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• Constructive criticsm on my linear sampling Gaussian blur

  - by Aequitas

  I've been attempting to implement a gaussian blur utilising linear sampling, I've come across a few articles presented on the web and a question posed here which dealt with the topic. I've now attempted to implement my own Gaussian function and pixel shader drawing reference from these articles. This is how I'm currently calculating my weights and offsets: int support = int(sigma * 3.0) weights.push_back(exp(-(0*0)/(2*sigma*sigma))/(sqrt(2*pi)*sigma)); total += weights.back(); offsets.push_back(0); for (int i = 1; i <= support; i++) { float w1 = exp(-(i*i)/(2*sigma*sigma))/(sqrt(2*pi)*sigma); float w2 = exp(-((i+1)*(i+1))/(2*sigma*sigma))/(sqrt(2*pi)*sigma); weights.push_back(w1 + w2); total += 2.0f * weights[i]; offsets.push_back(w1 / weights[i]); } for (int i = 0; i < support; i++) { weights[i] /= total; } Here is an example of my vertical pixel shader: vec3 acc = texture2D(tex_object, v_tex_coord.st).rgb*weights[0]; vec2 pixel_size = vec2(1.0 / tex_size.x, 1.0 / tex_size.y); for (int i = 1; i < NUM_SAMPLES; i++) { acc += texture2D(tex_object, (v_tex_coord.st+(vec2(0.0, offsets[i])*pixel_size))).rgb*weights[i]; acc += texture2D(tex_object, (v_tex_coord.st-(vec2(0.0, offsets[i])*pixel_size))).rgb*weights[i]; } gl_FragColor = vec4(acc, 1.0); Am I taking the correct route with this? Any criticism or potential tips to improving my method would be much appreciated.

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• questions on a particular algorithm

  - by paul smith

  Upon searching for a fast primr algorithm, I stumbled upon this: public static boolean isP(long n) { if (n==2 || n==3) return true; if ((n&0x1)==0 || n%3==0 || n<2) return false; long root=(long)Math.sqrt(n)+1L; // we check just numbers of the form 6*k+1 and 6*k-1 for (long k=6;k<=root;k+=6) { if (n%(k-1)==0) return false; if (n%(k+1)==0) return false; } return true; } My questions are: Why is long being used everywhere instead of int? Because with a long type the argument could be much larger than Integer.MAX thus making the method more flexible? In the second 'if', is n&0x1 the same as n%2? If so why didn't the author just use n%2? To me it's more readable. The line that sets the 'root' variable, why add the 1L? What is the run-time complexity? Is it O(sqrt(n/6)) or O(sqrt(n)/6)? Or would we just say O(n)?

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• Attempting my first fortran 95 program, to solve quadratic eqn. Getting weird errors.

  - by Damon

  So, I'm attempting my first program in Fortran, trying to solve quadratic eqn. I have double and triple checked my code and don't see anything wrong. I keep getting "Invalid character in name at (1)" and "Unclassifiable statement at (1)" at various locations. Any help would be greatly appreciated... ! This program solves quadratic equations ! of the form ax^2 + bx + c = 0. ! Record: ! Name: Date: Notes: ! Damon Robles 4/3/10 Original Code PROGRAM quad_solv IMPLICIT NONE ! Variables REAL :: a, b, c REAL :: discrim, root1, root2, COMPLEX :: comp1, comp2 CHARACTER(len=1) :: correct ! Prompt user for coefficients. WRITE(*,*) "This program solves quadratic equations " WRITE(*,*) "of the form ax^2 + bx + c = 0. " WRITE(*,*) "Please enter the coefficients a, b, and " WRITE(*,*) "c, separated by commas:" READ(*,*) a, b, c WRITE(*,*) "Is this correct: a = ", a, " b = ", b WRITE(*,*) " c = ", c, " [Y/N]? " READ(*,*) correct IF correct = N STOP IF correct = Y THEN ! Definition discrim = b**2 - 4*a*c ! Calculations IF discrim > 0 THEN root1 = (-b + sqrt(discrim))/(2*a) root2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "This equation has two real roots. " WRITE(*,*) "x1 = ", root1 WRITE(*,*) "x2 = ", root2 IF discrim = 0 THEN root1 = -b/(2*a) WRITE(*,*) "This equation has a double root. " WRITE(*,*) "x1 = ", root1 IF discrim < 0 THEN comp1 = (-b + sqrt(discrim))/(2*a) comp2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "x1 = ", comp1 WRITE(*,*) "x2 = ", comp2 PROGRAM END quad_solv Thanks in advance!

