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• An implementation of Sharir's or Aurenhammer's deterministic algorithm for calculating the intersect

  - by RGrey

  The problem of finding the intersection/union of 'N' discs/circles on a flat plane was first proposed by M. I. Shamos in his 1978 thesis: Shamos, M. I. “Computational Geometry” Ph.D. thesis, Yale Univ., New Haven, CT 1978. Since then, in 1985, Micha Sharir presented an O(n log2n) time and O(n) space deterministic algorithm for the disc intersection/union problem (based on modified Voronoi diagrams): Sharir, M. Intersection and closest-pair problems for a set of planar discs. SIAM .J Comput. 14 (1985), pp. 448-468. In 1988, Franz Aurenhammer presented a more efficient O(n log n) time and O(n) space algorithm for circle intersection/union using power diagrams (generalizations of Voronoi diagrams): Aurenhammer, F. Improved algorithms for discs and balls using power diagrams. Journal of Algorithms 9 (1985), pp. 151-161. Earlier in 1983, Paul G. Spirakis also presented an O(n^2) time deterministic algorithm, and an O(n) probabilistic algorithm: Spirakis, P.G. Very Fast Algorithms for the Area of the Union of Many Circles. Rep. 98, Dept. Comput. Sci., Courant Institute, New York University, 1983. I've been searching for any implementations of the algorithms above, focusing on computational geometry packages, and I haven't found anything yet. As neither appear trivial to put into practice, it would be really neat if someone could point me in the right direction!

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• How to spread changes in oriented graph?

  - by joseph

  Hello. I have oriented graph. Graph can be strongly connected. Every vertix can have a set of anything, for example letters. The set is user editable. Every vertix makes intersection of sets in previous vertices (only one step back). But now, there is problem: When I update set of one vertex, the change should expand to all vertices and uptate their intersection of sets of previous vertices. How to do every vertex have correct intersection after update of any vertex? Restriction: algorithm must avoid to stick in infinity. Any idea how to solve it?

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• Detecting coincident subset of two coincident line segments

  - by Jared Updike

  This question is related to: How do I determine the intersection point of two lines in GDI+? (great explanation of algebra but no code) How do you detect where two line segments intersect? (accepted answer doesn't actually work) But note that an interesting sub-problem is completely glossed over in most solutions which just return null for the coincident case even though there are three sub-cases: coincident but do not overlap touching just points and coincident overlap/coincident line sub-segment For example we could design a C# function like this: public static PointF[] Intersection(PointF a1, PointF a2, PointF b1, PointF b2) where (a1,a2) is one line segment and (b1,b2) is another. This function would need to cover all the weird cases that most implementations or explanations gloss over. In order to account for the weirdness of coincident lines, the function could return an array of PointF's: zero result points (or null) if the lines are parallel or do not intersect (infinite lines intersect but line segments are disjoint, or lines are parallel) one result point (containing the intersection location) if they do intersect or if they are coincident at one point two result points (for the overlapping part of the line segments) if the two lines are coincident

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• Python - alternative to list.remove(x)?

  - by Seafoid

  Hi, I wish to compare two lists. Generally this is not a problem as I usually use a nested for loop and append the intersection to a new list. In this case, I need to delete the intersection of A and B from A. A = [['ab', 'cd', 'ef', '0', '567'], ['ghy5'], ['pop', 'eye']] B = [['ab'], ['hi'], ['op'], ['ej']] My objective is to compare A and B and delete A intersection B from A, i.e., delete A[0][0] in this case. I tried: def match(): for i in A: for j in i: for k in B: for v in k: if j == v: A.remove(j) list.remove(x) throws a ValueError.

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• 2D SAT How to find collision center or point or area?

  - by Felipe Cypriano

  I've just implemented collision detection using SAT and this article as reference to my implementation. The detection is working as expected but I need to know where both rectangles are colliding. I need to find the center of the intersection, the black point on the image above. I've found some articles about this but they all involve avoiding the overlap or some kind of velocity, I don't need this. I just need to put a image on top of it. Like two cars crashed so I put an image on top of the collision. Any ideas? ## Update The information I've about the rectangles are the four points that represents them, the upper right, upper left, lower right and lower left coordinates. I'm trying to find an algorithm that can give me the intersection of these points.

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• Wavefront mesh: determine which face a point belongs to?

