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  • Determine arc-length of a Catmull-Rom spline

    - by Wouter
    I have a path that is defined by a concatenation of Catmull-Rom splines. I use the static method Vector2.CatmullRom in XNA that allows for interpolation between points with a value going from 0 to 1. Not every spline in this path has the same length. This causes speed differences if I let the weight go at a constant speed for every spline while proceeding along the path. I can remedy this by letting the speed of the weight be dependent on the length of the spline. How can I determine the length of such a spline? Should I just approximate by cutting the spline into 10 straight lines and sum their lengths? I'm using this for dynamic texture mapping on a generated mesh defined by splines.

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  • How can I use splne() with ggplot?

    - by David
    I would like to fit my data using spline(y~x) but all of the examples that I can find use a spline with smoothing, e.g. lm(y~ns(x), df=_). I want to use spline() specifically because I am using this to do the analysis represented by the plot that I am making. Is there a simple way to use spline() in ggplot? I have considered the hackish approach of fitting a line using geom_smooth(aes(x=(spline(y~x)$x, y=spline(y~x)$y)) but I would prefer not to have to resort to this. Thanks!

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  • Drawing a clamped uniform cubic B-spline using Cairo

    - by Tamás
    I have a bunch of coordinates which are the control points of a clamped uniform cubic B-spline on the 2D plane. I would like to draw this curve using Cairo calls (in Python, using Cairo's Python bindings), but as far as I know, Cairo supports Bézier curves only. I also know that the segments of a B-spline between two control points can be drawn using Bézier curves, but I can't find the exact formulae anywhere. Given the coordinates of the control points, how can I derive the control points of the corresponding Bézier curves? Is there any efficient algorithm for that?

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  • Can two mocha for After Effects X-Spline Layers be merged ?

    - by George Profenza
    Hello, I'm new to mocha for After Effects, but like the auto tracking feature. There are a few markers I'm adding, but there's one which is giving me a bit of a headache. I'm tracking a circle that moves around a larger object, so it moves in front of it initially, then behind, being occluded by the larger object, then in front again. I tried to track the circle in the first part(when it's in front, before being occluded) and in the second part(when it's in front again, coming out on the other side of the large object) using a single X-Spline. The problem is the second part starts in a different location and I don't know how to 'move' the X-Spline to the new position and track from there, without affecting the previous keyframes. As a workaround I use two X-Spline Layers, export the data to .txt files, then manually merge the two files into a new one containing keyframes from both X-Spline Layers. Is there an easier way to do this (either merging two X-Spline Layer, or using a single X-Spline Layer that can move to a new location without affecting previous keyframes) ? Any suggestion would help.

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  • Measuring the limit of a point on a smooth.spline in R

    - by Subtle Array
    I'm not sure if that's the right terminology. I've entered some data into R, and I've put a smoothingSpline through it using the following command. smoothingSpline = smooth.spline(year, rate, spar=0.35) plot(x,y) lines(smoothingSpline) Now I'd like to measure some limits (or where the curve is at a given y point), and maybe to some predictive analysis on points that extend beyond the graph. Are there commands in R for doing this?

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  • Is there a Java library with 3D spline functions?

    - by Liam
    In particular, I need a way to represent a curve/spline that passes through a set of known 3D points, and a way of finding other points on the curve/spline, by subdivision/interpolation. For example, if I have a set of points P0 to PN, I want to find 100 points between P0 and P1 that are on a spline that passes through P0 and P1. I see that Java3D's KBRotPosScaleSplinePathInterpolator performs such a calculation, but it is tied to that API's scenegraph model and I do not see how to return the values I need.

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  • Interpolation between two 3D points?

    - by meds
    I'm working with some splines which define a path a character follows (you can see a gameplay video here to get a better understanding of what's going on: http://www.youtube.com/watch?v=BndobjOiZ6g). Basically the characters 'forward' look direction is set to the 'forward' direction of the spline and when players tilt their phone left and right the character is strafed along its 'right' coordinate. The issue with this is (rather obviously) in performance, interpolating over a spline to find the nearest position and tangent relative to the player is an incredibly costly operation. To get by this I cache a finite number of positions in what I call 'SplineDetails', the class is as follows: public class SplineDetails { public SplineDetails() { Forward = Vector3.forward; Position = Vector3.one * float.MaxValue; Alpha = -1; } public float Alpha; // [0,1] measured along length of spline where 0 is the initial point and 1 is the end point of the spline public Vector3 Position; // the point of the spline at this alpha public Vector3 Forward; // the forward tangent of the spline at this alpha } I populate this with say 30 coordinates and I can give a rough estimate of a coordinate and 'forward' based on a position past in. It's not as accurate but it's much faster. But now I'd like to make the system work better by estimating positions and 'forward' directions by interpolating between two of the cached points though I'm stuck trying to figure out some logic. My first problem is, how can I determine between which two points the object is? Given each point can be placed at different intervals along the spline it could mean that two points in front or behind the object can be closer to the object. The other problem is to figure out the proportion between the two paths it's between, i.e. if there is a point a at coordinate (0,0,0) and point b at coordinate (1,0,0) if the object is at position (0.5,0,0) then the result it should give is '0.5' (as it is equal distance away from point a and point b). That's a simple example, but what if the object is at coordinate (0.5,3,0) for example?

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  • Using scipy.interpolate.splrep function

    - by Koustav Ghosal
    I am trying to fit a cubic spline to a given set of points. My points are not ordered. I CANNOT sort or reorder the points, since I need that information. But since the function scipy.interpolate.splrep works only on non-duplicate and monotonically increasing points I have defined a function that maps the x-coordinates to a monotonically increasing space. My old points are: xpoints=[4913.0, 4912.0, 4914.0, 4913.0, 4913.0, 4913.0, 4914.0, 4915.0, 4918.0, 4921.0, 4925.0, 4932.0, 4938.0, 4945.0, 4950.0, 4954.0, 4955.0, 4957.0, 4956.0, 4953.0, 4949.0, 4943.0, 4933.0, 4921.0, 4911.0, 4898.0, 4886.0, 4874.0, 4865.0, 4858.0, 4853.0, 4849.0, 4848.0, 4849.0, 4851.0, 4858.0, 4864.0, 4869.0, 4877.0, 4884.0, 4893.0, 4903.0, 4913.0, 4923.0, 4935.0, 4947.0, 4959.0, 4970.0, 4981.0, 4991.0, 5000.0, 5005.0, 5010.0, 5015.0, 5019.0, 5020.0, 5021.0, 5023.0, 5025.0, 5027.0, 5027.0, 5028.0, 5028.0, 5030.0, 5031.0, 5033.0, 5035.0, 5037.0, 5040.0, 5043.0] ypoints=[10557.0, 10563.0, 10567.0, 10571.0, 10575.0, 10577.0, 10578.0, 10581.0, 10582.0, 10582.0, 10582.0, 10581.0, 10578.0, 10576.0, 10572.0, 10567.0, 10560.0, 10550.0, 10541.0, 10531.0, 10520.0, 10511.0, 10503.0, 10496.0, 10490.0, 10487.0, 10488.0, 10488.0, 10490.0, 10495.0, 10504.0, 10513.0, 10523.0, 10533.0, 10542.0, 10550.0, 10556.0, 10559.0, 10560.0, 10559.0, 10555.0, 10550.0, 10543.0, 10533.0, 10522.0, 10514.0, 10505.0, 10496.0, 10490.0, 10486.0, 10482.0, 10481.0, 10482.0, 10486.0, 10491.0, 10497.0, 10506.0, 10516.0, 10524.0, 10534.0, 10544.0, 10552.0, 10558.0, 10564.0, 10569.0, 10573.0, 10576.0, 10578.0, 10581.0, 10582.0] Plots: The code for the mapping function and interpolation is: xnew=[] ynew=ypoints for c3,i in enumerate(xpoints): if np.isfinite(np.log(i*pow(2,c3))): xnew.append(np.log(i*pow(2,c3))) else: if c==0: xnew.append(np.random.random_sample()) else: xnew.append(xnew[c3-1]+np.random.random_sample()) xnew=np.asarray(xnew) ynew=np.asarray(ynew) constant1=10.0 nknots=len(xnew)/constant1 idx_knots = (np.arange(1,len(xnew)-1,(len(xnew)-2)/np.double(nknots))).astype('int') knots = [xnew[i] for i in idx_knots] knots = np.asarray(knots) int_range=np.linspace(min(xnew),max(xnew),len(xnew)) tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) y1= interpolate.splev(int_range,tck,der=0) The code is throwing an error at the function interpolate.splrep() for some set of points like the above one. The error is: File "/home/neeraj/Desktop/koustav/res/BOS5/fit_spline3.py", line 58, in save_spline_f tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) File "/usr/lib/python2.7/dist-packages/scipy/interpolate/fitpack.py", line 465, in splrep raise _iermessier(_iermess[ier][0]) ValueError: Error on input data But for other set of points it works fine. For example for the following set of points. xpoints=[1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1630.0, 1630.0, 1630.0, 1631.0, 1631.0, 1631.0, 1631.0, 1630.0, 1629.0, 1629.0, 1629.0, 1628.0, 1627.0, 1627.0, 1625.0, 1624.0, 1624.0, 1623.0, 1620.0, 1618.0, 1617.0, 1616.0, 1615.0, 1614.0, 1614.0, 1612.0, 1612.0, 1612.0, 1611.0, 1610.0, 1609.0, 1608.0, 1607.0, 1607.0, 1603.0, 1602.0, 1602.0, 1601.0, 1601.0, 1600.0, 1599.0, 1598.0] ypoints=[10570.0, 10572.0, 10572.0, 10573.0, 10572.0, 10572.0, 10571.0, 10570.0, 10569.0, 10565.0, 10564.0, 10563.0, 10562.0, 10560.0, 10558.0, 10556.0, 10554.0, 10551.0, 10548.0, 10547.0, 10544.0, 10542.0, 10541.0, 10538.0, 10534.0, 10532.0, 10531.0, 10528.0, 10525.0, 10522.0, 10519.0, 10517.0, 10516.0, 10512.0, 10509.0, 10509.0, 10507.0, 10504.0, 10502.0, 10500.0, 10501.0, 10499.0, 10498.0, 10496.0, 10491.0, 10492.0, 10488.0, 10488.0, 10488.0, 10486.0, 10486.0, 10485.0, 10485.0, 10486.0, 10483.0, 10483.0, 10482.0, 10480.0] Plots: Can anybody suggest what's happening ?? Thanks in advance......

