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  • Determining polygon intersection and containment

    - by Victor Liu
    I have a set of simple (no holes, no self-intersections) polygons, and I need to check that they don't intersect each other (one can be entirely contained in another; that is okay). I can check this by simply checking the per-vertex inside-ness of one polygon versus other polygons. I also need to determine the containment tree, which is the set of relationships that say which polygon contains any given polygon. Since no polygon can intersect any other, then any contained polygon has a unique container; the "next-bigger" one. In other words, if A contains B contains C, then A is the parent of B, and B is the parent of C, and we don't consider A the parent of C. The question: How do I efficiently determine the containment relationships and check the non-intersection criterion? I ask this as one question because maybe a combined algorithm is more efficient than solving each problem separately. The algorithm should take as input a list of polygons, given by a list of their vertices. It should produce a boolean B indicating if none of the polygons intersect any other polygon, and also if B = true, a list of pairs (P, C) where polygon P is the parent of child C. This is not homework. This is for a hobby project I am working on.

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  • Moving a Ball on iPhone

    - by Chandan Shetty SP
    I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius(I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches other circles please send your answers ASAP... I am waiting. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop. http://iphront.com/wp-content/uploads/2009/12/bdece528ea334033.jpg.jpg

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  • Why can't decimal numbers be represented exactly in binary?

    - by Barry Brown
    There have been several questions posted to SO about floating-point representation. For example, the decimal number 0.1 doesn't have an exact binary representation, so it's dangerous to use the == operator to compare it to another floating-point number. I understand the principles behind floating-point representation. What I don't understand is why, from a mathematical perspective, are the numbers to the right of the decimal point any more "special" that the ones to the left? For example, the number 61.0 has an exact binary representation because the integral portion of any number is always exact. But the number 6.10 is not exact. All I did was move the decimal one place and suddenly I've gone from Exactopia to Inexactville. Mathematically, there should be no intrinsic difference between the two numbers -- they're just numbers. By contrast, if I move the decimal one place in the other direction to produce the number 610, I'm still in Exactopia. I can keep going in that direction (6100, 610000000, 610000000000000) and they're still exact, exact, exact. But as soon as the decimal crosses some threshold, the numbers are no longer exact. What's going on? Edit: to clarify, I want to stay away from discussion about industry-standard representations, such as IEEE, and stick with what I believe is the mathematically "pure" way. In base 10, the positional values are: ... 1000 100 10 1 1/10 1/100 ... In binary, they would be: ... 8 4 2 1 1/2 1/4 1/8 ... There are also no arbitrary limits placed on these numbers. The positions increase indefinitely to the left and to the right.

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  • C# method to scale values?

    - by John S
    Hello, I have a value range from 0 to 255. There is a method that returns an array with a min and max values within this range, i.e: 13, 15, 20, 27, 50 ... 240 where 13 is the min and 240 is the max I need to scale these values so that 13 becomes 0 and 240 becomes 255 and scale all the other values between them proportionally. Is there any C# method that does that? thanks!

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  • Extend and Overload MS and Point Types

    - by dr d b karron
    Do I have make my own Point and Vector types to overload them ? Why does this not work ? namespace System . windows { public partial struct Point : IFormattable { public static Point operator * ( Point P , double D ) { Point Po = new Point ( ); return Po; } } } namespace SilverlightApplication36 { public partial class MainPage : UserControl { public static void ShrinkingRectangle ( WriteableBitmap wBM , int x1 , int y1 , int x2 , int y2 , Color C ) { wBM . DrawRectangle ( x1 , y1 , x2 , y2 , Colors . Red ); Point Center = Mean ( x1 , y1 , x2 , y2 ); wBM . SetPixel ( Center , Colors.Blue , 3 ); Point P1 = new Point ( x1 , y1 ); Point P2 = new Point ( x1 , y2 ); Point P3 = new Point ( x1 , y2 ); Point P4 = new Point ( x2 , y1 ); const int Steps = 10; for ( int i = 0 ; i < Steps ; i++ ) { double iF = (double)(i+1) / (double)Steps; double jF = ( 1.0 - iF ); Point P11 = **P1 * jF;** } }

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  • Express highest floating point quantity that is less than 1

    - by edA-qa mort-ora-y
    I was doing some rounding calculations and happened upon a question. How can I express the highest quantity less than 1 for a given floating point type? That is, how I write/represent value x such that x < 1, x + y >= 1 for any y > 0. In fractions this would be x = (q-1)/q where q is the precision of the type. For example, if you are counting in 1/999 increments then x = 998/999. For a given type (float, double, long double), how could one express the value x in code? I also wonder if such a value actually exists for all values of y. That is, as y's exponent gets smaller perhaps the relation doesn't hold anymore. So an answer with some range restriction on y is also acceptable. (The value of x I want still does exist, the relationship may just not properly express it.)

