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  • Sphere-Sphere intersection and Circle-Sphere intersection

    - by cagirici
    I have code for circle-circle intersection. But I need to expand it to 3-D. How do I calculate: Radius and center of the intersection circle of two spheres Points of the intersection of a sphere and a circle? Given two spheres (sc0,sr0) and (sc1,sr1), I need to calculate a circle of intersection whose center is ci and whose radius is ri. Moreover, given a sphere (sc0,sr0) and a circle (cc0, cr0), I need to calulate the two intersection points (pi0, pi1) I have checked this link and this link, but I could not understand the logic behind them and how to code them. I tried ProGAL library for sphere-sphere-sphere intersection, but the resulting coordinates are rounded. I need precise results.

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  • intersection of three sets in python?

    - by Phil Brown
    Currently I am stuck trying to find the intersection of three sets. Now these sets are really lists that I am converting into sets, and then trying to find the intersection of. Here's what I have so far: for list1 in masterlist: list1=thingList1 for list2 in masterlist: list2=thingList2 for list3 in masterlist: list3=thingList3 d3=[set(thingList1), set(thingList2), set(thingList3)] setmatches c= set.intersection(*map(set,d3)) print setmatches and I'm getting set([]) Script terminated. I know there's a much simpler and better way to do this, but I can't find one...

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  • Triangle - Rectangle Intersection in 2D

    - by Kevin Boyd
    I had previously asked this for 3D but now I changed my strategy and would like to do the intersection in 2D. The Rectangle is axis aligned and will always be in a fixed position, and has a constant shape and size, basically I want to clip the red areas of the triangles that extend outside the bounds of the rectangle The triangles could be in any position, shape or size, I my code I have a loop where I check the triangles one by one however I am still clueless about the math. I have identified 5 cases of triangle rectangle intersection as shown here. How do I find the intersection points of the triangle and the rectangle?

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  • Most efficient AABB - Ray intersection algorithm for input/output distance calculation

    - by Tobbey
    Thanks to the following thread : most efficient AABB vs Ray collision algorithms I have seen very fast algorithm for ray/AABB intersection point computation. Unfortunately, most of the recent algorithm are accelerated by omitting the "output" intersection point of the box. In my application, I would interested in getting both the the distance from source ray to input: t0 and source ray to output of bounding box: t1. I have seen for instance Eisemann designed a very fast version regarding plucker, smits, ... , but it does not compare the case when both input/output distance should be computed see: http://www.cg.cs.tu-bs.de/publications/Eisemann07FRA/ Does someone know where I can find more information on algorithm performances for the specific input/output problem ? Thank you in advance

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  • Line Intersection from parametric equation

    - by Sidar
    I'm sure this question has been asked before. However, I'm trying to connect the dots by translating an equation on paper into an actual function. I thought It would be interesting to ask here instead on the Math sites (since it's going to be used for games anyway ). Let's say we have our vector equation : x = s + Lr; where x is the resulting vector, s our starting point/vector. L our parameter and r our direction vector. The ( not sure it's called like this, please correct me ) normal equation is : x.n = c; If we substitute our vector equation we get: (s+Lr).n = c. We now need to isolate L which results in L = (c - s.n) / (r.n); L needs to be 0 < L < 1. Meaning it needs to be between 0 and 1. My question: I want to know what L is so if I were to substitute L for both vector equation (or two lines) they should give me the same intersection coordinates. That is if they intersect. But I can't wrap my head around on how to use this for two lines and find the parameter that fits the intersection point. Could someone with a simple example show how I could translate this to a function/method?

