I have a city square with people, cars, trees and buildings in pcl format. I need to automatically determine the ground plane and project this objects on that ground plane to get a 2D map with occupied places.
Any idea?
I think the best thing to do here would be to familiarise yourself with the following two PCL tutorials:
http://pointclouds.org/documentation/tutorials/planar_segmentation.php
http://pointclouds.org/documentation/tutorials/project_inliers.php
The first tutorial makes use of the RANSAC algorithm to find a dominant plane in a scene. I use it to find tables and floors in robotics scenarios. You would use it to find your dominant ground plane.
The second tutorial shows how to project points directly onto a plane. This is what you would use to make your 3D point cloud into a 2D one. Note that, despite the "inlier" keyword, you can pass your whole point cloud to be projected onto the plane.
Actually, if you are after "occupied" places, you might want to project all of the points that aren't in the ground plane (i.e. the outliers), and that are above it (you can use a PCL filter, such as PlaneClipper3D, for example, or just the complement of the outliers from the plane-segmentation operation.
If the plane that you end up with (containing all your projected points) is not in the coordinate frame you want, you may wish to rotate the whole lot, for example, to align with the coordinate axes so that all z-coordinates are zero. See pcl::transformPointCloud for this (the transform will be obtainable from the plane coefficients returned from the plane segmentation).
I hope this is helpful and not at too basic a level, though the question was rather general so I suppose it should be okay.
Related
I'm neither a geometry student or a native speaker, so apologies if my question isn't clear enough.
As part of my master's thesis, I have to plot bounded regions of the night sky onto a 2D plane. My current solution consists of a rectangular mapping where (ra, dec) values are plotted to (x,y) coordinates. While this approach works well enough for small regions in relatively low ascension values, the resulting plots get progressively distorted for higher ||dec|| values, as expected.
At some point I'll have to change this to a more versatile approach. Thing is, I'm not exactly clear on what to search for. I guess I have to be able to map angular coordinates to a square (or hexagon) subgrid, but most search results I get are concerned with full-surface mapping.
I know I won't be able to achieve a perfect, distortion-free plotting, but I don't require perfect solutions; only a more general projection that will work well near the poles. Something like this, where I put my Photoshop skills to work and try to simulate a 20ยบ region under my current approach and the one I'm looking for:
What I want:
What I have:
TL;DR: how do I convert between coordinates on a sphere (ra/dec) to cartesian coordinates on a locally-defined grid?
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 map of a mountainous landscape, http://skimap.org/data/989/60/1218033025.jpg. It contains a number of known points, the lat-longs of which can be easily found out using Google maps. I wish to be able to pin any latitude longitude coordinate on the map, of course within the bounds of the landscape.
For this, I tried an approach that seems to be largely failing. I assumed the map to be equivalent to an aerial photograph of the Swiss landscape, without any info about the altitude or other coordinates of the camera. So, I assumed the plane perpendicular to the camera lens normal to be Ax+By+Cz-d=0.
I attempt to find the plane constants, using the known points. I fix my origin at a point, with z=0 at the sea level. I take two known points in the landscape, and using the equation for a line in 3D, I find the length of the projection of this line segment joining the two known points, on the plane. I multiply it by another constant K to account for the resizing of this length on a static 2d representation of this 3D image. The length between the two points on a 2d static representation of this image on this screen can be easily found in pixels, and the actual length of the line joining the two points, can be easily found, since I can calculate the distance between the two points with their lat-longs, and their heights above sea level.
So, I end up with an equation directly relating the distance between the two points on the screen 2d representation, lets call it Ls, and the actual length in the landscape, L. I have many other known points, so plugging them into the equation should give me values of the 4 constants. For this, I needed 8 known points (known parameters being their name, lat-long, and heights above sea level), one being my orogin, and the second being a fixed reference point. The rest 6 points generate a system of 6 linear equations in A^2, B^2, C^2, AB, BC and CA. Solving the system using a online tool, I get the result that the system has a unique solution with all 6 constants being 0.
So, it seems that the assumption that the map is equivalent to an aerial photograph taken from an aircraft, is faulty. Can someone please give me some pointers or any other ideas to get this to work? Do open street maps have a Mercator projection?
I would say that this impossible to do in an automatic way. The skimap should be considered as an image rather than a map, a map is an projection of the real world into one plane, since this doesn't fit skimaps very well they are drawn instead.
The best way is probably to manually define a lot of points in the skimap with known or estimated coordinates and use them to estimate the points betwween. To get an acceptable result you probably have to assign coordinates to each pixel in the skimap.