  - by Mina Samy

  I have a 3D mesh Wavefront .obj file. Is there any algorithm that takes an arbitrary point coordinates as input and determines which face of the mesh that point belongs to ?? The mesh is rendered on the screen, then the user clicks on it, I want to determine which part of the mesh the user has clicked on ? Here's the code using LibGDX: Vector3 intersection=new Vector3(); Ray ray=camera.getPickRay(x, y); //vertices is an array that hold the coordinates of the mesh boolean ok=Intersector.intersectRayTriangles(ray, vertices, intersection); Thanks

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• Drag camera/view in a 3D world

  - by Dono

  I'm trying to make a Draggable view in a 3D world. Currently, I've made it using mouse position on the screen, but, when I move the distance traveled by my mouse is not equal to the distance traveled in the 3D world. So, I've tried to do that : Compute a ray from mouse position to 3D world. Calculate intersection with the ground. Check intersection difference old position <- new position. Translate camera with the difference. I've got a problem with this method: The ray is computed with the current camera's position I move the camera I compute the new ray with new camera position. The difference between old ray and new ray is now invalid. So, graphically my camera don't stop to move to previous/new position everytime. How can I do a draggable camera with another solution ? Thanks!

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• point light illumination using Phong model

  - by Myx

  Hello: I wish to render a scene that contains one box and a point light source using the Phong illumination scheme. The following are the relevant code snippets for my calculation: R3Rgb Phong(R3Scene *scene, R3Ray *ray, R3Intersection *intersection) { R3Rgb radiance; if(intersection->hit == 0) { radiance = scene->background; return radiance; } ... // obtain ambient term ... // this is zero for my test // obtain emissive term ... // this is also zero for my test // for each light in the scene, obtain calculate the diffuse and specular terms R3Rgb intensity_diffuse(0,0,0,1); R3Rgb intensity_specular(0,0,0,1); for(unsigned int i = 0; i < scene->lights.size(); i++) { R3Light *light = scene->Light(i); R3Rgb light_color = LightIntensity(scene->Light(i), intersection->position); R3Vector light_vector = -LightDirection(scene->Light(i), intersection->position); // check if the light is "behind" the surface normal if(normal.Dot(light_vector)<=0) continue; // calculate diffuse reflection if(!Kd.IsBlack()) intensity_diffuse += Kd*normal.Dot(light_vector)*light_color; if(Ks.IsBlack()) continue; // calculate specular reflection ... // this I believe to be irrelevant for the particular test I'm doing } radiance = intensity_diffuse; return radiance; } R3Rgb LightIntensity(R3Light *light, R3Point position) { R3Rgb light_intensity; double distance; double denominator; if(light->type != R3_DIRECTIONAL_LIGHT) { distance = (position-light->position).Length(); denominator = light->constant_attenuation + (light->linear_attenuation*distance) + (light->quadratic_attenuation*distance*distance); } switch(light->type) { ... case R3_POINT_LIGHT: light_intensity = light->color/denominator; break; ... } return light_intensity; } R3Vector LightDirection(R3Light *light, R3Point position) { R3Vector light_direction; switch(light->type) { ... case R3_POINT_LIGHT: light_direction = position - light->position; break; ... } light_direction.Normalize(); return light_direction; } I believe that the error must be somewhere in either LightDirection(...) or LightIntensity(...) functions because when I run my code using a directional light source, I obtain the desired rendered image (thus this leads me to believe that the Phong illumination equation is correct). Also, in Phong(...), when I computed the intensity_diffuse and while debugging, I divided light_color by 10, I was obtaining a resulting image that looked more like what I need. Am I calculating the light_color correctly? Thanks.

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• How could I make geometry advanced operations on bezier paths?

  - by yizzreel

  I have a library that draws regular bezier path figures (complex paths formed of a lot of bezier points), using midpoint approximation. I can draw them without problem, but I need to add support for advanced geometry operations: Nearest point of a curve, intersection, figure contains point, and more importantly, path combinations: difference, intersection, exclusive-or, union, ... Is there any good source to get all this? Thanks

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• In SQL, can we always write an inner join statement as a main query and subquery if we only want to

  - by Jian Lin

  In SQL, can we always write an inner join statement as a main query and subquery or vice versa if we only want to find the intersection? For example, select * from gifts g where g.giftID in (select giftID from sentGifts); can do a join and show the gifts sent in the sentGifts table, but it won't be able to show the sentTime because that is inside the subquery. But if all we care is to find the intersection, without caring what is being displayed, then we can always convert one to the other?

