I have two sets of X,Y co-ordinates as separate lists. Both represent the same irregular polygonal shape, but in different orientations and sizes/scale.
Need to write a program in C#, to compare both the points set, rotate any one of the shape such that it aligns with the another, so that they are in same orientation.
Tried searching for solution, and got to know using concave hull with angles difference can help, but could not find a good C# implementation for the same.
Can some one help me, if there is a minimal way to achieve this?
Edit: The two points-set might not be the same. One may contain more points than other.
I have contour co-ordinates of a shape and a PNG which is of same shape, but orientation is different. I want to read the PNG, calculate the angle to turn it to the fit the Contour.
Calculate image moments for point cloud
Evaluate orientation of both clouds with Theta angle.
Rotate one cloud by theta difference.
Use other moments (centroid etc) to find translation and scale
I have a set of 3D points that will fit neatly using using a line segment. I need to get the center of that line (no problem, a mean of X, Y and Z will work great for that). I also need to get a couple vectors that describes the orientation of the line in 3D space. In other words I need to describe how much the sampled data's X, Y and Z axis is rotated.
If you imagine an airplane (this is not an aviation application, just a handy example) and the 3d points are randomly spread in the area of the wings. I need to use these points to describe the orientation of the airplane in 3d space to determine exactly what direction the nose is pointed and the location of the tip of the wings.
I have been looking for linear fit libraries but they all seem to be for 2D data sets or are commercial
I could also fit two linear equations through the x/y and x/z data and use those but this seems wrong and a work around.
Does anybody have any thoughts on how to solve this problem?
I am trying to create a 2(or more) circles from a list of edgepoints which is sorted. A egdepoint is just a point. A list of edgepoints make the edge of a circle. Drawing a line between the edgepoints gives the black line in the pictures. So there is no radius and circles can vary in size.
It looks like this:
My idea is to split it like picture 2. Next, create circles like in this article. Ofcourse with the fist, middle and last point.
I created a method to detect whether the edgepoints are sorted clockwise or counter clockwise. Unfortunately I am stuck on how to detect these "split points" The picture can be rotated ofcourse.
The result should be 2(or more) list with edgepoints:
So how can I detect these "split points"? Or is there a better way to detect intersecting circles as separate?
Input: Something like Point[]. Output: Something like List[Circle]
Assume input is sorted by position around the outer edge of some picture that is made up of overlapping circles. Any points in the interior of the picture are not included.
I thought about it more and I think you can find the points easier if you consider slope. Points where the slope varies wildly are the points you are looking for.
[Revised thought - Find the transition points first, then the circles.]
Start by using a function to calculate the slope of a line segment between two points. As you go around a circle, you will have a reasonable change in slope (you will have to discover this by reviewing how close the points are together). Say you have points like { A, B, C, D, ...}. Compute the slope of A->B and B->C. If the points are evenly spaced, that difference or the average difference might be a tolerance (you have to be careful of transition points here - maybe compute an average over the entire set of points). If at some point the slope of K->L and L->M is very different from J->K and K->L then record that index as a transition point. Once you have traversed the whole set (include a test for Y->Z and Z->A as well if it is a closed shape), the recorded indexes should define the transition points. Use the mid-point of each segment as the third point for each circle. (e.g. if you identified I and M as transition points, then use I, K, and M to define a circle).
[Original thought - find the circles first]
Use the referenced article to determine the center of a circle based on three points. Then determine if it is really an interesting circle by testing some of the points around the reference points. (Say, pick every 5th or 10th point then verify with all the interior points). With more overlapping circles, this becomes a less effective process so you will have to define the algorithm carefully. Once you get all the reference circles, process through all of the edge points (assuming these are points on the exterior of the drawing). Using center, radius, a distance formula, and a tolerance, determine which points are on which circle. Points that fit the tolerance on more than one circle are the points you are looking for I think.
I read about rectangle structure in c# and the intersection function in it
My Question is: how to custom it such that I can have a 3D rectanlge, have x,y,z coordinates
and get it intersection with another one ?
Any idea
Just create your own. Here are some ideas:
a 3D rectangle not only has a width and a height, but also a plane
planes can be described with a normal vector and a point (origin)
the origin would be similar to the (x, y) in the 2D rectangle, that is, the "upper left" point, but any would do
intersecting with another rectangle could be as easy as intersecting the two plains and then checking to see if the intersection line "cuts" any of the rectangles
there are tons of math related websites to check for the formulas on how to do this
chances are pretty good, that in your application you won't need to do this in an optimized manner. Really. Just code it already and try it out. You can optimize later.
