I have a set of points like this (that I have clustered using R):
180.06576696, 192.64378568
180.11529253999998, 192.62311824
180.12106092, 191.78020965999997
180.15299478, 192.56909828000002
180.2260287, 192.55455869999997
These points are dispersed around a center point or centroid.
The problem is that the points are very close together and are, thus, difficult to see.
So, how do I move the points apart so that I can distinguish each point more clearly?
Thanks,
s
Maybe I'm overlooking some intricacy here, but...multiply by 10?
EDIT
Assuming the data you listed above are Cartesian (x,y) coordinate pairs, you can visualize them as a scatter plot using Google Charts. I've rounded your data to 3 decimal places, because Google Charts doesn't appear to handle higher precision than that.
I don't know the coordinates for your central point. In the above chart, I'm assuming it is somewhere nearby and not at (0,0). If it is at (0,0), then I imagine it will be difficult to visualize all of the data at once without some kind of "zoom-in" feature, scaling the data, or a very large screen.
slotishtype, without going into code, I think you first need to add in the following tweaking parameters to be used by the visualization code.
Given an x by y display box, fill the entire box, with input parameters [0.0 to 1.0]...
overlap: the allowance for points to be placed on top of each other
completeness: how important is it to display all of your data points
centroid_display: how important is it to see the centroid in the same output
These produce the dependent parameter
scale: the ratio between display distances to numerical distances
You will need code to
calculate the distance(s) to the centroid like you said,
and also the distances between data points, affecting the output based on the chosen input parameters.
I take inspiration from the fundamentals in the GraphViz dot manual. Look at the "Drawing Orientation, Size and Spacing" on p12.
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 currently working towards a 3D model of this, but I thought I would start with 2D. Basically, I have a grid of longitude and latitude with NO2 concentrations across it. What I want to produce, at least for now, is a total amount of Nitrogen Dioxide between two points. Like so:
2DGrid
Basically, These two points are at different lats and lons and as I stated I want to find the amount of something between them. The tricky thing to me is that the model data I'm working with is gridded so I need to be able to account for the amount of something along a line at the lat and lons at which that line cuts through said grid.
Another approach, and maybe a better one for my purposes, could be visualized like this:3DGrid
Ultimately, I'd like to be able to create a program (within any language honestly) that could find the amount of "something" between two points in a 3D grid. If you would like specfics, the bottom altitude is the surface, the top grid is the top of the atmosphere. The bottom point is a measurement device looking at the sun during a certain time of day (and therefore having a certain zenith and azimuth angle). I want to find the NO2 between that measurement device and the "top of the atmosphere" which in my grid is just the top altitude level (of which there are 25).
I'm rather new to coding, stack exchange, and even the subject matter I'm working with so the sparse code I've made might end up creating more clutter than purely asking the question and seeing what methods/code you might suggest?
Hopefully my question is beneficial!
Best,
Taylor
To traverse all touched cells, you can use Amanatides-Woo algorithm. It is suitable both for 2D and for 3D case.
Implementation clues
To account for quantity used from every cell, you can apply some model. For example, calculate path length inside cell (as difference of enter and exit coordinates) and divide by normalizing factor to get cell weight (for example, byCellSize*Sqrt(3) for 3D case as diagonal length).
I'm writing a data analysis program and part of it requires finding the volume of a shape. The shape information comes in the form of a lost of points, giving the radius and the angular coordinates of the point.
If the data points were uniformly distributed in coordinate space I would be able to perform the integral, but unfortunately the data points are basically randomly distributed.
My inefficient approach would be to find the nearest neighbours to each point and stitch the shape together like that, finding the volume of the stitched together parts.
Does anyone have a better approach to take?
Thanks.
IF those are surface points, one good way to do it would be to discretize the surface as triangles and convert the volume integral to a surface integral using Green's Theorem. Then you can use simple Gauss quadrature over the triangles.
Ok, here it is, along duffymo's lines I think.
First, triangulate the surface, and make sure you have consistent orientation of the triangles. Meaning that orientation of neighbouring triangle is such that the common edge is traversed in opposite directions.
Second, for each triangle ABC compute this expression: H*cross2D(B-A,C-A), where cross2D computes cross product using coordinates X and Y only, ignoring the Z coordinates, and H is the Z-coordinate of any convenient point in the triangle (although the barycentre would improve precision).
Third, sum up all the above expressions. The result would be the signed volume inside the surface (plus or minus depending on the choice of orientation).
Sounds like you want the convex hull of a point cloud. Fortunately, there are efficient ways of getting you there. Check out scipy.spatial.ConvexHull.
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!) ;)
Mapping a point cloud onto a 3D "fabric" then flattening.
So I have a scientific dataset consisting of a point cloud in 3D, this point cloud comprises points on a surface that is curved. In order to perform quantitative analysis I however need to map these point clouds onto a surface I can then flatten. I thought about using mapping tools sort of like in the case of the 3d world being flattened onto a map, but not sure how to even begin as I have no experience in cartography and maybe I'm trying to solve an easy problem with the wrong tools.
Just to briefly describe the dataset: imagine entirely transparent curtains on the window with small dots on them, if I could use that dot pattern to fit the material the dots are on I could then "straighten" it and do meaningful analysis on the spread of the dots. I'm guessing the procedure would be to first manually fit the "sheet" onto the point cloud data by using contours or something along those lines then flattening the sheet thus putting the points into a 2d array. Ultimately I'll probably also reduce that into a 1D but I assume I need the intermediate 2D step as the length of the 2nd dimension is variable (i.e. one end of the sheet is shorter than the other but still corresponds to the same position in terms of contours) I'm using Matlab and Amira though I'm always happy to learn new tools!
Any advice or hints how to approach are much appreciated!
You can use a space filling curve to reduce the 3d complexity to a 1d complexity. I use a hilbert curve to index lat-lng pairs on a 2d map. You can do the same with a 3d space but it's easier to start with a simple curve for example a z morton order curve. Space filling curves are often used in mapping applications. A space filling curve also adds some proximity information and a new sort order to the 3d points.
You can try to build a surface that approximates your dataset, then unfold the surface with the points you want. Solid3dtech.com has the tool to unfold the surfaces with the curves or points.