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  • Can I interpolate two HEX color values without converting them to RGB?

    - by navand
    I'm trying to make a Gradient Class for a Blackberry app. At first I thought about converting the HEX values to RGB and then interpolating them before converting the result back into HEX, but since I will be doing this for every pixel line of an area, and the calculations will be made by a mobile, I thought that maybe there's a more efficient way of doing it. Maybe involving those pesky bitwise operators which I know nothing of... or something. So, is there a way of interpolating without converting to RGB and back? If so, is it faster than the original way? In any case, can you help me make the most efficient color interpolation? Thank you in advance!

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  • Different background colors for the top and bottom of a UITableView

    - by Aaron Brethorst
    If you look at your Inbox in iPhone OS 3.0's Mail app, you'll see that swiping down displays a grayish background color above the UISearchBar. Now, if you scroll down to the bottom of the table, you'll see that the background color at that end is white. I can think of a couple ways of solving this problem, but they're pretty hacky: Change the table view's background color depending on the current scrollOffset by overriding -scrollViewDidScroll: Give the UITableView a clear background color and then set its superview's backgroundColor to a gradient pattern image. Does anyone know what the "best practice" solution is for this problem? thanks.

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  • How do i create winxp style controls

    - by KoolKabin
    Hi guys, I am trying to make my controls look as cool as xp theme enabled controls like gradient fill background in container controls and colour thames support etc I am not finding a way to start. from where can i start doing it? I am trying to do it in vb.net Edited: EnableXpVisualStyles() I found it to enable visual styles but didn't give me visual thames to apply. So in order to apply thames or colour schemes what should i do? What other commands should i use with combination with it? as I have seen my application giving ugly look even applying that command and other program showing nice loook in my win2003 server

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  • What's the most effective way to interpolate between two colors? (pseudocode and bitwise ops expecte

    - by navand
    Making a Blackberry app, want a Gradient class. What's the most effective way (as in, speed and battery life) to interpolate two colors? Please be specific. // Java, of course int c1 = 0xFFAA0055 // color 1, ARGB int c2 = 0xFF00CCFF // color 2, ARGB float st = 0 // the current step in the interpolation, between 0 and 1 /* Help from here on. Should I separate each channel of each color, convert them to decimal and interpolate? Is there a simpler way? interpolatedChannel = red1+((red2-red1)*st) interpolatedChannel = interpolatedChannel.toString(16) ^ Is this the right thing to do? If speed and effectiveness is important in a mobile app, should I use bitwise operations? Help me! */

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  • [CA_COLOR_OPAQUE] things that make a layer non-opaque. scaled CAGradientLayer?

    - by mahal tertin
    i spent some time with the environment variable CA_COLOR_OPAQUE = 1 and have my findings to share. things that make a CALayer non-opaque (slow, more memory, ...): * contents with alpha (like an NSImage with an icon) * NSImage/CGImage from a pdf as contents (even when the pdf does not contain any alpha and opaque=YES) * backgroundColor = nil * CATextLayer with text in a (because it is contents with alpha) * rounded corners? maybe/sometimes * masksToBounds? not necessarily as we scale most of tree with CATransform3DScale on sublayerTransform i found also these rather irritating non-opaque: * CAGradientLayer that is somewhere down in this scaled tree (even when set all the gradient colors without alpha) * edgeAntialiasingMask != 0 of a layer that is somewhere down in this scaled tree the last two do not make sense to me. why should it be non opaque? what do i see? if anyone has any thoughts on these findings, i'm happy to learn as i couldn't find such a list yet.

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  • Flex Panel Content Background Color

    - by Jerry
    Hello guys. I am trying to set the gradient background color for my panel via skins. I try to change my code but nothing seems to change. Not sure what to do. Thanks for any reply. My skin file /<!-- layer 2: background fill --/> <!--- Defines the appearance of the PanelSkin class's background. --> <s:Rect id="background" left="1" top="1" right="1" bottom="1"> <s:fill> <!--- @private Defines the PanelSkin class's background fill. The default color is 0xFFFFFF. --> <s:SolidColor id="backgroundFill" color="red"/> //Change to red but //nothing happen.... </s:fill> </s:Rect>

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  • Methods for making R plots look like Excel plots?