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• Resolving collisions between dynamic game objects

  - by TheBroodian

  I've been building a 2D platformer for some time now, I'm getting to the point where I am adding dynamic objects to the stage for testing. This has prompted me to consider how I would like my character and other objects to behave when they collide. A typical staple in many 2D platformer type games is that the player takes damage upon touching an enemy, and then essentially becomes able to pass through enemies during a period of invulnerability, and at the same time, enemies are able to pass through eachother freely. I personally don't want to take this approach, it feels strange to me that the player should receive arbitrary damage for harmless contact to an enemy, despite whether the enemy is attacking or not, and I would like my enemies' interactions between each other (and my player) to be a little more organic, so to speak. In my head I sort of have this idea where a game object (player, or non player) would be able to push other game objects around by manner of 'pushing' each other out of one anothers' bounding boxes if there is an intersection, and maybe correlate the repelling force to how much their bounding boxes are intersecting. The problem I'm experiencing is I have no idea what the math might look like for something like this? I'll show what work I've done so far, it sort of works, but it's jittery, and generally not quite what I would pass in a functional game: //Clears the anti-duplicate buffer collisionRecord.Clear(); //pick a thing foreach (GameObject entity in entities) { //pick another thing foreach (GameObject subject in entities) { //check to make sure both things aren't the same thing if (!ReferenceEquals(entity, subject)) { //check to see if thing2 is in semi-near proximity to thing1 if (entity.WideProximityArea.Intersects(subject.CollisionRectangle) || entity.WideProximityArea.Contains(subject.CollisionRectangle)) { //check to see if thing2 and thing1 are colliding. if (entity.CollisionRectangle.Intersects(subject.CollisionRectangle) || entity.CollisionRectangle.Contains(subject.CollisionRectangle) || subject.CollisionRectangle.Contains(entity.CollisionRectangle)) { //check if we've already resolved their collision or not. if (!collisionRecord.ContainsKey(entity.GetHashCode())) { //more duplicate resolution checking. if (!collisionRecord.ContainsKey(subject.GetHashCode())) { //if thing1 is traveling right... if (entity.Velocity.X > 0) { //if it isn't too far to the right... if (subject.CollisionRectangle.Contains(new Microsoft.Xna.Framework.Rectangle(entity.CollisionRectangle.Right, entity.CollisionRectangle.Y, 1, entity.CollisionRectangle.Height)) || subject.CollisionRectangle.Intersects(new Microsoft.Xna.Framework.Rectangle(entity.CollisionRectangle.Right, entity.CollisionRectangle.Y, 1, entity.CollisionRectangle.Height))) { //Find how deep thing1 is intersecting thing2's collision box; float offset = entity.CollisionRectangle.Right - subject.CollisionRectangle.Left; //Move both things in opposite directions half the length of the intersection, pushing thing1 to the left, and thing2 to the right. entity.Velocities.Add(new Vector2(-(((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); subject.Velocities.Add(new Vector2((((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); } } //if thing1 is traveling left... if (entity.Velocity.X < 0) { //if thing1 isn't too far left... if (entity.CollisionRectangle.Contains(new Microsoft.Xna.Framework.Rectangle(subject.CollisionRectangle.Right, subject.CollisionRectangle.Y, 1, subject.CollisionRectangle.Height)) || entity.CollisionRectangle.Intersects(new Microsoft.Xna.Framework.Rectangle(subject.CollisionRectangle.Right, subject.CollisionRectangle.Y, 1, subject.CollisionRectangle.Height))) { //Find how deep thing1 is intersecting thing2's collision box; float offset = subject.CollisionRectangle.Right - entity.CollisionRectangle.Left; //Move both things in opposite directions half the length of the intersection, pushing thing1 to the right, and thing2 to the left. entity.Velocities.Add(new Vector2((((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); subject.Velocities.Add(new Vector2(-(((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); } } //Make record that thing1 and thing2 have interacted and the collision has been solved, so that if thing2 is picked next in the foreach loop, it isn't checked against thing1 a second time before the next update. collisionRecord.Add(entity.GetHashCode(), subject.GetHashCode()); } } } } } } } } One of the biggest issues with my code aside from the jitteriness is that if one character were to land on top of another character, it very suddenly and abruptly resolves the collision, whereas I would like a more subtle and gradual resolution. Any thoughts or ideas are incredibly welcome and helpful.