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  • Python Least-Squares Natural Splines

    - by Eldila
    I am trying to find a numerical package which will fit a natural which minimizes weighted least squares. There is a package in scipy which does what I want for unnatural splines. import numpy as np import matplotlib.pyplot as plt from scipy import interpolate import random x = np.arange(0,5,1.0/2) xs = np.arange(0,5,1.0/500) y = np.sin(x+1) for i in range(len(y)): y[i] += .2*random.random() - .1 knots = np.array([1,2,3,4]) tck = interpolate.splrep(x,y,s=1,k=3,t=knots,task=-1) ynew = interpolate.splev(xs,tck,der=0) plt.figure() plt.plot(xs,ynew,x,y,'x')

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  • Akima interpolation of an array of doubles

    - by David Rutten
    Assuming I have an array of doubles, what's a good algorithm to sample this series using Akima interpolation? I'm too stupid to translate that mathematical description into code. // values is an array of doubles // idx is the index of the left-hand value for the current interpolation // t is the normalized parameter between values[idx] and values[idx+1] // Don't worry about array bounds, I'll handle that separately. public double InterpolateAkima(double[] values, int idx, double t) { ...? }

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  • How do I make cars on a one-dimensional track avoid collisions?

    - by user990827
    Using three.js, I use a simple spline to represent a road. Cars can only move forward on the spline. A car should be able to slow-down behind a slow moving car. I know how to calculate the distance between 2 cars, but how to calculate the proper speed in each game update? At the moment I simply do something like this: this.speed += (this.maxSpeed - this.speed) * 0.02; // linear interpolation to maxSpeed // the position on the spline (0.0 - 1.0) this.position += this.speed / this.road.spline.getLength(); This works. But how to implement the slow-down part? // transform from floats (0.0 - 1.0) into actual units var carInFrontPosition = carInFront.position * this.road.spline.getLength(); var myPosition = this.position * this.road.spline.getLength(); var distance = carInFrontPosition - myPosition; // WHAT TO DO HERE WITH THE DISTANCE? // HOW TO CALCULATE MY NEW SPEED? Obviously I have to somehow take current speed of the cars into account for calculation. Besides different maxSpeeds, I want each car to also have a different mass (causing it to accelerate slower/faster). But this mass has to be then also taken into account for braking (slowing down) so they don't crash into each other.

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  • Vector math, finding coördinates on a planar between 2 vectors

    - by Will Kru
    I am trying to generate a 3d tube along a spline. I have the coördinates of the spline (x1,y1,z1 - x2,y2,z2 - etc) which you can see in the illustration in yellow. At those points I need to generate circles, whose vertices are to be connected at a later stadium. The circles need to be perpendicular to the 'corners' of two line segments of the spline to form a correct tube. Note that the segments are kept low for illustration purpose. [apparently I'm not allowed to post images so please view the image at this link] http://img191.imageshack.us/img191/6863/18720019.jpg I am as far as being able to calculate the vertices of each ring at each point of the spline, but they are all on the same planar ie same angled. I need them to be rotated according to their 'legs' (which A & B are to C for instance). I've been thinking this over and thought of the following: two line segments can be seen as 2 vectors (in illustration A & B) the corner (in illustraton C) is where a ring of vertices need to be calculated I need to find the planar on which all of the vertices will reside I then can use this planar (=vector?) to calculate new vectors from the center point, which is C and find their x,y,z using radius * sin and cos However, I'm really confused on the math part of this. I read about the dot product but that returns a scalar which I don't know how to apply in this case. Can someone point me into the right direction? [edit] To give a bit more info on the situation: I need to construct a buffer of floats, which -in groups of 3- describe vertex positions and will be connected by OpenGL ES, given another buffer with indices to form polygons. To give shape to the tube, I first created an array of floats, which -in groups of 3- describe control points in 3d space. Then along with a variable for segment density, I pass these control points to a function that uses these control points to create a CatmullRom spline and returns this in the form of another array of floats which -again in groups of 3- describe vertices of the catmull rom spline. On each of these vertices, I want to create a ring of vertices which also can differ in density (amount of smoothness / vertices per ring). All former vertices (control points and those that describe the catmull rom spline) are discarded. Only the vertices that form the tube rings will be passed to OpenGL, which in turn will connect those to form the final tube. I am as far as being able to create the catmullrom spline, and create rings at the position of its vertices, however, they are all on a planars that are in the same angle, instead of following the splines path. [/edit] Thanks!

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  • Is there a decent vector / spline library for php?

    - by Brendan Heywood
    Does anyone know of the best way to render clean vectors into a php image and then serve it as a jpeg/png? Specifically I want to draw lines, polygons and splines which are anti-aliased and then serve them up as jpegs. Preferably also with an alpha option when rendering. What would be spectacular is a php library with a similar API to Raphael (without the animation) - not only because Raphael has a great API but also because I'm already using it on my website for the dynamic bits but also need to bake jpeg's in parallel for static consumption.

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  • Interpolation of time series data in R

    - by Pierreten
    I'm not sure what i'm missing here, but i'm basically trying to compute interpolated values for a time series; when I directly plot the series, constraining the interpolation points with "interpolation.date.vector", the plot is correct: plot(date.vector,fact.vector,ylab='Quantity') lines(spline(date.vector,fact.vector,xout=interpolation.date.vector)) When I compute the interpolation, store it in an intermediate variable, and then plot the results; I get a radically incorrect result: intepolated.values <- spline(date.vector,fact.vector,xout=interpolation.date.vector) plot(intepolated.values$x,intepolated.values$y) lines(testinterp$x,testinterp$y) Doesn't the lines() function have to execute the spline() function to retrieve the interpolated points in the same way i'm doing it?