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• C# Why can't I find Sum() of this HashSet. says "Arithmetic operation resulted in an overflow."

  - by user2332665

  I was trying to solve this problem projecteuler,problem125 this is my solution in python(just for understanding the logic) import math lim=10**8 found=set() for start in xrange(1,int(math.sqrt(lim))): sos = start*start for i in xrange(start+1,int(math.sqrt(lim))): sos += (i*i) if sos >= lim: break s=str(int(sos)) if s==s[::-1]: found.add(sos) print sum(found) the same code I wrote in C# is as follows using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication1 { class Program { public static bool isPalindrome(string s) { string temp = ""; for (int i=s.Length-1;i>=0;i-=1){temp+=s[i];} return (temp == s); } static void Main(string[] args) { int lim = Convert.ToInt32(Math.Pow(10,8)); var found = new HashSet<int>(); for (int start = 1; start < Math.Sqrt(lim); start += 1) { int s = start *start; for (int i = start + 1; start < Math.Sqrt(lim); i += 1) { s += i * i; if (s > lim) { break; } if (isPalindrome(s.ToString())) { found.Add(s); } } } Console.WriteLine(found.Sum()); } } } the code debugs fine until it gives an exception at Console.WriteLine(found.Sum()); (line31). Why can't I find Sum() of the set found

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• Iphone -- maintaining a list of strings and a corresponding typedef enum

  - by William Jockusch

  Suppose I have the following: typedef enum functionType {ln, sin, sqrt} functionType; NSArray *functions = [NSArray arrayWithObjects: @"ln", @"sin", @"sqrt", nil]; Suppose further that *functions will not change at runtime. Question -- is there any way to set up a single structure which updates both of these? So that I only have to keep track of one list, instead of two. To explain what is going on -- the idea is that string input from the user will be stored in a variable of type functionType. Later on, I will have code like this: double valueOfFunction: (functionType) function withInput: (double) input switch (function) { case ln: return ln(input); case sin: return sin(input); case sqrt: return sqrt(input); //etc . . . could grow to include a lot of functions. } And valueOfFunction needs to be fast. So I don't want to be doing string comparisons there.

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• Fortran severe (40) Error... Help?!

  - by Taka

  I can compile but when I run I get this error "forrtl: severe (40): recursive I/O operation, unit -1, file unknown" if I set n = 29 or more... Can anyone help with where I might have gone wrong? Thanks. PROGRAM SOLUTION IMPLICIT NONE ! Variable Declaration INTEGER :: i REAL :: dt DOUBLE PRECISION :: st(0:9) DOUBLE PRECISION :: stmean(0:9) DOUBLE PRECISION :: first_argument DOUBLE PRECISION :: second_argument DOUBLE PRECISION :: lci, uci, mean REAL :: exp1, n REAL :: r, segma ! Get inputs WRITE(*,*) 'Please enter number of trials: ' READ(*,*) n WRITE(*,*) dt=1.0 segma=0.2 r=0.1 ! For n Trials st(0)=35.0 stmean(0)=35.0 mean = stmean(0) PRINT *, 'For ', n ,' Trials' PRINT *,' 1 ',st(0) ! Calculate results DO i=0, n-2 first_argument = r-(1/2*(segma*segma))*dt exp1 = -(1/2)*(i*i) second_argument = segma*sqrt(dt)*((1/sqrt(2*3.1416))*exp(exp1)) st(i+1) = st(i) * exp(first_argument+second_argument) IF(st(i+1)<=20) THEN stmean(i+1) = 0.0 st(i+1) = st(i) else stmean(i+1) = st(i+1) ENDIF PRINT *,i+2,' ',stmean(i+1) mean = mean+stmean(i+1) END DO ! Output results uci = mean+(1.96*(segma/sqrt(n))) lci = mean-(1.96*(segma/sqrt(n))) PRINT *,'95% Confidence Interval for ', n, ' trials is between ', lci, ' and ', uci PRINT *,'' END PROGRAM SOLUTION

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• Stack overflow in OCaml and F# but not in Haskell

