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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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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • 6^x = 5 equation, how to solve it?

    - by Tom
    If it would be 6^x = 1 or 6^x = 6 or 6^x = 36 it would be extremely easy, but how to solve this equation: 6^x = 5 I don't need an answer, I want to find out how to solve equations like this one, I need solution. Thanks.

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  • How to interpolate rotations?

    - by uhuu
    I have two vectors describing rotations; a start rotation A and a target rotation B. How would I best go about interpolating A by a factor F to approach B? Using a simple lerp on the vectors fails to work when more than one dimension needs to be interpolated (i.e. produces undesirable rotations). Maybe building quaternions from the rotation vectors and using slerp is the way to go. But how, then, could I extract a vector describing the new rotation from the resulting quaternion? Thanks in advance.

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  • summing functions handles in matlab

    - by user552231
    Hi I am trying to sum two function handles, but it doesn't work. for example: y1=@(x)(x*x); y2=@(x)(x*x+3*x); y3=y1+y2 The error I receive is "??? Undefined function or method 'plus' for input arguments of type 'function_handle'." This is just a small example, in reality I actually need to iteratively sum about 500 functions that are dependent on each other. EDIT The solution by Clement J. indeed works but I couldn't manage to generalize this into a loop and ran into a problem. I have the function s=@(x,y,z)((1-exp(-x*y)-z)*exp(-x*y)); And I have a vector v that contains 536 data points and another vector w that also contains 536 data points. My goal is to sum up s(v(i),y,w(i)) for i=1...536 Thus getting one function in the variable y which is the sum of 536 functions. The syntax I tried in order to do this is: sum=@(y)(s(v(1),y,z2(1))); for i=2:536 sum=@(y)(sum+s(v(i),y,z2(i))) end

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  • Apache mod_rewrite rules problems

    - by ni
    domain.com/index/ to domain.com/index.php domain.com/index/hello to domain.com/index.php/hello The site is use path_info,and the default rule not works: RewriteRule ^([^/]+)/(.*)$ $1.php/$2 [L] I change to: RewriteRule ^([^/.]+)((/[^/]+)*)/?$ $1.php$2 [L] That was strange domain.com/index/ to domain.com/index.php works fine domain.com/index/hello to domain.com/index.php/hello not work and it says No input file specified. Php is run in fast cgi mode in apache

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  • Question about the mathematical properties of hashes

    - by levand
    Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value. Let A be the set of all possible 256 bit binary values. A is extremely large, but finite. Let B be the set of all possible binary values. B is infinite. Let C be the set of values obtained by running SHA-256 on every member of B. Obviously this can't be done in practice, but I'm guessing we can still do mathematical analysis of it. My Question: By necessity, C ? A. But does C = A?

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  • Can we find out the difference between 2 RGb colors to find out a 3rd color?

    - by AK
    2 colors are mixed together. If i have the RGB for the resultant color and RGB for one of the colors mixed, then somehow i could calculate the 2nd color? I will try to explain visually what i am trying to say. Here is a flickr link http://www.flickr.com/photos/48150615@N08/4407414157 I know that the circle in the middle has an opacity of 20% Is there any way to know the color value of the circle so that i can deduct that to get the same color value as the background color.

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  • Arrange points in sequence.

    - by Himadri
    I have some points in 3D which are in a single plane. I want to arrange them in clock wise or counter clockwise order. The points can create a concave or convex polygon in a single plane. Can any body give any suggestions?

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  • apache httpclient and spawning a browser that will share the session

    - by Nick
    I'm have a java program that uses Apache httpclient api. This is used to login to and communicate to a webapp. Once logged in, there's a situation in which the program issues an execute process to open up firefox to hit the webapp and allow the user to see data in the browser. Since the java program is already logged in, is there a way to share that current session PHPSESSID so that the spawned firefox is already logged in and working in that same session?

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  • C - How to implement Set data structure?

    - by psihodelia
    Is there any tricky way to implement a set data structure (a collection of unique values) in C? All elements in a set will be of the same type and there is a huge RAM memory. As I know, for integers it can be done really fast'N'easy using value-indexed arrays. But I'd like to have a very general Set data type. And it would be nice if a set could include itself.

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  • Interesting task using random numbers only

    - by psihodelia
    Given any number of the random real numbers from the interval [0,1] is there exist any method to construct a floating point number with zero decimal part? Your algorithm can use only random() function calls and no variables or constants. No constants and variables are allowed, no type casting is allowed. You can use for/while, if/else or any other programming language operands.

