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• R glm standard error estimate differences to SAS PROC GENMOD

  - by Michelle

  I am converting a SAS PROC GENMOD example into R, using glm in R. The SAS code was: proc genmod data=data0 namelen=30; model boxcoxy=boxcoxxy ~ AGEGRP4 + AGEGRP5 + AGEGRP6 + AGEGRP7 + AGEGRP8 + RACE1 + RACE3 + WEEKEND + SEQ/dist=normal; FREQ REPLICATE_VAR; run; My R code is: parmsg2 <- glm(boxcoxxy ~ AGEGRP4 + AGEGRP5 + AGEGRP6 + AGEGRP7 + AGEGRP8 + RACE1 + RACE3 + WEEKEND + SEQ , data=data0, family=gaussian, weights = REPLICATE_VAR) When I use summary(parmsg2) I get the same coefficient estimates as in SAS, but my standard errors are wildly different. The summary output from SAS is: Name df Estimate StdErr LowerWaldCL UpperWaldCL ChiSq ProbChiSq Intercept 1 6.5007436 .00078884 6.4991975 6.5022897 67911982 0 agegrp4 1 .64607262 .00105425 .64400633 .64813891 375556.79 0 agegrp5 1 .4191395 .00089722 .41738099 .42089802 218233.76 0 agegrp6 1 -.22518765 .00083118 -.22681672 -.22355857 73401.113 0 agegrp7 1 -1.7445189 .00087569 -1.7462352 -1.7428026 3968762.2 0 agegrp8 1 -2.2908855 .00109766 -2.2930369 -2.2887342 4355849.4 0 race1 1 -.13454883 .00080672 -.13612997 -.13296769 27817.29 0 race3 1 -.20607036 .00070966 -.20746127 -.20467944 84319.131 0 weekend 1 .0327884 .00044731 .0319117 .03366511 5373.1931 0 seq2 1 -.47509583 .00047337 -.47602363 -.47416804 1007291.3 0 Scale 1 2.9328613 .00015586 2.9325559 2.9331668 -127 The summary output from R is: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.50074 0.10354 62.785 < 2e-16 AGEGRP4 0.64607 0.13838 4.669 3.07e-06 AGEGRP5 0.41914 0.11776 3.559 0.000374 AGEGRP6 -0.22519 0.10910 -2.064 0.039031 AGEGRP7 -1.74452 0.11494 -15.178 < 2e-16 AGEGRP8 -2.29089 0.14407 -15.901 < 2e-16 RACE1 -0.13455 0.10589 -1.271 0.203865 RACE3 -0.20607 0.09315 -2.212 0.026967 WEEKEND 0.03279 0.05871 0.558 0.576535 SEQ -0.47510 0.06213 -7.646 2.25e-14 The importance of the difference in the standard errors is that the SAS coefficients are all statistically significant, but the RACE1 and WEEKEND coefficients in the R output are not. I have found a formula to calculate the Wald confidence intervals in R, but this is pointless given the difference in the standard errors, as I will not get the same results. Apparently SAS uses a ridge-stabilized Newton-Raphson algorithm for its estimates, which are ML. The information I read about the glm function in R is that the results should be equivalent to ML. What can I do to change my estimation procedure in R so that I get the equivalent coefficents and standard error estimates that were produced in SAS? To update, thanks to Spacedman's answer, I used weights because the data are from individuals in a dietary survey, and REPLICATE_VAR is a balanced repeated replication weight, that is an integer (and quite large, in the order of 1000s or 10000s). The website that describes the weight is here. I don't know why the FREQ rather than the WEIGHT command was used in SAS. I will now test by expanding the number of observations using REPLICATE_VAR and rerunning the analysis.

