There are 2 areas (java.awt.geom.Area) area1 and area2. I need to verify if area2 is inside area1? (area1 contains area2).
I have tried:
areaDelta = (Area)area1.clone();
areaDelta.add(area2);
return areaDelta.equals(area1);
But it doesnt always work as it should (If the bounds of area2 are on the bounds of area1, it returns true, should return false).
In fact I have 2 polygons (java.awt.Polygon) and I need the Polygon.contains(Polygon) method, may be this can be easier then for areas.
Any ideas?
Polygons can be convex and non-convex.
Since you have Polygon.contains(Point), you can achieve what you need by testing if every point of your second polygon is inside the first polygon (I dream of a JDK version which would implement every basic need of a programmer, like .NET).
EDIT: To handle concave polygons, you first need to split your polygons into convex ones, then you'll be able to properly use the method mentioned above. I used two different polygon decomposition algorithms in one of my applications, and I would suggest you to look at their code:
Bayazit Decomposer
Ewjordan Decomposer
Related
I'm making a program that needs to detect the collision between 2 non-axis aligned boxes. My program only needs an indication if 2 non-axis aligned boxes are colliding. I would like to have the most simple and efficient algorithm possible.
Here I visualized the problem.
So as you can see squares 1,2 and 3 would return true because they collided with the green squares.
4 would return false because it isn't colliding.
I do have all the boxes of both colors in separate array lists.
Does anybody know a library or algorithm for this problem? Thanks in advance.
Check out the Area class in the java.awt.geom package.
http://docs.oracle.com/javase/6/docs/api/java/awt/geom/Area.html
I don't know how "easy" your game really is, how many shapes you'd have to check for (I'm thinking efficiency here), but if you have your different color shapes in different lists, a kind of brute force iteration may work for you. Not a clue if it would be efficient enough for you. I use box2D to tell me the collisions, but sounds like that may be overkill for you.
The brute force method I'm thinking of would be to utilize libgdx's Intersector class (check out the API, it has lots of methods). Iterate through your rectangles comparing to the others. Something like IntersectRectangles() gives you a boolean if two rectangles overlap (ie: collide).
This may be too inefficient/hacky, and a physics library may be too much. So one of the other answers provided may be the sweet spot.
A commonly-used approach involves quadtrees. There's a good write-up and tutorial here, which explains how to use quadtrees to perform collision detection in 2D space.
The general idea is that your game area will keep being partitioned by four as your add objects. Each partition is called a node and each node will maintain a reference to objects that exist in the corresponding partition. Objects are placed into nodes based on where they are in the 2D space. If a node does not fit cleanly into a partition, it is inserted into the parent node. Using this method, you don't have to perform an expensive check against every other object in your 2D space, because you can be sure that objects in different nodes (at the same level; i.e., sibling nodes) will not collide. So you only have to perform your collision detection on a small subset of objects.
Note that this just tells you which objects are occupying a certain area; it's a more efficient way to hone in on objects that are likely to be colliding. After that you have to check if the objects are actually colliding. There is another write-up here that goes over various techniques to accomplish this.
There are two algorithms/data-structures you need to consider for this problem:
A spatial data-structure to store your rotated quads, to efficiently determine which pairs of quads need to be tested against each other. Other answers have already addressed this. If the number of quads is small enough then you can just test all the red quads against all the green quads, which is O(m * n).
An algorithm to perform the actual test of one rotated quad against another. One of the simplest is the Separating Axis Theorem.
The basic idea behind the SAT is that if you can find at least one line where all the points of one convex object are on one side of it, and all the points of the other are on the other side, then the two are not colliding. The potential lines that you need to test are just the edges of both of the objects.
To implement it you need to implement a point-line test to tell you which side of an edge a point is on. This is done by calculating the normal to the edge, and then calculating the dot product of the edge normal and a vector from a point on the edge to the point you are testing. The sign of the dot product tells you which side the point is on (positive means the outside the edge, for an outward pointing normal). Whether you count zero (on the line) as outside or inside depends on whether you want objects that are just touching but not penetrating to count as a collision, if you do then the dot product must be greater than zero to count as outside.
For example if the points on objects are in clockwise order, and edgeA and edgeB are the two points of an edge on one object, and pointC is a point on the other object, the test is done like this (not using function calls, to show the math):
boolean isOutsideEdge(PointF edgeA, PointF edgeB, PointF pointC)
{
float normalX = edgeA.Y - edgeB.y;
float normalY = edgeB.X - edgeA.x;
float vectorX = pointC.x - edgeA.x;
float vectorY = pointC.y - edgeA.y;
return (normalX * vectorX) + (normalY * vectorY) > 0.0f;
}
Then the algorithm is:
For each edge on quad A, if all the corner points on quad B are on the outward facing side of the edge, then A and B are not colliding, stop processing and return false.
For each edge on quad B, if all the corner points on quad A are on the outward facing side of the edge, then A and B are not colliding, stop processing and return false.
If all those tests have been performed and none have returned false, then A and B are colliding, so return true.
The SAT can be generalized to arbitrary convex polygons.