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  • Retain numerical precision in an R data frame?

    - by David
    When I create a dataframe from numeric vectors, R seems to truncate the value below the precision that I require in my analysis: data.frame(x=0.99999996) returns 1 (see update 1) I am stuck when fitting spline(x,y) and two of the x values are set to 1 due to rounding while y changes. I could hack around this but I would prefer to use a standard solution if available. example Here is an example data set d <- data.frame(x = c(0.668732936336141, 0.95351462456867, 0.994620622127435, 0.999602102672081, 0.999987126195509, 0.999999955814133, 0.999999999999966), y = c(38.3026509783688, 11.5895099585560, 10.0443344234229, 9.86152339768516, 9.84461434575695, 9.81648333804257, 9.83306725758297)) The following solution works, but I would prefer something that is less subjective: plot(d$x, d$y, ylim=c(0,50)) lines(spline(d$x, d$y),col='grey') #bad fit lines(spline(d[-c(4:6),]$x, d[-c(4:6),]$y),col='red') #reasonable fit Update 1 Since posting this question, I realize that this will return 1 even though the data frame still contains the original value, e.g. > dput(data.frame(x=0.99999999996)) returns structure(list(x = 0.99999999996), .Names = "x", row.names = c(NA, -1L), class = "data.frame") Update 2 After using dput to post this example data set, and some pointers from Dirk, I can see that the problem is not in the truncation of the x values but the limits of the numerical errors in the model that I have used to calculate y. This justifies dropping a few of the equivalent data points (as in the example red line).

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  • Windows CE Chat Transcript (March 30, 2010)