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  • BoundingBox Intersection Problems

    - by Deukalion
    When I try to render two cubes, same sizes, one beside the other. With the same proportions (XYZ). My problem is, why do a Box1.BoundingBox.Contains(Box2.BoundingBox) == ContaintmentType.Intersects - when it clearly doesn't? I'm trying to place objects with BoundingBoxes as "intersection" checking, but this simple example clearly shows that this doesn't work. Why is that? I also try checking height of the next object to be placed, by checking intersection, adding each boxes height += (Max.Y - Min.Y) to a Height value, so when I add a new Box it has a height value. This works, but sometimes due to strange behavior it adds extra values when there isn't anything there. This is an example of what I mean: BoundingBox box1 = GetBoundaries(new Vector3(0, 0, 0), new Vector3(128, 64, 128)); BoundingBox box2 = GetBoundaries(new Vector3(128, 0, 0), new Vector3(128, 64, 128)); if (box1.Contains(box2) == ContainmentType.Intersects) { // This will be executed System.Windows.Forms.MessageBox.Show("Intersects = True"); } if (box1.Contains(box2) == ContainmentType.Disjoint) { System.Windows.Forms.MessageBox.Show("Disjoint = True"); } if (box1.Contains(box2) == ContainmentType.Contains) { System.Windows.Forms.MessageBox.Show("Contains = True"); } Test Method: public BoundingBox GetBoundaries(Vector3 position, Vector3 size) { Vector3[] vertices = new Vector3[8]; vertices[0] = position + new Vector3(-0.5f, 0.5f, -0.5f) * size; vertices[1] = position + new Vector3(-0.5f, 0.5f, 0.5f) * size; vertices[2] = position + new Vector3(0.5f, 0.5f, -0.5f) * size; vertices[3] = position + new Vector3(0.5f, 0.5f, 0.5f) * size; vertices[4] = position + new Vector3(-0.5f, -0.5f, -0.5f) * size; vertices[5] = position + new Vector3(-0.5f, -0.5f, 0.5f) * size; vertices[6] = position + new Vector3(0.5f, -0.5f, -0.5f) * size; vertices[7] = position + new Vector3(0.5f, -0.5f, 0.5f) * size; return BoundingBox.CreateFromPoints(vertices); } Box 1 should start at x -64, Box 2 should start at x 64 which means they never overlap. If I add Box 2 to 129 instead it creates a small gap between the cubes which is not pretty. So, the question is how can I place two cubes beside eachother and make them understand that they do not overlap or actually intersect? Because this way I can never automatically check for intersections or place cube beside eachother.

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  • how to calculate intersection time and place of multiple moving arcs

    - by user20733
    I have rocks orbiting moons, moons orbiting planets, planets orbiting suns, and suns orbiting black holes, and the current system could have many many layers of orbitage. the position of any object is a function of time and relative to the object it orbits. (so far so good). now I want to know for a given 2 objects(A,B), a start time and a speed, how can I work out the when and where to go. I can work out where A and B is given a time. so i just need. 1: direction to travel in from A to B(remember B is moving(not in a straight line)) 2: Time to get to b in a straight line. travel must be in a straight line with the shortest possible distance. as an extension to this question, how will i know if its better to wait, EG is it faster to stay on object A and wait for a hour when the objects may be closer, than to set off from A to B at the start. Cheers, it hurt my brain.

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  • Ray-box Intersection Theory

    - by Myx
    Hello: I wish to determine the intersection point between a ray and a box. The box is defined by its min 3D coordinate and max 3D coordinate and the ray is defined by its origin and the direction to which it points. Currently, I am forming a plane for each face of the box and I'm intersecting the ray with the plane. If the ray intersects the plane, then I check whether or not the intersection point is actually on the surface of the box. If so, I check whether it is the closest intersection for this ray and I return the closest intersection. The way I check whether the plane-intersection point is on the box surface itself is through a function bool PointOnBoxFace(R3Point point, R3Point corner1, R3Point corner2) { double min_x = min(corner1.X(), corner2.X()); double max_x = max(corner1.X(), corner2.X()); double min_y = min(corner1.Y(), corner2.Y()); double max_y = max(corner1.Y(), corner2.Y()); double min_z = min(corner1.Z(), corner2.Z()); double max_z = max(corner1.Z(), corner2.Z()); if(point.X() >= min_x && point.X() <= max_x && point.Y() >= min_y && point.Y() <= max_y && point.Z() >= min_z && point.Z() <= max_z) return true; return false; } where corner1 is one corner of the rectangle for that box face and corner2 is the opposite corner. My implementation works most of the time but sometimes it gives me the wrong intersection. I was wondering if the way I'm checking whether the intersection point is on the box is correct or if I should use some other algorithm. Thanks.