EDIT:
Wait. On second thoughts: An origin, a height, a width and a normal vector won't really cut it, since you don't have a sense of "up" as you do in 2D.
So, scratch that. Thinking about it reveals that the width and the height in 2D are actually vectors two, except that their direction is implied: Width is the length of a vector in x direction, Height is the length of a vector in y direction.
So, model your rectangle like this:
a point (Origin)
a vector Width (this is often called u in maths)
a vector Height (this is often called v in maths)
the normal vector is not necessary anymore since it is can be calculated by the vectorial product of Width x Height
The three other points of your rectangle can then be calculated as:
Origin + Width
Origin + Width + Height
Origin + Height
The rectangle class you have linked to models a 2D rectangle (I don't know what a 3D rectangle would be, BTW).
Pretty much the whole System.Drawing namespace deals with 2D, so you can't customise it that way.
The System.Drawing parent namespace contains types that support basic GDI+ graphics functionality. Child namespaces support advanced two-dimensional and vector graphics functionality, advanced imaging functionality, and print-related and typographical services.
(emphasis mine)
(about the intersection function)
You cannot create such a function.
The intersecting function of 2 rectangles in 2D is interesting because it returns you a third rectangle (than can be empty).
Intersection of 2 "3D rectangles" in space is not always a 3D rectange!
(for example take 2 identical rectangles and rotate one, then take the intersection...)
So you cannot just create a rectangle object, then an intersection function that returns a rectangle object.
You need more complete 3D object management library.
remark:
A 3D rectangle is delimited by 6 planes.
so you can identify it by 6 constraints on x,y,z
Then the intersection of 2 3D rectangles will just be a 3D object identified by 12 contraints.
If these 12 constraints can be simplfied to 6 ones it can be a rectange (but it's not always the case)
and if it cannot then it's not a rectangle.
I have 1 red polygon say and 50 randomly placed blue polygons - they are situated in geographical 2D space. What is the quickest/speediest algorithim to find the the shortest distance between a red polygon and its nearest blue polygon?
Bear in mind that it is not a simple case of taking the points that make up the vertices of the polygon as values to test for distance as they may not necessarily be the closest points.
So in the end - the answer should give back the closest blue polygon to the singular red one.
This is harder than it sounds!
I doubt there is better solution than calculating the distance between the red one and every blue one and sorting these by length.
Regarding sorting, usually QuickSort is hard to beat in performance (an optimized one, that cuts off recursion if size goes below 7 items and switches to something like InsertionSort, maybe ShellSort).
Thus I guess the question is how to quickly calculate the distance between two polygons, after all you need to make this computation 50 times.
The following approach will work for 3D as well, but is probably not the fastest one:
Minimum Polygon Distance in 2D Space
The question is, are you willing to trade accuracy for speed? E.g. you can pack all polygons into bounding boxes, where the sides of the boxes are parallel to the coordinate system axes. 3D games use this approach pretty often. Therefor you need to find the maximum and minimum values for every coordinate (x, y, z) to construct the virtual bounding box. Calculating the distances of these bounding boxes is then a pretty trivial task.
Here's an example image of more advanced bounding boxes, that are not parallel to the coordinate system axes:
Oriented Bounding Boxes - OBB
However, this makes the distance calculation less trivial. It is used for collision detection, as you don't need to know the distance for that, you only need to know if one edge of one bounding box lies within another bounding box.
The following image shows an axes aligned bounding box:
Axes Aligned Bounding Box - AABB
OOBs are more accurate, AABBs are faster. Maybe you'd like to read this article:
Advanced Collision Detection Techniques
This is always assuming, that you are willing to trade precision for speed. If precision is more important than speed, you may need a more advanced technique.
You might be able to reduce the problem, and then do an intensive search on a small set.
Process each polygon first by finding:
Center of polygon
Maximum radius of polygon (i.e., point on edge/surface/vertex of the polygon furthest from the defined center)
Now you can collect, say, the 5-10 closest polygons to the red one (find the distance center to center, subtract the radius, sort the list and take the top 5) and then do a much more exhaustive routine.
For polygon shapes with a reasonable number of boundary points such as in a GIS or games application it might be quicker easier to do a series of tests.
For each vertex in the red polygon compute the distance to each vertex in the blue polygons and find the closest (hint, compare distance^2 so you don't need the sqrt() )
Find the closest, then check the vertex on each side of the found red and blue vertex to decide which line segments are closest and then find the closest approach between two line segments.
