I have two lines, I use "ST_LineCrossingDirection" to detect if the two lines cross each other.
If they do cross, how do I check the length of the overlap? Is there a function that returns a metric to indicate the size of their overlap?
For example, lines that do intersect but are perpendicular, length of overlap would be minimum. For lines that intersect, and run on the same route for some distance, the length of the overlap could quanity "overlap distance"
Any tips to get this?
Thanks
ST_Intersection will give you a collection of pieces of the lines that are mutual, if you want a bit more tolerance use ST_Buffer on one of the lines first. Then do a Sum() of the ST_Length of those pieces.
I had to use ST_length(ST_LineFromMultiPoint(ST_Intersection(geom1, geom2))) since intersection was giving me a multipoint geometry object.
Thanks for you help!
Related
I have created a line chart which has the date as X-axis and Y-axis as calculated median value and its grouped according to "FileName". Problem is that some of the "FileName" has same median values which makes line overlap thus not able to see all the lines. Attached image shows only 5 lines but there are total 10 lines. After running query I found out other 5 has 50 as the median which makes it overlap with one of the line.
I tried using transparency and secondary axis but wasn't able to achieve the desired result. Is there any other solution to try out ? Thanks!
This is more of a data presentation issue than something specific to SSRS. If you are stuck on using a line chart, then I've only used two options:
1) Increment lines to different widths. For example, in a chart with 3 lines, the width is set to 5,3,1 pts.
2) Change the values insignificantly to offset the lines. Obviously this depends on the data being visualized as shifting the line slight (multiply by 0.1) may be allowable or highly discouraged depending on your situation.
Trying to do either option with 10 lines (and up to 5+ stacking) is not going to be very good.
I think Viking is right and you might want to check out other visualization options. Grouped column charts perhaps or just split your chart into multiple charts on the page (i.e. four separate trend charts)
I am writing a simple GUI library and am using quadtrees to determine which, if any, objects are interacted with during a mouse event. I was looking through a number of quadtree libraries on github and they all contained a method for adding a rectangular object to a quadtree.
The method, in all cases, simply checked to see if the rectangle intersected with the given quadtree:
return quadtree.x2 >= rect.x1
and quadtree.x1 <= rect.x2
and quadtree.y2 >= rect.y1
and quadtree.y1 <= rect.y2
However, this gives an unwanted result in one of the simplest cases: Imagine a 100x100 square area. I place four 50x50 square objects into the area with coordinates (0,0), (0,50), (50,0), and (50,50). If these objects had been placed into a 100x100 quadtree with a maximum capacity of one object, I would (visually) expect that the first layer of the quadtree would split and that the four resulting trees would each exactly contain one of the squares.
If I use the above method to determine which tree the squares are placed into, though, I find that each object intersects with all four trees. This would cause each of the trees to rapidly split until the maximum depth is reached.
The only way I see to avoid this is to use two checks:
return (quadtree.x2 > rect.x1
and quadtree.x1 < rect.x2
and quadtree.y2 > rect.y1
and quadtree.y1 < rect.y2)
or (quadtree.x2 == rect.x1
and quadtree.x1 == rect.x2
and quadtree.y2 == rect.y1
and quadtree.y1 == rect.y2)
(in the simplest case. Larger objects would have to be viewed within a bounding box since, for example, an object with coordinates (0,0), w=100, h=100 would belong in the upper-left quadtree as well.)
I could also calculate the overlap between the rectangles and the quadtrees to see if it's non-zero.
Am I missing something? It seems like this should be an ideal situation for a quadtree, yet, in most implementations, it's a huge mess.
I wouldn't call this an ideal situation, because the four rectangles overlap by a fractional amount. For example, if we assume a (fictional) floating precision of 10^(-10), every 'point' is actually a small rectangle with 10^(-10) length, and thus the rectangles overlap by 10^(-10). This is why you get the deep tree.
But I also think the tree could be improved with a slightly modified overlap checking. With your code, the sub-nodes all overlap by a tiny amount. It would work better with excluding the minimum (or maximum values), for example:
return quadtree.x2 >= rect.x1
and quadtree.x1 < rect.x2
and quadtree.y2 >= rect.y1
and quadtree.y1 < rect.y2
So the lower left coordinate of a node is actually outside of that node. This would at least avoid points turning up in several nodes (such as the point (50,50)), and the lower left rectangle would be stored in only one node.
I want to make randomized numbers but if they are too close, I want to make it a reroll or make it a number further away from the the other number or try to make it a little more spread out.
I guess I am not sure what exactly I want :/
Thanks in advance
EDIT: So the reason i am making randomized numbers is for spawning positions for units on sides of the screen so i want units to not be too close to each other essentially to make it look better.
I want to make randomized numbers but if they are too close, I want to
make it a reroll or make it a number further away from the the other
number or try to make it a little more spread out.
A random number generator sometimes produces numbers that are near each other.
If you don't want them so close together, maybe what you need is fixed numbers each with a small random perturbation.
Let's say you choose numbers 10, 20, 30, 40, and 50. Then, you run a random number generator that gives you a number between -3 and +3. You add this random number to each one in turn. This produces numbers that aren't uniform, but they're not too close to one another.
