I can calculate the distance between two points using:
SELECT ST_Distance(
ST_GeomFromText('SRID=4326;POINT(54.5972850 -5.930119)')
, ST_GeomFromText('SRID=4326;POINT(54.516827 -5.958130)'),
false);
However, my goal is to create a rough circular zone (this can be square, hexagon, octagon .etc) around each point and then check if the zones overlap.
I am looking at ST_Overlaps as a possible solution but I am not sure how to convert these points into polygons to be compared. My ideal result would be something like:
SELECT ST_Overlaps(
ST_CreateCircularPolygon(geom1, 1000, 6)
ST_CreateCircularPolygon(geom2, 10000, 4)
);
Where:
ST_CreateCircularPolygon(geomerty, metreRadius, numberOfRadialPoints (e.g. 6 creates a hexagonal polygon))
Any guidance would be much appreciated!
You can use the quad_seg parameter of st_buffer to specify the number of segments per quarter of a circle. That is, the total number of segments in the output will be a factor of 4.
To produce a square:
select st_asText(st_buffer(st_geomFromText('Point(10 10)'), 1, 'quad_segs=1'));
st_astext
------------------------------------------------------
POLYGON((11 10,10 9,9 10,9.99999999999999 11,11 10))
(1 row)
Octagon:
select st_asText(st_buffer(st_geomFromText('Point(10 10)'), 1, 'quad_segs=2'));
st_astext
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
POLYGON((11 10,10.7071067811865 9.29289321881345,10 9,9.29289321881345 9.29289321881345,9 10,9.29289321881345 10.7071067811865,9.99999999999999 11,10.7071067811865 10.7071067811866,11 10))
(1 row)
Since you want to work in meters but have unprojected coordinates, you can cast your geometry to geography, apply a buffer in meters and cast back to geometry. Let's note that st_buffer in geography will internally cast to a geometry in UTM, do the buffer, then cast back to geography (a lot of casting, but it's handy!)
That being said, a square is not a circle and it sounds very very wrong to assume otherwise. The orientation of the square is not obvious: should a corner be at the north? or should a segment be facing norht? or should the square be rotated? by how much?
You will save yourself a lot of trouble by using a real circle. In this case, don't use st_buffer at all, nor st_distance but rather st_dwithin which can leverage spatial indexes
Related
I am developing a SLAM algorithm in C, and I have implemented the FAST corner finding method which gives me some strong keypoints in the image. The next step is to get the center of the keypoints with a sub-pixel accuracy, therefore I extract a 3x3 patch around each of them, and do a Least Squares fit of a two dimensional quadratic:
Where f(x,y) is the corner saliency measure of each pixel, similar to the FAST score proposed on the original paper, but modified to also provide a saliency measure in non corner pixels.
And the least squares:
With being the estimated parameters.
I can now calculate the location of the peak of the fitted quadratic, by taking the gradient equal to zero, achieving my original goal.
The issue arises on some corner cases, where the local peak is closer to the edge of the window, resulting in a fit with low residuals but a peak of the quadratic way outside the window.
An example:
The corner saliency and a contour of the fitted quadratic:
The saliency (blue) and fit (red) as 3D meshes:
Numeric values of this example are (row-major ordering):
[336, 522, 483, 423, 539, 153, 221, 412, 234]
And the resulting sub pixel center of (2.6, -17.1) being wrong.
How can I constrain the fit so the center is within the window?
I'm open to alternative methods for finding the sub pixel peak.
The obvious answer is to reject 3x3 (or 5x5, whatever you use) boxes whose discrete maximum is not at the center. In other words, to use a quadratic approximation only to refine the location of a maximum that must be located inside the box.
More generally, in such cases the first questions to ask is not "How do I constrain my model-fitting procedure to shoehorn a solution for this edge case?", but rather
"Does my model apply to this edge case?" and "Is this edge case even worth spending time on, or can I just ignore it?"
I tried my own code to fit a 2D quadratic function to the 3x3 values, using a stable least-squares solving algorithm, and also found a maximum outside of the domain. The 3x3 patch of data does not match a quadratic function, and therefore the fit is not useful.
Fitting a 2D quadratic to a 3x3 neighborhood requires a degree of smoothness in the data that you don't seem to have in your FAST output.
