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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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  • 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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  • Drawing Directed Acyclic Graphs: Using DAG property to improve layout/edge routing?

    - by Robert Fraser
    Hi, Laying out the verticies in a DAG in a tree form (i.e. verticies with no in-edges on top, verticies dependent only on those on the next level, etc.) is rather simple. However, is there a simple algorithm to do this that minimizes edge crossing? (For some graphs, it may be impossible to completely eliminate edge crossing.) A picture says a thousand words, so is there an algorithm that would suggest: instead of:

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  • Faster way to compare two sets of points in N-dimensional space?

    - by Amit
    List1 contains a high number (~7^10) of N-dimensional points (N <=10), List2 contains the same or fewer number of N-dimensional points (N <=10). My task is this: I want to check which point in List2 is closest (euclidean distance) to a point in List1 for every point in List1 and subsequently perform some operation on it. I have been doing it the simple- the nested loop way when I didn't have more than 50 points in List1, but with 7^10 points, this obviously takes up a lot of time. What is the fastest way to do this? Any concepts from Computational Geometry might help?

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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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  • Fastest way to find the rotation of a vector

    - by kriss
    I have two 2D vectors, say u and v, defined by cartesian coordinates. Imagine that vectors are needles of a clock. I'm looking for the fastest way to find out, using python, if v is after or before u (or in other words find out in wich half plane is v, regarding to position of u). For the purpose of the problem if vectors are aligned answer should be before. It seems easy using some trigonometry, but I believe there should be a faster way using coordinates only. My test case: def after(u, v): """code here""" after((4,2), (6, 1)) : True after((4,2), (3, 3)) : False after((4,2), (2, 1)) : False after((4,2), (3, -3)) : True after((4,2), (-2, -5)) : True after((4,2), (-4, -2)) : False

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  • simple rank formula

    - by Graham
    I'm looking for a mathmatical ranking formula. Sample is 2008 2009 2010 A 5 6 4 B 6 7 5 C 7 8 2 I want to add a rank column for each period code field rank 2008 2009 2010 2008 2009 2010 B 6 7 5 2 1 1 A 5 6 4 3 2 2 C 7 2 2 1 3 3 please do not reply with methods that loop thru the rows and columns, incrementing the rank value as it goes, that's easy. I'm looking for a formula much like finding the percent total (item / total). I know i've seen this before but an havning a tough time locating it. Thanks in advance!

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  • Efficient Multiplication of Varying-Length #s [Conceptual]

    - by Milan Patel
    Write the pseudocode of an algorithm that takes in two arbitrary length numbers (provided as strings), and computes the product of these numbers. Use an efficient procedure for multiplication of large numbers of arbitrary length. Analyze the efficiency of your algorithm. I decided to take the (semi) easy way out and use the Russian Peasant Algorithm. It works like this: a * b = a/2 * 2b if a is even a * b = (a-1)/2 * 2b + a if a is odd My pseudocode is: rpa(x, y){ if x is 1 return y if x is even return rpa(x/2, 2y) if x is odd return rpa((x-1)/2, 2y) + y } I have 3 questions: Is this efficient for arbitrary length numbers? I implemented it in C and tried varying length numbers. The run-time in was near-instant in all cases so it's hard to tell empirically... Can I apply the Master's Theorem to understand the complexity...? a = # subproblems in recursion = 1 (max 1 recursive call across all states) n / b = size of each subproblem = n / 1 - b = 1 (problem doesn't change size...?) f(n^d) = work done outside recursive calls = 1 - d = 0 (the addition when a is odd) a = 1, b^d = 1, a = b^d - complexity is in n^d*log(n) = log(n) this makes sense logically since we are halving the problem at each step, right? What might my professor mean by providing arbitrary length numbers "as strings". Why do that? Many thanks in advance

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  • Why isnt int pow(int base, int exponent) in the standard C++ libraries?

    - by Dan O
    I feel like I must just be unable to find it. Is there any reason that the c++ pow function does not implement the "power" function for anything except floats and doubles? I know the implementation is trivial, I just feel like I'm doing work that should be in a standard library. A robust power function (ie handles overflow in some consistent, explicit way) is not fun to write.