  - by Fernand Pajot

  I've been comparing for fun different languages for speed in execution of the following program: for i from 1 to 1000000 sum the product i*(sqrt i) One of my implementations (not the only one) is constructing a list [1..1000000] and then folding with a specific funtion. The program works fine and fast in Haskell (even when using foldl and not foldl') but stack overflows in OCaml and F#. Here is the Haskell code: test = foldl (\ a b -> a + b * (sqrt b)) 0 create 0 = [] create n = n:(create (n-1)) main = print (test (create 1000000)) And here is the OCaml one: let test = List.fold_left (fun a b -> a +. (float_of_int b) *. (sqrt (float_of_int b))) 0. ;; let rec create = function | 0 -> [] | n -> n::(create (n-1)) ;; print_float (test (create 1000000));; Why does the OCaml/F# implementation stack overflows?

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• How to write a code Newton Raphson code in R involving integration and Bessel function

  - by Ahmed

  I have want to estimate the parameters of the function which involves Bessel function and integration. However, when i tried to run it, i got a message that "Error in f(x, ...) : could not find function "BesselI" ". I don't know to fix it and would appreciate any related proposal. library(Bessel) library(maxLik) library(miscTools) K<-300 f <- function(theta,lambda,u) {exp(-u*theta)*BesselI(2*sqrt(t*u*theta*lambda),1)/u^0.5} F <- function(theta,lambda){integrate(f,0,K,theta=theta,lambda=lambda)$value} tt<-function(theta,lambda){(sqrt(lambda)*exp(-t*lambda)/(2*sqrt(t*theta)))(theta(2*t*lambda-1)*F(theta,lambda)} loglik <- function(param) { theta <- param[1] lambda <- param[2] ll <-sum(log(tt(theta,lambda))) } t<-c(24,220,340,620,550,559,689,543) res <- maxNR(loglik, start=c(0.001,0.0005),print.level=1,tol = 1e-08) summary(res)

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• 0/1 Knapsack with irrational weights

  - by user356106

  Consider the 0/1 knapsack problem. The standard Dynamic Programming algorithm applies only when the capacity as well as the weights to fill the knapsack with are integers/ rational numbers. What do you do when the capacity/weights are irrational? The issue is that we can't memoize like we do for integer weights because we may need potentially infinite decimal places for irrational weights - leading to an infinitely large number of columns for the Dynamic Programming Table . Is there any standard method for solving this? Any comments on the complexity of this problem? Any heuristics? What about associated recurrences like (for example): f(x)=1, for x< sqrt(2) f(x)=f(x-sqrt(2))+sqrt(3)

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• Raycasting tutorial / vector math question

  - by mattboy

  I'm checking out this nice raycasting tutorial at http://lodev.org/cgtutor/raycasting.html and have a probably very simple math question. In the DDA algorithm I'm having trouble understanding the calcuation of the deltaDistX and deltaDistY variables, which are the distances that the ray has to travel from 1 x-side to the next x-side, or from 1 y-side to the next y-side, in the square grid that makes up the world map (see below screenshot). In the tutorial they are calculated as follows, but without much explanation: //length of ray from one x or y-side to next x or y-side double deltaDistX = sqrt(1 + (rayDirY * rayDirY) / (rayDirX * rayDirX)); double deltaDistY = sqrt(1 + (rayDirX * rayDirX) / (rayDirY * rayDirY)); rayDirY and rayDirX are the direction of a ray that has been cast. How do you get these formulas? It looks like pythagorean theorem is part of it, but somehow there's division involved here. Can anyone clue me in as to what mathematical knowledge I'm missing here, or "prove" the formula by showing how it's derived?

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• Fitting a rectangle into screen with XNA

  - by alecnash

  I am drawing a rectangle with primitives in XNA. The width is: width = GraphicsDevice.Viewport.Width and the height is height = GraphicsDevice.Viewport.Height I am trying to fit this rectangle in the screen (using different screens and devices) but I am not sure where to put the camera on the Z-axis. Sometimes the camera is too close and sometimes to far. This is what I am using to get the camera distance: //Height of piramid float alpha = 0; float beta = 0; float gamma = 0; alpha = (float)Math.Sqrt((width / 2 * width/2) + (height / 2 * height / 2)); beta = height / ((float)Math.Cos(MathHelper.ToRadians(67.5f)) * 2); gamma = (float)Math.Sqrt(beta*beta - alpha*alpha); position = new Vector3(0, 0, gamma); Any idea where to put the camera on the Z-axis?