    - by brianjd
    I've been poking around with R graphical parameters trying to make my plots look a little more professional (e.g., las=1, bty="n" usually help). But not quite there. Started playing with tikzDevice. A huge improvement! Amazing how much better things look when the font sizes and styles in the figure match those of the surrounding document. Still, not quite there. What I'm ultimately looking for are those professional gradient shading, rounded corners, and shadow effects found in MS Excel plots. I know they're probably considered chart junk, but I like them. They're just nice looking. Q: How can I get these effects into my R plots? Do people usually just export to Inkscape and doodle over there? It would be nice if there were a literate programming approach. Is there an R package that handles these effects outright?

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  • Visual Studio 2010 element names for theming

    - by Anthony Potts
    I am trying to figure out what the element name for the tooltip is in Visual studio so that I can change the style using the extension found here. Anyone know what that is? I am using the default theme which seems to have a white to light grey gradient on it. This is less than optimal since the text for the functions are also white. In a more general question (and perhaps better), is there anything that maps the names as they are found in the theme to where they are in the IDE.

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  • flex application transparent backbround

    - by simplemagik
    i have some problems with embedding swf into html page. Customer asked me to add some round corners to my application. I added. Then the design of the has changed and instead of black background i got ragial gradient( So, i need to make the corners of the swf transparent, but don't know how. wmode=transparent and backgroudAlpha param doesn't work. Need some help... :/ It's important that one solution i found works on Flash Builder Beta 2, but didn't work on Adobe flash builder 4.

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  • Background image fixed with vertical scroll bar in IE

    - by Rich
    I have a gradient background image in my web application, it goes from dark at the top to light at the bottom. In Firefox, this image is handled properly, where upon scrolling vertically downwards on the page, the dark top section disappears. However, when I started testing in IE (I'm using IE8) the background image stays fixed behind the screen as you vertically scroll, meaning the dark top section of the background image is always rendered at the top of the IE view. I've set the background tag to have scroll defined, which from all I can tell should solve the problem, but IE is not happy. background: #470077 url( images/abcd.jpg ) repeat-x scroll; I made sure to be clearing the data in IE in case it was caching the old style before I added scroll. Textual representation of issue (x = darkest, o = dark, _ = light, - = lightest) Firefox: top of page xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx oooooooooooooooooooooooo oooooooooooooooooooooooo ___________________________ ___________________________ scrolled down a bit oooooooooooooooooooooooo ___________________________ ___________________________ -------------------------------------- -------------------------------------- -------------------------------------- IE: top of page xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx oooooooooooooooooooooooo oooooooooooooooooooooooo ___________________________ ___________________________ scrolled down a bit xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx oooooooooooooooooooooooo oooooooooooooooooooooooo ___________________________ ___________________________

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  • to avoid page refresh during button click event in asp.net

    - by ush
    public partial class _Default : System.Web.UI.Page { protected void Page_Load(object sender, EventArgs e) { if (!IsPostBack) // If page loads for first time { Session["update"] = Server.UrlEncode(System.DateTime.Now.ToString()); // Assign the Session["update"] with unique value //=============== Page load code ========================= //============== End of Page load code =================== } } protected void Button1_Click(object sender, EventArgs e) { if (Session["update"].ToString() == ViewState["update"].ToString()) // If page not Refreshed { //=============== On click event code ========================= Label1.Text = TextBox1.Text; //lblDisplayAddedName.Text = txtName.Text; //=============== End of On click event code ================== // After the event/ method, again update the session Session["update"] = Server.UrlEncode(System.DateTime.Now.ToString()); } else // If Page Refreshed { // Do nothing } } protected override void OnPreRender(EventArgs e) { ViewState["update"] = Session["update"]; } } this is not working for high resolution gradient background

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  • Errors in UILabel

    - by Todd Davies
    I'm trying to use the FXlabel when following this (Adding a gradient label section) tutorial. This is some of the code inside my viewDidLoad method: self.logoLabel = [[FXLabel alloc] initWithFrame:CGRectMake(14, 11, 280, 87)]; [logoLabel setFont:[UIFont boldSystemFontOfSize:45]]; [logoLabel setTextColor:[UIColor whiteColor]]; [logoLabel setShadowColor:[UIColor blackColor]]; [logoLabel setShadowOffset:CGSizeMake(0, 2)]; [logoLabel setTextAlignment:UITextAlignmentCenter]; [logoLabel setBackgroundColor:[UIColor clearColor]]; [logoLabel setText:@"Attorney Biz"]; [logoLabel setGradientStartColor:[UIColor colorWithRed:163.0/255 green:203.0/255 blue:222.0/255 alpha:1.0]]; [logoLabel setGradientEndColor:[UIColor whiteColor]]; Unfortnuately, I get an error "No visible @interface for 'UILabel' declares the selector 'setGradientStartColor'" at the second-to-last line and "No visible @interface for 'UILabel' declares the selector 'setGradientEndColor'" Can somebody explain how to remove these errors?