If a re-roll would be sufficient, you could just save the previous value, and then on the next iteration, if the difference between the two numbers is too small, call Math.rand() again. Maybe your sample space is too small?
Get random position
If it's not good (too close to some other or what ever) go to step 1.
There you go! You got valid position. :)
...
Or...pre-calculate all valid positions, place them in some array and use rnd function to get array indexes - what array elements will use. That should be the faster solution (if you have huge number of units)...
A line segment can be defined by a pair of points. There are well-known algorithms for finding whether two line segments in 2D space intersect. But what if we make it a bit trickier by adding a width to the line?
Imagine you have a line segment defined by a pair of points and a width. What you end up with is a rectangle whose sides are not necessarily aligned with the coordinate axes. (So you can't use the standard "rectangle overlap" functions.) What would be the best way to determine if two such line segments overlap?
I'd recommend to use The Method of Separating Axes to find out whether the rotated rectangles (thick line segments) overlap. This method is fast and simple.
A line with a width can be regarded as two parallel lines, separated by the width that you're talking about. So two lines which each have a width corresponds to four lines. Just work out whether any of these 4 lines intersect and you're done, aren't you?
Update: A comment points out that this will miss overlapping parallel lines. I think that's all it will miss, so that case could be handled as a special case.
I'm trying to diagnose and fix a bug which boils down to X/Y yielding an unstable result when X and Y are small:
In this case, both cx and patharea increase smoothly. Their ratio is a smooth asymptote at high numbers, but erratic for "small" numbers. The obvious first thought is that we're reaching the limit of floating point accuracy, but the actual numbers themselves are nowhere near it. ActionScript "Number" types are IEE 754 double-precision floats, so should have 15 decimal digits of precision (if I read it right).
Some typical values of the denominator (patharea):
0.0000000002119123
0.0000000002137313
0.0000000002137313
0.0000000002155502
0.0000000002182787
0.0000000002200977
0.0000000002210072
And the numerator (cx):
0.0000000922932995
0.0000000930474444
0.0000000930582124
0.0000000938123574
0.0000000950458711
0.0000000958000159
0.0000000962901528
0.0000000970442977
0.0000000977984426
Each of these increases monotonically, but the ratio is chaotic as seen above.
At larger numbers it settles down to a smooth hyperbola.
So, my question: what's the correct way to deal with very small numbers when you need to divide one by another?
I thought of multiplying numerator and/or denominator by 1000 in advance, but couldn't quite work it out.
The actual code in question is the recalculate() function here. It computes the centroid of a polygon, but when the polygon is tiny, the centroid jumps erratically around the place, and can end up a long distance from the polygon. The data series above are the result of moving one node of the polygon in a consistent direction (by hand, which is why it's not perfectly smooth).
This is Adobe Flex 4.5.
I believe the problem most likely is caused by the following line in your code:
sc = (lx*latp-lon*ly)*paint.map.scalefactor;
If your polygon is very small, then lx and lon are almost the same, as are ly and latp. They are both very large compared to the result, so you are subtracting two numbers that are almost equal.
To get around this, we can make use of the fact that:
x1*y2-x2*y1 = (x2+(x1-x2))*y2 - x2*(y2+(y1-y2))
= x2*y2 + (x1-x2)*y2 - x2*y2 - x2*(y2-y1)
= (x1-x2)*y2 - x2*(y2-y1)
So, try this:
dlon = lx - lon
dlat = ly - latp
sc = (dlon*latp-lon*dlat)*paint.map.scalefactor;
The value is mathematically the same, but the terms are an order of magnitude smaller, so the error should be an order of magnitude smaller as well.
Jeffrey Sax has correctly identified the basic issue - loss of precision from combining terms that are (much) larger than the final result.
The suggested rewriting eliminates part of the problem - apparently sufficient for the actual case, given the happy response.
You may find, however, that if the polygon becomes again (much) smaller and/or farther away from the origin, inaccuracy will show up again. In the rewritten formula the terms are still quite a bit larger than their difference.
Furthermore, there's another 'combining-large&comparable-numbers-with-different-signs'-issue in the algorithm. The various 'sc' values in subsequent cycles of the iteration over the edges of the polygon effectively combine into a final number that is (much) smaller than the individual sc(i) are. (if you have a convex polygon you will find that there is one contiguous sequence of positive values, and one contiguous sequence of negative values, in non-convex polygons the negatives and positives may be intertwined).
What the algorithm is doing, effectively, is computing the area of the polygon by adding areas of triangles spanned by the edges and the origin, where some of the terms are negative (whenever an edge is traversed clockwise, viewing it from the origin) and some positive (anti-clockwise walk over the edge).
You get rid of ALL the loss-of-precision issues by defining the origin at one of the polygon's corners, say (lx,ly) and then adding the triangle-surfaces spanned by the edges and that corner (so: transforming lon to (lon-lx) and latp to (latp-ly) - with the additional bonus that you need to process two triangles less, because obviously the edges that link to the chosen origin-corner yield zero surfaces.
For the area-part that's all. For the centroid-part, you will of course have to "transform back" the result to the original frame, i.e. adding (lx,ly) at the end.