Problem I have a binary image with traversable and blocked cells. On this map points of interest (POIs) are set. My goal is to create a graph from these POIs respecting obstacles (see images) which represents all possible and truly distinct paths. Two paths are truly distinct if they can not be joined into one path. E.g. if the outside of the building in picture 1 was accessible a path around the building could not be merged with one through the building.
Researched I have looked at maze solvers and various shortest path finding algorithms (e.g. A*, Theta*, Phi*) and while they'd be useful for this problem they only search for a path between two points and don't consider already established routes.
Best Guess I am considering using Phi* to search for all possible routes and merge afterwards using magic (ideas?), but this will not give me truly distinct alternatives.
Can someone help?
P.S.: I'm using C++ and am not really eager to do this by myself, so if there is a library which already does this... :)
I found (and decided to use) a parallel thinning algorithm (Zhan-Suen for now) to create an image skeleton. This effectively makes the assumption that the geometry shapes the common routes, which is fine I think.
By using the Rutovitz crossing number I can extract bifurcations and crossings from the resulting skeleton. Then I'll determine the shortest line of sight from my Points of Interest (using Bresenham's algorithm) to the extracted crossings to connect them to the graph.
I hope this will help someone along the road :)
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I am creating a line from point shapefile which is auto generated. First time when I create that line in ArcGIS, I got a line like this because the points are not in a order:
after that I ordered the points according to it's location and got a line like this:
But unable to create a line like this:
Please give me any solution to fix this in ArcGIS or R programming. If you need the shapefile I can provide you.
I think there is no bullet proof way to restore the line, as same dataset can obviously represent different lines, so you would need to use some heuristics to do this. What Rafael described is very good top-bottom heuristics if you can reliably detect start and end points.
Another heuristics could be a bottom-up process to stitch nearby segments into a line. Find nearby points for every point, sort and connect the two nearest points. Continue this process, making sure each point has at most two connections, and that there are no loops.
A simpler approach that might just work if the line follows in general some direction is your idea of sorting points. But instead of ordering by x or y coordinate, find a linear approximation of these points, project each point to this straight line, and sort using the coordinate of the projection.
One way to go about this would be to treat it as a graph problem.
Create a weighted fully connected graph where the nodes are the points and the edge weight distance between its endpoints. Heuristically identify the “starting” and “ending” points of the line (for example, pick the bottom-leftmost point as start and top-rightmost and end).
Then you can use a shortest path algorithm to generate the order in which you connect the points.
Our project is focused on optimizing routes within a warehouse in R.
We have multiple locations "from" and "to" all numbered. There are also some constraints, like you have to follow specific pathways only.
(blue - starting location, red - points to go, grey - walls (constraints, cant go through))
What is the optimal way to start off?
Without exactly understanding what you mean by "S-shape pathways", I think you could model your problem as a network flow problem, also known as min-cut/max-flow problem. This would be a linear model, you could use the lpSolveAPI package for that.
Okay, so I have one OBJ file which I read into PCLpointcloud2. Now I want to feed it into a K-dTree. Which is not taking PCLPointCloud2 as input. I want to query any general point if it lies on the surface of my OBJ file.
I am finding it hard to understand their documentation. So how can it be done?
Plus, kindly point me to a good reference easily interpretable. And what is "PointT" BTW? Is it custom build type defined by us? please elaborate.
Look at the code in the provided tool pcl_mesh_sampling (in the PCL code directory under tools/mesh_sampling.cpp). It is relatively simple. It loads a model from PLY or OBJ then for each triangle it samples random points from the triangle. The final point cloud then undergoes a voxel-grid sample to make the points relatively uniform. Alternatively, you can just run the pcl_mesh_sampling program on your obj file to get an output PCD which you can then visualise with pcl_viewer before loading the PCD file into your own code.
Once you have the final point cloud, you can build and use a KD-Tree as per http://pointclouds.org/documentation/tutorials/kdtree_search.php
PointT is the template argument. The point cloud library can handle a variety of point types, from simple PointXYZ (having just x,y,z) to more complicated points like PointXYZRGBNormal (having x,y,z,normal_x,normal_y,normal_z, curvature, r, g, and b channels). Each algorithm is templated on the point type that you want to use. It would probably be easier if you used PointXYZ with your OBJ file, so use pcl::PointXYZ for all your template arguments. For more on templates see http://www.tutorialspoint.com/cplusplus/cpp_templates.htm and http://pointclouds.org/documentation/tutorials/adding_custom_ptype.php.