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• Trace code pascal [on hold]

  - by mghaffari

  I haven't worked with Pascal so far, and my problem is understanding the recursive aspects that prm assignment operators and how the final (correct) value is derived. Would someone please explain that line for me. Program test(output); FUNCTION prm(az:integer) : real; begin if az = 1 then prm := sqrt(12) else prm := sqrt(12*prm(az-1)); end; begin writeln(prm(30):0:2); end.

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• Determining the angle to fire a shot when target and shooter moves, and bullet moves with shooter velocity added in

  - by Azaral

  I saw this question: Predicting enemy position in order to have an object lead its target and followed the link in the answer to stack overflow. In the stack overflow page I used the 2nd answer, the one that is a large mathematical derivation. My situation is a little different though. My first question though is will the answer provided in the stack overflow page even work to begin with, assuming the original circumstances of moving target and stationary shooter. My situation is a little different than that situation. My target moves, the shooter moves, and the bullets from the shooter start off with the velocities in x and y added to the bullets' x and y velocities. If you are sliding to the right, the bullets will remain in front of you as you move so as long as your velocity remains constant. What I'm trying to do is to get the enemy to be able to determine where they need to shoot in order to hit the player. Unless the player and enemy is stationary, the velocity from the ship adding to the velocity of the bullets will cause a miss. I'd rather like to prevent that. I used the formula in the stack overflow answer and did what I thought were the appropriate adjustments. I've been banging at this for the last four hours and I just can't make it click. It is probably something really simple and boneheaded that I am missing (that seems to be a lot of my problems lately). Here is the solution presented from the stack overflow answer: It boils down to solving a quadratic equation of the form: a * sqr(x) + b * x + c == 0 Note that by sqr I mean square, as opposed to square root. Use the following values: a := sqr(target.velocityX) + sqr(target.velocityY) - sqr(projectile_speed) b := 2 * (target.velocityX * (target.startX - cannon.X) + target.velocityY * (target.startY - cannon.Y)) c := sqr(target.startX - cannon.X) + sqr(target.startY - cannon.Y) Now we can look at the discriminant to determine if we have a possible solution. disc := sqr(b) - 4 * a * c If the discriminant is less than 0, forget about hitting your target -- your projectile can never get there in time. Otherwise, look at two candidate solutions: t1 := (-b + sqrt(disc)) / (2 * a) t2 := (-b - sqrt(disc)) / (2 * a) Note that if disc == 0 then t1 and t2 are equal. If there are no other considerations such as intervening obstacles, simply choose the smaller positive value. (Negative t values would require firing backward in time to use!) Substitute the chosen t value back into the target's position equations to get the coordinates of the leading point you should be aiming at: aim.X := t * target.velocityX + target.startX aim.Y := t * target.velocityY + target.startY Here is my code, after being corrected by Sam Hocevar (thank you again for your help!). It still doesn't work. For some reason it never enters the section of code inside the if(disc = 0) (obviously because it is always less than zero but...). However, if I plug the numbers from my game log on the enemy and player positions and velocities it outputs a valid firing solution. I have looked at the code side by side a couple of times now and I can't find any differences. There has got to be something simple I'm missing here. If someone else could look at this code and determine what is going on here I'd appreciate it. I know it's not going through that section because if it were, shouldShoot would become true and the enemy would be blasting away at the player. This section calls the function in question, CalculateShootHeading() if(shouldMove) { UseEngines(); } x += xVelocity; y += yVelocity; CalculateShootHeading(); if(shouldShoot) { ShootWeapons(); } UpdateWeapons(); This is CalculateShootHeading(). This is inside the enemy class so x and y are the enemy's x and y and the same with velocity. One output from my game log gives Player X = 2108, Player Y = -180.956, Player X velocity = 10.9949, Player Y Velocity = -6.26017, Enemy X = 1988.31, Enemy Y = -339.051, Enemy X velocity = 1.81666, Enemy Y velocity = -9.67762, 0 enemy projectiles. The output from the console tester is Bullet position = 2210.49, -239.313 and Player Position = 2210.49, -239.313. This doesn't make any sense. The only thing that could be different is the code or the input into my function in the game and I've checked that and I don't think that it is wrong as it's updated before this and never changed. float const bulletSpeed = 30.f; float const dx = playerX - x; float const dy = playerY - y; float const vx = playerXVelocity - xVelocity; float const vy = playerYVelocity - yVelocity; float const a = vx * vx + vy * vy - bulletSpeed * bulletSpeed; float const b = 2.f * (vx * dx + vy * dy); float const c = dx * dx + dy * dy; float const disc = b * b - 4.f * a * c; shouldShoot = false; if (disc >= 0.f) { float t0 = (-b - std::sqrt(disc)) / (2.f * a); float t1 = (-b + std::sqrt(disc)) / (2.f * a); if (t0 < 0.f || (t1 < t0 && t1 >= 0.f)) { t0 = t1; } if (t0 >= 0.f) { float shootx = vx + dx / t0; float shooty = vy + dy / t0; heading = std::atan2(shooty, shootx) * RAD2DEGREE; } shouldShoot = true; }