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  • Distance between hyperplanes

    - by michael dillard
    I'm trying to teach myself some machine learning, and have been using the MNIST database (http://yann.lecun.com/exdb/mnist/) do so. The author of that site wrote a paper in '98 on all different kinds of handwriting recognition techniques, available at http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf. The 10th method mentioned is a "Tangent Distance Classifier". The idea being that if you place each image in a (NxM)-dimensional vector space, you can compute the distance between two images as the distance between the hyperplanes formed by each where the hyperplane is given by taking the point, and rotating the image, rescaling the image, translating the image, etc. I can't figure out enough to fill in the missing details. I understand that most of these are indeed linear operators, so how does one use that fact to then create the hyperplane? And once we have a hyperplane, how do we take its distance with other hyperplanes?

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  • Subdividing 3D mesh into arbitrarily sized pieces

    - by Groky
    I have a mesh defined by 4 points in 3D space. I need an algorithm which will subdivide that mesh into subdivisions of an arbitrary horizontal and vertical size. If the subdivision size isn't an exact divisor of the mesh size, the edge pieces will be smaller. All of the subdivision algorithms I've found only subdivide meshes into exact powers of 2. Does anyone know of one that can do what I want? Failing that, my thoughts about a possible implementation is to rotate the mesh so that it is flat on the Z axis, subdivide in 2D and then translate back into 3D. That's because my mind finds 3D hard ;) Any better suggestions? Using C# if that makes any difference.

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  • How to detect if a certain range resides (partly) within an other range?

    - by Tom
    Lets say I've got two squares and I know their positions, a red and blue square: redTopX; redTopY; redBotX; redBotY; blueTopX; blueTopY; blueBotX; blueBotY; Now, I want to check if square blue resides (partly) within (or around) square red. This can happen in a lot of situations, as you can see in this image I created to illustrate my situation better: Note that there's always only one blue and one red square, I just added multiple so I didn't have to redraw 18 times. My original logic was simple, I'd check all corners of square blue and see if any of them are inside square red: if ( ((redTopX >= blueTopX) && (redTopY >= blueTopY) && (redTopX <= blueBotX) && (redTopY <= blueBotY)) || //top left ((redBotX >= blueTopX) && (redTopY >= blueTopY) && (redBotX <= blueBotX) && (redTopY <= blueBotY)) || //top right ((redTopX >= blueTopX) && (redBotY >= blueTopY) && (redTopX <= blueBotX) && (redBotY <= blueBotY)) || //bottom left ((redBotX >= blueTopX) && (redBotY >= blueTopY) && (redBotX <= blueBotX) && (redBotY <= blueBotY)) //bottom right ) { //blue resides in red } Unfortunately, there are a couple of flaws in this logic. For example, what if red surrounds blue (like in situation 1)? I thought this would be pretty easy but am having trouble coming up with a good way of covering all these situations.. can anyone help me out here? Regards, Tom

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  • Pretty Pixel-level Picture Painting, Programatically

    - by dreeves
    My mac laptop has 1,024,000 pixels. What's the simplest way to turn my display completely black and go nuts with writing little programs to twiddle pixels to my heart's delight? To make it more concrete, say I wanted to implement the Chaos Game to draw a Sierpinski triangle, at the pixel level, with nothing else on the screen. What are ways to do that?

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  • Problems with mod_rewrite and 301 redirects from one dynamic url to another

    - by user349891
    Hey all, I'm having all kinds of problems with a bunch of apache redirects just now and could really use some help! I'm wating to put in a 301 redirect for a load of urls from a client's old site to their new site in the following format; Old - page.php?pageNum_rs_all=0&totalRows_rs_all=112 New - page/sub?foo=bar The values in the query sting for the old site don't in any way tie up to any ids or references on the new site, I only want to match that specific request and redirect to the new page. It feels like I've tried just about every combination of rewriterule I can find online but still nothing seems to be working. This is running on Apache 2.2. The rule I started with (and keep going back to) is; RewriteRule ^/page.php\?pageNum_rs_all=0&totalRows_rs_all=112 /page/sub?foo=bar [R=301,L,NE] Any help would be greatly appreciated! c.

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  • Radius of multiple latitude/longitude points

    - by zekial
    I have a program that takes as input an array of lat/long points. I need to perform a check on that array to ensure that all of the points are within a certain radius. So, for example, the maximum radius I will allow is 100 miles. Given an array of lat/long (coming from a MySQL database, could be 10 points could be 10000) I need to figure out if they will all fit in a circle with radius of 100 miles. Kinda stumped on how to approach this. Any help would be greatly appreciated.

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