I ran into a problem that I don't know how to address, if anyone has any ideas I would be very grateful.
So I have a NxM matrix and number of points (minimum 4) that represent a shape resting on the matrix as show in the figure (Each point is represented by a number, ignore the black/white points):
I know how to match each point to the x,y coordinate inside the matrix.
But let's say I want to calculate the average of the values inside the polygon, how can I do it?
Many thanks to all the helpers
I tried to parametrize the polygon to a new square, but without success...
You need to use a polygon filling algorithm (also called scan conversion). In a nutshell, you intersect the polygon with all horizontals through the matrix rows and find intervals covered by the inside of the polygon. Accumulate the matrix values spanned by these intervals.
Related
I am trying to solve the following problem in Python. The problem comes from an image processing problem when i use the Finite Element Method.
In my problem, I have a set of triangles and a ray. Each triangle consists of three 3-D points, and the ray is in the form of a 3-D point and a 3-D vector. How can I determine the first triangle that is passed through by the ray? Now I do not even have an algorithm for this. Any inputs will be appreciated.
The first thing I would do, is translate the whole data set, subtracting the 3D ray origin. Then rotate the data set so that the ray's 3D vector aligns with the X-axis. See How to find the orthonormal transformation that will rotate a vector to the x axis?.
Now the problem has been converted to filter for triangles that cross the X-axis with a non-negative X-coordinate, and among those find the one whose crossing point has the minimal X-coordinate. So
For each triangle check where its plane crosses the X-axis. See Determine point of interesction of plane with axis given points of plane
Then throw away the triangles where that crossing point (on the X-axis) is not within the bounds of the triangle (check for each of the three edges that this point is at the "inner" side of it). See Check whether a point is within a 3D Triangle
Throw away the triangles whose crossing point has a negative X-coordinate.
Among the remaining triangles (that really cross the X-axis on the positive side) find the one with the minimum crossing point in terms of X-coordinate.
I am fairly new to openCV and am not sure how to proceed.
I have this thresholded image:
And using this image, I need to calculate the distance between two points. The points are also unknown. Illustrated here:
I need to calculate 'd' value. It is the distance from the midpoint of the middle line to where the top line would have been. I am not sure how to proceed with identifying the points and getting the distance, any help would be appreciated!
While I'm not sure about the selecting points part of your problem, calculating the distance between two points is trivial. You can imagine your two points as the beginning and end of the hypotenuse of a right triangle, and use Pythagoreans Theorem to find the length of that hypotenuse.
The math module has a distance method which takes two points, or you can just write the function yourself very simply.
I'm looking for some solutions that, given a set S of circles with 2D-center points and radii, returns a minimal sub-set M in S that covers entirely a specific circle with 2d-center point and radius. This last circle is not in S.
I've chosen circles, but it doesn't matter if we change them to squares, hexagons, etc.
You have two distinct problems: you need to turn the geometric problem into a combinatoric problem, and then you need to solve the combinatoric problem. For the latter, you are looking at a minimum set cover problem, and there should be plenty of literature on that. Personally I like Knuth's Dancing Links approach to enumerate all solutions of a set cover, but I guess for a single minimal solution you can do better. A CPLEX formulation (to match your tag) would use a binary variable for each row, and a ≥1 constraint for each column.
So now about turning geometry into combinatorics. All the lines of all your circles divide the plane into a bunch of areas. The areas are delimited by lines. Of particular relevance are the points where two or more circles meet. The exact shape of the line between these points is less relevant, and you might imagine pulling those arcs straight to come up with a more classical planar graph representation. So compute all the pair-wise intersections between all your circles. Order all intersections of a single circle by angle and connect them with graph edges in that order. Do so for all circles. Then you can do a kind of bucket fill to determine for each circle which graph faces are within and which are outside.
Now you have your matrix for the set cover: every graph face which is inside the big circle is a column you need to cover. Every circle is a row and covers some of these faces, and you know which.
Dear Stackoverflow community,
I have contours of irregular polygons as unordered datapoints (like on the figure here: https://s16.postimg.org/pum4m0pn9/figure_4.png), and I am trying to order them (ie. to create a polygon).
I cannot use the convex hull envelope because of the non convex shape of the polygon. I cannot ase a minimum distance criterion because some points of other parts of the contour lie closer (example: point A has to be joined with B, but is closer to C). I cannot use a clockwise ordering because of the irregular shape of the contour.
Do anyone knos a way to implement (preferentially in Python) an algorithm that would reorder the datapoints from a starting point?
look here finding holes in 2D point set for some ideas on how to solve this
I would create point density map (similar to above linked answer)
create list of all lines
so add to it all possible combination of lines (between close points)
not intersecting empty area in map
remove all intersecting lines
apply closed loop / connectivity analysis on the lines
then handle the rest of unused points
by splitting nearest line by them ...
depending on you map grid size and point density you may need to blend/smooth the map to cover gaps
if grid size is too big then you can miss details like on the image between points A,C
if it is too small then significant gaps may occur near low density areas
But as said this has more then one solution so you need to tweak this a bit to make the wanted output perhaps some User input for shaking the solution a bit until wanted solution found...
[notes]
you can handle this as more covex polygons ...
add line only if winding rule met
stop when no more lines found
start again with unused points
and in the end try to connect found non closed polygons ...
So I'm working on a piece of code to take positional data for a RC Plane Crop Duster and compute the total surface area transversed (without double counting any area). I cannot figure out how to calculate the area for a given period of operation.
Given the following Table Calculate the area the points cover.
x,y
1,2
1,5
4,3
6,6
3,4
3,1
Any Ideas? I've browsed Greens Theorem and I'm left without a practical concept in which to code.
Thanks for any advise
Build the convex hull from the given points
Algorithms are described here
See a very nice python demo + src
Calculate its area
Python code is here
Someone mathier than me may have to verify the information here. But it looks legit: http://www.wikihow.com/Calculate-the-Area-of-a-Polygon and fairly easy to apply in code.
I'm not entirely sure that you're looking for "Surface area" as much as you're looking for Distance. It seems like you want to calculate the distance between one point and the next for that list. If that's the case, simply use the Distance Formula.
If the plane drops a constant width of dust while flying between those points, then the area is simply the distance between those points times the width of the spray.
If your points are guaranteed to be on an integer grid - as they are in your example - (and you really are looking for enclosed area) would Pick's Theorem help?
You will have to divide the complex polygon approximately into standard polygons (triangles, rectangles etc) and then find area of all of them. This is just like regular integration (only difference is that you are yet to find a formula to approximate your data).
The above points are when you assume that you are forming a closed polygon with your data.
Use to QHull to triangulate the region, then sum the areas of the resulting triangles.
Python now conveniently has a library that implements the method Lior provided. https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.ConvexHull.html will calculate the convex hull for any N dimensional space and calculate the area/volume for you as well. See the example and return value attributes towards the bottom of the page for details.