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• In SQL, if we rename INNER JOIN as INTERSECT JOIN, LEFT OUTER JOIN as LEFT UNION JOIN, and FULL OUTE

  - by Jian Lin

  In SQL, the name Join gives an idea of "merging" or a sense of "union", making something bigger. But in fact, as in the other post http://stackoverflow.com/questions/2706051/in-sql-a-join-is-actually-an-intersection-and-it-is-also-a-linkage-or-a-sidew it turns out that a Join (Inner Join) is actually an Intersection. So if we think of Join = Inner Join = Intersect Join Left Outer Join = Left Union Join Full Outer Join = Full Union Join = Union Join then we always get a feel of what's happening, and maybe never forget what they are easily. In a way, we can think of Intersect as "making it less", therefore it is excluding something. That's why the name "Join" won't go with the idea of "Intersect". But in fact, both Intersect and Union can be thought of as: Union: bringing something together and merge them unconditionally. Intersect: bringing something together and merge them based on some condition. so the "bringing something together" is probably what "Join" is all about. It is like, Intersection is a "half glass of water" -- we can thinking of it as "excluding something" or as "bringing something together and accepting the common ones". So if the word "Intersect Join" is used, maybe a clear picture is there, and "Union Join" can be a clear picture too. Maybe the word "Inner Join" and "Outer Join" is very clear when we use SQL a lot. Somehow, the word "Outer" tends to give a feeling that it is "outside" and excluding something rather than a "Union".

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• Examples of monoids/semigroups in programming

  - by jkff

  It is well-known that monoids are stunningly ubiquitous in programing. They are so ubiquitous and so useful that I, as a 'hobby project', am working on a system that is completely based on their properties (distributed data aggregation). To make the system useful I need useful monoids :) I already know of these: Numeric or matrix sum Numeric or matrix product Minimum or maximum under a total order with a top or bottom element (more generally, join or meet in a bounded lattice, or even more generally, product or coproduct in a category) Set union Map union where conflicting values are joined using a monoid Intersection of subsets of a finite set (or just set intersection if we speak about semigroups) Intersection of maps with a bounded key domain (same here) Merge of sorted sequences, perhaps with joining key-equal values in a different monoid/semigroup Bounded merge of sorted lists (same as above, but we take the top N of the result) Cartesian product of two monoids or semigroups List concatenation Endomorphism composition. Now, let us define a quasi-property of an operation as a property that holds up to an equivalence relation. For example, list concatenation is quasi-commutative if we consider lists of equal length or with identical contents up to permutation to be equivalent. Here are some quasi-monoids and quasi-commutative monoids and semigroups: Any (a+b = a or b, if we consider all elements of the carrier set to be equivalent) Any satisfying predicate (a+b = the one of a and b that is non-null and satisfies some predicate P, if none does then null; if we consider all elements satisfying P equivalent) Bounded mixture of random samples (xs+ys = a random sample of size N from the concatenation of xs and ys; if we consider any two samples with the same distribution as the whole dataset to be equivalent) Bounded mixture of weighted random samples Which others do exist?

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• Meaning of offset in pygame Mask.overlap methods

  - by Alan

  I have a situation in which two rectangles collide, and I have to detect how much did they collide so so I can redraw the objects in a way that they are only touching each others edges. It's a situation in which a moving ball should hit a completely unmovable wall and instantly stop moving. Since the ball sometimes moves multiple pixels per screen refresh, it it possible that it enters the wall with more that half its surface when the collision is detected, in which case i want to shift it position back to the point where it only touches the edges of the wall. Here is the conceptual image it: I decided to implement this with masks, and thought that i could supply the masks of both objects (wall and ball) and get the surface (as a square) of their intersection. However, there is also the offset parameter which i don't understand. Here are the docs for the method: Mask.overlap Returns the point of intersection if the masks overlap with the given offset - or None if it does not overlap. Mask.overlap(othermask, offset) -> x,y The overlap tests uses the following offsets (which may be negative): +----+----------.. |A | yoffset | +-+----------.. +--|B |xoffset | | : :

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• Algorithm to shoot at a target in a 3d game

