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  • Algorithm: Determine shape of two sectors delineated by an arbitrary path, and then fill one.

    - by Arseniy Banayev
    NOTE: This is a challenging problem for anybody who likes logic problems, etc. Consider a rectangular two-dimensional grid of height H and width W. Every space on the grid has a value, either 0 1 or 2. Initially, every space on the grid is a 0, except for the spaces along each of the four edges, which are initially a 2. Then consider an arbitrary path of adjacent (horizontally or vertically) grid spaces. The path begins on a 2 and ends on a different 2. Every space along the path is a 1. The path divides the grid into two "sectors" of 0 spaces. There is an object that rests on an unspecified 0 space. The "sector" that does NOT contain the object must be filled completely with 2. Define an algorithm that determines the spaces that must become 2 from 0, given an array (list) of values (0, 1, or 2) that correspond to the values in the grid, going from top to bottom and then from left to right. In other words, the element at index 0 in the array contains the value of the top-left space in the grid (initially a 2). The element at index 1 contains the value of the space in the grid that is in the left column, second from the top, and so forth. The element at index H contains the value of the space in the grid that is in the top row but second from the left, and so forth. Once the algorithm finishes and the empty "sector" is filled completely with 2s, the SAME algorithm must be sufficient to do the same process again. The second (and on) time, the path is still drawn from a 2 to a different 2, across spaces of 0, but the "grid" is smaller because the 2s that are surrounded by other 2s cannot be touched by the path (since the path is along spaces of 0). I thank whomever is able to figure this out for me, very very much. This does not have to be in a particular programming language; in fact, pseudo-code or just English is sufficient. Thanks again! If you have any questions, just leave a comment and I'll specify what needs to be specified.

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  • Largest triangle from a set of points

    - by Faken
    I have a set of random points from which i want to find the largest triangle by area who's verticies are each on one of those points. So far I have figured out that the largest triangle's verticies will only lie on the outside points of the cloud of points (or the convex hull) so i have programmed a function to do just that (using Graham scan in nlogn time). However that's where I'm stuck. The only way I can figure out how to find the largest triangle from these points is to use brute force at n^3 time which is still acceptable in an average case as the convex hull algorithm usually kicks out the vast majority of points. However in a worst case scenario where points are on a circle, this method would fail miserably. Dose anyone know an algorithm to do this more efficiently? Note: I know that CGAL has this algorithm there but they do not go into any details on how its done. I don't want to use libraries, i want to learn this and program it myself (and also allow me to tweak it to exactly the way i want it to operate, just like the graham scan in which other implementations pick up collinear points that i don't want).

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  • smallest perimiter rectangle with given integer area and integer sides

    - by remuladgryta
    Given an integer area A, how can one find integer sides w and h of a rectangle such that w*h = A and w+h is as small as possible? I'd rather the algorithm be simple than efficient (although within reasonable efficiency). What would be the best way to accomplish this? Finding out the prime factors of A, then combining them in some way that tries to balance w and h? Finding the two squares with integer sides with areas closest to A and then somehow interpolating between them? Any other method i'm not thinking of?

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  • Find the centroid of a polygon with weighted vertices

    - by Calle Kabo
    Hi, I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight? Simplified illustration of what I mean using straight line: 5kg-----------------5kg ^center of gravity 10kg---------------5kg ^center of gravity offset du to weight of vertices Of course, I know how to calculate the center of gravity on a straight line with weighted vertices, but how do I do it on a polygon with weighted vertices? Thanks for your time!

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  • Efficiently remove points with same slope

    - by Ram
    Hi, In one of mine applications I am dealing with graphics objects. I am using open source GPC library to clip/merge two shapes. To improve accuracy I am sampling (adding multiple points between two edges) existing shapes. But before displaying back the merged shape I need to remove all the points between two edges. But I am not able to find an efficient algorithm that will remove all points between two edges which has same slope with minimum CPU utilization. Currently all points are of type PointF Any pointer on this will be a great help.

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  • 3D line plane intersection, with simple plane

    - by clamp
    hello, i have two points in 3D space which have X-coordinates with different signum. so one of them lies definitely on one side of the X-plane and one on the other. now i want to find the intersection of this plane and the line made up by the two points in the most simple and optimized way. i know how to do general line plane intersection, but since in this case the plane is just the x-plane, i think there should be some shortcuts i can take. thanks!