So I decided to go with box2d in the end. This was the best solution because of the diffrent mask-qualifiers, the objects didn't collide but it could be easily checked wether they should be colliding.
I had to make my own contactlistener that overrides the default contactlistener. Here I could do anything if any 2 objects collided.
Thanks everyone for the help.
So, I'd like to figure out a function that allows you to determine if two cubes of arbitrary rotation and size intersect.
If the cubes are not arbitrary in their rotation (but locked to a particular axis) the intersection is simple; you check if they intersect in all three dimensions by checking their bounds to see if they cross or are within one another in all three dimensions. If they cross or are within in only two, they do not intersect. This method can be used to determine if the arbitrary cubes are even candidates for intersection, using their highest/lowest x, y, and z to create an outer bounds.
That's the first step. In theory, from that information we can tell which 'side' they are on from each other, which means we can eliminate some of the quads (sides) from our intersection. However, I can't assume that we have that information, since the rotation of the cubes may make it difficult to determine simply.
My thought is to take each pair of quads, find the intersection of their planes, then determine if that line intersects with at least one edge of each of the pairs of sides. If any pair of sides has a line of intersection that intersects with any of their edges, the quads intersect. If none intersect, the two cubes do not intersect.
We can then determine the depth of the intersection on the second cube by where the plane-intersection line intersects with its edge(s).
This is simply speculative, however. Is there a better, more efficient way to determine the intersection of these two cubes? I can think of a number of different ways to do this, and I can also tell that they could be very different in terms of amount of computation required.
I'm working in Java at the moment, but C/C++ solutions are cool too (I can port them); even psuedocode since it is perhaps a big question.
To find the intersection (contact) points of two arbitrary cubes in three dimensions, you have to do it in two phases:
Detect collisions. This is usually two phases itself, but for simplicity, let's just call it "collision detection".
The algorithm will be either SAT (Separating axis theorem), or some variant of polytope expansion/reduction. Again, for simplicity, let's assume you will be using SAT.
I won't explain in detail, as others have already done so many times, and better than I could. The "take-home" from this, is that collision detection is not designed to tell you where a collision has taken place; only that it has taken place.
Upon detection of an intersection, you need to compute the contact points. This is done via a polygon clipping algorithm. In this case, let's use https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm
There are easier, and better ways to do this, but SAT is easy to grasp in 3d, and SH clipping is also easy to get your head around, so is a good starting point for you.
You should take a look at the field of computer graphics. They have many means. E.g. Weiler–Atherton clipping algorithm. There are also many datastructures that could ease up the process for you. To mention AABBs (Axis-aligned bounding boxes).
Try using the separating axis theorem. it should apply in 3d as it does in 2d.
If you create polygons from the sides of the cubes then another approach is to use Constructive Space Geometry (CSG) operations on them. By building a Binary Space Partitioning (BSP) tree of each cube you can perform an intersection on them. The result of the intersection is a set of polygons representing the intersection. In your case if the number of polygons is zero then the cubes don't intersect.
I would add that this approach is probably not a good real time solution, but you didn't indicate if this needed to happen in frame refresh time or not.
Since porting is an option you can look at the Javascript library that does CSG located at
http://evanw.github.io/csg.js/docs/
I've ported this library to C# at
https://github.com/johnmott59/CGSinCSharp
I have a series of Polygons, created using the JTS Topology Suite. Each polygon is a set of points, longitudes and latitudes that form a shape, as shown below.
((lat1,lon1),(lat2,lon2),....(lat1,lon1))
I want to find each of these polygons neighbours, the other shapes that are physically next to them. I have thought of looking for matching points, but obviously that won't work in all cases. I was wondering if there is any package that will check to see if polygons share the same edge that I could use in this situation? Or if not then another way to do this in Java.
Thanks.
Since you are looking for shared edges, you can create a hash table uses the edge as the key and a list of polygons that have that edge as its item.
Then you go through each polygon and fill up the table. Which is linear in the number of edges.
Then you go through the table and look for edges that are tied to multiple polygons, which is what you are looking for. This is linear in the number of unique edges.
I'm not sure how Java implement hash tables, so it might be a bit of work to get this setup. Make sure the edges are sorted to prevent the edge (A,B) being different from the edge (B,A), which will mess up the algorithm.
As for libraries, seems like what you're trying to do might be a bit specialized, and thus not sure you'll find library implementations, hence why I outlined an algorithm.
There was in fact a very simple way to do this. I created an arraylist containing an array of objects. The object referenced the name/id of the polygon, the actual polygon coordinates and then a string that would contain ids of any neighbours.
In JTS Topology suite there is a method that you can call on polygons called touches that returns a boolean; so I had a double for loop, going through my arraylist twice and calling the method touches on polygon(i) so:
arraylist<object[]>..
//where in the array the objects are
object[0] = id
object[1] = polygon
object[2] = neighbours
for (int i=0;i<arraylist;i++)
for (int j=0;j<arraylist;j++)
if (i)[1].touches(j)[1]
update i[2]..
It's probably not the best method but it seems to work.