There are many other methods to find the sub-pixel location of the maximum. One that I like because it is more stable and less computationally intensive is the fitting of a "separable" quadratic function. In short, you fit a quadratic function to the three values around the local maximum in one dimension, and then another in the other dimension. Instead of solving 6 parameters with 9 values, this solves 3 parameters with 3 values, twice. The solution is guaranteed stable, as long as the center pixel is larger or equal to all pixels in the 4-connected neighborhood.
z1 = [f(-1,0), f(0,0), f(1,0)]^T
[1,-1,0]
X = [0,0,0]
[1,1,0]
solve: X b1 = z1
and
z2 = [f(0,-1), f(0,0), f(0,1)]^T
[1,-1,0]
X = [0,0,0]
[1,1,0]
solve: X b2 = z2
Now you get the x-coordinate of the centroid from b1 and the y-coordinate from b2.
What is the Difference between Geodist(sfield,x,y) and dist(2,x,y,a,b) in Apache Solr for Geo-Spacial Searches ??
dist(2,x,y,0,0) :- calculates the Euclidean distance between (0,0) and (x,y) for each document. Return the Distance between two Vectors (points) in an n-dimensional space.
I was earlier using geodist() distance function for Geo-Spatial searches on my website but its response time was large. so have done a POC(proof of concept) for different distance functions and found that dist(2,x,y,0,0) distance function is relatively taking half of the time. But I want to know the reason behind this and the algorithms which both functions are using to calculate the distance.
I have to make a difference matrix for the same to convey it further.
The main difference is that geodist() is intended to work with spatial field types.
Most spatial implementation are based on Lucene's Points API, which is a BKD Index. This field type is strictly limited to coordinates in lat/lon decimal degrees. Behind the scenes, latitude and longitude are indexed as separate numbers. Four main field types are available for spatial search :
LatLonPointSpatialField
LatLonType (now deprecated) and its non-geodetic twin PointType
SpatialRecursivePrefixTreeFieldType (RPT for short), including RptWithGeometrySpatialField, a derivative
BBoxField (for areas, 4 instances of another field type referred to by numberType)
In geodist (sfield, x, y), sfield is a spatial field type that represents two points (lat,lon), so the direct equivalent using dist() would be to implement dist (2, sfieldX, sfieldY, x, y) with sfieldX and sfieldY being respectively the (lat,lon) coordinates of sfield.
Using dist (power, a, b, ...) you can't query a spatial field type. In order to perform the same spatial search, you would have to specify every point's dimension separately. It would require 2 indexed fields (or values per field at least) for 2 dimensions, 3 for 3d, and so on. That makes a huge difference because you would have to index every coordinates of each point separately.
Besides, you can also use geodist() as is with the BBoxField field type that indexes a single rectangle per document field and supports searching via a bounding box. To do the same with dist() you would have to compute the center point of the box to input each one of its coordinates as a function argument, so it would be too much hassle to yield the same result if you want to use an area as parameter.
Lastly, LatLonPointSpatialField for example does distance calculations based on Haversine formula (Great Circle), BBoxField does it a little faster because the rectangular shape is faster to compute. It's true that dist() may be even faster but remember that requires more field to be indexed, a lot of preprocess at query time to be able to yield the same calculated distance, and, as mentioned by Mats, it wouldn't take the earth' curvature into account.
An euclidean distance doesn't account for the curvature of the earth. If you're only sorting by the distance, the behavior can be OK - but only if your hits are within a small geographical area (the value of a unit compared to meters greatly change when you're getting closer to the poles).
There's an extensive and good answer that explains the difference between a Euclidean distance and a proper geographical distance (usually calculated using haversine) available at the GIS Stack Exchange.
Although at small scales any smooth surface looks like a plane, the accuracy of the Pythagorean formula depends on the coordinates used. When those coordinates are latitude and longitude on a sphere (or ellipsoid), we can expect that
Distances along lines of longitude will be reasonably accurate.
Distances along the Equator will be reasonably accurate.
All other distances will be erroneous, in rough proportion to the differences in latitude and longitude.
I would like to buffer the warning polygon by two miles can anyone help me with
this so if ema personal are with in to miles of the warning the are listed, I've been trying to use ST Buffer (to expand the polygon coverage for the search) but cant seem to get it right? Is it in Meters (3218.69)? I'm using the latest opengeo suite.
SELECT DISTINCT ON (ema.name)
ST_X(ema.geom),ST_Y(ema.geom),ema."name", torpoly.expire
FROM ema INNER JOIN torpoly ON ST_Within(ema.geom, ST_BUFFER(torpoly.geom)
ORDER BY ema."name"
Your options are either:
Use an appropriate projected coordinate system for the region that uses linear units in metres or feet (UTM, State plane, etc.). All distance calculations on geometry types use a Cartesian coordinate system, which is quick and simple.