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  • Fusion Table Layer Caching issue

    - by user1854791
    I have created a series of fusion table layers and apply filtering to one of the layers in response to checkbox click events. The base layer of the map contains a gradient applied over county boundaries. When the base layer is unchecked, the filtered layer loses it's styling. I have added unique timestamps to all queries to avoid caching, however I get the feeling that these image tiles are still be cached for this situation. Is there any way to force the google fusion tables api to invalidate a cached image? Test site here: http://map.inquestmarketing.com/new.html Unchecking the Other - Consumer Prospects checkbox reproduces the issue. This is a pure client app, all of the source is in the single page.

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  • Indexing an image in-between already made content

    - by Christophersson
    I have a pre-code page coded as follows: <div id="linearBg"> <div id="wrapper"> <div class="logo"></div> <div class="navigation"></div> <div class="video"></div> <div class="content"></div> </div> </div> Where linearBg is a gradient background, the back board of the website. Wrapper is the container for the inner div's, and the rest are content oriented. So i've already implemented this with styles and all sorts, but the thing is I want to add: <div class="watermark"></div> underneath/behind both the content and video div, sort of like a reverse watermark, I've tried z-indexing but i'm not an expert. Could you guide me on to do make this possible? Thanks in advance

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  • Rendering sub tools on vertical toolbar

    - by user146780
    I was wondering how ex Photoshop and Expression Design render sub tools. These show up when for example you hold your mouse down on the fill tool, a sub menu comes up to your right with the fill and gradient tools. I'm just not sure how to go about this because this sub menu would essentially have to be an extension of my toolbar, but then it would find itself on my Frame control. How is this handled? Would it be a good idea to just paint on my frame?

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • nautilus selected item color

    - by shantanu
    See in the image, selected item "build" colour is black as background colour. How can i change the selected item colour gtk3 theme's nautilus.css script Which section colour need to modify: /* desktop mode */ .nautilus-desktop.nautilus-canvas-item { color: @bg_color; text-shadow: 1 1 alpha (#001B33, 0.8); } .nautilus-desktop.nautilus-canvas-item:active { background-image: none; background-color: alpha (@selected_bg_color, 0.84); border-radius: 4; color: @fg_color; } .nautilus-desktop.nautilus-canvas-item:selected { background-image: none; background-color: alpha (@bg_color, 0.84); border-radius: 4; color: @selected_fg_color; } .nautilus-desktop.nautilus-canvas-item:active, .nautilus-desktop.nautilus-canvas-item:prelight, .nautilus-desktop.nautilus-canvas-item:selected { text-shadow: none; } /* browser window */ NautilusTrashBar.info, NautilusXContentBar.info, NautilusSearchBar.info, NautilusQueryEditor.info { /* this background-color controls the symbolic icon in the entry */ background-color: mix (@fg_color, @base_color, 0.3); border-radius: 0; border-style: solid; border-width: 0 1 1 1; } NautilusSearchBar .entry { } .nautilus-cluebar-label { color: @fg_color; font: bold; } #nautilus-search-button *:active, #nautilus-search-button *:active:prelight { color: @dark_fg_color; } NautilusFloatingBar { background-color: @info_bg_color; border-radius: 3 3 0 0; border-style: solid; border-width: 1; border-color: darker (@info_bg_color); -unico-border-gradient: none; } NautilusFloatingBar .button { -GtkButton-image-spacing: 0; -GtkButton-inner-border: 0; } /* sidebar */ NautilusWindow .sidebar, NautilusWindow .sidebar .view { background-color: @bg_color; color: @fg_color; } NautilusWindow .sidebar .frame { } NautilusWindow > GtkTable > .pane-separator { background-color: @bg_color; border-color: @bg_color; border-width: 0 0 0 0; border-style: solid; }

