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  • How to Zip one IEnumerable with itself

    - by wageoghe
    I am implementing some math algorithms based on lists of points, like Distance, Area, Centroid, etc. Just like in this post: http://stackoverflow.com/questions/2227828/find-the-distance-required-to-navigate-a-list-of-points-using-linq That post describes how to calculate the total distance of a sequence of points (taken in order) by essentially zipping the sequence "with itself", generating the sequence for Zip by offsetting the start position of the original IEnumerable by 1. So, given the Zip extension in .Net 4.0, assuming Point for the point type, and a reasonable Distance formula, you can make calls like this to generate a sequence of distances from one point to the next and then to sum the distances: var distances = points.Zip(points.Skip(1),Distance); double totalDistance = distances.Sum(); Area and Centroid calculations are similar in that they need to iterate over the sequence, processing each pair of points (points[i] and points[i+1]). I thought of making a generic IEnumerable extension suitable for implementing these (and possibly other) algorithms that operate over sequences, taking two items at a time (points[0] and points[1], points[1] and points[2], ..., points[n-1] and points[n] (or is it n-2 and n-1 ...) and applying a function. My generic iterator would have a similar signature to Zip, but it would not receive a second sequence to zip with as it is really just going to zip with itself. My first try looks like this: public static IEnumerable<TResult> ZipMyself<TSequence, TResult>(this IEnumerable<TSequence> seq, Func<TSequence, TSequence, TResult> resultSelector) { return seq.Zip(seq.Skip(1),resultSelector); } With my generic iterator in place, I can write functions like this: public static double Length(this IEnumerable<Point> points) { return points.ZipMyself(Distance).Sum(); } and call it like this: double d = points.Length(); and double GreensTheorem(Point p1, Point p1) { return p1.X * p2.Y - p1.Y * p2.X; } public static double SignedArea(this IEnumerable<Point> points) { return points.ZipMyself(GreensTheorem).Sum() / 2.0 } public static double Area(this IEnumerable<Point> points) { return Math.Abs(points.SignedArea()); } public static bool IsClockwise(this IEnumerable<Point> points) { return SignedArea(points) < 0; } and call them like this: double a = points.Area(); bool isClockwise = points.IsClockwise(); In this case, is there any reason NOT to implement "ZipMyself" in terms of Zip and Skip(1)? Is there already something in LINQ that automates this (zipping a list with itself) - not that it needs to be made that much easier ;-) Also, is there better name for the extension that might reflect that it is a well-known pattern (if, indeed it is a well-known pattern)? Had a link here for a StackOverflow question about area calculation. It is question 2432428. Also had a link to Wikipedia article on Centroid. Just go to Wikipedia and search for Centroid if interested. Just starting out, so don't have enough rep to post more than one link,

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  • Google earth GEOdata ?

    - by Quandary
    Question: Is it possible to use/retrieve Geodata from Google-Earth ? What I want to do is take a little area, get terrain information (coordinates, height, elevation) and simulate how the selected area would be flooded at specified amounts of rain for a specified amount of hours.

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  • Compute bounding quad of a sphere with vertex shader

    - by Ben Jones
    I'm trying to implement an algorithm from a graphics paper and part of the algorithm is rendering spheres of known radius to a buffer. They say that they render the spheres by computing the location and size in a vertex shader and then doing appropriate shading in a fragment shader. Any guesses as to how they actually did this? The position and radius are known in world coordinates and the projection is perspective. Does that mean that the sphere will be projected as a circle? Thanks!

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  • Draw fitted line (OpenCV)

    - by Sunny
    I'm using OpenCV to fit a line from a set of points using cvFitLine() cvFitLine() returns a normalized vector that is co-linear to the line and a point on the line. See details here Using this information how can I get the equation of a line so that I can draw the line?