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• Model Fit of Binary GLM with more than 1 or 2 predictors

  - by Salmo salar

  I am trying to predict a binary GLM with multiple predictors. I can do it fine with one predictor variable however struggle when I use multiple Sample data: structure(list(attempt = structure(c(1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L), .Label = c("1", "2"), class = "factor"), searchtime = c(137, 90, 164, 32, 39, 30, 197, 308, 172, 48, 867, 117, 63, 1345, 38, 122, 226, 397, 0, 106, 259, 220, 170, 102, 46, 327, 8, 10, 23, 108, 315, 318, 70, 646, 69, 97, 117, 45, 31, 64, 125, 17, 240, 63, 549, 1651, 233, 406, 334, 168, 127, 47, 881), mean.search.flow = c(15.97766667, 14.226, 17.15724762, 14.7465, 39.579, 23.355, 110.2926923, 71.95709524, 72.73666667, 32.37466667, 50.34905172, 27.98471429, 49.244, 109.1759778, 77.71733333, 37.446875, 101.23875, 67.78534615, 21.359, 36.54257143, 34.13961111, 64.35253333, 80.98554545, 61.50857143, 48.983, 63.81072727, 26.105, 46.783, 23.0605, 33.61557143, 46.31042857, 62.37061905, 12.565, 42.31983721, 15.3982, 14.49625, 23.77425, 25.626, 74.62485714, 170.1547778, 50.67125, 48.098, 66.83644444, 76.564875, 80.63189189, 136.0573243, 136.3484, 86.68688889, 34.82169565, 70.00415385, 64.67233333, 81.72766667, 57.74522034), Pass = structure(c(1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L), .Label = c("0", "1"), class = "factor")), .Names = c("attempt", "searchtime", "mean.search.flow", "Pass"), class = "data.frame", row.names = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 38L, 39L, 40L, 50L, 51L, 53L, 54L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L)) First model with single predictor M2 <- glm(Pass ~ searchtime, data = DF3, family = binomial) summary(M2) drop1(M2, test = "Chi") Plot works fine P1 <- predict(M2, newdata = MyData, type = "link", se = TRUE) plot(x=MyData$searchtime, exp(P1$fit) / (1+exp(P1$fit)), type = "l", ylim = c(0,1), xlab = "search time", ylab = "pobability of passage") lines(MyData$searchtime, exp(P1$fit+1.96*P1$se.fit)/ (1 + exp(P1$fit + 1.96 * P1$se.fit)), lty = 2) lines(MyData$searchtime, exp(P1$fit-1.96*P1$se.fit)/ (1 + exp(P1$fit - 1.96 * P1$se.fit)), lty = 2) points(DF3$searchtime, DF3$Search.and.pass) Second model M2a <- glm(Pass ~ searchtime + mean.search.flow+ attempt, data = DF3, family = binomial) summary(M2a) drop1(M2a, test = "Chi") How do I plot this with "dummy" data? I have tried along the lines of Model.matrix and expand.grid, as you would do with glmer, but fail straight away due to the two categorical variables along with factor(attempt)

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• Java Math.cos() Method Does Not Return 0 When Expected

  - by dimo414

  Using Java on a Windows 7 PC (not sure if that matters) and calling Math.cos() on values that should return 0 (like pi/2) instead returns small values, but small values that, unless I'm misunderstanding, are much greater than 1 ulp off from zero. Math.cos(Math.PI/2) = 6.123233995736766E-17 Math.ulp(Math.cos(Math.PI/2)) = 1.232595164407831E-32 Is this in fact within 1 ulp and I'm simply confused? And would this be an acceptable wrapper method to resolve this minor inaccuracy? public static double cos(double a){ double temp = Math.abs(a % Math.PI); if(temp == Math.PI/2) return 0; return Math.cos(a); }

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• MathType and LibreOffice Math comparison

  - by Agmenor

  In my office my team and I are going to type texts in the future which will include mathematical signs. Two programs are being proposed: LibreOffice Writer + Math or Microsoft Office + MathType. I would like to advocate for the first solution, but I need to know what technical advantages and disadvantages each program has. Compatibility with Ubuntu is an evident and important characteristic for LibreOffice, but could you give some other aspects? As a side question, do you advice any other program, even if not WYSIWYG and thus not my preference in this case?

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• Getting to math applications gradually

  - by den-javamaniac

  I'm currently getting a formal degree related to computation, in particular my current focus is numerical programming, scientific computing and machine learning. I'd love to apply that knowledge in game dev and expand it with statistics, probability theory, and graph theory (probably even linear algebra). The question is: which spheres of gamedev are filled with such math stuff, is it possible to advance in those without being a part of a group of people and how to get to it gradually? P.S.: I've got experience with commercial java dev and am getting my hands on C/C++ at the moment, however, I'm opened to go ahead and try Unity3D and etc.