  - by Sebastian Bugiu

  For those of you remembering Descent Freespace it had a nice feature to help you aim at the enemy when shooting non-homing missiles or lasers: it showed a crosshair in front of the ship you chased telling you where to shoot in order to hit the moving target. I tried using the answer from http://stackoverflow.com/questions/4107403/ai-algorithm-to-shoot-at-a-target-in-a-2d-game?lq=1 but it's for 2D so I tried adapting it. I first decomposed the calculation to solve the intersection point for XoZ plane and saved the x and z coordinates and then solving the intersection point for XoY plane and adding the y coordinate to a final xyz that I then transformed to clipspace and put a texture at those coordinates. But of course it doesn't work as it should or else I wouldn't have posted the question. From what I notice the after finding x in XoZ plane and the in XoY the x is not the same so something must be wrong. float a = ENG_Math.sqr(targetVelocity.x) + ENG_Math.sqr(targetVelocity.y) - ENG_Math.sqr(projectileSpeed); float b = 2.0f * (targetVelocity.x * targetPos.x + targetVelocity.y * targetPos.y); float c = ENG_Math.sqr(targetPos.x) + ENG_Math.sqr(targetPos.y); ENG_Math.solveQuadraticEquation(a, b, c, collisionTime); First time targetVelocity.y is actually targetVelocity.z (the same for targetPos) and the second time it's actually targetVelocity.y. The final position after XoZ is crossPosition.set(minTime * finalEntityVelocity.x + finalTargetPos4D.x, 0.0f, minTime * finalEntityVelocity.z + finalTargetPos4D.z); and after XoY crossPosition.y = minTime * finalEntityVelocity.y + finalTargetPos4D.y; Is my approach of separating into 2 planes and calculating any good? Or for 3D there is a whole different approach? sqr() is square not sqrt - avoiding a confusion.

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• share code between check and process methods

  - by undu

  My job is to refactor an old library for GIS vector data processing. The main class encapsulates a collection of building outlines, and offers different methods for checking data consistency. Those checking functions have an optional parameter that allows to perform some process. For instance: std::vector<Point> checkIntersections(int process_mode = 0); This method tests if some building outlines are intersecting, and return the intersection points. But if you pass a non null argument, the method will modify the outlines to remove the intersection. I think it's pretty bad (at call site, a reader not familiar with the code base will assume that a method called checkSomething only performs a check and doesn't modifiy data) and I want to change this. I also want to avoid code duplication as check and process methods are mostly similar. So I was thinking to something like this: // a private worker std::vector<Point> workerIntersections(int process_mode = 0) { // it's the equivalent of the current checkIntersections, it may perform // a process depending on process_mode } // public interfaces for check and process std::vector<Point> checkIntersections() /* const */ { workerIntersections(0); } std::vector<Point> processIntersections(int process_mode /*I have different process modes*/) { workerIntersections(process_mode); } But that forces me to break const correctness as workerIntersections is a non-const method. How can I separate check and process, avoiding code duplication and keeping const-correctness?

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• Triangle Picking Picking Back faces