Use the geography type, which does distance calculations on objects with EPSG:4326 (lat/lon) with distance units in metres. If you don't want to change the data types, you can use a geom::geography cast, and maybe make an index on that cast.
And never do ST_Within(.., ST_Buffer()) for this type of analysis. It is slower and imperfect. Instead, use ST_DWithin, which finds all geometry/geography objects within a distance threshold of each other, which is just like a buffer. This function may use a spatial GiST index, if present.
I understand that you cannot check if a geography point touches for example a geography polygon (see here) using something like this, which is possible in the geometry world:
WHERE A.Geo.STTouches(#s0) = 1
Is there a way to achieve this in the geography world? I guess a solution would be to transform the geography polygon + geography point into their geometry equivalents?
PS:
This should also work with complex polygons - such as this one with holes:
POLYGON ((99.999999999999986 5.3926387744713564E-14, 101.00000000000001 5.3926387744713564E-14, 100.99999999999987 1.0000000000000155, 100.00000000000013 1.0000000000000155, 99.999999999999986 5.3926387744713564E-14), (100.20000000000003 0.19999999999992918, 100.19999999999989 0.79999999999990257, 100.80000000000011 0.79999999999990234, 100.79999999999998 0.19999999999992912, 100.20000000000003 0.19999999999992918))
I'm assuming that my statement of your wanting to track whether or not the given point intersects with the boundary of your polygon. The below should do the trick:
SELECT #point.STIntersects(#polygon.RingN(1));
In essence, you're getting the outer boundary with RingN(1) (I'm making an assumption that this is a simple polygon, so the first ring should be the outer boundary) and then checking whether that intersects with the point you care about.
Edit: If you want to check if a given point lies on the boundary of any ring in the given polygon, something like this should do the trick:
select n.n as [IntersectedRingNumber],
#polygon.RingN(n) as [IntersectedRing]
from dbo.Numbers as n
where n <= #polygon.NumRings()
and #point.STIntersects(#polygon.RingN(n)) = 1;
I search for the fastest or simplest method to compute the outer angle at any point of a convex polygon. That means, always the bigger angle, whereas the two angles in question add up to 360 degrees.
Here is an illustration:
Now I know that I may compute the angles between the two vectors A-B and C-B which involves the dot product, normalization and cosine. Then I would still have to determine which of the two resulting angles (second one is 180 degrees minus first one) I want to take two times added to the other one.
However, I thought there might be a much simpler, less tricky solution, probably using the mighty atan2() function. I got stuck and ask you about this :-)
UPDATE:
I was asked what I need the angle for. I need to calculate the area of this specific circle around B, but only of the polygon that is described by A, B, C, ...
So to calculate the area, I need the angle to use the formula 0.5*angle*r*r.
Use the inner-product (dot product) of the vectors describing the lines to get the inner angle and subtract from 360 degrees?
Works best if you already have the lines in point-vector form, but you can get vectors from point-to-point form pretty easily (i.e. by subtraction).
Taking . to be the dot product we have
v . w = |v| * |w| * cos(theta)
where v and w are vectors and theta is the angle between the lines. And the dot product can be computed from the components of the vectors by
v . w = SUM(v_i * w_i : i=0..3) // 3 for three dimensions. Use more or fewer as needed
here the subscripts indicate components.
Having actually read the question:
The angle returned from inverting the dot-product will always be less than 180 degrees, so it is always the inner angle.
Use this formula:
beta = 360° - arccos(<BA,BC>/|BA||BC|)
Where <,> is the scalar product and BA (BC) are the vectors from B to A (B to C).
I need to calculate the area of the circle outside of the polygon that is described by A, B, C, ...
It sounds like you're taking the wrong approach, then. You need to calculate the area of the circumcircle, then subtract the area of the polygon.
If you need the angle there is no way around normalizing the vectors and do a dot or cross-product. You often have a choice if you want to calculate the angle via asin, acos or atan but in the end that does not make a difference to execution speed.
However, It would be nice if you could tell us what you're trying to archive. If we have a better picture of what you're doing we might be able to give you some hints how to solve the problem without calculating the angle at the first place.
Lots of geometric algorithms can be rewritten to work with cross and dot-products only. Euler-angles are rarely needed.