You could do something like the following: http://magazin.unic.com/en/2012/02/16/making-of-interactive-mobile-piste-map-by-laax/
I am solving the exact same issue. It is pretty hard and lots of maths. Taking me a few weeks to solve it. Interpolation is the key as well with lots of manual mapping. I would say that for a ski mountain it will take at least 1000/1500 points to be able to get the very basic. So, not a trivial task unless you can automate the collection of these points (what I am doing!) ;)
Am following this tutorial for my 2d game collision handling , this tutorial explains about the collision used in one of my favorite game "N". How they used separate axis theorem more efficiently for collision between AABB vs AABB and AABB vs Circle. http://www.metanetsoftware.com/technique/tutorialA.html. I understand the implementation of AABB vs AABB collision handling but I couldn't understand AABB vs Circle collision detection especially voronoi regions.Totally confused how/where to start.
AABB vs AABB collision detection
Find the axis along all the edge by finding the normal of each edge.
Projection all the vertices to the
resultant Axis , final result should
be a scalar value.
The resultant scalar value in turn
is used to find whether collision is
present or not.
Can someone please explain how to handle collision AABB vc Circle - vise versa?
Since collisions with a circle always come down to a comparison against the radius (in your case, via projection), having the closest line segment (edge of the polygon) and the normal vector are the only building blocks you need. The normal vector is easily computed from the points of the line segment (something like unit(y2-y1, x1-x2) ... the negative reciprocal of the slope). Figuring out which edge is closest is the building block that remains. Voronoi regions give us the last building block.
You understand collisions between axis-aligned bounding boxes. I assume you also understand collisions between two circles. I'm assuming you don't understand voronoi regions. So, where to start? Voronoi diagrams. I highly suggest that you find a diagrammed explanation. This link is quite good. However, depending on how lost you are, perhaps a little additional background (seriously, though, no explanation can beat the visual):
A voronoi diagram is one of the ubiquitous data structures of computational geometry. Any computational geometry book will discuss the Voronoi diagram. It answers a simple question: where is the closest post office? Given a set of points in a plane (post offices), a voronoi diagram separates the plane into different regions, each containing one of the points. If you are in a particular region, you know which point (post office) is closest to you. If you were a circle, this would be nice for collision detection for a simple reason: the closest point is the most important one to test for collisions.
Note that if you want to mathematically derive a voronoi diagram, you simply consider all point pairs and calculate all bisecting lines. Then you intersect all of the bisecting lines and throw away the segments that are unimportant because some other point is closer to the point of interest (which happens at every intersection). This leads to a terribly inefficient algorithm, though. The efficient implementation involves another ubiquitous thing in computational geometry: the line-sweep algorithm. Its details can be found elsewhere; the important bit is that it provides a method of considering only the important points at any stage of the algorithm.
The voronoi regions in your tutorial are a little more complex. Instead of just points, we have line segments. Fortunately, the line-sweep algorithm handles this nicely. You mostly have to worry about the start or end of the line segments. Conceptually, not much changes once you have the basic algorithm down. Again, this is exceptionally helpful for collision detection with a circle: given the voronoi region, you know which line segment to test collisions against.
Does that even help? Feedback appreciated. I'll be happy to clarify anything. Explaining voronoi diagrams without visuals is probably a bad idea.
I need to convert arbitrary triangulated 3D mesh to cloud of particles that are uniformly spaced.
First thought was to try find a way to fill one 3D triangle. And then fill each triangle of mesh, removing duplicated particles on edges, but that's just hard and too much work. I was hoping for some more-math way.
Can anyone point me to an algorithm which can help me do my task correctly... well, at least approximatively?
Thanks
There are two main options:
Voxelization of mesh. Easy to implement the conversion of mesh to voxels, but it's inaccurate since uniform spacing cannot be achieved: distance between cubes can be x, x*sqrt(2) or x*sqrt(3) depending if neighbor cubes are in same plane and adjacent.
Poisson disk sampling on surface. Hard to implement and lack of research material and code, but mathematically very correct. Some links:
http://research.microsoft.com/apps/pubs/default.aspx?id=135760
http://web.mysites.ntu.edu.sg/cwfu/public/Shared%20Documents/dualtiling/index.html
You could convert the TIN to raster using a GIS package or software such as R, then retrieve one point at the center of each pixel representing the value. (Example in ArcGIS)
EDIT: If the irregular 3D mesh has multiple heights per {x, y} a similar approach would be to sample the mesh using a voxel "grid" and keep one value per voxel. GRASS GIS has the functionality to take the vertices of the TIN (3d mesh) and convert them to voxels, then back to a regular 3d cloud.