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  • Producing a smooth mesh from density cloud and marching cubes

    - by Wardy
    Based on my results from this question I decided to build myself a 3D noise map containing float values in place of my existing boolean point values. The effect I'm trying to produce is something like this, rather than typical rolling hills; which should explain the "missing cubes" in the image below. If I render my density map in normal "minecraft mode" (1 block per point in the density map) varying the size of the cube based on the value in my density map (floats in the range 0 to 1) I get something like this: I'm now happy that I can produce a density map for the marching cubes algorithm (which will need a little tweaking) but for some reason when I run it through my implementation it's not producing what I expect. My problem is that I'm getting something like the first image in this answer to my previous question, when I want to achieve the effect in the second image. Upon further investigation I can't see how marching cubes does the "move vertex along the edge" type logic (i.e. the difference between the two images on my previous link). I see that it does do some interpolation, but I'm not convinced I have the correct understanding of what I think it should do, because the code in question appears to give the same result regardless of whether I use boolean or float values. I took the code from here which is a C# implementation of marching cubes, but instead of using the MarchingCubesPrimitive I modified it to accept an object of type IDrawable, containing lists for the various collections (vertices, normals, UVs, indices), the logic was otherwise untouched. My understanding is that given a very low isovalue the accuracy level of the surface being rendered should increase, so in short "less 45 degree slows more rolling hills" type mesh output. However this isn't what I'm seeing. Have I missed something or is the implementation flawed and need to be fixed? EDIT: A little more detail on what I am seeing when I "marching cube" the data. Ok so firstly, ignore the fact that the meshes created by the chunks don't "connect" (i'll probably raise another question about this later). Then look at the shaping of the island, it's too ... square, from the voxels rendered as boxes you get the impression there's a clean soft gradual hill and yet from the image there are sharp falling edges even in the most central areas where the gradient in the first image looks the most smooth. The data is "regenerated" each time I run this so no 2 islands come out the same, and it's purely random so not based on noise, but still, how can it look so smooth in 1 image and so not smooth in the other?

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  • Bad results converting PDF to EPS on Linux

    - by Tim
    I'm having some trouble converting PDFs (created by Adobe Illustrator on a Mac) to EPS. I have tried several things but I am wondering if there is a better option. The following list is ordered by decreasing quality: inkscape --export-area-page --export-eps=out.eps in.pdf using the graphical program Inkscape works best, but is a bit slow; pdftops -eps in.pdf out.eps uses Poppler and works good and is fast; pdf2ps in.pdf out.eps uses ghostscript and works ok for simple documents; convert in.pdf out.eps uses ImageMagick and always rasterizes the image. I haven't tested the following: acroread -toPostScript use acroread (Linux only) Some issues I've found: Transparency is not supported in EPS, but instead of flattening the layers, most programs rasterize the image producing big files and ugly graphs. Inkscape does this best by only rasterizing the unsupported area. Gradients are rendered properly by Inkscape, but Poppler somehow chops up the gradient into many shapes of different colors. Greek symbols are seemingly not supported by Ghostscript and are rasterized (using pdf2ps). What are your experiences for this kind of task? Did I forgot certain programs and/or command line options that improve quality? I found some posts on this, but not a (thorough) comparison of possibilities, please correct me if I'm wrong. Related posts How to convert PDF to EPS? on TeX

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  • unable to access Internet by wireless but can by cable

    - by Jeff King
    i'M GOING MAD! UNtil last friday I had been successfully using wifi with the supplier as VIRGIN through their Motorola SB 4200 cable Modem and the wireless router being the Linksys WRT 54G router. Supported were three lap tops and an EPSON 510W printer and this had been running with no issue for about 3 years. Back to last friday, we started suffering significant delays and then the network collapsed with no wireless access. I was able to connect a single laptop direct to the cable modem and internet access was restored to just that one device. I thought that the problem was the router so I tried a backup D-Link device with no success. I have subsequently bought another cable modem AND a netgear router plus addidtional ethernet cables but with no success. The best that happens is that the signal appears good but I cannot get access to the internet. A yellow question mark appears on the 'gradient' icon. Each laptop and router works elsewhere so I'm stumped. Mind you I am a real novice so I'm not surprised. Please can anyone tell me what I'm doing wrong?