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• Problem using glm::lookat

  - by omikun

  I am trying to rotate a sprite so it is always facing a 3D camera. Object GLfloat vertexData[] = { // X Y Z U V 0.0f, 0.8f, 0.0f, 0.5f, 1.0f, -0.8f,-0.8f, 0.0f, 0.0f, 0.0f, 0.8f,-0.8f, 0.0f, 1.0f, 0.0f, }; Per frame transform glm::mat4 newTransform = glm::lookAt(glm::vec3(0), gCamera.position(), gCamera.up()); shaders->setUniform("camera", gCamera.matrix()); shaders->setUniform("model", newTransform); In the vertex shader: gl_Position = camera * model * vec4(vert, 1); The object will track the camera if I move the camera up or down, but if I move the camera left/right (spin the camera around the object's y axis), it will rotate in the other direction so I end up seeing its front twice and its back twice as I rotate around it 360. If I use -gCamera.up() instead, it would track the camera side to side, but spin the opposite direction when I move the camera up/down. What am I doing wrong?

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• Understanding math used to determine if vector is clockwise / counterclockwise from your vector

  - by MTLPhil

  I'm reading Programming Game AI by Example by Mat Buckland. In the Math & Physics primer chapter there's a listing of the declaration of a class used to represent 2D vectors. This class contains a method called Sign. It's implementation is as follows //------------------------ Sign ------------------------------------------ // // returns positive if v2 is clockwise of this vector, // minus if anticlockwise (Y axis pointing down, X axis to right) //------------------------------------------------------------------------ enum {clockwise = 1, anticlockwise = -1}; inline int Vector2D::Sign(const Vector2D& v2)const { if (y*v2.x > x*v2.y) { return anticlockwise; } else { return clockwise; } } Can someone explain the vector rules that make this hold true? What do the values of y*v2.x and x*v2.y that are being compared actually represent? I'd like to have a solid understanding of why this works rather than just accepting that it does without figuring it out. I feel like it's something really obvious that I'm just not catching on to. Thanks for your help.

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• Math-font from the ubuntu font family?

  - by Wauzl

  Does anyone know if there will be (or already are) any possibilities to use the ubuntu font family for mathematical typesetting in LaTeX? It says “Dalton Maag, a London-based studio, has laid the foundations for the Ubuntu font project with a beautiful design that aims to produce every character to support every language and interest in the world.” on the project web site of ubuntu. So I would expect something like this because maths is an interest.

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• PCF shadow shader math causing artifacts

  - by user2971069

  For a while now I used PCSS for my shadow technique of choice until I discovered a type of percentage closer filtering. This method creates really smooth shadows and with hopes of improving performance, with only a fraction of texture samples, I tried to implement PCF into my shader. This is the relevant code: float c0, c1, c2, c3; float f = blurFactor; float2 coord = ProjectedTexCoords; if (receiverDistance - tex2D(lightSampler, coord + float2(0, 0)).x > 0.0007) c0 = 1; if (receiverDistance - tex2D(lightSampler, coord + float2(f, 0)).x > 0.0007) c1 = 1; if (receiverDistance - tex2D(lightSampler, coord + float2(0, f)).x > 0.0007) c2 = 1; if (receiverDistance - tex2D(lightSampler, coord + float2(f, f)).x > 0.0007) c3 = 1; coord = (coord % f) / f; return 1 - (c0 * (1 - coord.x) * (1 - coord.y) + c1 * coord.x * (1 - coord.y) + c2 * (1 - coord.x) * coord.y + c3 * coord.x * coord.y); This is a very basic implementation. blurFactor is initialized with 1 / LightTextureSize. So the if statements fetch the occlusion values for the four adjacent texels. I now want to weight each value based on the actual position of the texture coordinate. If it's near the bottom-right pixel, that occlusion value should be preferred. The weighting itself is done with a simple bilinear interpolation function, however this function takes a 2d vector in the range [0..1] so I have to convert my texture coordinate to get the distance from my first pixel to the second one in range [0..1]. For that I used the mod operator to get it into [0..f] range and then divided by f. This code makes sense to me, and for specific blurFactors it works, producing really smooth one pixel wide shadows, but not for all blurFactors. Initially blurFactor is (1 / LightTextureSize) to sample the 4 adjacent texels. I now want to increase the blurFactor by factor x to get a smooth interpolation across maybe 4 or so pixels. But that is when weird artifacts show up. Here is an image: Using a 1x on blurFactor produces a good result, 0.5 is as expected not so smooth. 2x however doesn't work at all. I found that only a factor of 1/2^n produces an good result, every other factor produces artifacts. I'm pretty sure the error lies here: coord = (coord % f) / f; Maybe the modulo is not calculated correctly? I have no idea how to fix that. Is it even possible for pixel that are further than 1 pixel away?