    - by Bruce Eitman
    For those of you who missed the chat today, here is the raw transcript.   By raw, I mean that I copied and pasted the discussion without any edits. This is divided into two parts, the top part is the answers from the Microsoft Experts and the bottom part is the questions from the audience. Answers from Microsoft:   Karel Danihelka [MS] (Expert)[2010-3-30 12:2]: Hi everyone, my name is Karel Danihelka and I am developer in partner response team. Sing Wee [MS] (Expert)[2010-3-30 12:2]: Hi, I'm Sing Wee, part of the CoreOS/BSP Test Team. GLanger_MS (Expert)[2010-3-30 12:2]: Hi, I'm Glen Langer, program manager on the Core Team. Karel Danihelka [MS] (Expert)[2010-3-30 12:3]: Q: I need to implement hardware timers on my windows CE 6.0 device to trigger events at microsecond intervals. Where should i start? A: Until you are using CPU with GHz frequency your only chance is use interrupt handler and implement all funcionality there. But it will be really tricky and may reduce system performance. If period will be near to millisecond timeframe you can use normal thread wait for event pattern. Karel Danihelka [MS] (Expert)[2010-3-30 12:5]: Q: I want to partition my NAND Flash device. One partition to use for hive ragistry and the other for the apps and data. The only way to do it is programmatically or setting some registry values ? A: It need to be set in registry - generally you need mark this partition as boot partition. Karel Danihelka [MS] (Expert)[2010-3-30 12:7]: Q: My CPU is Intel celeron M processor 1Ghz. A: In this case you can try use normal approach - in interrupt handler return SYSINTR and start thread in device driver which will spin thread waiting on event attached to this SYSINTR. Karel Danihelka [MS] (Expert)[2010-3-30 12:7]: Q: If i need to implement it using interrupt handlers, What are all the files that I should look at? A: Good quesiton - I would recommend documentation and there was BSP development book to download for free. mikehall_ms (Moderator)[2010-3-30 12:8]: Q: Hi guys, what's the formal way to report bugs back to the core team / product team? The mechanism of calling the support phone number every time is really onerous and time-consuming. Is there another mechanism? A: Using product support is the formal way to report bugs/issues - Product support can then create an issue that can be tracked. Karel Danihelka [MS] (Expert)[2010-3-30 12:9]: Q: But the operation for creating the partitions ? A: This is tricky - if you will make it autopartition & autoformat it will be created by filesystem. But generally it depends on your boot loader. mikehall_ms (Moderator)[2010-3-30 12:10]: Q: Is Windows Phone 7 related to Windows CE? If so, can you tell me what version of Windows CE is the basis? Is it in fact the new version of Windows Mobile? A: At MIX 2010 Charlie Kindel presented a session that described some of the core technologies that make up Windows Phone 7 Series, including the underlying operating system (Windows CE) and the new ISV programming model based on Silverlight and .NET - check out the Mix Online Videos to get more information. davbo-msft (Moderator)[2010-3-30 12:10]: Q: Is Windows Phone 7 related to Windows CE? If so, can you tell me what version of Windows CE is the basis? Is it in fact the new version of Windows Mobile? A: This forum is to discussed released products in the industry. Windows Mobile & Windows CE are based on the same Windows CE Kernel/system. Windows CE is focused on deliverying the OS for embedded customers in the market where Windows Mobile is focused on deliverying compelling Windows Phone platform. davbo-msft (Moderator)[2010-3-30 12:11]: Q: Is Windows Phone 7 related to Windows CE? If so, can you tell me what version of Windows CE is the basis? Is it in fact the new version of Windows Mobile? A: http://en.wikipedia.org/wiki/Windows_CE Wikipedia gives a good breakdown of the version history. Travis Hobrla [MS] (Expert)[2010-3-30 12:13]: Q: I created a OS design with KITL and kernel debugger enabled. But I am unable to connect to the target for debugging. I am getting the following error when i try to connect with the device. PB Debugger Cannot initialize the Kernel Debugger. PB Debugger Debugger could not initialize connection. PB Debugger The Kernel Debugger is waiting to connect with target. PB Debugger The Kernel Debugger has been disconnected successfully. A: One possibility is that a rogue cesvchost.exe has co-opted the debugger. I am assuming this is CE 6.0? Can you try exiting visual studio and manually killing the cesvchost.exe process from the Task Manager? davbo-msft (Moderator)[2010-3-30 12:14]: Q: Hi guys, what's the formal way to report bugs back to the core team / product team? The mechanism of calling the support phone number every time is really onerous and time-consuming. Is there another mechanism? A: For info on contacting Microsoft support refer to the support page on the Embedded website: http://msdn.microsoft.com/en-us/windowsembedded/dd897633.aspx Sing Wee [MS] (Expert)[2010-3-30 12:16]: Q: Do u mean ISR/IST implementation? How can i register an interrupt? What kind of interrupt should i register? A: A good introduction to interrupts in WinCE 6.0 can be found here (aside from the documentation on MSDN): http://download.microsoft.com/download/9/c/f/9cffaa58-4000-48d6-a4b2-5fed9e4e6410/Chapter%206%20-%20Developing%20Device%20Drivers.pdf mikehall_ms (Moderator)[2010-3-30 12:16]: Q: What will be different in Windows Compact 7 from CE 6.0? A: Unfortunately we cannot discuss unreleased products on this chat - keep an eye on the Windows Embedded web site and blogs to keep up to date with product announcements. Travis Hobrla [MS] (Expert)[2010-3-30 12:16]: Q: I am using CE 6.0. There is no cesvchost process running in my system. A: What operating system are you using? Karel Danihelka [MS] (Expert)[2010-3-30 12:16]: Q: So...I have to modify file system code to create 2 partition at system startup ?!! I haven't understood.... A: You don't need to modify code, there are registry settings to achive this (look to documentation). But you may need to create partition table in boot loader. Unfortunatelly there isn't simple way how to do it. davbo-msft (Moderator)[2010-3-30 12:18]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? A: Windows Embedded CE 6.0 R3 includes Sliverlight for Windows Embedded. Refer to New Features overview on the embedded web site. http://www.microsoft.com/windowsembedded/en-us/products/windowsce/default.mspx. Silverlight - The power of Silverlight brought to Windows Embedded CE to create rich applications and user interfaces is new part of Windows CE Embedded. mikehall_ms (Moderator)[2010-3-30 12:20]: Q: The link for developing device drivers is not working. can u please check that? A: http://msdn.microsoft.com/en-us/library/ms923714.aspx davbo-msft (Moderator)[2010-3-30 12:20]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? A: Sorry misunderstood the question I thought you were asking if embedded CE could handle Silverlight. Please repost so that the question goes back into the active queue because once answered no way to put the status back to open. Travis Hobrla [MS] (Expert)[2010-3-30 12:21]: Q: sorry! Windows XP SP3 A: Can you try exiting VS2005 and confirming cesvchost.exe is not running, then renaming C:\Documents and Settings\USERNAME\Local Settings\Application Data\Microsoft\CoreCon\1.0 to 1.0_backup, then restarting VS2005? Sing Wee [MS] (Expert)[2010-3-30 12:24]: Q: Can I have the book's name please? A: I believe the downloadable version is related to the last link I sent. If you go to the following website, I believe you can download the whole thing: http://msdn.microsoft.com/en-us/windowsembedded/ce/cc294468.aspx davbo-msft (Moderator)[2010-3-30 12:24]: Q: If one has an image on a Silverlight page, it seems to be cached. How would one refresh that cache after changing the underlying image? A: change the URI of the image or use a writeable bitmap if they want to manually toggle the pixels Sing Wee [MS] (Expert)[2010-3-30 12:25]: A: Whoops, hit [ENTER] too early. On the right side, you'll see there an "Exam Preparation Kit" link that can be downloaded in several different languages. Sing Wee [MS] (Expert)[2010-3-30 12:25]: Q: Can I have the book's name please? A: Whoops, hit [ENTER] too early. On the right side, you'll see there an "Exam Preparation Kit" link that can be downloaded in several different languages. Karel Danihelka [MS] (Expert)[2010-3-30 12:26]: Q: I have a NAND Flash on my target device. On this flash I have the hive registry and an application.I have observed that when the NAND flash is fully, the system startup time is longer....is there a degradation of NAND use that influences the startup time ? Why ? A: Yes - on boot flash abstraction library (old one) read metadata from all sectors to rebuild physical - logical mapping table. davbo-msft (Moderator)[2010-3-30 12:27]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? A: Need addition info on this question. Can you provide more details on what you are trying to do in Silverlight? davbo-msft (Moderator)[2010-3-30 12:27]: Q: If one has an image on a Silverlight page, it seems to be cached. How would one refresh that cache after changing the underlying image? A: Additonal Info: if you want to manually touch the pixels use WriteableBitmap if you want to use the underlying HWND then use IXRVisualHost::GetHWND() davbo-msft (Moderator)[2010-3-30 12:28]: Q: Writable bitmap, is there an example of the syntax? A: if you want to manually touch the pixels use WriteableBitmap if you want to use the underlying HWND then use IXRVisualHost::GetHWND() davbo-msft (Moderator)[2010-3-30 12:29]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? A: Can I get more information about this question about what you are trying to accomplish in Silverlight? davbo-msft (Moderator)[2010-3-30 12:31]: Q: IXRVisualHost::GetHWND() exactly what I needed Thanks, A: Your welcome Sing Wee [MS] (Expert)[2010-3-30 12:31]: Q: ok. thanks for the book's link A: No problem. Travis Hobrla [MS] (Expert)[2010-3-30 12:32]: Q: Typically for SoC devices you name your hardware specific libraries in the form "SOCDIRNAME_LIBNAME". In our platform "OMAP35XX_TPS659XX_TI_V1" if you do this we cause the catalog parser to die... For example if we have a library "Musbfn_OMAP35XX_TPS659XX_TI_V1.dll" entering this in the catalogs pbcxml file in a <module> section causes the XML parser to fail with : Error 3 The 'urn:Microsoft.PlatformBuilder/Catalog:Module' element is        invalid - The value '012345678901234567890123456789.dll' is invalid         according to its datatype         'urn:Microsoft.PlatformBuilder/Catalog:CatalogFileName' - The actual         length is greater than the MaxLength value. A: There are a couple workarounds I can think of. I believe the Module element is only used when doing SYSGEN parsing to make sure dependent SYSGENs are present when the item is selected, so I believe it is optional to the catalog. The other obvious workaround is to shorten the soc name. I realize neither of these solutions is ideal. This is not something we anticipated when we tested CE6.0, sorry. Travis Hobrla [MS] (Expert)[2010-3-30 12:33]: Q: I am getting this error only when I select the KdStub as the debugger in Target device connectivity. A: Right, but KdStub is the debugger that you should use. Have you tried the steps I suggested? Travis Hobrla [MS] (Expert)[2010-3-30 12:36]: Q: If I select Active KTIL, My OS doesn't boots. It says "loading NK.EXE at 0x<xxxxx> location" after that nothing comes in the debug log. A: Can you look at the serial debug output and see what is happening there? Often it can give you a clue to the KITL driver malfunctioning. Travis Hobrla [MS] (Expert)[2010-3-30 12:38]: Q: I have tried that and I am getting the same error. A: I am assuming you have a device created in Target -> Connectivity Options in Platform Builder. What are the Kernel download / Kernel transport for your device? Travis Hobrla [MS] (Expert)[2010-3-30 12:40]: Q: KITL: *** Device Name CEPC56059 *** WARN: KITL will run in polling mode VBridge:: built on [Jul 10 2009] time [10:20:14] VBridgeInit()...TX = [16384] bytes -- Rx = [16384] bytes Tx buffer [0xA1B84860] to [0xA1B88860]. Rx buffer [0xA1B88880] to [0xA1B8C880]. VBridge:: NK add MAC: [0-60-65-2-DA-FB] Connecting to Desktop KITL: Connected host IP: 1 Port: 1086 .. this is the output of the serial debug A: This looks reasonable and does not give clues as to why boot would halt at that point. If you capture a network trace or turn on KITL debug zones via dpCurSettings in kitl.dll, do you see KITL active after this? Travis Hobrla [MS] (Expert)[2010-3-30 12:41]: Q: Both is happening via Ethernet. A: Only thing I have left to suggest is a Platform Builder installation Repair, then. Karel Danihelka [MS] (Expert)[2010-3-30 12:42]: Q: Hi, I saw that the ATADISK is quite generic and des not have any optimizations. Do you have any advice to consider while tryin to improve the performance of it? A: If I remember correctly sample code has support for some specific hardware controllers (little obsolete now). This should be good start point (if you will not decide take existing driver as sample and write you own). Travis Hobrla [MS] (Expert)[2010-3-30 12:44]: Q: I didn't do that. I have to try. A: I think that's the next valid step. You need to figure out whether KITL is hanging or the device - use instrumented serial debug messages and network trace to determine this. Sing Wee [MS] (Expert)[2010-3-30 12:46]: Q: KITL: *** Device Name CEPC56059 *** WARN: KITL will run in polling mode VBridge:: built on [Jul 10 2009] time [10:20:14] VBridgeInit()...TX = [16384] bytes -- Rx = [16384] bytes Tx buffer [0xA1B84860] to [0xA1B88860]. Rx buffer [0xA1B88880] to [0xA1B8C880]. VBridge:: NK add MAC: [0-60-65-2-DA-FB] Connecting to Desktop KITL: Connected host IP: 1 Port: 1086 .. this is the output of the serial debug A: Neo, have you by any chance tried looking into your firewall to see if it might be blocking traffic on any particular ports? Wireshark/netmon might be able to help you here if that's the issue. davbo-msft (Moderator)[2010-3-30 12:48]: Q: I lost spell check, how can i get it back A: Hello - can you give additional details about your question? Is this related to a Windows CE Embedded application? masatos_MSFT (Expert)[2010-3-30 12:51]: Q: When attempting to run the CETK cellcore tests the documentation states the pre-requisites include "stinger.ini", "ltk.ini" but windows CE doesn't provide these or document what they fully need to contain. Implicitly you also need "datatrans.xml" which isn't supplied. If you get around this error and steal these from Windows Mobile instead, when you try and run the CETK tests you get a data abort in radiometricsdll.dll. How should we invoke the cellcore parts of CETK? A: Hi Pev, what version of Windows CE and CETK are you using? I do not have the expertise to answer this question, but can find somebody who can. Travis Hobrla [MS] (Expert)[2010-3-30 12:52]: Q: I don't see a kitlcore.dll in my OS. is my debug image fails to load because of that? A: kitl.dll should be all that's needed, kitlcore.lib is linked into that. Travis Hobrla [MS] (Expert)[2010-3-30 12:55]: Q: I've got a platform (not developed by myself) where I2C bus support has to be provided through the OAL as the kernel needs to talk to devices such as the power management IC and gas gauge so a 'proper' I2C driver hanging off device manager isn't possible. This happens to be a polled driver, so obviously it hits the system hard when either under lots of traffic or an error condition occurs and the driver constantly polls. I originally thought that there was no straightforward way to make such code interrupt driven in the kernel (as it's a cludge) but I realised that that's exactly what ETHDBG drivers do. Is there any reason why I shouldn't have a go at implementing a similar mechanism for our kernel resident I2C driver? If not, are there any obvious pitfalls - I've not seen any other BSP's do this in the past... A: You can make a 'proper' driver that calls down into the OAL to do the actual I2C transactions. Alternatively you can build an interrupt-based version in the OAL where you handle everything in the ISR. There is nothing wrong with that so long as the rest of your drivers and app threads can handle longer times with interrupts off while you are servicing I2C interrupts. Sing Wee [MS] (Expert)[2010-3-30 12:55]: Q: I am having trouble with my mouse, I have the microsoft wireless mobile mouse 3000, when I push the scroll button I am suppose to have autoscroll instead it shows other web pages,Can you help me out tell me what to do!!! A: Sorry, this current chat is about Windows Embedded Compact. Hope you're able to find an answer to your question elsewhere. davbo-msft (Moderator)[2010-3-30 12:56]: Q: Is the Silverlight Animation "Spline" a BezierSpline? A: Spline - http://msdn.microsoft.com/en-us/library/ee501495.aspx<BR< a>>   masatos_MSFT (Expert)[2010-3-30 12:57]: Thanks for the info Pev. I will follow up with the CETK experts here and get back to you. davbo-msft (Moderator)[2010-3-30 12:59]: Q: Spline- bad link A: http://msdn.microsoft.com/en-us/library/ee501495.aspx davbo-msft (Moderator)[2010-3-30 13:0]: Q: Sorry, got to tirm the ">" A: No Worries http://msdn.microsoft.com/en-us/library/ee501495.aspx davbo-msft (Moderator)[2010-3-30 13:0]: Hello everyone, we are just about out of time. Thank you for joining us for our Windows Embedded CE 6.0 chat today! <http://www.Microsoft.com/Embedded>; A special thank you to the product group members for coming out. The transcript of today’s chat will be posted online as soon as possible, to <http://msdn.microsoft.com/en-us/chats>;. We’ll see you again for another chat next month. Please check <http://msdn.microsoft.com/en-us/chats>; for the list of upcoming chats. If you still have unanswered questions, let me suggest that you post them on one of our newsgroups on <http://msdn.microsoft.com/en-us/windowsembedded/ce/default.aspx> -Windows Embedded CE 6.0 R3 Now Available! <http://msdn.microsoft.com/windowsembedded/ce/dd630616.aspx>; davbo-msft (Moderator)[2010-3-30 13:1]: Q: hi everybody. I would like to know if there is something know about a bug in RTC API (VOIP), especially when using SIP. According the to the analysis with application verifyier there is a heap link in rtcdllmedia.dll. All of the unreleased chunks seem to have a size of 6560 bytes. A: I will follow up with the Networking Team for a response. davbo-msft (Moderator)[2010-3-30 13:1]: Q: Hi, we've problems with debugging of applications (= breakpoints in Platform Builder will be ignored) over KITL on Windows CE 5.0, if the PDB files are large (over 60MB). Are there any limitations to size of the PDB files? A: I will follow up with the tools team for a response and post with the transcript. Sing Wee [MS] (Expert)[2010-3-30 13:1]: Q: I am unable to use the target control in my development environment. any ideas? A: Make sure you have SYSGEN_SHELL=1 set in your build environment. davbo-msft (Moderator)[2010-3-30 13:3]: Q: what are the main differences between Object Store and RAM disk ? They are both in RAM...are there performance differences ? access differences ? A: