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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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  • The bigger value in a matrix row

    - by marionmaiden
    How can I get the 2 biggers numbers of a matrix row? If the matrix have a bigger number in other row, it can't be shown. For example, let's suppose I have the following matrix int mat[][] ={{1,2,3}{4,5,6}{7,8,9}}; if I search the 2 biggers numbers from the row 0, it should return me 1 and 2.

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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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  • Find all ways to insert zeroes into a bit pattern

    - by James
    I've been struggling to wrap my head around this for some reason. I have 15 bits that represent a number. The bits must match a pattern. The pattern is defined in the way the bits start out: they are in the most flush-right representation of that pattern. So say the pattern is 1 4 1. The bits will be: 000000010111101 So the general rule is, take each number in the pattern, create that many bits (1, 4 or 1 in this case) and then have at least one space separating them. So if it's 1 2 6 1 (it will be random): 001011011111101 Starting with the flush-right version, I want to generate every single possible number that meets that pattern. The # of bits will be stored in a variable. So for a simple case, assume it's 5 bits and the initial bit pattern is: 00101. I want to generate: 00101 01001 01010 10001 10010 10100 I'm trying to do this in Objective-C, but anything resembling C would be fine. I just can't seem to come up with a good recursive algorithm for this. It makes sense in the above example, but when I start getting into 12431 and having to keep track of everything it breaks down.

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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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  • 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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  • 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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  • 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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  • 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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  • How to calculate the normal of points on a 3D cubic Bézier curve given normals for its start and end points?

    - by Robert
    I'm trying to render a "3D ribbon" using a single 3D cubic Bézier curve to describe it (the width of the ribbon is some constant). The first and last control points have a normal vector associated with them (which are always perpendicular to the tangents at those points, and describe the surface normal of the ribbon at those points), and I'm trying to smoothly interpolate the normal vector over the course of the curve. For example, given a curve which forms the letter 'C', with the first and last control points both having surface normals pointing upwards, the ribbon should start flat, parallel to the ground, slowly turn, and then end flat again, facing the same way as the first control point. To do this "smoothly", it would have to face outwards half-way through the curve. At the moment (for this case), I've only been able to get all the surfaces facing upwards (and not outwards in the middle), which creates an ugly transition in the middle. It's quite hard to explain, I've attached some images below of this example with what it currently looks like (all surfaces facing upwards, sharp flip in the middle) and what it should look like (smooth transition, surfaces slowly rotate round). Silver faces represent the front, black faces the back. Incorrect, what it currently looks like: Correct, what it should look like: All I really need is to be able to calculate this "hybrid normal vector" for any point on the 3D cubic bézier curve, and I can generate the polygons no problem, but I can't work out how to get them to smoothly rotate round as depicted. Completely stuck as to how to proceed!

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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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  • 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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  • 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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  • 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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  • Adding Colours (Colors) Together like Paint (Blue + Yellow = Green, etc)

    - by glenstorey
    I'm making an iOS game using cocos2d libraries. Lets say you have two objects that have two separate colours - defined in RGB as Blue: 0,0,255 Yellow: 255,255,0 I want to add blue and yellow to make green. To over complicate things, let's say that the Blue object is bigger than the Yellow object (for the sake of argument let's say that the ratio is 2:1), I'm adding twice as much blue as yellow - how to I calculate this new (light green) colour correctly. I understand LAB * Color Space is useful for this sort of 'natural colour' kind of thing, but I'm not sure how to use it - especially in the context of a cocos2d object which (AFAIK) is limited to using RGB in its colour schemes. I'd really appreciate practical help on how to implement this. Thanks heaps!

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