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• Math > Logic for a Logarithmic Score Meter

  - by oodavid

  I'm trying to implement a score meter whereby I specify a maximum value (say 15,000) and I can render values on it in a logarithmic manner ie: +------+---+--+-++ +------+---+--+-++ |== | |====== | +------+---+--+-++ +------+---+--+-++ 200 pts 1,000 pts +------+---+--+-++ +------+---+--+-++ |============= | |================| +------+---+--+-++ +------+---+--+-++ 5,000 pts 15,000 pts + The upper bound needs to be variable, and need to be able to convert a score to a percentage, using the above mockup as an example: score2pct(15000, 200) = 0.2 score2pct(15000, 1000) = 0.4 score2pct(15000, 5000) = 0.8 score2pct(15000, 15000) = 1 Does anyone have any pointers for me?

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• Why is math taught "backwards"? [closed]

  - by Yorirou

  A friend of mine showed me a pretty practical Java example. It was a riddle. I got excited and quickly solved the problem. After it, he showed me the mathematical explanation of my solution (he proved why is it good), and it was completely clear for me. This seems like natural approach for me: solve problems, and generalize. This is very familiar to me, I do it all the time when I am programming: I write a function. When I have to write a similar function, I generalize the problem, grab the generic parts, and refactor them to a function, and solve the original problems as a specialization of the general function. At the university (or at least where I study), things work backwards. The professors shows just the highest possible level of the solutions ("cryptic" mathematical formulas). My problem is that this is too abstract for me. There is no connection of my previous knowledge (== reality in my sense), so even if I can understand it, I can't really learn it properly. Others are learning these formulas word-by-word, and get good grades, since they can write exactly the same to the test, but this is not an option for me. I am a curious person, I can learn interesting things, but I can't learn just text. My brain is for storing toughts, not strings. There are proofs for the theories, but they are also really hard to understand because of this, and in most of the cases they are omitted. What is the reason for this? I don't understand why is it a good idea to show the really high level of abstraction and then leave the practical connections (or some important ideas / practical motivations) out?

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• OpenGL - have object follow mouse

  - by kevin james

  I want to have an object follow around my mouse on the screen in OpenGL. (I am also using GLEW, GLFW, and GLM). The best idea I've come up with is: Get the coordinates within the window with glfwGetCursorPos. The window was created with window = glfwCreateWindow( 1024, 768, "Test", NULL, NULL); and the code to get coordinates is double xpos, ypos; glfwGetCursorPos(window, &xpos, &ypos); Next, I use GLM unproject, to get the coordinates in "object space" glm::vec4 viewport = glm::vec4(0.0f, 0.0f, 1024.0f, 768.0f); glm::vec3 pos = glm::vec3(xpos, ypos, 0.0f); glm::vec3 un = glm::unProject(pos, View*Model, Projection, viewport); There are two potential problems I can already see. The viewport is fine, as the initial x,y, coordinates of the lower left are indeed 0,0, and it's indeed a 1024*768 window. However, the position vector I create doesn't seem right. The Z coordinate should probably not be zero. However, glfwGetCursorPos returns 2D coordinates, and I don't know how to go from there to the 3D window coordinates, especially since I am not sure what the 3rd dimension of the window coordinates even means (since computer screens are 2D). Then, I am not sure if I am using unproject correctly. Assume the View, Model, Projection matrices are all OK. If I passed in the correct position vector in Window coordinates, does the unproject call give me the coordinates in Object coordinates? I think it does, but the documentation is not clear. Finally, to each vertex of the object I want to follow the mouse around, I just increment the x coordinate by un[0], the y coordinate by -un[1], and the z coordinate by un[2]. However, since my position vector that is being unprojected is likely wrong, this is not giving good results; the object does move as my mouse moves, but it is offset quite a bit (i.e. moving the mouse a lot doesn't move the object that much, and the z coordinate is very large). I actually found that the z coordinate un[2] is always the same value no matter where my mouse is, probably because the position vector I pass into unproject always has a value of 0.0 for z. Edit: The (incorrectly) unprojected x-values range from about -0.552 to 0.552, and the y-values from about -0.411 to 0.411.