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  • .NET Ascertaining mouse is on line drawn between two arbitrary points

    - by johnc
    I have an arrow drawn between two objects on a Winform. What would be the simplest way to determine that my mouse is currently hovering over, or near, this line. I have considered testing whether the mouse point intersects a square defined and extrapolated by the two points, however this would only be feasible if the two points had very similar x or y values. I am thinking, also, this problem is probably more in the realms of linear algebra rather than simple trigonometry, and whilst I do remember the simpler aspects of matrices, this problem is beyond my knowledge of linear algebra. On the other hand, if a .NET library can cope with the function, even better.

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  • Coloring close points

    - by ooboo
    I have a dense set of points in the plane. I want them colored so that points that are close to each other have the same color, and a different color if they're far away. For simplicity assume that there are, say, 5 different colors to choose from. Turns out I've not the slightest idea how to do that .. I'm using Tkinter with Python, by the way

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  • Ray-triangle intersetion

    - by gamemaker
    Hello! How can I test intersesion ray and triangle, and if it exist how to get distance from ray origin to intersection point?? What optimization I can use, if in my program I've got to check 1 ray to ~10000 triangles ??

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  • Two parallel line segments intersection

    - by Judarkness
    I know there are many algorithms to verify whether two line segments are intersected. But once they encountered parallel condition, they just tell the user a big "No" and pretend there is no overlap, share end point, or end point collusion. I know I can can calculate the distance between 2 lines segments. If the distance is 0, check the end points located in the other line segments or not. And this means I have to use a lot of if else and && || conditions. This is not difficult, but my question is "Is there a trick( or mathematics) method to calculate this special parallel case?"

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  • Find the set of largest contiguous rectangles to cover multiple areas

    - by joelpt
    I'm working on a tool called Quickfort for the game Dwarf Fortress. Quickfort turns spreadsheets in csv/xls format into a series of commands for Dwarf Fortress to carry out in order to plot a "blueprint" within the game. I am currently trying to optimally solve an area-plotting problem for the 2.0 release of this tool. Consider the following "blueprint" which defines plotting commands for a 2-dimensional grid. Each cell in the grid should either be dug out ("d"), channeled ("c"), or left unplotted ("."). Any number of distinct plotting commands might be present in actual usage. . d . d c c d d d d c c . d d d . c d d d d d c . d . d d c To minimize the number of instructions that need to be sent to Dwarf Fortress, I would like to find the set of largest contiguous rectangles that can be formed to completely cover, or "plot", all of the plottable cells. To be valid, all of a given rectangle's cells must contain the same command. This is a faster approach than Quickfort 1.0 took: plotting every cell individually as a 1x1 rectangle. This video shows the performance difference between the two versions. For the above blueprint, the solution looks like this: . 9 . 0 3 2 8 1 1 1 3 2 . 1 1 1 . 2 7 1 1 1 4 2 . 6 . 5 4 2 Each same-numbered rectangle above denotes a contiguous rectangle. The largest rectangles take precedence over smaller rectangles that could also be formed in their areas. The order of the numbering/rectangles is unimportant. My current approach is iterative. In each iteration, I build a list of the largest rectangles that could be formed from each of the grid's plottable cells by extending in all 4 directions from the cell. After sorting the list largest first, I begin with the largest rectangle found, mark its underlying cells as "plotted", and record the rectangle in a list. Before plotting each rectangle, its underlying cells are checked to ensure they are not yet plotted (overlapping a previous plot). We then start again, finding the largest remaining rectangles that can be formed and plotting them until all cells have been plotted as part of some rectangle. I consider this approach slightly more optimized than a dumb brute-force search, but I am wasting a lot of cycles (re)calculating cells' largest rectangles and checking underlying cells' states. Currently, this rectangle-discovery routine takes the lion's share of the total runtime of the tool, especially for large blueprints. I have sacrificed some accuracy for the sake of speed by only considering rectangles from cells which appear to form a rectangle's corner (determined using some neighboring-cell heuristics which aren't always correct). As a result of this 'optimization', my current code doesn't actually generate the above solution correctly, but it's close enough. More broadly, I consider the goal of largest-rectangles-first to be a "good enough" approach for this application. However I observe that if the goal is instead to find the minimum set (fewest number) of rectangles to completely cover multiple areas, the solution would look like this instead: . 3 . 5 6 8 1 3 4 5 6 8 . 3 4 5 . 8 2 3 4 5 7 8 . 3 . 5 7 8 This second goal actually represents a more optimal solution to the problem, as fewer rectangles usually means fewer commands sent to Dwarf Fortress. However, this approach strikes me as closer to NP-Hard, based on my limited math knowledge. Watch the video if you'd like to better understand the overall strategy; I have not addressed other aspects of Quickfort's process, such as finding the shortest cursor-path that plots all rectangles. Possibly there is a solution to this problem that coherently combines these multiple strategies. Help of any form would be appreciated.