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  • MacBook Pro (2007 - ATI-Card) Screen goes half black then shuts down the entire computer

    - by BluePerry
    Hey, when I'm starting my MBP I get about 10-60 seconds of the booting process before the screen goes half black (Its like applying a black to transparent gradient from the left side of the screen to the middle of the screen). After a 5 seconds the entire screen blacks out and the MBP shuts down. There have been issues with heat and some minor artifacts on the screen in the past but nothing serious as far as I know. Everything could be resolved by rebooting or letting the MBP cool down a bit. I would like to identify the problem now. There are 3 possibilities I can think of right now: My graphics card is defect and shuts down after a few seconds. (But if thats true, I find it kind of hard to explain the HALF black screen) My LCD-Panel is defect and sends back wrong signals so the system shuts down??? (I not sure about that) My fan or/and thermal sensors are defect and forcing the graphics card to shut down. Can anyone point if I'm right or if there yet another reason for this. I'd be thankful for any hint or tips. Cheers, Per

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  • Improved appointment rendering in RadScheduler for ASP.NET AJAX, Q1 2010

    Now that Q1 2010 release is out in the wild, we can sit down and discuss some of the changes we decided to make in the new release. One of them is the new appointment rendering of RadScheduler - a potentially breaking change, but a much needed one. If you have problems with your old custom skins, include the old base stylesheet along with your RadScheduler and set EnableEmbeddedBaseStylesheet=false in your RadScheduler. You can find the said base stylesheet attached to this post.   While trying to improve the performance of RadScheduler, I noticed that the number of resources slows down the rendering and overall performance considerably. This had to be expected - the images to support the appointment rounded corners (and the predefined resources) were quite large. However, I didnt take into account that all browsers keep for performance reasons their images uncompressed in memory and with the color depth of the current desktop. A simple calculation later I discovered that the appointment sprite itself is taking 25MB memory when loaded. Add 5 resources to the fray and you have 150MB memory down with a single blow. As it turns out - a sprite image is not a panacea, if it gets too big - dont be afraid to break it in two. The loading time may suffer, but your browser suffers more while rendering a 25MB monster. First I thought of undertaking the aforementioned solution - breaking the appointment sprite in two and thus reducing the two appointment sprites to mere 2MB uncompressed. Then I thought - the rounded corners are small - I can use borders and backgrounds to simulate rounded appointment borders while still keeping the same HTML structure. The gradients can be done with a single 10x50px image plus we have a gain - border colors and backgrounds can be changed on the fly.  I started with five rendering elements at first, then tried with four and finally I settled on only three elements.  Behold the new appointment rendering (quite simple really):       On the left you can see that the first container has only top and bottom borders and a background. In fact, the background isnt even needed since it will be obscured by the elements on top of it. The whole first container is only needed for the four dots that reside in the four corners of the appointment. On top of this container is another one that holds the left and right borders and slightly lighter background to create the illusion of a second lighter border beside the other two. At last on top of all others is placed the text container that also holds the top and bottom borders and the gradient background. On the right you can see the final result - Im quite happy with it and I hope you will be too. After creating the new rendering we took another step further - we decided to use alpha gradients for the resource rendering, thus supporting any color appointments with rounded corners and gradients. You can see some examples below:We plan on adding BorderColor and BackColor properties  to the ResourceStyles definitions for Q1 SP1. However with the new rendering in Q1 2010 we do support BackColor and BorderColor appointment properties - you only need to set AppointmentStyleMode=Default to keep RadScheduler from switching to Simple appointment rendering. Here is one screenshot of RadScheduler with appointments set to different colors: I hope that you will enjoy working with the new appointments in RadScheduler. RadScheduler base stylesheet Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • Improved appointment rendering in RadScheduler for ASP.NET AJAX, Q1 2010