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• Sunrise / set calculations

  - by dassouki

  I'm trying to calculate the sunset / rise times using python based on the link provided below. My results done through excel and python do not match the real values. Any ideas on what I could be doing wrong? My Excel sheet can be found under .. http://transpotools.com/sun_time.xls # Created on 2010-03-28 # @author: dassouki # @source: [http://williams.best.vwh.net/sunrise_sunset_algorithm.htm][2] # @summary: this is based on the Nautical Almanac Office, United States Naval # Observatory. import math, sys class TimeOfDay(object): def calculate_time(self, in_day, in_month, in_year, lat, long, is_rise, utc_time_zone): # is_rise is a bool when it's true it indicates rise, # and if it's false it indicates setting time #set Zenith zenith = 96 # offical = 90 degrees 50' # civil = 96 degrees # nautical = 102 degrees # astronomical = 108 degrees #1- calculate the day of year n1 = math.floor( 275 * in_month / 9 ) n2 = math.floor( ( in_month + 9 ) / 12 ) n3 = ( 1 + math.floor( in_year - 4 * math.floor( in_year / 4 ) + 2 ) / 3 ) new_day = n1 - ( n2 * n3 ) + in_day - 30 print "new_day ", new_day #2- calculate rising / setting time if is_rise: rise_or_set_time = new_day + ( ( 6 - ( long / 15 ) ) / 24 ) else: rise_or_set_time = new_day + ( ( 18 - ( long/ 15 ) ) / 24 ) print "rise / set", rise_or_set_time #3- calculate sun mean anamoly sun_mean_anomaly = ( 0.9856 * rise_or_set_time ) - 3.289 print "sun mean anomaly", sun_mean_anomaly #4 calculate true longitude true_long = ( sun_mean_anomaly + ( 1.916 * math.sin( math.radians( sun_mean_anomaly ) ) ) + ( 0.020 * math.sin( 2 * math.radians( sun_mean_anomaly ) ) ) + 282.634 ) print "true long ", true_long # make sure true_long is within 0, 360 if true_long < 0: true_long = true_long + 360 elif true_long > 360: true_long = true_long - 360 else: true_long print "true long (360 if) ", true_long #5 calculate s_r_a (sun_right_ascenstion) s_r_a = math.degrees( math.atan( 0.91764 * math.tan( math.radians( true_long ) ) ) ) print "s_r_a is ", s_r_a #make sure it's between 0 and 360 if s_r_a < 0: s_r_a = s_r_a + 360 elif true_long > 360: s_r_a = s_r_a - 360 else: s_r_a print "s_r_a (modified) is ", s_r_a # s_r_a has to be in the same Quadrant as true_long true_long_quad = ( math.floor( true_long / 90 ) ) * 90 s_r_a_quad = ( math.floor( s_r_a / 90 ) ) * 90 s_r_a = s_r_a + ( true_long_quad - s_r_a_quad ) print "s_r_a (quadrant) is ", s_r_a # convert s_r_a to hours s_r_a = s_r_a / 15 print "s_r_a (to hours) is ", s_r_a #6- calculate sun diclanation in terms of cos and sin sin_declanation = 0.39782 * math.sin( math.radians ( true_long ) ) cos_declanation = math.cos( math.asin( sin_declanation ) ) print " sin/cos declanations ", sin_declanation, ", ", cos_declanation # sun local hour cos_hour = ( math.cos( math.radians( zenith ) ) - ( sin_declanation * math.sin( math.radians ( lat ) ) ) / ( cos_declanation * math.cos( math.radians ( lat ) ) ) ) print "cos_hour ", cos_hour # extreme north / south if cos_hour > 1: print "Sun Never Rises at this location on this date, exiting" # sys.exit() elif cos_hour < -1: print "Sun Never Sets at this location on this date, exiting" # sys.exit() print "cos_hour (2)", cos_hour #7- sun/set local time calculations if is_rise: sun_local_hour = ( 360 - math.degrees(math.acos( cos_hour ) ) ) / 15 else: sun_local_hour = math.degrees( math.acos( cos_hour ) ) / 15 print "sun local hour ", sun_local_hour sun_event_time = sun_local_hour + s_r_a - ( 0.06571 * rise_or_set_time ) - 6.622 print "sun event time ", sun_event_time #final result time_in_utc = sun_event_time - ( long / 15 ) + utc_time_zone return time_in_utc #test through main def main(): print "Time of day App " # test: fredericton, NB # answer: 7:34 am long = 66.6 lat = -45.9 utc_time = -4 d = 3 m = 3 y = 2010 is_rise = True tod = TimeOfDay() print "TOD is ", tod.calculate_time(d, m, y, lat, long, is_rise, utc_time) if __name__ == "__main__": main()