I will follow up with the Core Team and get a response posted with the transcript to MSDN  The Questions   [2010-3-30 12:57]: Thanks for the info Pev. I will follow up with the CETK experts here and get back to you. [2010-3-30 12:59]:   [2010-3-30 13:0]:   [2010-3-30 13:0]: Hello everyone, we are just about out of time. Thank you for joining us for our Windows Embedded CE 6.0 chat today! <http://www.Microsoft.com/Embedded>; A special thank you to the product group members for coming out. The transcript of today’s chat will be posted online as soon as possible, to <http://msdn.microsoft.com/en-us/chats>;. We’ll see you again for another chat next month. Please check <http://msdn.microsoft.com/en-us/chats>; for the list of upcoming chats. If you still have unanswered questions, let me suggest that you post them on one of our newsgroups on <http://msdn.microsoft.com/en-us/windowsembedded/ce/default.aspx> -Windows Embedded CE 6.0 R3 Now Available! <http://msdn.microsoft.com/windowsembedded/ce/dd630616.aspx>; [2010-3-30 13:1]: [2010-3-30 13:1]: [2010-3-30 13:1]: [2010-3-30 13:3]: neo (Guest)[2010-3-30 11:37]: Hi all KellyG (Guest)[2010-3-30 11:37]: Hi KellyG (Guest)[2010-3-30 11:37]: I have a question unrelated to windows Ce embedded, can you please help me?? neo (Guest)[2010-3-30 11:38]: I need to implement hardware timers on my windows CE 6.0 device to trigger events at microsecond intervals! c neo (Guest)[2010-3-30 11:38]: yes. post it. May be i cud give a try KellyG (Guest)[2010-3-30 11:38]: My Product key listed on my tower is not the product key I need for microsoft office, but that is the only product key listed. neo (Guest)[2010-3-30 11:39]: I hope this is a chat for windows embedded. please post ur queries in office forums KellyG (Guest)[2010-3-30 11:39]: it is but i could not find a forum for office neo (Guest)[2010-3-30 11:40]: I think moderators will help u out. @ davbo-msft: can u help this guy? neo (Guest)[2010-3-30 11:41]: Q: I need to implement hardware timers on my windows CE 6.0 device to trigger events at microsecond intervals. Where should i start? davbo-msft (Moderator)[2010-3-30 11:50]: Our chat today covers the topic of Windows Embedded CE! 1. This chat will last for one hour. During this hour, our Experts will respond to as many questions as they can. Please understand that there may be some questions we cannot respond to due to lack of information or because the information is not yet public. 2. We encourage you to submit questions for our Experts. To do so, type your questions in the send box, select the “ask the Experts” box and click SEND. Questions sent directly to the Guest Chat room will not be answered by the Experts, but we encourage other community members to assist. 3. We ask that you stay on topic for the duration of the chat. This helps the Guests and Experts follow the conversation more easily. We invite you to ask off topic questions after this chat is over, but not during. 4. Please abide by the Chat Code of Conduct. Chat code of conduct: <http://msdn.microsoft.com/chats/chatroom.aspx?ctl=hlp#Conduct>; Pev (Guest)[2010-3-30 11:54]: Evening! davbo-msft (Moderator)[2010-3-30 11:54]: Hello everyone this is Dave Boyce - I worked in the Multimedia area for Windows CE. neo (Guest)[2010-3-30 11:55]: hello dave neo (Guest)[2010-3-30 11:55]: The chat code of conduct link is not working! Pev (Guest)[2010-3-30 11:56]: Best be polite just in case then ;-) neo (Guest)[2010-3-30 11:56]: davbo-msft (Moderator)[2010-3-30 11:57]: I'll check out the issue w/ the link paolopat (Guest)[2010-3-30 12:0]: Hello davbo-msft (Moderator)[2010-3-30 12:0]: We are pleased to welcome our Experts for today’s chat. I will have them introduce themselves now. Chat will begin in a couple of minutes. <http://www.Microsoft.com/Embedded>; paolopat (Guest)[2010-3-30 12:3]: Hello Experts ! neo (Guest)[2010-3-30 12:3]: Welcome all! paolopat (Guest)[2010-3-30 12:3]: Q: I want to partition my NAND Flash device. One partition to use for hive ragistry and the other for the apps and data. The only way to do it is programmatically or setting some registry values ? neo (Guest)[2010-3-30 12:3]: Q: I need to implement hardware timers on my windows CE 6.0 device to trigger events at microsecond intervals. Where should i start? neo (Guest)[2010-3-30 12:5]: Q: My CPU is Intel celeron M processor 1Ghz. Pev (Guest)[2010-3-30 12:5]: neo: if your silicon has multiple general purpose timers, pick one that's not in use for the system timer / profiler and set it up to trigger irqs for your purpose. You can't guarantee hard realtime type responses though... GarySwalling (Guest)[2010-3-30 12:5]: Q: Is Windows Phone 7 related to Windows CE? If so, can you tell me what version of Windows CE is the basis? Is it in fact the new version of Windows Mobile? Pev (Guest)[2010-3-30 12:6]: Q: Hi guys, what's the formal way to report bugs back to the core team / product team? The mechanism of calling the support phone number every time is really onerous and time-consuming. Is there another mechanism? paolopat (Guest)[2010-3-30 12:6]: Q: But the operation for creating the partitions ? neo (Guest)[2010-3-30 12:6]: Q: If i need to implement it using interrupt handlers, What are all the files that I should look at? GPM (Guest)[2010-3-30 12:6]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? Jhony (Guest)[2010-3-30 12:7]: Q: I created a OS design with KITL and kernel debugger enabled. But I am unable to connect to the target for debugging. I am getting the following error when i try to connect with the device. PB Debugger Cannot initialize the Kernel Debugger. PB Debugger Debugger could not initialize connection. PB Debugger The Kernel Debugger is waiting to connect with target. PB Debugger The Kernel Debugger has been disconnected successfully. Charles (Guest)[2010-3-30 12:7]: What will be different in Windows Compact 7 from CE 6.0? neo (Guest)[2010-3-30 12:8]: Can I have the book's name please? kiefs_dev (Guest)[2010-3-30 12:8]: Q: hi everybody. I would like to know if there is something know about a bug in RTC API (VOIP), especially when using SIP. According the to the analysis with application verifyier there is a heap link in rtcdllmedia.dll. All of the unreleased chunks seem to have a size of 6560 bytes. paolopat (Guest)[2010-3-30 12:10]: Q: So...I have to modify file system code to create 2 partition at system startup ?!! I haven't understood.... neo (Guest)[2010-3-30 12:10]: Q: Do u mean ISR/IST implementation? How can i register an interrupt? What kind of interrupt should i register? neo (Guest)[2010-3-30 12:11]: Q: Can I have the book's name please? Charles (Guest)[2010-3-30 12:11]: Q: What will be different in Windows Compact 7 from CE 6.0? PaulT (Guest)[2010-3-30 12:11]: neo: I'd say that you really need the docs for YOUR BSP, not generic documents for BSPs in general. Each BSP may be architected differently. If you're using the CEPC BSP, then the documentation that comes with Platform Builder is a reasonable place to look. GPM (Guest)[2010-3-30 12:11]: Q: If one has an image on a Silverlight page, it seems to be cached. How would one refresh that cache after changing the underlying image? Elektrobit (Guest)[2010-3-30 12:12]: Q: Hi, we've problems with debugging of applications (= breakpoints in Platform Builder will be ignored) over KITL on Windows CE 5.0, if the PDB files are large (over 60MB). Are there any limitations to size of the PDB files? Jhony (Guest)[2010-3-30 12:15]: Q: I am using CE 6.0. There is no cesvchost process running in my system. alexquisi (Guest)[2010-3-30 12:15]: Q: Hi, I saw that the ATADISK is quite generic and des not have any optimizations. Do you have any advice to consider while tryin to improve the performance of it? Jhony (Guest)[2010-3-30 12:17]: Windows XP service pack 1 Jhony (Guest)[2010-3-30 12:17]: Q: sorry! Windows XP SP3 neo (Guest)[2010-3-30 12:19]: Q: The link for developing device drivers is not working. can u please check that? paolopat (Guest)[2010-3-30 12:20]: Q: I have a NAND Flash on my target device. On this flash I have the hive registry and an application.I have observed that when the NAND flash is fully, the system startup time is longer....is there a degradation of NAND use that influences the startup time ? Why ? Pev (Guest)[2010-3-30 12:20]: Q: When attempting to run the CETK cellcore tests the documentation states the pre-requisites include "stinger.ini", "ltk.ini" but windows CE doesn't provide these or document what they fully need to contain. Implicitly you also need "datatrans.xml" which isn't supplied. If you get around this error and steal these from Windows Mobile instead, when you try and run the CETK tests you get a data abort in radiometricsdll.dll. How should we invoke the cellcore parts of CETK? Pev (Guest)[2010-3-30 12:21]: Hi all, Pev (Guest)[2010-3-30 12:21]: oops Pev (Guest)[2010-3-30 12:21]: :-D Pev (Guest)[2010-3-30 12:24]: Typically for SoC devices you name your hardware specific libraries in the form "SOCDIRNAME_LIBNAME". In our platform "OMAP35XX_TPS659XX_TI_V1" if you do this we cause the catalog parser to die... For example if we have a library "Musbfn_OMAP35XX_TPS659XX_TI_V1.dll" entering this in the catalogs pbcxml file in a <module> section causes the XML parser to fail with : Pev (Guest)[2010-3-30 12:25]: Q: Error 3 The 'urn:Microsoft.PlatformBuilder/Catalog:Module' element is        invalid - The value '012345678901234567890123456789.dll' is invalid         according to its datatype         'urn:Microsoft.PlatformBuilder/Catalog:CatalogFileName' - The actual         length is greater than the MaxLength value. GPM (Guest)[2010-3-30 12:25]: Q: Writable bitmap, is there an