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  • Raytracing (LoS) on 3D hex-like tile maps

    - by herenvardo
    Greetings, I'm working on a game project that uses a 3D variant of hexagonal tile maps. Tiles are actually cubes, not hexes, but are laid out just like hexes (because a square can be turned to a cube to extrapolate from 2D to 3D, but there is no 3D version of a hex). Rather than a verbose description, here goes an example of a 4x4x4 map: (I have highlighted an arbitrary tile (green) and its adjacent tiles (yellow) to help describe how the whole thing is supposed to work; but the adjacency functions are not the issue, that's already solved.) I have a struct type to represent tiles, and maps are represented as a 3D array of tiles (wrapped in a Map class to add some utility methods, but that's not very relevant). Each tile is supposed to represent a perfectly cubic space, and they are all exactly the same size. Also, the offset between adjacent "rows" is exactly half the size of a tile. That's enough context; my question is: Given the coordinates of two points A and B, how can I generate a list of the tiles (or, rather, their coordinates) that a straight line between A and B would cross? That would later be used for a variety of purposes, such as determining Line-of-sight, charge path legality, and so on. BTW, this may be useful: my maps use the (0,0,0) as a reference position. The 'jagging' of the map can be defined as offsetting each tile ((y+z) mod 2) * tileSize/2.0 to the right from the position it'd have on a "sane" cartesian system. For the non-jagged rows, that yields 0; for rows where (y+z) mod 2 is 1, it yields 0.5 tiles. I'm working on C#4 targeting the .Net Framework 4.0; but I don't really need specific code, just the algorithm to solve the weird geometric/mathematical problem. I have been trying for several days to solve this at no avail; and trying to draw the whole thing on paper to "visualize" it didn't help either :( . Thanks in advance for any answer

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  • Get most left|right|top|bottom point contained in box

    - by skyman
    I'm storing Points Of Interest (POI) in PostgreSQL database, and retrieve them via PHP script to Android application. To reduce internet usage I want my mobile app to know if there are any points in the neighborhood of currently displayed area. My idea is to store bounds of the rectangle containing all points already retrieved (in other words: nearest point on the left (West) of most west already retrieved, nearest point above (North) of most north already retrieved etc.) and I will make next query when any edge of screen goes outside of this bounds. Currently I can retrieve points which are in "single screen" (in the area covered by currently displayed map) using: SELECT * FROM ch WHERE loc <@ (box '((".-$latSpan.", ".$lonSpan."),(".$latSpan.", ".-$lonSpan."))' + point '".$loc."') Now I need to know four most remote points in each direction, than I will be able to retrieve next four "more remote" points. Is there any possibility to get those points (or box) directly from PostgreSQL (maybe using some "aggregate points to box" function)?

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  • Soft Shadows in Raytracing 3D to 2D

    - by Myx
    Hello: I wish to implement soft shadows produced by area lights in my raytracer. I'm having trouble generating the random samples. So I have a scene in which I have an area light (represented as a circle) whose world (x,y,z) coordinates of the center are given, the radius is given, the normal of the plane on which the circle lies is given, as well as the color and attenuation factors. The sampling scheme I wish to use is the following: generate samples on the quadrilateral that encompasses the circle and discard points outside the circle until the required number of samples within the circle have been found. I'm having trouble understanding how I can transform the 3D coordinates of the center of the circle to its 2D representation (I don't think I can assume that the projection of the circle is on the x-y axis and thus just get rid of the z-component). I think the plane normal information should be used but I'm not sure how. Any and all suggestions are appreciated.

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  • Compute average distance from point to line segment and line segment to line segment

    - by Fred
    Hi everyone, I'm searching for an algorithm to calculate the average distance between a point and a line segment in 3D. So given two points A(x1, y1, z1) and B(x2, y2, z2) that represent line segment AB, and a third point C(x3, y3, z3), what is the average distance between each point on AB to point C? I'm also interested in the average distance between two line segments. So given segment AB and CD, what is the average distance from each point on AB to the closest point on CD? I haven't had any luck with the web searches I've tried, so any suggestions would be appreciated. Thanks.

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  • Find unique vertices from a 'triangle-soup'

    - by sum1stolemyname
    I am building a CAD-file converter on top of two libraries (Opencascade and DWF Toolkit). However, my question is plattform agnostic: Given: I have generated a mesh as a list of triangular faces form a model constructed through my application. Each Triangle is defined through three vertexes, which consist of three floats (x, y & z coordinate). Since the triangles form a mesh, most of the vertices are shared by more then one triangle. Goal: I need to find the list of unique vertices, and to generate an array of faces consisting of tuples of three indices in this list. What i want to do is this: //step 1: build a list of unique vertices for each triangle for each vertex in triangle if not vertex in listOfVertices Add vertex to listOfVertices //step 2: build a list of faces for each triangle for each vertex in triangle Get Vertex Index From listOfvertices AddToMap(vertex Index, triangle) While I do have an implementation which does this, step1 (the generation of the list of unique vertices) is really slow in the order of O(n!), since each vertex is compared to all vertices already in the list. I thought "Hey, lets build a hashmap of my vertices' components using std::map, that ought to speed things up!", only to find that generating a unique key from three floating point values is not a trivial task. Here, the experts of stackoverflow come into play: I need some kind of hash-function which works on 3 floats, or any other function generating a unique value from a 3d-vertex position.