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• Do you have to be good at math to be a good programmer?

  - by Charles Roper

  It seems that conventional wisdom suggests that good programmers are also good at math. Or that the two are somehow intrinsically linked. Many programming books I have read provide many examples that are solutions to math problems, or are somehow related to math as if these examples are what make sense to most people. So the question I would like to float is: do you have to be good at math to be a good programmer?

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• Rotate sprite to face 3D camera

  - by omikun

  I am trying to rotate a sprite so it is always facing a 3D camera. shaders->setUniform("camera", gCamera.matrix()); glm::mat4 scale = glm::scale(glm::mat4(), glm::vec3(5e5, 5e5, 5e5)); glm::vec3 look = gCamera.position(); glm::vec3 right = glm::cross(gCamera.up(), look); glm::vec3 up = glm::cross(look, right); glm::mat4 newTransform = glm::lookAt(glm::vec3(0), gCamera.position(), up) * scale; shaders->setUniform("model", newTransform); In the vertex shader: gl_Position = camera * model * vec4(vert, 1); The object will track the camera if I move the camera up or down, but if I rotate the camera around it, it will rotate in the other direction so I end up seeing its front twice and its back twice as I rotate around it 360. What am I doing wrong?

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• Should certain math classes be required for a Computer Science degree?

  - by sunpech

  For a Computer Science (CS) degree at many colleges and universities, certain math courses are required: Calculus, Linear Algebra, and Discrete Mathematics are few examples. However, since I've started working in the real world as a software developer, I have yet to truly use some the knowledge I had at once acquired from taking those classes. Discrete Math might be the only exception. My questions: Should these math classes be required to obtain a computer science degree? Or would they be better served as electives? I'm challenging even that the certain math classes even help with required CS classes. For example, I never used linear algebra outside of the math class itself. I hear it's used in Computer Graphics, but I never took those classes-- yet linear algebra was required for a CS degree. I personally think it could be better served as an elective rather than requirement because it's more specific to a branch of CS rather than general CS. From a Slashdot post CS Profs Debate Role of Math In CS Education: 'For too long, we have taught computer science as an academic discipline (as though all of our students will go on to get PhDs and then become CS faculty members) even though for most of us, our students are overwhelmingly seeking careers in which they apply computer science.'