  - by Tangeleno

  I'm having a bit of trouble with 3D picking, at first I thought my ray was inaccurate but it turns out that the picking is happening on faces facing the camera and faces facing away from the camera which I'm currently culling. Here's my ray creation code, I'm pretty sure the problem isn't here but I've been wrong before. private uint Pick() { Ray cursorRay = CalculateCursorRay(); Vector3? point = Control.Mesh.RayCast(cursorRay); if (point != null) { Tile hitTile = Control.TileMesh.GetTileAtPoint(point); return hitTile == null ? uint.MaxValue : (uint)(hitTile.X + hitTile.Y * Control.Generator.TilesWide); } return uint.MaxValue; } private Ray CalculateCursorRay() { Vector3 nearPoint = Control.Camera.Unproject(new Vector3(Cursor.Position.X, Control.ClientRectangle.Height - Cursor.Position.Y, 0f)); Vector3 farPoint = Control.Camera.Unproject(new Vector3(Cursor.Position.X, Control.ClientRectangle.Height - Cursor.Position.Y, 1f)); Vector3 direction = farPoint - nearPoint; direction.Normalize(); return new Ray(nearPoint, direction); } public Vector3 Camera.Unproject(Vector3 source) { Vector4 result; result.X = (source.X - _control.ClientRectangle.X) * 2 / _control.ClientRectangle.Width - 1; result.Y = (source.Y - _control.ClientRectangle.Y) * 2 / _control.ClientRectangle.Height - 1; result.Z = source.Z - 1; if (_farPlane - 1 == 0) result.Z = 0; else result.Z = result.Z / (_farPlane - 1); result.W = 1f; result = Vector4.Transform(result, Matrix4.Invert(ProjectionMatrix)); result = Vector4.Transform(result, Matrix4.Invert(ViewMatrix)); result = Vector4.Transform(result, Matrix4.Invert(_world)); result = Vector4.Divide(result, result.W); return new Vector3(result.X, result.Y, result.Z); } And my triangle intersection code. Ripped mainly from the XNA picking sample. public float? Intersects(Ray ray) { float? closestHit = Bounds.Intersects(ray); if (closestHit != null && Vertices.Length == 3) { Vector3 e1, e2; Vector3.Subtract(ref Vertices[1].Position, ref Vertices[0].Position, out e1); Vector3.Subtract(ref Vertices[2].Position, ref Vertices[0].Position, out e2); Vector3 directionCrossEdge2; Vector3.Cross(ref ray.Direction, ref e2, out directionCrossEdge2); float determinant; Vector3.Dot(ref e1, ref directionCrossEdge2, out determinant); if (determinant > -float.Epsilon && determinant < float.Epsilon) return null; float inverseDeterminant = 1.0f/determinant; Vector3 distanceVector; Vector3.Subtract(ref ray.Position, ref Vertices[0].Position, out distanceVector); float triangleU; Vector3.Dot(ref distanceVector, ref directionCrossEdge2, out triangleU); triangleU *= inverseDeterminant; if (triangleU < 0 || triangleU > 1) return null; Vector3 distanceCrossEdge1; Vector3.Cross(ref distanceVector, ref e1, out distanceCrossEdge1); float triangleV; Vector3.Dot(ref ray.Direction, ref distanceCrossEdge1, out triangleV); triangleV *= inverseDeterminant; if (triangleV < 0 || triangleU + triangleV > 1) return null; float rayDistance; Vector3.Dot(ref e2, ref distanceCrossEdge1, out rayDistance); rayDistance *= inverseDeterminant; if (rayDistance < 0) return null; return rayDistance; } return closestHit; } I'll admit I don't fully understand all of the math behind the intersection and that is something I'm working on, but my understanding was that if rayDistance was less than 0 the face was facing away from the camera, and shouldn't be counted as a hit. So my question is, is there an issue with my intersection or ray creation code, or is there another check I need to perform to tell if the face is facing away from the camera, and if so any hints on what that check might contain would be appreciated.

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• PropertyGrid: Merging multiple dynamic properties when editing multiple objects

  - by Andrei Stanescu

  Hi, Let's say I have a class A and a class B. I would like to edit using .NET PropertyGrid multiple instances of A and B simultaneously. The desired behavior would be to have the intersection of properties displayed. If A and B have static (written in the source code) properties everything works fine. Selecting A and B instances will only display the intersection of properties. However, if A and B also have dynamic properties (returned as a PropertyDescriptorCollection through the GetProperties() method) the behavior is wrong. When selecting multiple objects I will only see those static properties and none of the dynamic ones. When I select only one instance I can see all properties (static and dynamic). Anybody any ideas? I couldn't find anything on the internet.

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• Grouping rectangles (getting the bounding boxes of rects)

  - by hyn

  What is a good, fast way to get the "final" bounding boxes of a set of random (up to about 40, not many) rectangles? By final I mean that all bounding boxes don't intersect with any other. Brute force way: in a double for loop, for each rect, test for intersection against every other rect. The intersecting rects become a new rect (replaced), indicating the bounding box. Start over and repeat until no intersection is detected. Because the rects are random every time, and the rect count is relatively small, collision detection using spatial hashing seems like overkill. Is there a way to do this more effectively?

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• Using set in Python inside a loop

  - by user210481

  I have the following list in Python: [[1, 2], [3, 4], [4, 6], [2, 7], [3, 9]] I want to group them into [[1,2,7],[3,4,6,7]] My code to do this looks like this: l=[[1, 2], [3, 4], [4, 6], [2, 7], [3, 9]] lf=[] for li in l: for lfi in lf: if lfi.intersection(set(li)): lfi=lfi.union(set(li)) break else: lf.append(set(li)) lf is my final list. I do a loop over l and lf and when I find an intersection between an element from l and another from lf, I would like to merge them (union) But I can't figure out why this is not working. The first to elements of the list l are being inserted with the append command, but the union is not working. My final list lf looks like [set([1, 2]), set([3, 4])] It seems to be something pretty basic, but I'm not familiar with sets. I appreciate any help Thanks