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• Circular movement - eliminating speed ups near Y = 0

  - by Fibericon

  I have a basic algorithm to rotate an enemy around a 200 unit radius circle with center 0. This is how I'm achieving that: if (position.Y <= 0 && position.X > -200) { position.X -= 2; position.Y = 0 - (float)Math.Sqrt((200 * 200) - (position.X * position.X)); } else { position.X += 2; position.Y = (float)Math.Sqrt((200 * 200) - (position.X * position.X)); } It does work, and I've ensured that at no point does either X or Y equal NaN. However, when Y approaches 0, it seems to go significantly faster. This surprises me, because the Y values are locked to the X, which is being incremented by a steady amount. What can I do to smooth the speed?

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• Microsoft Excel not graphing

  - by SmartLemon

  Im not sure if this is a math question or a su question. The experiment was relating the period of one "bounce" when you hang a weight on a spring and let it bounce. I have this data here, one being mass and one being time. The time is an average of 5 trials, each one being and average of 20 bounces, to minimize human error. t 0.3049s 0.3982s 0.4838s 0.5572s 0.6219s 0.6804s 0.7362s 0.7811s 0.8328s 0.869s The mass is the mass that was used in each trial (they aren't going up in exact differences because each weight has a slight difference, nothing is perfect in the real world) m 50.59g 100.43g 150.25g 200.19g 250.89g 301.16g 351.28g 400.79g 450.43g 499.71g My problem is that I need to find the relationship between them, I know m = (k/4PI^2)*T^2 so I can work out k like that but we need to graph it. I can assume that the relationship is a sqrt relation, not sure on that one. But it appears to be the reverse of a square. Should it be 1/x^2 then? Either way my problem is still present, I have tried 1/x, 1/x^2, sqrt, x^2, none of them produce a straight line. The problem for SU is that when I go to graph the data on Excel I set the y axis data (which is the weights) and then when I go to set the x axis (which is the time) it just replaces the y axis with what I want to be the x axis, this is only happening when I have the sqrt of "m" as the y axis and I try to set the x axis as the time. The problem of math is that, am I even using the right thing? To get a straight line it would need to be x = y^1/2 right? I thought I was doing the right thing, it is what we were told to do. I'm just not getting anything that looks right.

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• about cosine similarity

  - by jaskirat

  hi i m finding cosine similarity between documents ..i did like dis D1=(8,0,0,1) where 8,0,0,1 are the tf-idf scores of the terms t1, t2, t3 , t4 D2=(7,0,0,1) cos(theta) = (56 + 0 + 0 + 1) / sqrt(64 + 49) sqrt(1 +1 ) which comes out to be cos(theta)= 5 now what do i evaluate from this value...i dont get it wat does cos(theta)=5 signify about the similarity between them...pls reply ..Am i doing things right ??????????..pls do reply guys.. will be thank ful to you..