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  • circles and triangles problem

    - by Faken
    Hello everyone, I have an interesting problem here I've been trying to solve for the last little while: I have 3 circles on a 2D xy plane, each with the same known radius. I know the coordinates of each of the three centers (they are arbitrary and can be anywhere). What is the largest triangle that can be drawn such that each vertice of the triangle sits on a separate circle, what are the coordinates of those verticies? I've been looking at this problem for hours and asked a bunch of people but so far only one person has been able to suggest a plausible solution (though i have no way of proving it). The solution that we have come up with involves first creating a triangle about the three circle centers. Next we look at each circle individually and calculate the equation of a line that passes through the circle's center and is perpendicular to the opposite edge. We then calculate two intersection points of the circle. This is then done for the next two circles with a result of 6 points. We iterate over the 8 possible 3 point triangles that these 6 points create (the restriction is that each point of the big triangle must be on a separate circle) and find the maximum size. The results look reasonable (at least when drawn out on paper) and it passes the special case of when the centers of the circles all fall on a straight line (gives a known largest triangle). Unfortunate i have no way of proving this is correct or not. I'm wondering if anyone has encountered a problem similar to this and if so, how did you solve it? Note: I understand that this is mostly a math question and not programming, however it is going to be implemented in code and it must be optimized to run very fast and efficient. In fact, I already have the above solution in code and tested to be working, if you would like to take a look, please let me know, i chose not to post it because its all in vector form and pretty much impossible to figure out exactly what is going on (because it's been condensed to be more efficient). Lastly, yes this is for school work, though it is NOT a homework question/assignment/project. It's part of my graduate thesis (abet a very very small part, but still technically is part of it). Thanks for your help.

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  • Does Quartz2D test intersection of rect by line before drawing it.

    - by ddnv
    I'm drawing a big scheme that consist of a lot of lines. I do it in the drawRect: method of UIView. The scheme is larger than the layer of view and I check each line and draw it only if it intersects the visible rect. But at one moment I thought, should I do this? Maybe Quartz is already doing this test? So the question is: When I use function CGContextAddLineToPoint() does the Core Graphics tests this line for intersection with layer rect or it just draw it anyway?

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  • Cuboid inside generic polyhedron

    - by DOFHandler
    I am searching for an efficient algorithm to find if a cuboid is completely inside or completely outside or (not-inside and not-outside) a generic (concave or convex) polyhedron. The polyhedron is defined by a list of 3D points and a list of facets. Each facet is defined by the subset of the contour points ordinated such as the right-hand normal points outward the solid. Any suggestion? Thank you

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  • Reverse-projection 2D points into 3D

    - by ehsan baghaki
    Suppose we have a 3d Space with a plane on it with an arbitary equation : ax+by+cz+d=0 now suppose that we pick 3 random points on that plane: (x0,y0,z0) (x1,y1,z1) (x1,y1,z1) now i have a different point of view(camera) for this plane. i mean i have a different camera that will look at this plane from a different point of view. From that camera point of view these points have different locations. for example (x0,y0,z0) will be (x0',y0') and (x1,y1,z1) will be (x1',y1') and (x2,y2,z2) will be (x2',y2') from the new camera point of view. So here is my a little hard question! I want to pick a point for example (X,Y) from the new camera point of view and tell where it will be on that plane. All i know is that 3 points and their locations on 3d space and their projection locations on the new camera view. Do you know the coefficients of the plane-equation and the camera positions (along with the projection), or do you only have the six points? - Nils i know the location of first 3 points. therefore we can calculate the coefficients of the plane. so we know exactly where the plane is from (0,0,0) point of view. and then we have the camera that can only see the points! So the only thing that camera sees is 3 points and also it knows their locations in 3d space (and for sure their locations on 2d camera view plane). and after all i want to look at camera view, pick a point (for example (x1,y1)) and tell where is that point on that plane. (for sure this (X,Y,Z) point should fit on the plane equation). Also i know nothing about the camera location.