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• Equivalence Classes

  - by orcik

  I need to write a program for equivalence classes and get this outputs... (equiv '((a b) (a c) (d e) (e f) (c g) (g h))) => ((a b c g h) (d e f)) (equiv '((a b) (c d) (e f) (f g) (a e))) => ((a b e f g) (c d)) Basically, A set is a list in which the order doesn't matter, but elements don't appear more than once. The function should accept a list of pairs (elements which are related according to some equivalence relation), and return a set of equivalence classes without using iteration or assignment statements (e.g. do, set!, etc.). However, set utilities such as set-intersection, set-union and a function which eliminates duplicates in a list and built-in functions union, intersection, and remove-duplicates are allowed. Thanks a lot! By the way, It's not a homework question. A friend of mine need this piece of code to solve smilar questions.

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• Real life usage of the projective plane theory

  - by Elazar Leibovich

  I'm learning about the theory of the projective plane. Very generally speaking, it is an extension of the plane, which includes additional points which are defined as the intersection points of two parallel lines. In the projective plane, every two lines have an interesection point. Whether they're parallel or not. Every point in the projective plane can be represented by three numbers (you actually need less than that, but nevemind now). Is there any real life application which uses the projective plane? I can think that, for instance, a software which needs to find the intersections of a line, can benefit from always having an intersection point which might lead to simpler code, but is it really used?

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• Finding all points common to two circles

  - by Dustin I.

  In Python, how would one find all points common to two circles? For example, imagine a Venn diagram-like intersection of two (equally sized) circles, with center-points (x1,y1) and (x2,y2) and radii r1=r2. Additionally, we already know the two points of intersection of the circles are (xi1,yi1) and (xi2,yi2). How would one generate a list of all points (x,y) contained in both circles in an efficient manner? That is, it would be simple to draw a box containing the intersections and iterate through it, checking if a given point is within both circles, but is there a better way?

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• Linked lists in Java - help with assignment

  - by user368241

  Representation of a string in linked lists In every intersection in the list there will be 3 fields : The letter itself. The number of times it appears consecutively. A pointer to the next intersection in the list. The following class CharNode represents a intersection in the list : public class CharNode { private char _data; private int _value; private charNode _next; public CharNode (char c, int val, charNode n) { _data = c; _value = val; _next = n; } public charNode getNext() { return _next; } public void setNext (charNode node) { _next = node; } public int getValue() { return _value; } public void setValue (int v) { value = v; } public char getData() { return _data; } public void setData (char c) { _data = c; } } The class StringList represents the whole list : public class StringList { private charNode _head; public StringList() { _head = null; } public StringList (CharNode node) { _head = node; } } Add methods to the class StringList according to the details : (I will add methods gradually according to my specific questions) (Pay attention, these are methods from the class String and we want to fulfill them by the representation of a string by a list as explained above) public int indexOf (int ch) - returns the index in the string it is operated on of the first appeareance of the char "ch". If the char "ch" doesn't appear in the string, returns -1. If the value of fromIndex isn't in the range, returns -1. Pay attention to all the possible error cases. Write what is the time complexity and space complexity of every method that you wrote. Make sure the methods you wrote are effective. It is NOT allowed to use ready classes of Java. It is NOT allowed to move to string and use string operations. Here is my try to write the method indexOf (int ch). Kindly assist me with fixing the bugs so I can move on. public int indexOf (int ch) { int count = 0; charNode pose = _head; if (pose == null ) { return -1; } for (pose = _head; pose!=null && pose.getNext()!='ch'; pose = pose.getNext()) { count++; } if (pose!=null) return count; else return -1; }

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• Equivalence Classes LISP

  - by orcik

  I need to write a program for equivalence classes and get this outputs... (equiv '((a b) (a c) (d e) (e f) (c g) (g h))) => ((a b c g h) (d e f)) (equiv '((a b) (c d) (e f) (f g) (a e))) => ((a b e f g) (c d)) Basically, A set is a list in which the order doesn't matter, but elements don't appear more than once. The function should accept a list of pairs (elements which are related according to some equivalence relation), and return a set of equivalence classes without using iteration or assignment statements (e.g. do, set!, etc.). However, set utilities such as set-intersection, set-union and a function which eliminates duplicates in a list and built-in functions union, intersection, and remove-duplicates are allowed. Thanks a lot!

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