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  • Python: Trying to get index of an intersection

    - by user1620716
    I have the following line of code: for i in [i for i,x in enumerate(catdate) if x == set(NNSRCfile['datetimenew']).intersection(catdate)]: print i I am trying to find the index of the intersection for the two components above. Both are lengthy lists that have several commonalities. The intersection part works perfectly; however, the for loop seems to output nothing. (ie: there is nothing that is printed). Python outputs no error, and when I run the code in IPython, I notice that i is equivalent to to the very last element in the list "catdate", instead of listing the indices of "catdate" that are equivalent to the intersection values. Any help is greatly appreciated!

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  • Finding intersection of two spheres

    - by Onkar Deshpande
    Hi, Consider the following problem - I am given 2 links of length L0 and L1. P0 is the point that the first link starts at and P1 is the point that I want the end of second link to be at in 3-D space. I am supposed to write a function that should take in these 3-D points (P0 and P1) as inputs and should find all configurations of the links that put the second link's end point at P1. My understanding of how to go about it is - Each link L0 and L1 will create a sphere S0 and S1 around itself. I should find out the intersection of those two spheres (which will be a circle) and print all points that are on the circumference of that circle. I saw gmatt's first reply on the http://stackoverflow.com/questions/1406375/finding-intersection-points-between-3-spheres but could not understand it properly since the images did not show up. I also saw a formula for finding out the intersection at mathworld[dot]wolfram[dot]com/Sphere-SphereIntersection[dot]html . I could find the radius of intersection by the method given on mathworld. Also I can find the center of that circle and then use the parametric equation of circle to find the points. The only doubt that I have is will this method work for the points P0 and P1 mentioned above ? Please comment and let me know your thoughts.

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  • What is a technique for 2D ray-box intersection that is suitable for old console hardware?

    - by DJCouchyCouch
    I'm working on a Sega Genesis homebrew game (it has a 7mhz 68000 CPU). I'm looking for a way to find the intersection between a particle sprite and a background tile. Particles are represented as a point with a movement vector. Background tiles are 8 x 8 pixels, with an (X,Y) position that is always located at a multiple of 8. So, really, I need to find the intersection point for a ray-box collision; I need to find out where along the edge of the tile the ray/particle hits. I have these two hard constraints: I'm working with pixel locations (integers). Floating point is too expensive. It doesn't have to be super exact, just close enough. Multiplications, divisions, dot products, et cetera, are incredibly expensive and are to be avoided. So I'm looking for an efficient algorithm that would fit those constraints. Any ideas? I'm writing it in C, so that would work, but assembly should be good as well.

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  • Quickest algorithm for finding sets with high intersection

    - by conradlee
    I have a large number of user IDs (integers), potentially millions. These users all belong to various groups (sets of integers), such that there are on the order of 10 million groups. To simplify my example and get to the essence of it, let's assume that all groups contain 20 user IDs (i.e., all integer sets have a cardinality of 100). I want to find all pairs of integer sets that have an intersection of 15 or greater. Should I compare every pair of sets? (If I keep a data structure that maps userIDs to set membership, this would not be necessary.) What is the quickest way to do this? That is, what should my underlying data structure be for representing the integer sets? Sorted sets, unsorted---can hashing somehow help? And what algorithm should I use to compute set intersection)? I prefer answers that relate C/C++ (especially STL), but also any more general, algorithmic insights are welcome. Update Also, note that I will be running this in parallel in a shared memory environment, so ideas that cleanly extend to a parallel solution are preferred.