Update (reply to latest comment)
Added here because this reply is too long for a comment.
I think I see what you are getting at. So when you sample points from the point cloud & build a KD-tree of the object surface, and for each point you keep track which faces are nearby that point (probably all the faces adjacent to the face from which the point was sampled should be sufficient? Just one face is definitely insufficient). Then when the query point is given, you find the nearest point in the KD-tree and check whether the query point is on the "outside" or inside of the full list of nearby faces associated with that point in the KD-tree. If it's on the "inside" of all of them perhaps it is an interior point. But I cannot guarantee that this is true. That is my thinking on that question at the moment. But I do wonder if you want a mesh-based approach really. By the way, if you break your mesh up into convex parts then you can have nice guarantees when processing each convex part.
I'm maintaining software which uses PCL. I'm myself not much experienced in PCL, I've only tried some examples and tried to understand the official PCL-Ducumentation (which is unfortunately mainly sparse, doxygen-generated text). My impression is, only a PCL contributors have real change to use the library efficiently.
One feature I have to fix in the software is aligning two clouds. The clouds are two objects, which should be stacked together with a layer in-between (The actual task is to calculate the volume of the layer ).
I hope the picture explains the task well. The objects are scanned both from the sides to be stacked (one from above and the other from below). On both clouds the user selects manually two points. Then, as I hope there should be a mean in PCL to align two clouds providing the two clouds and the coordinates of the points. The alignment is required only in X-Y Plane.
Unfortunately I can't find out which function should I use for this, partly because the PCL documentation is IHMO really humble, partly because of lack of experience.
My desperate idea was to stack the clouds using P1 as the origin of both and then rotate the second cloud manually using the calculated angle between P11,P21 and P12,P22. This works, but since the task appears to me very common, I'd expect PCL to provide a dedicated function for that.
Could you point me to a proper API-function, code-snippet, example, similar project or a good book helping to understand PCL API and usage?
Many thanks!
I think this problem does not need PCL. It is simple enough to form the correct linear equation and solve it.
If you want to use PCL without worrying about the maths too much (though, if the above is a mystery to you, then studying some computational geometry would be very useful), here is my suggestion.
Most PCL operations work on 3D point clouds. I understand from your question that you only have 2D point clouds OR you don't care about the 3rd dimension. In this case if I were you I would represent the points as a 3D point cloud and set the z dimension to zero.
You will only need two point clouds with 3 points as that is how many points you are feeding to the transformation estimation algorithm. The first 2 points in the clouds will be the points chosen by the user. The third one will be any point that you have chosen that you know is the same in both clouds. You need this third one otherwise the transform is still ambiguous if it is a general transform that is being computed. You can calculate however such a point as you know 2 points already and you know that all the points are on a common plane (as you have projected them by losing the z values). Just don't choose it co-linear with the other two points. For example, halfway between the two points and 2cm in the perpendicular direction (ensuring to go in the correct direction).
Then you can use the estimateRigidTransformation functions to find the transform.
http://docs.pointclouds.org/1.7.0/classpcl_1_1registration_1_1_transformation_estimation_s_v_d.html
This function is also good for over-determined problems (it is the workhorse of the ICP algorithm in PCL) but as long as you have enough points to determine the transform it should work.
I have a small library of a few shortest path search algorithms. They were developed for simple undirected graphs (the normal representation - vertices and edges). Now I'd like to somehow apply them on a bit different scenario - where the maps are represented as 2-dimensional shapes, connected by shared edges (edges of the polygons, that is). In this scenario, the search can start/end either at a map object or some point (x,y). What would be the best approach? Try to apply the algorithms onto shapes? or try to extract a 'normal' graph out of the shapes (I have preprocessing time available)? Any advice would be much appreciated, as I'm really not sure which way to go, and I don't have enough time (and skill) to explore many options...
Thanks a lot
What's the "path" you're looking for? A list of the shapes to traverse? (Otherwise you just draw a straight line between start+end points.)
It's easy to preprocess it into a format where the shapes are vertices and are connected by edges when the shapes share a polygon side. Then, just pass it off to your existing library to get the answer.