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• Finding the nth number of primes

  - by Braxton Smith

  I can not figure out why this won't work. Please help me from math import sqrt pN = 0 numPrimes = 0 num = 1 def checkPrime(x): '''Check\'s whether a number is a prime or not''' prime = True if(x==2): prime = True elif(x%2==0): prime=False else: root=int(sqrt(x)) for i in range(3,root,2): if(x%i==0): prime=False break return prime n = int(input("Find n number of primes. N being:")) while( numPrimes != n ): if( checkPrime( num ) == True ): numPrimes += 1 pN = num print("{0}: {1}".format(numPrimes,pN)) num += 1 print("Prime {0} is: {1}".format(n,pN))

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• fit a ellipse in Python given a set of points xi=(xi,yi)

  - by Gianni

  I am computing a series of index from a 2D points (x,y). One index is the ratio between minor and major axis. To fit the ellipse i am using the following post when i run these function the final results looks strange because the center and the axis length are not in scale with the 2D points center = [ 560415.53298363+0.j 6368878.84576771+0.j] angle of rotation = (-0.0528033467597-5.55111512313e-17j) axes = [0.00000000-557.21553487j 6817.76933256 +0.j] thanks in advance for help import numpy as np from numpy.linalg import eig, inv def fitEllipse(x,y): x = x[:,np.newaxis] y = y[:,np.newaxis] D = np.hstack((x*x, x*y, y*y, x, y, np.ones_like(x))) S = np.dot(D.T,D) C = np.zeros([6,6]) C[0,2] = C[2,0] = 2; C[1,1] = -1 E, V = eig(np.dot(inv(S), C)) n = np.argmax(np.abs(E)) a = V[:,n] return a def ellipse_center(a): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] num = b*b-a*c x0=(c*d-b*f)/num y0=(a*f-b*d)/num return np.array([x0,y0]) def ellipse_angle_of_rotation( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] return 0.5*np.arctan(2*b/(a-c)) def ellipse_axis_length( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g) down1=(b*b-a*c)*( (c-a)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) down2=(b*b-a*c)*( (a-c)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) res1=np.sqrt(up/down1) res2=np.sqrt(up/down2) return np.array([res1, res2]) if __name__ == '__main__': points = [(560036.4495758876, 6362071.890493258), (560036.4495758876, 6362070.890493258), (560036.9495758876, 6362070.890493258), (560036.9495758876, 6362070.390493258), (560037.4495758876, 6362070.390493258), (560037.4495758876, 6362064.890493258), (560036.4495758876, 6362064.890493258), (560036.4495758876, 6362063.390493258), (560035.4495758876, 6362063.390493258), (560035.4495758876, 6362062.390493258), (560034.9495758876, 6362062.390493258), (560034.9495758876, 6362061.390493258), (560032.9495758876, 6362061.390493258), (560032.9495758876, 6362061.890493258), (560030.4495758876, 6362061.890493258), (560030.4495758876, 6362061.390493258), (560029.9495758876, 6362061.390493258), (560029.9495758876, 6362060.390493258), (560029.4495758876, 6362060.390493258), (560029.4495758876, 6362059.890493258), (560028.9495758876, 6362059.890493258), (560028.9495758876, 6362059.390493258), (560028.4495758876, 6362059.390493258), (560028.4495758876, 6362058.890493258), (560027.4495758876, 6362058.890493258), (560027.4495758876, 6362058.390493258), (560026.9495758876, 6362058.390493258), (560026.9495758876, 6362057.890493258), (560025.4495758876, 6362057.890493258), (560025.4495758876, 6362057.390493258), (560023.4495758876, 6362057.390493258), (560023.4495758876, 6362060.390493258), (560023.9495758876, 6362060.390493258), (560023.9495758876, 6362061.890493258), (560024.4495758876, 6362061.890493258), (560024.4495758876, 6362063.390493258), (560024.9495758876, 6362063.390493258), (560024.9495758876, 6362064.390493258), (560025.4495758876, 6362064.390493258), (560025.4495758876, 6362065.390493258), (560025.9495758876, 6362065.390493258), (560025.9495758876, 6362065.890493258), (560026.4495758876, 6362065.890493258), (560026.4495758876, 6362066.890493258), (560026.9495758876, 6362066.890493258), (560026.9495758876, 6362068.390493258), (560027.4495758876, 6362068.390493258), (560027.4495758876, 6362068.890493258), (560027.9495758876, 6362068.890493258), (560027.9495758876, 6362069.390493258), (560028.4495758876, 6362069.390493258), (560028.4495758876, 6362069.890493258), (560033.4495758876, 6362069.890493258), (560033.4495758876, 6362070.390493258), (560033.9495758876, 6362070.390493258), (560033.9495758876, 6362070.890493258), (560034.4495758876, 6362070.890493258), (560034.4495758876, 6362071.390493258), (560034.9495758876, 6362071.390493258), (560034.9495758876, 6362071.890493258), (560036.4495758876, 6362071.890493258)] a_points = np.array(points) x = a_points[:, 0] y = a_points[:, 1] from pylab import * plot(x,y) show() a = fitEllipse(x,y) center = ellipse_center(a) phi = ellipse_angle_of_rotation(a) axes = ellipse_axis_length(a) print "center = ", center print "angle of rotation = ", phi print "axes = ", axes from pylab import * plot(x,y) plot(center[0:1],center[1:], color = 'red') show() each vertex is a xi,y,i point plot of 2D point and center of fit ellipse