    Now that Q1 2010 release is out in the wild, we can sit down and discuss some of the changes we decided to make in the new release. One of them is the new appointment rendering of RadScheduler - a potentially breaking change, but a much needed one. If you have problems with your old custom skins, include the old base stylesheet along with your RadScheduler and set EnableEmbeddedBaseStylesheet=false in your RadScheduler. You can find the said base stylesheet attached to this post.   While trying to improve the performance of RadScheduler, I noticed that the number of resources slows down the rendering and overall performance considerably. This had to be expected - the images to support the appointment rounded corners (and the predefined resources) were quite large. However, I didnt take into account that all browsers keep for performance reasons their images uncompressed in memory and with the color depth of the current desktop. A simple calculation later I discovered that the appointment sprite itself is taking 25MB memory when loaded. Add 5 resources to the fray and you have 150MB memory down with a single blow. As it turns out - a sprite image is not a panacea, if it gets too big - dont be afraid to break it in two. The loading time may suffer, but your browser suffers more while rendering a 25MB monster. First I thought of undertaking the aforementioned solution - breaking the appointment sprite in two and thus reducing the two appointment sprites to mere 2MB uncompressed. Then I thought - the rounded corners are small - I can use borders and backgrounds to simulate rounded appointment borders while still keeping the same HTML structure. The gradients can be done with a single 10x50px image plus we have a gain - border colors and backgrounds can be changed on the fly.  I started with five rendering elements at first, then tried with four and finally I settled on only three elements.  Behold the new appointment rendering (quite simple really):       On the left you can see that the first container has only top and bottom borders and a background. In fact, the background isnt even needed since it will be obscured by the elements on top of it. The whole first container is only needed for the four dots that reside in the four corners of the appointment. On top of this container is another one that holds the left and right borders and slightly lighter background to create the illusion of a second lighter border beside the other two. At last on top of all others is placed the text container that also holds the top and bottom borders and the gradient background. On the right you can see the final result - Im quite happy with it and I hope you will be too. After creating the new rendering we took another step further - we decided to use alpha gradients for the resource rendering, thus supporting any color appointments with rounded corners and gradients. You can see some examples below:We plan on adding BorderColor and BackColor properties  to the ResourceStyles definitions for Q1 SP1. However with the new rendering in Q1 2010 we do support BackColor and BorderColor appointment properties - you only need to set AppointmentStyleMode=Default to keep RadScheduler from switching to Simple appointment rendering. Here is one screenshot of RadScheduler with appointments set to different colors: I hope that you will enjoy working with the new appointments in RadScheduler. RadScheduler base stylesheet Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • Drawing custom graphics on the iPhone: CALayer vs. CGContext

    - by Henry Cooke
    Hi all, I have an application in which I'm doing some custom drawing, a bunch of lines on a gradient background, like so (ignore the text, they're just UILabels): At the moment, that's all done by starting a new CGContext, drawing stuff into it with CGContextDrawLinearGradient and CGContextStrokePath, then finally saving the resulting image with UIGraphicsGetImageFromCurrentImageContext. The positioning info is calculated while I'm laying out those labels, so it'd be a PITA (and duplication of effort) to calculate it all over again when the containing UIView is drawn with drawRect, so I'm drawing it ahead of time into a UIImage. All works fine, so far so good. However, I have a sneaking suspicion that it may be more efficient to use CALayers to do this drawing. My (cursory) understanding of the difference between the two approaches is that a CALayer is more like a bunch of instructions to draw stuff, and so takes up less memory until it's actually drawn onscreen, whereas drawing everything into a UIImage ahead of time means that you've got a sodding great bitmap kicking around in memory all the time, whether it's drawn or not. Is that a correct understanding? What is generally considered to be the best way of drawing custom images on the iPhone?

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  • CSS background-images and Z-Index problem

    - by dscher
    Hope someone has an easy answer on this. I have a header image which is just a 75px high gradient with a fade on the bottom. I have it set as the background image on my header and I want to throw in a left-sidebar on my page. There is a transparency on the header image and when I have my sidebar I can't get it to sit behind the header. You can see in this screenshot: link text The green sidebar won't "sit" behind the header. I have the header z-index set to 99 and the sidebar to 1. I tried the reverse to make sure I didn't mix up my numbers but that didn't work. Both are absolutely positioned. I'm attaching their CSS selectors in the hopes someone has an easy answer. Am sure I'm missing something basic: div.header { z-index: 99; background: transparent; background-image: url(images/header_bg.png); position: absolute; height: 85px; width: 100%; font-family: Helvetica, Verdana, Arial, sans-serif; } div#leftsidebar { height: 400px; border-right-style: dashed; border-right-width: 1px; z-index: -1; margin-top: 75px; width: 200px; position: absolute; background-color: #66ff66; } Thanks.

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