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  • C++ integer floor function

    - by Thomas
    I want to implement greatest integer function. int x = 5/3; My question is with greater numbers could there be a loss of precision as 5/3 would produce a double? EDIT: Greatest integer function is integer less than or equal to X. Example: 4.5 = 4 4 = 4 3.2 = 3 3 = 3 What I want to know is 5/3 going to produce a double? Because if so I will have loss of precision when converting to int. Hope this makes sense. RE-EDIT: What OP calls 'greatest integer' most of us call 'floor'.

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  • How to find the largest square in the number (Java)

    - by Ypsilon IV
    Hello everyone, I want to find the largest square in the number, but I am stuck at some point. I would really appreciate some suggestions. This is what I've done so far: I take the number on the input, factorize into prime numbers, and put the sequence of prime numbers to ArrayList. Numbers are sorted, in a sense, thus the numbers in the sequence are increasing. For example, 996 is 2 2 3 83 1000 is 2 2 2 5 5 5 100000 is 2 2 2 2 2 5 5 5 5 5 My idea now is to count number of occurrences of each elements in the sequence, so if the number of occurrences is divisible by two, then this is the square. In this way, I can get another sequence, where the right most element divisible by two is the largest square. What is the most efficient way to count occurrences in the ArrayList? Or is there any better way to find the largest square? Many thanks in advance!

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  • Android: Find coordinates of a certain point X meters from my location moving towards the point I am

    - by Aidan
    Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've done some Googling and checked the SDK but can't really find anything for such a thing. Does anyone know of a way? Example. Point A = Phones current location. Point B = A's orientation in relation to true north + 45 + max distance towards the direction your facing, Point C = A's orientation in relation to true north - 45 + max distance towards the direction your facing. So now you have a triangle constructed. pretty schweet huh? yeah.. I think so.. So now that I have my fancy Triangle I use something called Barycentric Coordinates ( http://en.wikipedia.org/wiki/Barycentric_coordinates_(mathematics) ). This will allow me to test another point and see if it is in the triangle. If it is, it means we're facing it AND it's within the right distance. So it should be displayed on screen. If I'm facing 90 degrees from true north. The distance it travels should be that direction. 90 degrees from true north. It should not be 100 degrees or something from true north! But the problem is I haven't yet figured out how I make the device realise it must go "out" the direction it is facing.

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  • Recursion problem in algorithm

    - by Marthin
    I'm not sure if this is the right place to post this, but the problem actually belongs to a programming assignment. Solve the recursion: T(0) = 2; T(n) = T(n-1) + 2; Solution: T(n) = 2(n+1) Could someone please show me how they got to that solution?

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  • How to fix this 7% where 6% , 5% works great.

    - by Stackfan
    Case 1 (discount 6%): Subtotal: 750.00 Discount: 45.00 Handling cost: 24.32 21% VAT: 0.00 Total (this is the amount you will deposit): 729.32 Case 2 (discount 7%): Subtotal: 1250.00 Discount: 87.50 Handling cost: 39.88 21% VAT: 0.00 Total (this is the amount you will deposit): 1202.38 Where i am applying this formula: (729.32 - 0.35) / 1.034/ 0.94 = 750.00 (<<--- CORRECT ) ? (1202.38 - 0.35) / 1.034/ 0.93 = 1250.01 (<<--- My problem why not 1250.00) ? How to correct the 7% formula to get exactly 1250.00 ? Instead of fraction error.

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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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  • simple dividing

    - by dontoo
    Lets say I am dividing 2592 / 324 = 8 Practically I must guess that 324 goes 8 times in 2592 without reminder. For example, first I try with 7 ( 7*324 = 2268, reminder 324, so 7 is wrong, so I try with 8 and 8 is correct) Is there anyway to do dividing without guessing( trying ), like multiplication ( all mechanically, digit by digit )?