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  • fast sphere-grid intersection

    - by Mat
    hi! given a 3D grid, a 3d point as sphere center and a radius, i'd like to quickly calculate all cells contained or intersected by the sphere. Currently i take the the (gridaligned) boundingbox of the sphere and calculate the two cells for the min anx max point of this boundingbox. then, for each cell between those two cells, i do a box-sphere intersection test. would be great if there was something more efficient thanks!

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  • Single Column Multiple Filter In Mysql Intersection

    - by Jeebus
    Here is a table CarID| Attribute | Value 1 | Color | Red 2 | Color | Blue 3 | Color | Red 1 | Type | Coupe 2 | Type | Hatch Back 3 | Type | Coupe 3 | Make | Honda 2 | Make | Toyota 1 | Make | Ford Now I would like to run a filter Like Select * From Cars WHERE (Attribute = Color AND Value = Red) AND (Attribute = Make AND Value = Honda).... and Hope to get the CarID as 3 ! This is simple case of Intersection of 2 queries but I don't know how to get it done in a single query. Any help appriciated.

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  • Take the intersection of an arbitrary number of lists in python

    - by thepandaatemyface
    Suppose I have a list of lists of elements which are all the same (i'll use ints in this example) [range(100)[::4], range(100)[::3], range(100)[::2], range(100)[::1]] What would be a nice and/or efficient way to take the intersection of these lists (so you would get every element that is in each of the lists)? For the example that would be: [0, 12, 24, 36, 48, 60, 72, 84, 96]

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  • Using ETS Select To Form An Intersection

    - by Ruhi
    i have the following ets structure: SomeTable = ets:new(sometable, [bag]). ets:insert(SomeTable, [ {set1,item1}, {set1,item2}, {set1,item3}, {set2,item1}, {set2,item2}, {set2,item4}]). i want to get intersection of set1 and set2 using ets:select and fun2ms, result will be [item1, item2]. i spent hours and hours trying to accomplist it with ets:select and fun2ms with no success. can you help me out using ets:select and fun2ms? thanks for all answers! ps: i know about sets module, but i have to use ets and this exact data structure.

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  • PHP intersection between array and object

    - by nickf
    I have an object, let's say it's like this: class Foo { var $b, $a, $r; function __construct($B, $A, $R) { $this->b = $B; $this->a = $A; $this->r = $R; } } $f = new Foo(1, 2, 3); I want to get an arbitrary slice of this object's properties as an array. $desiredProperties = array('b', 'r'); $output = magicHere($foo, $desiredProperties); print_r($output); // array( // "b" => 1, // "r" => 3 // )

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  • Great Circle & Ray intersection

    - by Karl T
    I have a Latitude, Longitude, and a direction of travel in degrees true north. I would like to calculate if I will intersect a line defined by two more Lat/Lon points. I figure the two points defining the line would create my great circle and my location and azimuth would define my ray (or possibly a small circle). Any ideas?

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  • Great Circle & Rhumb line intersection

    - by Karl T
    I have a Latitude, Longitude, and a direction of travel in degrees true north. I would like to calculate if I will intersect a line defined by two more Lat/Lon points. I figure the two points defining the line would create my great circle and my location and azimuth would define my Rhumb line. I am only interested in intersections that will occur with a few hundred kilometers so I do not need every possible solution. I have no idea where to begin.

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  • set / line intersection solution

    - by Xavier
    I have two lists in python and I want to know if they intersect at the same index. Is there a mathematical way of solving this? For example if I have [9,8,7,6,5] and [3,4,5,6,7] I'd like a simple and efficient formula/algorithm that finds that at index 3 they intersect. I know I could do a search just wondering if there is a better way. I know there is a formula to solve two lines in y = mx + b form by subtracting them from each other but my "line" isn't truly a line because its limited to the items in the list and it may have curves. Any help is appreciated.