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• The most efficient way of implementing pow() function in floating point

  - by user319873

  Hi, I am trying to implement my own version of pow() and sqrt() function as my custom library doesn't have pow()/sqrt() floating point support. Can anyone help?

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• Projection on a plane using a 2*3 matrix

  - by leipäjuusto

  Hello, I can easily draw the projection of a 3D set of points onto the plane with normal vector (1,1,1), by using the matrix (-sqrt(3)/2 sqrt(3)/2 0) (-1/2 -1/2 1). I want to do the same thing, but for a projection onto an arbitrary plane with normal vector (a,b,c) instead of (1,1,1). How to find the matrix? Thanks in advance!

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• Why can't c# calculate exact values of mathematical functions

  - by Timo Willemsen

  Hey everyone, Why can't c# do any exact operations. Math.Pow(Math.Sqrt(2.0),2) == 2.0000000000000004 I know how doubles work, I know where the rounding error is from, I know that it's almost the correct value, and I know that you can't store infinite numbers in a finite double. But why isn't there a way that c# can calculate it exactly, while my calculator can do it. Edit It's not about my calculator, I was just giving an example: http://www.wolframalpha.com/input/?i=Sqrt%282.000000000000000000000000000000000000000000000000000000000000000000000000000000001%29%5E2 Cheers

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• Special functions in Matlab

  - by favala

  I'm trying to get a picture like the following: http://upload.wikimedia.org/wikipedia/en/e/e6/Airy-3d.svg What am I doing wrong? [x,y]=meshgrid(-1:.1:1,-1:.1:1); surf(x,y,(2*besselj(1,2*pi*sqrt(x.^2+ y.^2)/sqrt(x.^2+ y.^2)).^2) Also... kind of a side note, but if I used ndgrid instead of meshgrid here my x's and y's would switch right?

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• Arcball Problems with UDK

  - by opdude

  I'm trying to re-create an arcball example from a Nehe, where an object can be rotated in a more realistic way while floating in the air (in my game the object is attached to the player at a distance like for example the Physics Gun) however I'm having trouble getting this to work with UDK. I have created an LGArcBall which follows the example from Nehe and I've compared outputs from this with the example code. I think where my problem lies is what I do to the Quaternion that is returned from the LGArcBall. Currently I am taking the returned Quaternion converting it to a rotation matrix. Getting the product of the last rotation (set when the object is first clicked) and then returning that into a Rotator and setting that to the objects rotation. If you could point me in the right direction that would be great, my code can be found below. class LGArcBall extends Object; var Quat StartRotation; var Vector StartVector; var float AdjustWidth, AdjustHeight, Epsilon; function SetBounds(float NewWidth, float NewHeight) { AdjustWidth = 1.0f / ((NewWidth - 1.0f) * 0.5f); AdjustHeight = 1.0f / ((NewHeight - 1.0f) * 0.5f); } function StartDrag(Vector2D startPoint, Quat rotation) { StartVector = MapToSphere(startPoint); } function Quat Update(Vector2D currentPoint) { local Vector currentVector, perp; local Quat newRot; //Map the new point to the sphere currentVector = MapToSphere(currentPoint); //Compute the vector perpendicular to the start and current perp = startVector cross currentVector; //Make sure our length is larger than Epsilon if (VSize(perp) > Epsilon) { //Return the perpendicular vector as the transform newRot.X = perp.X; newRot.Y = perp.Y; newRot.Z = perp.Z; //In the quaternion values, w is cosine (theta / 2), where //theta is the rotation angle newRot.W = startVector dot currentVector; } else { //The two vectors coincide, so return an identity transform newRot.X = 0.0f; newRot.Y = 0.0f; newRot.Z = 0.0f; newRot.W = 0.0f; } return newRot; } function Vector MapToSphere(Vector2D point) { local float x, y, length, norm; local Vector result; //Transform the mouse coords to [-1..1] //and inverse the Y coord x = (point.X * AdjustWidth) - 1.0f; y = 1.0f - (point.Y * AdjustHeight); length = (x * x) + (y * y); //If the point is mapped outside of the sphere //( length > radius squared) if (length > 1.0f) { norm = 1.0f / Sqrt(length); //Return the "normalized" vector, a point on the sphere result.X = x * norm; result.Y = y * norm; result.Z = 0.0f; } else //It's inside of the sphere { //Return a vector to the point mapped inside the sphere //sqrt(radius squared - length) result.X = x; result.Y = y; result.Z = Sqrt(1.0f - length); } return result; } DefaultProperties { Epsilon = 0.000001f } I'm then attempting to rotate that object when the mouse is dragged, with the following update code in my PlayerController. //Get Mouse Position MousePosition.X = LGMouseInterfacePlayerInput(PlayerInput).MousePosition.X; MousePosition.Y = LGMouseInterfacePlayerInput(PlayerInput).MousePosition.Y; newQuat = ArcBall.Update(MousePosition); rotMatrix = MakeRotationMatrix(QuatToRotator(newQuat)); rotMatrix = rotMatrix * LastRot; LGMoveableActor(movingPawn.CurrentUseableObject).SetPhysics(EPhysics.PHYS_Rotating); LGMoveableActor(movingPawn.CurrentUseableObject).SetRotation(MatrixGetRotator(rotMatrix));