If you are using JTS geometries anyway you can use the spatial relations that can be used with any Geometry object.
Use touches if you can ensure that at least one point between neighbours is in common and their interiors do not intersect.
Use intersects if you cannot ensure that the interiors do not intersect. Depending on the datasource this is probably the better choice.
Given the polygons a method to get the neighbours can look like this:
public ArrayList<Polygon> getNeighbourList(Polygon center, ArrayList<Polygon> possibleNeighbourList){
// result list
ArrayList realNeighbourList = new ArrayList();
for(Polygon p : possibleNeighbourList){
// check if current polygon is a neighbour of the center polygon by using the spatial relation touches or intersects
if(center.intersects(p)){
realNeighbourList.add(p);
}
}
return realNeighbourList;
}
I tried to find out thousands of point in million polygon via web services .At first i implemented the algorithm(Point in polygon) in java ,but it take a long time .And then i split the table in mysql and tried to using the multiple thread to solve it ,but still inefficiently. Is there any faster algorithm or implementation for solve this?
Plus description about the polygon. 2D ,static,complex polygon(also with hole).
Any Suggestion will be appreciate.
Testing a point against a million polygons is going to take a lot of time, no matter how efficient your point in polygon function is.
You need to narrow down the search list. Start by making a bounding box for each polygon and only selecting the polygons when the point is within the bounding box.
If the polygons are unchanging you could convert each polygon to a set of triangles. Testing to see if a point is in a triangle should be much faster than testing to see if it's in an arbitrary polygon. Even though the number of triangles will be much larger than the number of polygons, it might be faster overall.
If the collection of polygons is static it may be helpful to first register them onto a spatial data structure - an R-tree might be a good choice, assuming that the polygons do not overlap each other too much.
To test a point against the polygon collection the enclosing leaf in the tree would first be found (an O(log(n)) style operation) and then it would only be necessary to perform the full point-in-polygon test for the polygons that are associated with the enclosing leaf.
This approach should greatly speed up each point test, but requires an additional setup phase to build the R-tree.
Hope this helps.
If you deal with millions of polygons, you need some kind of space partitioning, or it's gonna be slow, no matter how optimized your hit-test function is or how many threads work on solving your query.
What kind of space partitioning ? it depends:
2D? 3D?
Is your polygon set static? If not, do it changes frequently?
What kind of request are you doing on this set?
What kind of polygon is it? Triangle? Convex? Concave? Complex? With holes?
We need more information to help you.
EDIT
Here is a simple space partitioning scheme.
Suppose there is a Cartesian grid over your 2D space with a given step.
When you add a polygon:
Compute its bounding box
Find all the grid cells that intersect with the bounding box
For each cell, add a line in a special table.
The table looks like this: cell_x, cell_y, polygon_id. Add the proper indexes (at least cell_x and cell_y)
Of course, you want to choose your grid step so most of the polygons lay in less than 10 cells, or else your cell table will quickly becomes huge.
It's now easy to find the polygons at a given point:
Compute in which cell your point belongs
Get all polygons associated to this cell
For each polygon, use your hit-test function
This solution is far from optimal, but easy to implements.
I thik here is the case where divide and conquer would do, you could try making subpolyons or simplifying some of the poonts, maybe try an heuristic approach, there are my 5 cents.
Using Java 2D I've patched several Bezier curves (CubicCurve2D) together to create a "blob". The problem I now face is how to:
Efficiently fill the blob with a given colour.
Efficiently determine whether a given point lies inside the blob.
I noticed thst CubicCurve2D implements Shape which provides numerous contains methods for determining "insideness" and that Graphics2D is able to fill a Shape via the fill(Shape) (which I believe uses Shape's getPathIterator methods to do this).
Given this I was hoping I could create a composite Shape, whereby my getPathIterator(AffineTransform) method would simply link the underlying PathIterators together. However, this is producing a NoSuchElementException once my shape contains more than one CubicCurve2D. Even if I do manage to achieve this I'm not convinced it will work as expected because a CubicCurve2D is always filled on the convex side, and my "blob" is composed of concave and convex curves. The "contains" problem is even harder as a point can legitimately lie within the blob but not within any of the individual curves.
Am I approaching this problem in the correct way (trying to implement Shape?) or is there an idiomatic way to do this that I'm unaware of? I would have thought that the problem of compositing geometric shapes would be fairly common.
Does anyone have any suggestions regarding how to solve this problem?
Thanks in advance.
I'm not sure I understand your question but composite shapes can be created with the class java/awt/geom/Area.
Looking to Shape for a solution is the right way to go about this. If you have a collection of curves that you are trying to assemble into a shape, I would suggest that you use a GeneralPath. Simply add your curves, or straight line segments, as required. Look to the interface to see the various append methods. Also note that you can 'complete' the shape by joining the last point to the starting point.
Once the path is closed, there are a number of different versions of contains() that can be used, please take the time to read each of their descriptions, as there are trade-offs in terms of speed and accuracy, depends on your application.
Also it is easy to get a shape from the path, and fill it, transform it, etc.