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• vector rotations for branches of a 3d tree

  - by freefallr

  I'm attempting to create a 3d tree procedurally. I'm hoping that someone can check my vector rotation maths, as I'm a bit confused. I'm using an l-system (a recursive algorithm for generating branches). The trunk of the tree is the root node. It's orientation is aligned to the y axis. In the next iteration of the tree (e.g. the first branches), I might create a branch that is oriented say by +10 degrees in the X axis and a similar amount in the Z axis, relative to the trunk. I know that I should keep a rotation matrix at each branch, so that it can be applied to child branches, along with any modifications to the child branch. My questions then: for the trunk, the rotation matrix - is that just the identity matrix * initial orientation vector ? for the first branch (and subsequent branches) - I'll "inherit" the rotation matrix of the parent branch, and apply x and z rotations to that also. e.g. using glm::normalize; using glm::rotateX; using glm::vec4; using glm::mat4; using glm::rotate; vec4 vYAxis = vec4(0.0f, 1.0f, 0.0f, 0.0f); vec4 vInitial = normalize( rotateX( vYAxis, 10.0f ) ); mat4 mRotation = mat4(1.0); // trunk rotation matrix = identity * initial orientation vector mRotation *= vInitial; // first branch = parent rotation matrix * this branches rotations mRotation *= rotate( 10.0f, 1.0f, 0.0f, 0.0f ); // x rotation mRotation *= rotate( 10.0f, 0.0f, 0.0f, 1.0f ); // z rotation Are my maths and approach correct, or am I completely wrong? Finally, I'm using the glm library with OpenGL / C++ for this. Is the order of x rotation and z rotation important?

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• 3D rotation matrices deform object while rotating

  - by Kevin

  I'm writing a small 3D renderer (using an orthographic projection right now). I've run into some trouble with my 3D rotation matrices. They seem to squeeze my 3D object (a box primitive) at certain angles. Here's a live demo (only tested in Google Chrome): http://dl.dropbox.com/u/109400107/3D/index.html The box is viewed from the top along the Y axis and is rotating around the X and Z axis. These are my 3 rotation matrices (Only rX and rZ are being used): var rX = new Matrix([ [1, 0, 0], [0, Math.cos(radiants), -Math.sin(radiants)], [0, Math.sin(radiants), Math.cos(radiants)] ]); var rY = new Matrix([ [Math.cos(radiants), 0, Math.sin(radiants)], [0, 1, 0], [-Math.sin(radiants), 0, Math.cos(radiants)] ]); var rZ = new Matrix([ [Math.cos(radiants), -Math.sin(radiants), 0], [Math.sin(radiants), Math.cos(radiants), 0], [0, 0, 1] ]); Before projecting the verticies I multiply them by rZ and rX like so: vert1.multiply(rZ); vert1.multiply(rX); vert2.multiply(rZ); vert2.multiply(rX); vert3.multiply(rZ); vert3.multiply(rX); The projection itself looks like this: bX = (pos.x + (vert1.x*scale)); bY = (pos.y + (vert1.z*scale)); Where "pos.x" and "pos.y" is an offset for centering the box on the screen. I just can't seem to find a solution to this and I'm still relativly new to working with Matricies. You can view the source-code of the demo page if you want to see the whole thing.

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• Do game studios hire people based on their math knowledge alone?

  - by Brent Horvath

  I have very little programming skills outside of very basic levels of Java, but I have excellent math and science knowledge. I was wondering what I could offer any potential team if I were to go into video game development? Do people hire people based on their math knowledge alone? I like to do other things such as writing or drawing, but math and science are the only skills in which I really excel in.

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• Should certain math classes be required for a Computer Science degree?

  - by sunpech

  For a Computer Science degree at many colleges and universities, certain math courses are required: Calculus, Linear Algebra, and Discrete Mathematics are few examples. However, since I've started working in the real world as a software developer, I have yet to truly use the knowledge I had at once acquired from taking those classes. My question is: Should these math classes be required to obtain a computer science degree? Or would they better served as electives? A Slashdot post: CS Profs Debate Role of Math In CS Education

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• Complete Math Library for use in OpenGL ES 2.0 Game?

  - by Bunkai.Satori

  Are you aware of a complete (or almost complete) cross platform math library for use in OpenGL ES 2.0 games? The library should contain: Matrix2x2, Matrix 3x3, Matrix4x4 classes Quaternions Vector2, Vector3, Vector4 Classes Euler Angle Class Operations amongh the above mentioned classes, conversions, etc.. Standardly used math operations in 3D graphics (Dot Product, Cross Product, SLERP, etc...) Is there such Math API available either standalone or as a part of any package? Programming Language: Visual C++ but planned to be ported to OS X and Android OS.