example of the syntax? Pev (Guest)[2010-3-30 12:25]: Q: Typically for SoC devices you name your hardware specific libraries in the form "SOCDIRNAME_LIBNAME". In our platform "OMAP35XX_TPS659XX_TI_V1" if you do this we cause the catalog parser to die... For example if we have a library "Musbfn_OMAP35XX_TPS659XX_TI_V1.dll" entering this in the catalogs pbcxml file in a <module> section causes the XML parser to fail with : Error 3 The 'urn:Microsoft.PlatformBuilder/Catalog:Module' element is        invalid - The value '012345678901234567890123456789.dll' is invalid         according to its datatype         'urn:Microsoft.PlatformBuilder/Catalog:CatalogFileName' - The actual         length is greater than the MaxLength value. Pev (Guest)[2010-3-30 12:25]: sorry, messed up submission there! GPM (Guest)[2010-3-30 12:26]: Q: I would like to get a handle to a Silverlight screen section, is that possiable? GPM (Guest)[2010-3-30 12:28]: Q: IXRVisualHost::GetHWND() exactly what I needed Thanks, PaulT (Guest)[2010-3-30 12:29]: GPM: You don't have to keep submitting the questions. The chat experts have an application that they're using to follow the chat and all Ask the Experts questions are logged. Jhony (Guest)[2010-3-30 12:29]: Q: I am getting this error only when I select the KdStub as the debugger in Target device connectivity. neo (Guest)[2010-3-30 12:30]: Q: ok. thanks for the book's link Pev (Guest)[2010-3-30 12:31]: Hm, did those two I submitted get picked up by anyone? neo (Guest)[2010-3-30 12:33]: Q: If I select Active KTIL, My OS doesn't boots. It says "loading NK.EXE at 0x<xxxxx> location" after that nothing comes in the debug log. PaulT (Guest)[2010-3-30 12:34]: Pev: PaulT (Guest)[2010-3-30 12:35]: Pev: I'm sure they did. The guys who are actually on the chat may not be experts in that part of things. That's usually the explanation when you don't get an answer in 10 minutes or so. Pev (Guest)[2010-3-30 12:36]: Ah, fair enough Susie (Guest)[2010-3-30 12:36]: My Outlook Express incoming mail is corrput. No ONE has been able to fix the problem, Dell or Norton. I have dial up I'm in a rural area Jhony (Guest)[2010-3-30 12:37]: Q: I have tried that and I am getting the same error. Pev (Guest)[2010-3-30 12:37]: Susie : Use Thunderbird instead :-D PaulT (Guest)[2010-3-30 12:37]: Susie: Sorry, but this chat is not about Windows, but Embedded (like what runs on a phone). Your best chance is to find a local expert or talk to your ISP. paolopat (Guest)[2010-3-30 12:37]: Q: what are the main differences between Object Store and RAM disk ? They are both in RAM...are there performance differences ? access differences ? Susie (Guest)[2010-3-30 12:38]: My computer knowlege is very limited, what is Thunderbird? Pev (Guest)[2010-3-30 12:38]: A different email client :-D neo (Guest)[2010-3-30 12:39]: Q: KITL: *** Device Name CEPC56059 *** WARN: KITL will run in polling mode VBridge:: built on [Jul 10 2009] time [10:20:14] VBridgeInit()...TX = [16384] bytes -- Rx = [16384] bytes Tx buffer [0xA1B84860] to [0xA1B88860]. Rx buffer [0xA1B88880] to [0xA1B8C880]. VBridge:: NK add MAC: [0-60-65-2-DA-FB] Connecting to Desktop KITL: Connected host IP: 1 Port: 1086 .. this is the output of the serial debug Susie (Guest)[2010-3-30 12:39]: Do I need to uninstall Outlook Express youngboyzie (Guest)[2010-3-30 12:39]: I need to start battery calibration for my new battery for my dell inspiron 1525 laptop and should be able to reach the BIOS screen by hitting f2 but this isnt working... help? Pev (Guest)[2010-3-30 12:39]: Nah, you can run it instead - you'll still need help from your ISP to configure it I expect Jhony (Guest)[2010-3-30 12:39]: Q: Both is happening via Ethernet. PaulT (Guest)[2010-3-30 12:40]: youngboyzie: You're off-topic. This is not a general chat for Windows and certainly not for Dell. You'll have to ask Dell how to get to setup; it's their machine. bill (Guest)[2010-3-30 12:41]: I lost spell check, how can i get et back neo (Guest)[2010-3-30 12:42]: Q: I didn't do that. I have to try. Jhony (Guest)[2010-3-30 12:43]: Q: Ok. I will do it then. bill (Guest)[2010-3-30 12:43]: Q: I lost spell check, how can i get it back PaulT (Guest)[2010-3-30 12:44]: bill: This isn't a general Windows chat. There are some Web forums that you might try. GarySwalling (Guest)[2010-3-30 12:45]: Q: Thanks, I found the Phone 7 presentation at http://live.visitmix.com/MIX10/Sessions/CL13 GPM (Guest)[2010-3-30 12:45]: Q: Is the Silverlight Animation "Spline" a BezierSpline? neo (Guest)[2010-3-30 12:46]: Q: ok. I'll do it. thanks Pev (Guest)[2010-3-30 12:46]: Whowever was asking about KITL connection : I've had this loads in the past. I think I started debugging last time by using wireshark to see what was happening on the network then setting up the OAL_ETHER and OAL_FUNC and OAL_VERBOSE as well as OAL_KITL flags to see what was actually happening in the driver.... Pev (Guest)[2010-3-30 12:47]: I'd generally make sure that you're testing though a 10baseT hub (instead of anything faster) and forcing Active KITL in polled mode too... neo (Guest)[2010-3-30 12:48]: Q: I disabled the firewall in my PC. Pev (Guest)[2010-3-30 12:50]: Q: I've got a platform (not developed by myself) where I2C bus support has to be provided through the OAL as the kernel needs to talk to devices such as the power management IC and gas gauge so a 'proper' I2C driver hanging off device manager isn't possible. This happens to be a polled driver, so obviously it hits the system hard when either under lots of traffic or an error condition occurs and the driver constantly polls. I originally thought that there was no straightforward way to make such code interrupt driven in the kernel (as it's a cludge) but I realised that that's exactly what ETHDBG drivers do. Is there any reason why I shouldn't have a go at implementing a similar mechanism for our kernel resident I2C driver? If not, are there any obvious pitfalls - I've not seen any other BSP's do this in the past... neo (Guest)[2010-3-30 12:51]: Q: I don't see a kitlcore.dll in my OS. is my debug image fails to load because of that? Pev (Guest)[2010-3-30 12:52]: Q: Hi masatos, I'm using Windows Embedded CE 6.0 with R3 and patched to feb 2010's QFE's (with it's associated CETK version) this is a machine with only CE 6.0 on (no conflicts with earlier CE or WM...) neo (Guest)[2010-3-30 12:54]: ok. Got it neo (Guest)[2010-3-30 12:54]: Q: ok. Got it Roundman (Guest)[2010-3-30 12:55]: Q: I am having trouble with my mouse, I have the microsoft wireless mobile mouse 3000, when I push the scroll button I am suppose to have autoscroll instead it shows other web pages,Can you help me out tell me what to do!!! Pev (Guest)[2010-3-30 12:55]: Hey neo, debugging kitl issues is really frustrating but dont lose heart :-) neo (Guest)[2010-3-30 12:55]: @ pev : u fixed the problem of KITL after that? neo (Guest)[2010-3-30 12:56]: I am getting the same error again and again. I even cleaned my environment and tried in a fresh PC. But didn't succeed yet Pev (Guest)[2010-3-30 12:56]: Well, eventually - my experiences probably won't help you as different platforms have different reasons for doing that neo (Guest)[2010-3-30 12:56]: I think so PaulT (Guest)[2010-3-30 12:58]: neo: Have you searched the old messages in microsoft.public.windowsce.platbuilder? It seems to me that there was a packet size situation where it was possible to have problems with KITL connections based on a setting on the PC. Google Groups, groups.google.com, Advanced Groups Search will allow you to search a single newsgroup or a set of newsgroups easily. GPM (Guest)[2010-3-30 12:58]: Q: Spline- bad link PaulT (Guest)[2010-3-30 12:58]: GPM: without the > at the end does it work? It seems to for me... neo (Guest)[2010-3-30 12:58]: But some times if i try to connect to the device again. The Image information is seen in the serial debug. what does that mean?Download BIN file information: ----------------------------------------------------- [0]: Base Address=0x220000 Length=0x18DAADC Received a broadcast message !CheckUDP: Not UDP (proto = 0x00000001) after this i am getting the old errors. PB debugger cannot initialize ... GPM (Guest)[2010-3-30 12:59]: Q: Sorry, got to tirm the ">" neo (Guest)[2010-3-30 12:59]: ok paul. I ll look into that. davbo-msft (Moderator)[2010-3-30 13:0]: Hello everyone, we are just about out of time. Thank you for joining us for our Windows Embedded CE 6.0 chat today! <http://www.Microsoft.com/Embedded>; A special thank you to the product group members for coming out. The transcript of today’s chat will be posted online as soon as possible, to <http://msdn.microsoft.com/en-us/chats>;. We’ll see you again for another chat next month. Please check <http://msdn.microsoft.com/en-us/chats>; for the list of upcoming chats. If you still have unanswered questions, let me suggest that you post them on one of our newsgroups on <http://msdn.microsoft.com/en-us/windowsembedded/ce/default.aspx> -Windows Embedded CE 6.0 R3 Now Available! <http://msdn.microsoft.com/windowsembedded/ce/dd630616.aspx>; neo (Guest)[2010-3-30 13:1]: Q: I am unable to use the target control in my development environment. any ideas? Pev (Guest)[2010-3-30 13:1]: Sure, if KITL isn't connected target control won't work as it runs over kitl... neo (Guest)[2010-3-30 13:1]: ok .thanks pev neo (Guest)[2010-3-30 13:2]: yes. sysgen_shell is set to 1 neo (Guest)[2010-3-30 13:2]: Q: yes. sysgen_shell is set to 1 Marcelovk (Guest)[2010-3-30 13:2]: Q: Is there any way to extract the default command lines of the tests in CETK? I want to have it running unconnected from the desktop.   Copyright © 2010 – Bruce Eitman All Rights Reserved