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  • Inverse relationship of two variables

    - by Jam
    this one is maybe pretty stupid.. Or I am just exhausted or something, but I just cant seem to solve it.. Problem : two variables X and Y, value of Y is dependent on value of X. X can have values ranging from some value to some value (lets say from 0 to 250) and y can have different values (lets say from 0.1 to 1.0 or something..) - but it is inverse relatonship (what I mean is: if value of X is e.g. 250, then value of Y would be 0.1 and when X decreases up to 0, value of Y raises up to 1.0.. So how should I do it? lets say I have function: -- double computeValue (double X) { /computation/ return Y; } Also, is there some easy way to somehow make the scaling of the function not so linear? - For example when X raises, Y decreases slower at first but then more rapidly in the end.. (rly dont know how to say it but I hope you guys got it) Thanks in advance for this stupid question :/

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  • If we make a number every millisecond, how much data would we have in a day?

    - by Roger Travis
    I'm a bit confused here... I'm being offered to get into a project, where would be an array of certain sensors, that would give off reading every millisecond ( yes, 1000 reading in a second ). Reading would be a 3 or 4 digit number, for example like 818 or 1529. This reading need to be stored in a database on a server and accessed remotely. I never worked with such big amounts of data, what do you think, how much in terms of MBs reading from one sensor for a day would be?... 4(digits)x1000x60x60x24 ... = 345600000 bits ... right ? about 42 MB per day... doesn't seem too bad, right? therefor a DB of, say, 1 GB, would hold 23 days of info from 1 sensor, correct? I understand that MySQL & PHP probably would not be able to handle it... what would you suggest, maybe some aps? azure? oracle? ... Thansk!

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  • How to maintain decimal percision in calculations

    - by Blankman
    I need to sum 2 decimal values together, then divide by 2 and convert to string. My calculation currently is trimming to 2 decimal places, but I want to keep as many decimals as I can. city.Latitude = ( (lat.North + lat.South) / 2 ).ToString(); the values for lat.North and lat.Souch are like: 55.32342322

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  • Learning Basic Mathematics

    - by NeedsToKnow
    I'm going to just come out and say it. I'm 20 and can't do maths. Two years ago I passed the end-of-high-school mathematics exam (but not at school), and did pretty well. Since then, I haven't done a scrap of mathematics. I wondered just how bad I had gotten, so I was looking at some simple algebra problems. You know, the kind you learn halfway through highschool. 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Couldn't do them. I've got half a year left until I start a Computer Science undergraduate degree. I love designing and creating programs, and I remember I loved mathematics back when I did it. Basically, I've had a pretty bad education, but I want to be knowledgable in these areas. I was thinking of buying some high school textbooks and reading them, but I'm not sure this is the right way to go. I need to start off at some basic level and work towards a greater understanding. My question is: What should I study, how should I study, and what books can you recommend? Thanks!

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  • Position elements without overlap

    - by eWolf
    I have a number of rectangular elements that I want to position in a 2D space. I calculate an ideal position for each element. Now my problem is that many elements overlap as very often the ideal positions are concentrated in one region. I want to avoid overlap as much as possible (doesn't have to be perfect, though). How can I do this? I've heard physics simulations are suitable for this - is that correct? And can anyone provide an example/tutorial? By the way: I'm using XNA, if you know any .NET library that does exactly this job - tell me!

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  • A simple algorithm for polygon intersection

    - by Elazar Leibovich
    I'm looking for a very simple algorithm for computing the polygon intersection/clipping. That is, given polygons P, Q, I wish to find polygon T which is contained in P and in Q, and I wish T to be maximal among all possible polygons. I don't mind the run time (I have a few very small polygons), I can also afford getting an approximation of the polygons' intersection (that is, a polygon with less points, but which is still contained in the polygons' intersection). But it is really important for me that the algorithm will be simple (cheaper testing) and preferably short (less code). edit: please note, I wish to obtain a polygon which represent the intersection. I don't need only a boolean answer to the question of whether the two polygons intersect.