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• What kind of math should I be expecting in advanced programming?

  - by I_Question_Things_Deeply

  And I don't mean just space shooters and such, because in non-3D environments it's obvious that not much beyond elementary math is needed to implement. Most of the programming in 2D games is mostly going to involve basic arithmetic, algorithms for enemy AI and dimensional worlds, rotation, and maybe some Algebra as well depending on how you want to design. But I ask because I'm not really gifted with math at all. I get frustrated and worn out just by doing Pre-Algebra, so Algebra 2 and Calculus would likely be futile for me. I guess I'm not so "right-brained" when it comes down to pure numbers and math formulas, but the bad part is that I'm no art-expert either. What do you people here suppose I should do? Go along avoiding as much of the extremely difficult maths I can't fathom, or try to ease into more complex math as I excel at programming?

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• Braces (syntax) highlighting in OpenOffice Math formula text editor

  - by Oleksandr Bolotov

  When you use OpenOffice Math, in upper part you see formula and formula text editor in lower part. Almost like this: %sigma = 2 %mu %epsilon + %lambda Tr(%epsilon)I So my questions are: How to replace OpenOffice Math's formula text editor with own text editor? ... or how to enable braces (syntax) highlighting in embedded editor? ... are there any extensions for anything like this? I need this because sometimes it's too much braces and stuff and it's hard to distinguish which braces match each other. Please do not suggest me to use MathType Mathematica (or anything) instead of OpenOffice Math (because I'm almost happy with it:)

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• Fixed point math in c#?

  - by x4000

  Hi there, I was wondering if anyone here knows of any good resources for fixed point math in c#? I've seen things like this (http://2ddev.72dpiarmy.com/viewtopic.php?id=156) and this (http://stackoverflow.com/questions/79677/whats-the-best-way-to-do-fixed-point-math), and a number of discussions about whether decimal is really fixed point or actually floating point (update: responders have confirmed that it's definitely floating point), but I haven't seen a solid C# library for things like calculating cosine and sine. My needs are simple -- I need the basic operators, plus cosine, sine, arctan2, PI... I think that's about it. Maybe sqrt. I'm programming a 2D RTS game, which I have largely working, but the unit movement when using floating-point math (doubles) has very small inaccuracies over time (10-30 minutes) across multiple machines, leading to desyncs. This is presently only between a 32 bit OS and a 64 bit OS, all the 32 bit machines seem to stay in sync without issue, which is what makes me think this is a floating point issue. I was aware from this as a possible issue from the outset, and so have limited my use of non-integer position math as much as possible, but for smooth diagonal movement at varying speeds I'm calculating the angle between points in radians, then getting the x and y components of movement with sin and cos. That's the main issue. I'm also doing some calculations for line segment intersections, line-circle intersections, circle-rect intersections, etc, that also probably need to move from floating-point to fixed-point to avoid cross-machine issues. If there's something open source in Java or VB or another comparable language, I could probably convert the code for my uses. The main priority for me is accuracy, although I'd like as little speed loss over present performance as possible. This whole fixed point math thing is very new to me, and I'm surprised by how little practical information on it there is on google -- most stuff seems to be either theory or dense C++ header files. Anything you could do to point me in the right direction is much appreciated; if I can get this working, I plan to open-source the math functions I put together so that there will be a resource for other C# programmers out there. UPDATE: I could definitely make a cosine/sine lookup table work for my purposes, but I don't think that would work for arctan2, since I'd need to generate a table with about 64,000x64,000 entries (yikes). If you know any programmatic explanations of efficient ways to calculate things like arctan2, that would be awesome. My math background is all right, but the advanced formulas and traditional math notation are very difficult for me to translate into code.

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• Recommended Math textbooks for programmers

  - by Tony

  I learned math in a non-English environment, I recently read some books about algorithm analysis, I found some math concepts were confusing, and seemed not the same as what I've learned. What math textbooks would you recommend that covers math concepts from the scratch and suitable for self-learning ?

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