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  • troubles with integration on matlab

    - by user648666
    I'd like some help please I really need to solve this problem. Well before anything thank you for your time... My problem: I have a matrix (826x826 double) and I want to integrate this matrix with respect to a vector of (826x1 double) I don't have the functions of any of this. Is there a command or an algorithm to take the integral of a matrix with respect to a vector? Please I really need help, I'm such a newbie at matlab. Sincerely. George

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  • getting the value of a filter at an arbitrary time

    - by Andiih
    Context: I'm trying to improve the values returned by the iPhone CLLocationManager, although this is a more generally applicable problem. The key is that CLLocationManger returns data on current velocity as and when it feels like it, rather than at a fixed sample rate. I'd like to use a feedback equation to improve accuracy v=(k*v)+(1-k)*currentVelocity where currentVelocity is the speed returned by didUpdateToLocation:fromLocation: and v is the output velocity (and also used for the feedback element). Because of the "as and when" nature of didUpdateToLocation:fromLocation: I could calculate the time interval since it was last called, and do something like for (i=0;i<timeintervalsincelastcalled;i++) v=(k*v)+(1-k)*currentVelocity which would work, but is wasteful of cycles. Especially as I probably want timeintervalsincelastcalled to be measured as 10ths of a second. Is there a way to solve this without the loop ? i.e. rework (integrate?) the formula so I put an interval into the equation and get the same answer as I would have by iteration ?

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  • what is the best algorithm to use for this problem

    - by slim
    Equilibrium index of a sequence is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. For example, in a sequence A: A[0]=-7 A[1]=1 A[2]=5 A[3]=2 A[4]=-4 A[5]=3 A[6]=0 3 is an equilibrium index, because: A[0]+A[1]+A[2]=A[4]+A[5]+A[6] 6 is also an equilibrium index, because: A[0]+A[1]+A[2]+A[3]+A[4]+A[5]=0 (sum of zero elements is zero) 7 is not an equilibrium index, because it is not a valid index of sequence A. If you still have doubts, this is a precise definition: the integer k is an equilibrium index of a sequence if and only if and . Assume the sum of zero elements is equal zero. Write a function int equi(int[] A); that given a sequence, returns its equilibrium index (any) or -1 if no equilibrium indexes exist. Assume that the sequence may be very long.

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  • All non-prime factorings

    - by Tony Veijalainen
    Let's say we have numbers factors, for example 1260: >>> factors(1260) [2, 2, 3, 3, 5, 7] Which would be best way to do in Python combinations with every subproduct possible from these numbers, ie all factorings, not only prime factoring, with sum of factors less than max_sum? If I do combinations from the prime factors, I have to refactor remaining part of the product as I do not know the remaining part not in combination. Example results would be: [4, 3, 3, 5, 7] (one replacement) [3, 6, 14, 5] (two replacements)

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  • Shortest command to calculate the sum of a column of output on Unix?

    - by Andrew
    I'm sure there is a quick and easy way to calculate the sum of a column of values on Unix systems (using something like awk or xargs perhaps), but writing a shell script to parse the rows line by line is the only thing that comes to mind at the moment. For example, what's the simplest way to modify the command below to compute and display the total for the SEGSZ column (70300)? ipcs -mb | head -6 IPC status from /dev/kmem as of Mon Nov 17 08:58:17 2008 T ID KEY MODE OWNER GROUP SEGSZ Shared Memory: m 0 0x411c322e --rw-rw-rw- root root 348 m 1 0x4e0c0002 --rw-rw-rw- root root 61760 m 2 0x412013f5 --rw-rw-rw- root root 8192

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  • How to make simple mathematical operations and displaying the result in a textbox

    - by Audel
    Hi, I know is a rather simple question but I just can't find an appropriate example in google or anywhere. I've got this piece int numberOfPlays = int.Parse(textBox2.Text); numberOfPlays = (numberOfPlays++); textBox2.Text = (numberOfPlays.ToString()); MessageBox.Show(numberOfPlays.ToString()); So basically what I want to do is to get the value of the textBox2, make it an integer and then add 1 to it. I can't think of any more details right now, so if i'm not clear enough please ask Thanks in advance

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