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  • Which SQL statements to execute with intersection / junction tables

    - by user1455103
    Here a simplified database layout One condo can hold multiple properties (flats, garage boxes, etc) - 1->n relationship One owner can have multiple properties in the same condo and properties can have more than one owner (m->n changed to 1->n with the junction table) One condo can have multiple owners - 1->n Some additional clarification: A owner is a member of a condo. A condo is made of properties belonging to owners BUT a owner is not linked to a property directly (there can be no relation between a property and a owner for a certain time BUT there will ALWAYS be a relation between a owner and a condo). Reason for this: the agent managing the condo will first create a list of owners and a list of properties. It is only later thet he will "link" each property to one or multiple owners (or inversely) I'm quite new to SQL. What SQL statements should I execute to: SELECT, for a specific condo (WHERE condition), the properties and their respective owners (all properties should be listed even if owners are null) SELECT, for a specific condo (WHERE condition), the owners along with their properties (all owners should be listed even if properties are null) UPDATE / DELETE existing owners (I'm uncertain about how to handle the operation for the junction tables. Should I first check if there is an entry in the junction table or not ?) UPDATE / DELETE existing properties (same concern) INSERT new owners (should I use two different SQL statements depending if the owner should be linked to a property or NOT - IF condition ?) INSERT new properties (same question as above) Could you be as clear and generic as possible so that it can be reused ? :-)

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  • Ray intersection and child camera

    - by lutangar
    I've been playing with three.js for few weeks now and got few inconsistencies on ray casting. Here is a simplified version demonstrating one of the bug I encoutered : http://jsfiddle.net/eMrhb/12/ The camera is added to the sphere mesh for further use of TrackBallControl for example. scene.add(mesh); mesh.add(camera); Clicking a few times on the sphere and opening the console, show us none of the expected intersections between the ray and the mesh. Adding the camera to the scene (http://jsfiddle.net/eMrhb/9/), solves the problem: scene.add(mesh); scene.add(camera); But I could use a much more complex hierarchy between my scene objects and the camera to suit my needs. Is this a limitation? If it is, is there any workarounds I could use?

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  • Ray-Box Intersection during Scene traversal with matrix transforms

    - by Myx
    Hello: There are a few ways that I'm testing my ray-box intersections: Using the ComputeIntersectionBox(...) method, that takes a ray and a box as arguments and computes the closest intersection of the ray and the box. This method works by forming a plane with each of the faces of the box and finding an intersection with each of the planes. Once an intersection is found, a check is made whether or not the point is on the surface of the box by checking that the intersection point is between the corner points. When I look at rays after running this algorithm on two different boxes, I obtain the correct intersections. Using ComputeIntersectionScene(...) method without using the matrix transformations on a scene that has two spheres, a dodecahedron (a triangular mesh), and two boxes. ComputeIntersectionScene(...) recursively traverses all of the nodes of the scene graph and computes the closest intersection with the given ray. This test in particular does not apply any transformations that parent nodes may have that also need to be applied to their children. With this test, I also obtain the correct intersections. Using ComputeIntersectionScene(...) method WITH the matrix transformations. This test works like the one above except that before finding an intersection between the ray and a node in the scene, the ray is transformed into the node's coordinate frame using the inverse of the node's transformation matrix and after the intersection has been computed, this intersection is transformed back into the world coordinates by applying the transformation matrix to the intersection point. When testing with the third method on the same scene file as described in 2, testing with 4 rays (thus one ray intersects the one sphere, one ray the the other sphere, one ray one box, and one ray the other box), only the two spheres get intersected and the two boxes do not get intersections. When I debug looking into my ComputeIntersectionBox(...) method, it actually tells me that the ray intersects every plane on the box but each intersection point does not lie on the box. This seems to be strange behavior, since when using test 2 without transformations, I obtain the correct box intersections (thus, I believe my ray-box intersection to be correct) and when using test 3 WITH transformations, I obtain the correct sphere intersections (thus, I believe my transformed ray should be OK). Any suggestions where I could be going wrong? Thank you in advance.

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