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• Calculate car filled up times

  - by Ivan

  Here is the question: The driving distance between Perth and Adelaide is 1996 miles. On the average, the fuel consumption of a 2.0 litre 4 cylinder car is 8 litres per 100 kilometres. The fuel tank capacity of such a car is 60 litres. Design and implement a JAVA program that prompts for the fuel consumption and fuel tank capacity of the aforementioned car. The program then displays the minimum number of times the car’s fuel tank has to be filled up to drive from Perth to Adelaide. Note that 62 miles is equal to 100 kilometres. What data will you use to test that your algorithm works correctly? Here is what I've done so far: import java.util.Scanner;// public class Ex4{ public static void main( String args[] ){ Scanner input = new Scanner( System.in ); double distance, consumption, capacity, time; distance = Math.sqrt(1996/62*100); consumption = Math.sqrt(8/100); capacity = 60; time = Math.sqrt(distance*consumption/capacity); System.out.println("The car's fuel tank need to be filled up:" + time + "times"); } } I can compile it but the problem is that the result is always 0.0, can anyone help me what's wrong with it ?

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• What am I doing wrong with my Shoes program?

  - by dmonroe4919

  #Shoes.app(:title => "Collinear Points", :width => 450, :height => 350) do def calculate math.sqrt(((@[email protected]_f)**2)+((@[email protected]_f)**2)+((@[email protected]_f)**2)) end def compute math.sqrt(((@[email protected]_f)**2)+((@[email protected]_f)**2)+((@[email protected]_f)**2)) end def capture math.sqrt(((@[email protected]_f)**2)+((@[email protected]_f)**2)+((@[email protected]_f)**2)) end stack(:width => '100%', :margin => 20) do para('Calculate Collinear Points') para(' x y z') end flow(:width => '100%' ) do para('Point A: ') @alphax = edit_line(:width => 100, height => 35) {@collinear.text = calculate} @alphay = edit_line(:width => 100, height => 35) {@collinear.text = calculate} @alphaz = edit_line(:width => 100, height => 35) {@collinear.text = calculate} end flow(:width => '100%' ) do para('Point B: ') @betax = edit_line(:width => 100, height => 35) {@collinear.text = compute} @betay = edit_line(:width => 100, height => 35) {@collinear.text = compute} @betaz = edit_line(:width => 100, height => 35) {@collinear.text = compute} end flow(:width => '100%' ) do para('Point C: ') @gammax = edit_line(:width => 100, height => 35) {@collinear.text = capture} @gammay = edit_line(:width => 100, height => 35) {@collinear.text = capture} @gammaz = edit_line(:width => 100, height => 35) {@collinear.text = capture} end button("Configure") @button.click do c = calculate+compute=capture case c when c=true alert("Points are collinear, equation is ") when c=false alert("Points are non-collinear") end end

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