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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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  • Typical Applications of Linear System Solver in Game Developemnt

    - by craftsman.don
    I am going to write a custom solver for linear system. I would like to survey the typical problems involved the linear system solving in games. So that I can custom optimization on these problems based on the shape of the matrix. currently I am focus on these problems: B-Spline editing (I use a linear solve to resolve the C0, C1, C2 continuity) Constraint in Simulation (especially Position-Constraint, cloth) Both of them are Banded Matrix. I want to hear about some other applications of a linear system in games. Thank you.

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  • Narrow-phase collision detection algorithms

    - by Marian Ivanov
    There are three phases of collision detection. Broadphase: It loops between all objecs that can interact, false positives are allowed, if it would speed up the loop. Narrowphase: Determines whether they collide, and sometimes, how, no false positives Resolution: Resolves the collision. The question I'm asking is about the narrowphase. There are multiple algorithms, differing in complexity and accuracy. Hitbox intersection: This is an a-posteriori algorithm, that has the lowest complexity, but also isn't too accurate, Color intersection: Hitbox intersection for each pixel, a-posteriori, pixel-perfect, not accuratee in regards to time, higher complexity Separating axis theorem: This is used more often, accurate for triangles, however, a-posteriori, as it can't find the edge, when taking last frame in account, it's more stable Linear raycasting: A-priori algorithm, useful for semi-realistic-looking physics, finds the intersection point, even more accurate than SAT, but with more complexity Spline interpolation: A-priori, even more accurate than linear rays, even more coplexity. There are probably many more that I've forgot about. The question is, in when is it better to use SAT, when rays, when splines, and whether there is anything better.

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  • Line smoothing in Cocoa Touch

    - by Sam Kaplan
    How would I smooth a line (UIBeizerPath) or a set of points? Right now it draws it jagged. I read about spline interpolation, could anyone point me to an implementation of this in cocoa or C or give me an alternate line smoothing algorithm.

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  • How to troubleshoot a Highcharts script that's not rendering data when date is added and hanging the JS engine with large datasets?

    - by ylluminate
    I have a Highchart JS graph that I'm building in Rails (although I don't think Ruby has real bearing on this problem unless it's the Date output format) to which I'm adding the timestamp of each datapoint. Presently the array of floats is rendering fine without timestamps, however when I add the timestamp to the series it fails to rend. What's worse is that when the series has hundreds of entries all sorts of problems arise, not the least of which is the browser entirely hanging and requiring a force quit / kill. I'm using the following to build the array of arrays data series: series1 = readings.map{|row| [(row.date.to_i * 1000), (row.data1.to_f if BigDecimal(row.data1) != BigDecimal("-1000.0"))] } This yields a result like this: series: [{"name":"Data 1","data":[[1326262980000,1.79e-09],[1326262920000,1.29e-09],[1326262860000,1.22e-09],[1326262800000,1.42e-09],[1326262740000,1.29e-09],[1326262680000,1.34e-09],[1326262620000,1.31e-09],[1326262560000,1.51e-09],[1326262500000,1.24e-09],[1326262440000,1.7e-09],[1326262380000,1.24e-09],[1326262320000,1.29e-09],[1326262260000,1.53e-09],[1326262200000,1.23e-09],[1326262140000,1.21e-09]],"color":"blue"}] Yet nothing appears on the graph as noted. Notwithstanding, when I compare the data series in one of their very similar examples here: http://www.highcharts.com/demo/spline-irregular-time It appears that really the data series are formatted identically (except in mine I use the timestamp vs date method). This leads me to think I've got a problem with the timestamp output, but I'm just not able to figure out where / how as I'm converting the date output to an integer multipled by 1000 to convert it to milliseconds as per explained in a similar Railscasts tutorial. I would very much appreciate it if someone could point me in the right direction here as to what I may be doing wrong. What could cause no data to appear on the graph in smaller sized sets (<100 points) and when into the hundreds causes an apparent hang in the javascript engine in this case? Perhaps ultimately the key lies here as this is the entire js that's being generated and not rendering: jQuery(function() { // 1. Define JSON options var options = { chart: {"defaultSeriesType":"spline","renderTo":"chart_name"}, title: {"text":"Title"}, legend: {"layout":"vertical","style":{}}, xAxis: {"title":{"text":"UTC Time"},"type":"datetime"}, yAxis: [{"title":{"text":"Left Title","margin":10}},{"title":{"text":"Right Groups Title"},"opposite":true}], tooltip: {"enabled":true}, credits: {"enabled":false}, plotOptions: {"areaspline":{}}, series: [{"name":"Data 1","data":[[1326262980000,1.79e-08],[1326262920000,1.69e-08],[1326262860000,1.62e-08],[1326262800000,1.42e-08],[1326262740000,1.29e-08],[1326262680000,1.34e-08],[1326262620000,1.31e-08],[1326262560000,1.51e-08],[1326262500000,1.64e-08],[1326262440000,1.7e-08],[1326262380000,1.64e-08],[1326262320000,1.69e-08],[1326262260000,1.53e-08],[1326262200000,1.23e-08],[1326262140000,1.21e-08]],"color":"blue"},{"name":"Data 2","data":[[1326262980000,9.79e-09],[1326262920000,9.78e-09],[1326262860000,9.8e-09],[1326262800000,9.82e-09],[1326262740000,9.88e-09],[1326262680000,9.89e-09],[1326262620000,1.3e-06],[1326262560000,1.32e-06],[1326262500000,1.33e-06],[1326262440000,1.33e-06],[1326262380000,1.34e-06],[1326262320000,1.33e-06],[1326262260000,1.32e-06],[1326262200000,1.32e-06],[1326262140000,1.32e-06]],"color":"red"}], subtitle: {} }; // 2. Add callbacks (non-JSON compliant) // 3. Build the chart var chart = new Highcharts.StockChart(options); });

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  • Rotating object along bezier curve: not rotating enough?

    - by Paul
    I tried to follow the instructions from the threads on the forum (Cocos2d rotating sprite while moving with CCBezierBy) with Unity, in order to rotate my object as it moves along a bezier curve. But it does not rotate enough, the angle is too low, it goes up to 6 instead of 90 for example, as you can see on this image (the y eulerAngle is at 6, I would expect it to be around 90 with this curve) : Would you know why it does this? And how to make the rotation toward the next point? Here is the code (in c# with Unity) : (I am comparing x and z to get the angle, and adding the angle to eulerAngles.y so that it rotates around the y axis) void Update () { if ( Input.GetKey("d") ) start = true; if ( start ){ myTime = Time.time; start = false; } float theTime = (Time.time - myTime) *0.5f; if ( theTime < 1 ) { car.position = Spline.Interp( myArray, theTime );//creates the bezier curve counterBezier += Time.deltaTime; //compare 2 positions after 0.1f if ( counterBezier > 0.1f ){ counterBezier = 0; cbDone = false; newpos = car.position; float angle = Mathf.Atan2(newpos.z - oldpos.z, newpos.x - oldpos.x); angle += car.eulerAngles.y; car.eulerAngles = new Vector3(0,angle,0); } else if ( counterBezier > 0 && !cbDone ){ oldpos = car.position; cbDone = true; } Thanks

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