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  • Cone-Line Segment Intersection 2D

    - by nophnoph
    Hi everyone, I would like to know is there any way to determine if a cone is intersecting with a (finite)line segment. The cone actually a circle located at P(x,y) with theta degree field of view and radius r. The simple visualization can be found here (sorry i can't post the picture here) I'm trying to do it in C# but I don't have any idea how to that, so for now this is what I'm doing : Check if the line segment is intersecting with the circle If the line segment is intersecting with the circle then I check every single point in the line segment using a function I found here. But I don't think this is the best way to do it. Does anyone have an idea? For additional info, I need this function to make some kind of simple vision simulator. Thanks in advance :)

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  • Determining if a coordinate is on a line

    - by TGCBraun
    I´m coding a little app that allows the user to draw multiple shapes and then remove or resize them. It´s working perfectly on rectangles and ovals, but I´m having issues with lines. Here´s a method that I wrote to find if the clicked spot on the screen is part of a specific line: public boolean containsLocation(int x, int y) { int m = (getY2() - getY()) / (getX2() - getX()); int b = getY() - (m * getX()); if (y == (m * x) + b) { return true; } return false; I´m using the famous y = mx + b formula and replacing y and x to find if the clicked spot is part of the line. The problem is when I click on the screen to remove the line, it only works if I click on the very fist coordinate (x,y) where the line starts. Nothing happens when I click anywhere else along the line. Can anyone shed a light on what I´m doing wrong? Thanks a lot.

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  • Generating a beveled edge for a 2D polygon

    - by Metaphile
    I'm trying to programmatically generate beveled edges for geometric polygons. For example, given an array of 4 vertices defining a square, I want to generate something like this. But computing the vertices of the inner shape is baffling me. Simply creating a copy of the original shape and then scaling it down will not produce the desired result most of the time. My algorithm so far involves analyzing adjacent edges (triples of vertices; e.g., the bottom-left, top-left, and top-right vertices of a square). From there, I need to find the angle between them, and then create a vertex somewhere along that angle, depending on how deep I want the bevel to be. And because I don't have much of a math background, that's where I'm stuck. How do I find that center angle? Or is there a much simpler way of attacking this problem?

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  • Uniforme distance between points

    - by Reonarudo
    Hello, How could I, having a path defined by several points that are not in a uniform distance from each other, redefine along the same path the same number of points but with a uniform distance. I'm trying to do this in Objective-C with NSArrays of CGPoints but so far I haven't had any luck with this. Thank you for any help. EDIT I was wondering if it would help to reduce the number of points, like when detecting if 3 points are collinear we could remove the middle one, but I'm not sure that would help.

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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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  • WPF, convert Path.DataProperty to Segment objects

    - by user275587
    I was wondering if there was a tool to convert a path data like "M 0 0 l 10 10" to it's equivalent line/curve segment code. Currently I'm using: string pathXaml = "<Path xmlns=\"http://schemas.microsoft.com/winfx/2006/xaml/presentation\" xmlns:x=\"http://schemas.microsoft.com/winfx/2006/xaml\" Data=\"M 0 0 l 10 10\"/>"; Path path = (Path)System.Windows.Markup.XamlReader.Load(pathXaml); It appears to me that calling XamlParser is much slower than explicitly creating the line segments. However converting a lot of paths by hand is very tedious.

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  • Open source jigsaw piece generator

    - by codecowboy
    Hi, Does anyone know of a C-based open source class / framework which can generate a random jigsaw puzzle from an image or generate a random puzzle template which could then be applied to an image? The puzzle pieces must have male and female notches/holes. There should be more than one template so that the puzzle does not become too easy. The target system is iOS / Mac. If not, how would you approach this problem? The puzzle pieces should be as close to a real jigsaw piece shape as possible and the system must be dynamic so that the user can use their own photos or download photos. thanks!

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  • Reconstructing simple 3d enviroment(room) from photo

    - by Riz
    I have photo of a room with three walls and floor/ceiling or both. I am trying to reconstruct this room in 3d asking user for minimal input. Right now I use 8 points defined by user, angles of left and right wall(they can be quite different from 90) and one size "InLeftBottom-InRightBottom"(I need to have real size of this room for later use). I have no info about user's camera(I can read EXIF to get FOV and use constant height but this can be only used as additional info). Is this possible to ask user for less info? Maybe it's possible to get wall angles without user interaction? Or maybe I am completly wrong and should use different approach?

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