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  • Converting from Latitude/Longitude to Cartesian Coordinates with a World File and map image.

    - by Heath
    I have a java applet that allows users to import a jpeg and world file from the local system. The user can then "click" draw lines on the image that was imported. Each endpoint of each line contains a set of X/Y and Lat/Long values. The XY is standard java coordinate space, the applet uses an affine transform calculation with the world file to determine the lat/long for every point on the canvas. I have a requirement that allows a user to type a distance into a text field and use the arrow key to draw a line in a certain direction (Up, Down, Left, Right) from a single selected point on the screen. I know how to determine the lat/long of a point given a source lat/long, distance, and bearing. So a user types "100" in the text field and presses the Right arrow key a line should be drawn 100 feet to the right from the currently selected point. My issue is I don't know how to convert the distance( which is in feet ) into the distance in pixels. This would then tell my where to plot the point.

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  • Implementation of any Hamiltonian Path Problem algorithm

    - by Julien
    Hi all ! Here is my problem : I have an array of points, the points have three properties : the "x" and "y" coordinates, and a sequence number "n". The "x" and "y" are defined for all the points, the "n" are not. You can access and write them calling points[i]-x, points[i]-y, points[i]-n. i.e. : points[i]->n = var var = points[i]->n So the title maybe ruined the surprise, but I'm looking for a possible implementation of a solution to the Hamiltonian path problem : I need to set the "n" number of each point, so that the sequence is the shortest path (not cycle, the edges have to be disjoint) that goes exactly once through each point. I looked for a solution and I found The Bellman Ford Algorithm but I think it doesn't work since the problem doesn't specify that it has to go through all of the points is it correct ? If it is, does somebody has another algorithm and the implementation ? If the Bellman Ford Algorithm works, how would I implement it ? Thanks a lot, Julien

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  • How to detect if an ellipse intersects(collides with) a circle

    - by php html
    I want to improve a collision system. Right now I detect if 2 irregular objects collide if their bounding rectangles collide. I want to obtain the for rectangle the corresponding ellipse while for the other one to use a circle. I found a method to obtain the ellipse coordinates but I have a problem when I try to detect if it intersects the circle. Do you know a algorithm to test if a circle intersects an ellipse?

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  • How to calculate the length of a Path2D in Java?

    - by Sanoj
    I have some paths represented by Path2D. The Path consist of multiple CubicCurve2D or Line2D segments that are connected to each other. I would like to calculate or get the length from the start to the end of a Path. How can I calculate it or get it? Is it possible? I have checked the API documentation, but couldn't find any useful methods.

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  • formula for best approximation for center of 2D rotation with small angles

    - by RocketSurgeon
    This is not a homework. I am asking to see if problem is classical (trivial) or non-trivial. It looks simple on a surface, and I hope it is truly a simple problem. Have N points (N = 2) with coordinates Xn, Yn on a surface of 2D solid body. Solid body has some small rotation (below Pi/180) combined with small shifts (below 1% of distance between any 2 points of N). Possibly some small deformation too (<<0.001%) Same N points have new coordinates named XXn, YYn Calculate with best approximation the location of center of rotation as point C with coordinates XXX, YYY. Thank you

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  • Bounding Boxes for Circle and Arcs in 3D

    - by David Rutten
    Given curves of type Circle and Circular-Arc in 3D space, what is a good way to compute accurate bounding boxes (world axis aligned)? Edit: found solution for circles, still need help with Arcs. C# snippet for solving BoundingBoxes for Circles: public static BoundingBox CircleBBox(Circle circle) { Point3d O = circle.Center; Vector3d N = circle.Normal; double ax = Angle(N, new Vector3d(1,0,0)); double ay = Angle(N, new Vector3d(0,1,0)); double az = Angle(N, new Vector3d(0,0,1)); Vector3d R = new Vector3d(Math.Sin(ax), Math.Sin(ay), Math.Sin(az)); R *= circle.Radius; return new BoundingBox(O - R, O + R); } private static double Angle(Vector3d A, Vector3d B) { double dP = A * B; if (dP <= -1.0) { return Math.PI; } if (dP >= +1.0) { return 0.0; } return Math.Acos(dP); }

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  • WPF: Combine Geometries / Canvas for Geometries?

