]

It may help if you divide the problem into it's two parts
a) the physics of whatever is going on ( for instance the temperature of a point may be influenced by than more than one heat source , but then the heat flow is material dependant and must be spatially mapped )
b) the presentation method or graphics , which is dependant on the program etc.

For simple cases I like to use Qbasic(4.0), to explore ideas -- maths is well represented and the graphics simple to set up , if you can solve the problem in miniature then it's just a matter of scaling with appropriate software.
Ray.

 

[H-bar None]

I've seen these problems modeled these before.

Computational Physics deals with this type of problem constantly. Computional Physics is a combination of physics, computer science. Try this link:

http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/

I can imagine some pure mathematicians having issues with this, as your problem falls within the dreaded realm of Applied Mathematics.

There are some Signal Processing algorithims for managing large data sets. I would go to The Society of Industrial Mathematics website:
http://www.siam.org/journals/problems/index.htm

I'm not too advanced in my field of study, so forgive my naivete. I might be able to add some specific help a little later.