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  • Detecting periodic repetitions in the data stream

    - by pulegium
    Let's say I have an array of zeros: a = numpy.zeros(1000) I then introduce some repetitive 'events': a[range(0, 1000, 30)] = 1 Question is, how do I detect the 'signal' there? Because it's far from the ideal signal if I do the 'regular' FFT I don't get a clear indication of where my 'true' signal is: f = abs(numpy.fft.rfft(a)) Is there a method to detect these repetitions with some degree of certainty? Especially if I have few of those mixed in, for example here: a[range(0, 1000, 30)] = 1 a[range(0, 1000, 110)] = 1 a[range(0, 1000, 48)] = 1 I'd like to get three 'spikes' on the resulting data...

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  • How to solve generic algebra using solver/library programmatically? Matlab, Mathematica, Wolfram etc?

    - by DevDevDev
    I'm trying to build an algebra trainer for students. I want to construct a representative problem, define constraints and relationships on the parameters, and then generate a bunch of Latex formatted problems from the representation. As an example: A specific question might be: If y < 0 and (x+3)(y-5) = 0, what is x? Answer (x = -3) I would like to encode this as a Latex formatted problem like. If $y<0$ and $(x+constant_1)(y+constant_2)=0$ what is the value of x? Answer = -constant_1 And plug into my problem solver constant_1 > 0, constant_1 < 60, constant_1 = INTEGER constant_2 < 0, constant_2 > -60, constant_2 = INTEGER Then it will randomly construct me pairs of (constant_1, constant_2) that I can feed into my Latex generator. Obviously this is an extremely simple example with no real "solving" but hopefully it gets the point across. Things I'm looking for ideally in priority order * Solve algebra problems * Definition of relationships relatively straight forward * Rich support for latex formatting (not just writing encoded strings) Thanks!

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  • signed angle between two 3d vectors with same origin within the same plane? recipe?

    - by Advanced Customer
    Was looking through the web for an answer but it seems like there is no clear recipe for it. What I need is a signed angle of rotation between two vectors Va and Vb lying within the same 3D plane and having the same origin knowing that: the plane contatining both vectors is an arbitrary and is not parallel to XY or any other of cardinal planes Vn - is a plane normal both vectors along with the normal have the same origin O = { 0, 0, 0 } Va - is a reference for measuring the left handed rotation at Vn The angle should be measured in such a way so if the plane would be XY plane the Va would stand for X axis unit vector of it. I guess I should perform a kind of coordinate space transformation by using the Va as the X-axis and the cross product of Vb and Vn as the Y-axis and then just using some 2d method like with atan2() or something. Any ideas? Formulas?

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  • C++: Best text accumulator

    - by MInner
    Text gets accumulates piecemeal before being sent to client. Now we use own class that allocates memory for each piece as char massive. (Anyway, works like char[][] + std::list<char*>). Then we build the whole string, convert it into std::sting and then create boost::asio::streambuf using it. That's slow enough, I assume. Correct me if I'm wrong. I know, in many cases simple FILE type from stdio.h is used. How does it works? Allocates memory at every write into it. So, is it faster and is there any way to read into boost::asio::streambuf from FILE?

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  • Reverse engineering a bezier curve

    - by Martin
    Given a few sample points on a bézier curve, is it possible to work out the set of possible parameters of the curve? In my specific application there is a limited set of endpoints the curve may have, so I want to generate the set of possible curves, enumerate all of them and pick out all the ones which may end on a valid end point.

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  • Looking for framework for plotting scientific data: 2d/3d ...

    - by Ivan
    I need to visualize some scientific calculations. I generally prefer reusing code if there is already a good available instead of inventing wheels each time, that's why I am asking. I need a C# code to draw charts (just outputting a bitmap is ok) of 2d (y=f(x)) and 3d (z=f(x,y)) digital data sets (where any axis can be float, int or datetime), sometimes combined. If I go here and click 3D in the navigation bar on the left, there I can see what I need. But the cheapest version costs $759 there, looks scary for a hobby project of an east-european student :-(

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  • Good computer science lecture series

    - by joemoe
    Since we have a thread on books.. what are your recommendations of publicly accessible video lecture series related to programming, computer science, or mathematics? Please post specific courses, not websites with courses. :) This is the video equivalent of this thread: http://stackoverflow.com/questions/194812/list-of-freely-available-programming-books

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  • Looking for interesing formula

    - by Thinker
    I'm creating a game, where players can make an alloy. To make it less predictable, and more interesting, I thought that durability and hardness of an alloy can't be calculated by simple formula, because it will be extremely easy to find extrema, where alloy have best statistics. So the questions is, is there any formula for a function, where extrema can be found only by investigating all points? Input values will be in percents: 0.0%-100.0%. I think, it should look like this: half sound wave

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