See http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/ (it's easy to simply for the 2d case)
This screening technique is intended to reduce the number of distance computations you need to perform in the average case, without compromising the accuracy of the result. It works on convex and concave polygons.
Find the the minimum distance between each pair of vertexes such that one is a red vertex and one is a blue. Call it r. The distance between the polygons is at most r. Construct a new region from the red polygon where each line segment is moved outward by r and is joined to its neighbors by an arc of radius r is centered at the vertex. Find the distance from each vertex inside this region to every line segment of the opposite color that intersects this region.
Of course you could add an approximate method such as bounding boxes to quickly determine which of the blue polygons can't possibly intersect with the red region.
Maybe the Frechet Distance is what your looking for?
Computing the Fréchet distance between two polygonal curves
Computing the Fréchet Distance Between Simple Polygons
I know you said "the shortest distance" but you really meant the optimal solution or a "good/very good" solution is fine for your problem?
Because if you need to find the optimal solution, you have to calculate the distance between all of your source and destination poligon bounds (not only vertexes). If you are in 3D space then each bound is a plane. That can be a big problem (O(n^2)) depending on how many vertexes you have.
So if you have vertex count that makes that squares to a scarry number AND a "good/very good" solution is fine for you, go for a heuristic solution or approximation.
You might want to look at Voronoi Culling. Paper and video here:
http://www.cs.unc.edu/~geom/DVD/
I would start by bounding all the polygons by a bounding circle and then finding an upper bound of the minimal distance.
Then i would simply check the edges of all blue polygons whose lower bound of distance is lower than the upper bound of minimal distance against all the edges of the red polygon.
upper bound of min distance = min {distance(red's center, current blue's center) + current blue's radius}
for every blue polygon where distance(red's center, current blue's center) - current blue's radius < upper bound of min distance
check distance of edges and vertices
But it all depends on your data. If the blue polygons are relatively small compared to the distances between them and the red polygon, then this approach should work nicely, but if they are very close, you won't save anything (many of them will be close enough). And another thing -- If these polygons don't have many vertices (like if most of them were triangles), then it might be almost as fast to just check each red edge against each blue edge.
hope it helps
As others have mentioned using bounding areas (boxes, circles) may allow you to discard some polygon-polygon interactions. There are several strategies for this, e.g.
Pick any blue polygon and find the distance from the red one. Now pick any other polygon. If the minimum distance between the bounding areas is greater than the already found distance you can ignore this polygon. Continue for all polygons.
Find the minimum distance/centroid distance between the red polygon and all the blue polygons. Sort the distances and consider the smallest distance first. Calculate the actual minimum distance and continue through the sorted list until the maximum distance between the polygons is greater than the minimum distance found so far.
Your choice of circles/axially aligned boxes, or oriented boxes can have a great affect on performance of the algorithm, dependent on the actual layout of the input polygons.
For the actual minimum distance calculation you could use Yang et al's 'A new fast algorithm for computing the distance between two disjoint convex polygons based on Voronoi diagram' which is O(log n + log m).
Gotta run off to a funeral in a sec, but if you break your polygons down into convex subpolies, there are some optimizations you can do. You can do a binary searches on each poly to find the closest vertex, and then I believe the closest point should either be that vertex, or an adjacent edge. This means you should be able to do it in log(log m * n) where m is the average number of vertices on a poly, and n is the number of polies. This is kind of hastey, so it could be wrong. Will give more details later if wanted.
You could start by comparing the distance between the bounding boxes. Testing the distance between rectangles is easier than testing the distance between polygons, and you can immediately eliminate any polygons that are more than nearest_rect + its_diagonal away (possibly you can refine that even more). Then, you can test the remaining polygons to find the closest polygon.
There are algorithms for finding polygon proximity - I'm sure Wikipedia has a good review of them. If I recall correctly, those that only allow convex polygons are substantially faster.
I believe what you are looking for is the A* algorithm, its used in pathfinding.
The naive approach is to find the distance between the red and 50 blue objects -- so you're looking at 50 3d Pythagorean calculations + sorting to find the answer. That would only really work for finding the distance between center points though.
If you want arbitrary polygons, maybe your best best is a raytracing solution that emits rays from the surface of the red polygon with respect to the normal, and reports when another polygon is hit.
A hybrid might work -- we could find the distance from the center points, assuming we had some notion of the relative size of the blue polygons, we could cull the result set to the closest among those, then use raytracing to narrow down the truly closest polygon(s).