    - by stefan.at.wpf
    Hello, I have 2 geometries A and B which I'd like to combine like shown at the end of the following drawing: http://www.imagebanana.com/view/9vm6zoy/geocombine.png How could one do this? Is there something like a "virtual canvas for geometries" where I can place A and B, move B accordingly and then get a geometrie from this? Thanks for any hint!

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  • Parallel curve like algorithm for graphs

    - by skrat
    Is there a well know algorithm for calculating "parallel graph"? where by parallel graph I mean the same as parallel curve, vaguely called "offset curve", but with a graph instead of a curve. Given this picture how can I calculate points of black outlined polygons?

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  • comparing two angles

    - by Elazar Leibovich
    Given four points in the plane, A,B,X,Y, I wish to determine which of the following two angles is smaller ?ABX or ?ABY. I'd rather not use cos or sqrt, in order to preserve accuracy. In the case where A=(-1,0),B=(0,0), I can compare the two angles ?ABX and ?ABY, by calculating the dot product of the vectors X,Y, and watch it's sign. What I can do in this case is: Determine whether or not ABX turns right or left If ABX turns left check whether or not Y and A are on the same side of the line on segment BX. If they are - ?ABX is a smaller than ABY. If ABX turns right, then Y and A on the same side of BX means that ?ABX is larger than ?ABY. But this seems too complicated to me. Any simpler approach?

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  • Union of complex polygons

    - by grenade
    Given two polygons: POLYGON((1 0, 1 8, 6 4, 1 0)) POLYGON((4 1, 3 5, 4 9, 9 5, 4 1),(4 5, 5 7, 6 7, 4 4, 4 5)) How can I calculate the union (combined polygon)? Dave's example uses SQL server to produce the union, but I need to accomplish the same in code. I'm looking for a mathematical formula or code example in any language that exposes the actual math. I am attempting to produce maps that combine countries dynamically into regions. I asked a related question here: http://stackoverflow.com/questions/2653812/grouping-geographical-shapes

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  • Algorithm to merge adjacent rectangles into polygon

    - by Glitch
    I guess that my problem is related to "convex hull", but no the same. All shapes in the drawing are rectangles with same width and height. Many are adjacent to each other. I want to combine those adjacent rectangles into polygons. Unlike "convex hull", the resuled polygons could be "hollow" inside. Is there any open source algorithm available?

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  • How do I arbitrarily distort a textured polygon?

    - by Archagon
    I'd like to write a program that lets me arbitrarily distort a textured polygon by dragging its vertices. I want the texture to distort fluidly and without overlap, assuming the new polygon doesn't intersect itself. I should also be able to repeat the process with the new shape, and with a minimum amount of loss. Are there any algorithms for doing this?

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  • How to find two most distant points?

    - by depesz
    This is a question that I was asked on a job interview some time ago. And I still can't figure out sensible answer. Question is: you are given set of points (x,y). Find 2 most distant points. Distant from each other. For example, for points: (0,0), (1,1), (-8, 5) - the most distant are: (1,1) and (-8,5) because the distance between them is larger from both (0,0)-(1,1) and (0,0)-(-8,5). The obvious approach is to calculate all distances between all points, and find maximum. The problem is that it is O(n^2), which makes it prohibitively expensive for large datasets. There is approach with first tracking points that are on the boundary, and then calculating distances for them, on the premise that there will be less points on boundary than "inside", but it's still expensive, and will fail in worst case scenario. Tried to search the web, but didn't find any sensible answer - although this might be simply my lack of search skills.

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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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  • uniform generation of points on 3D box

    - by Myx
    Hello: I would like to generate random points on a 3D box defined by its (minx, miny, minz) and (maxx, maxy, maxz) corners. I was thinking of generating a random point inside of the box and then somehow projecting it onto one of the box sides. However, I don't have explicit plane information for the box sides and this seems like it will not produce a uniform distribution of points since if some sides of the box are bigger than others, those sides should have more points generated on them. Any suggestions are appreciated. Thanks.

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