I am solving the steady state heat equation with linear finite element and siplex triangular element. The domain is divided into two subdomains and they have different conductivity, let say conductivity is k=0.2 for the first subdomain and 0.1 for the second one. my problem is that I don't know how to deal with interface,what kind of boundary condition should I impose there? I appreciate your help in advance.
Bests,
Related
I have been exploring the GPS data mining literature esp. for problems like anomalous trajectory detection, time travel prediction, etc and one very common method I see is dividing the data or map into grids. Can any one please explain the logic of this? Are the coordinates euclidean in this case? Is grid decomposition really necessary?
I would be grateful if someone can also give/ quote some links or materials I should explore. I am new to this field, so please pardon me if the question is very obvious.
Thanks & Regards,
Lesnar
No they are not euclidean. But they don't have to be. The grids are not rectangles anymore, but can be treated as such for some operations.
If you create a lat/long grid, then each cell by means of meters is not rectangular. However it defines a zone where you add a counter, which has a clear inside/outside definition. And you can use cartesian operations (Rectangle.inside())
So the lat / lon span is constant for each cell, but not the longitudinal meters span, which shrinks by cos(latitude).
If one needs a grid with equal grid cells sizes by means of meters, then one
has to transform the geo coordinates before.
I'm asking if there are any ideas of how to cluster different body segments using the depth map from the Kinect device? There are two problems, the first one is how to identify different body parts from each other, for example: lower arm from upper arm. The second one is how to identify a body part if there is an occluded part?
I hope if anyone could guide me solve this.
Many Thanks for your kind assistance
You can use skeleton recognition middlewares (e.g. Nite) to get the coordinates of the joints of the body (such as shoulder, elbow, fingertip). After reading the Z (depth) value of the joints, you can consider only the points which has a Z value close to the body joints' Z values.
For example if the middleware tells you that the Z value of the hand is 2000mm, you can safely assume that all the pixels/points that are part of fingers and palm will have a Z value around 1900-2100mm, and the wall or desk behind or in front of the user will have a much different Z value. So you can just disregard any point outside 1900-2100mm.
You should also disregard any points that are far from the joints. For example there might be a book that is exactly 2000mm far from the camera, but located far from the user.
Sort of a programming question, sort of a general logic question. Imagine a circular base with a pattern of circles:
And another circle, mounted above and able to rotate, with holes that expose the colored circles below:
There must be an optimal pattern of either the colored circles or the openings (or both) that will allow for all N possible combinations of colors... but I have no idea how to attack the problem! At this point, combinations of 2 seem probably the easiest and would be fine as a starting point (red/blue, red/green, red/white, etc).
I would imagine there will need to be gaps in the colors, unlike the example above. Any suggestions welcome!
Edit: clarified the question (hopefully!) thanks to feedback from Robert Harvey
For two holes, you could look for a perfect matching in a bipartite graph, each permutation described by two nodes, one in each partition. Nodes would be connected if they share one element, i.e. the (blue,red) node from the first partition connected to the (red,green) node of the second. The circles arranged in the same distance would allow for both of these patterns. A perfect matching in that graph would correspond to chains or cycles of permutations where two of them always share a single color. A bit like dominoes. If you had a set of cycles of the same length, you could interleave them to form the pattern on the lower disk. I'm not sure how easy it will be to obtain these same length cycles, though, and I also don't know how to generalize this to more than two elements in each permutation.
I have some way points with longitudes and latitudes which builds a trajectory and I want to calculate a parallel trajectory at a specific distance!
I would appreciate any help!
Best regards,
Tara
You can use the Dijkstra's algorithm.
More explanation here:
http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
If you want that both the trajectory and the parallel trajectory will be composed of geodesics - you can't.
The path between two points is usually defined by a geodesic. Geodesic is a generalization of the notion of a straight line, or a straight line segment to curved spaces. Geodesic is the shortest route between two points on the Earth's surface, namely, a segment of a great circle.
Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Therefore, there are no parallel geodesics.
I'm looking for references to algorithms for plotting on a mechanical pen plotter.
Specifically, I have a list of straight vectors, each representing a line to be plotted. First I want to remove duplicate vectors, so each line is only plotted once. That's easy enough.
Second, there are many vectors that intersect, sometimes at endpoints, but not always. They can be plotted in any order, but I want to find an order that reduces the number of times the pen must be lifted, preferably to a minimum though I understand that may take a long time to compute, if it's computable at all. Vectors that intersect can be broken into smaller vectors if that helps. But generally, if the pen is moving in a straight line, it's best to keep it moving that way as long as possible. So, two parallel vectors joined end to end could be combined into a single vector, etc.
This sounds like some variety of graph theory problem, but I don't know much about that. Can anyone point me to references or algorithms I need to study? Or maybe example code?
Thanks,
Neil
The problem is an example of the Chinese postman problem which is an NP-complete problem. The most wellknown NP-complete problem is the Travelling Salesman. Common for all NP-complete problems are that they can all be translated into eachother. There are no known algorithms for solving any of them in a time that is polynomial dependent of the number of nodes in the input, they are non-polynomial (NP).
For your case I would suggest some simple heuristics. Don't overdo it, just pick anything quite simple like going in a straight line as long as possible and then lift the pen to the closest available starting point and go on from there.