math

how to subtract circle from an arbitrary polygon

Given an arbitary polygon with vertices stored in either clockwise/counterclockwise fashion (depicted as a black rectangle in the diagram), I need to be able to subtract an arbitrary number of circles (in red on the diagram) from that polygon. Removing a circle could possibly split the polygon into two seperate polygons (as depicted by t...

getting the value of a filter at an arbitrary time

Context: I'm trying to improve the values returned by the iPhone CLLocationManager, although this is a more generally applicable problem. The key is that CLLocationManger returns data on current velocity as and when it feels like it, rather than at a fixed sample rate. I'd like to use a feedback equation to improve accuracy v=(k*v)+(1-...

Fast dot product for a very special case

Given a vector X of size L, where every scalar element of X is from a binary set {0,1}, it is to find a dot product z=dot(X,Y) if vector Y of size L consists of the integer-valued elements. I suggest, there must exist a very fast way to do it. Let's say we have L=4; X[L]={1, 0, 0, 1}; Y[L]={-4, 2, 1, 0} and we have to find z=X[0]*Y[0] +...

Naive Bayesian classification (spam filtering) - Doubt in one calculation? Which one is right? Plz clarify

Hi guys, I am implementing Naive Bayesian classifier for spam filtering. I have doubt on some calculation. Please clarify me what to do. Here is my question. In this method, you have to calculate P(S|W) -> Probability that Message is spam given word W occurs in it. P(W|S) -> Probability that word W occurs in a spam message. P(W...

Project Euler #163 understanding

I spent quite a long time searching for a solution to this problem. I drew tons of cross-hatched triangles, counted the triangles in simple cases, and searched for some sort of pattern. Unfortunately, I hit the wall. I'm pretty sure my programming/math skills did not meet the prereq for this problem. So I found a solution online in ord...

Find the centroid of a polygon with weighted vertices

Hi, I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight? Simplified illustration of what I mean using straight line: 5kg-------------...

draw an arc given 3 points in SWT

iam using the swt java library and iam having a problem. the gc draw arc method takes the following arguments GC.drawArc(int x, int y, int width, int height, int startAngle, int endAngle); but i want to be able to draw the arc using 3 arguments : the source ,destination and control points. is there any formula to convert between tho...

Why is Java not telling me when I can't use Integer?

For a small project (Problem 10 Project Euler) i tried to sum up all prime numbers below 2 millions. So I used a brute force method and iterated from 0 to 2'000'000 and checked if the number is a prime. If it is I added it to the sum: private int sum = 0; private void calculate() { for (int i = 0; i < 2000000; i++) { if (i.isP...

Mathematical problem

I have the following function: function getLevel(points) { var level = -1 + Math.sqrt(4 + points/20); // Round down to nearest level return Math.floor(level); } The above function calculates the level of a player based on their points, my problem is that I need a function like this to calculate the points needed for a given lev...

Create a circle using a Catmull-Rom Spline

I have a class where you enter control points for a catmull-rom spline, and then it returns a list of points running along the spline. What points would I need to enter to create a circle? ...

Idea of developing "Calendar" from scratch

What's the broad math idea behind the calendar if you need to build one from scratch without depending on OS or other libraries ? ...

Is the binormal of a vertex the cross between its normal and tangent?

I'm trying to find out what a binormal is in the context of graphics programming but coming up short, I saw on a site that the binormal was being calculated as the corss between the normal and tangent (i.e. cross(normal, tangent)), is this the correct way to calculate a binormal? ...

How do I find the millionth number in the series: 2 3 4 6 9 13 19 28 42 63 ... ?

It takes about minute to achieve 3000 in my comp but I need to know the millionth number in the series. The definition is recursive so I cannot see any shortcuts except to calculate everything before the millionth number. How can you fast calculate millionth number in the series? Series Def n_{i+1} = \floor{ 3/2 * n_{i} } and n_{0}=2....

optimization math computation (multiplication and summing)

Suppose you want to compute the sum of the square of the differences of items: $\sum_{i=1}^{N-1} (x_i - x_{i+1})^2$ the simplest code (the input is std::vector<double> xs, the ouput sum2) is: double sum2 = 0.; double prev = xs[0]; for (vector::const_iterator i = xs.begin() + 1; i != xs.end(); ++i) { sum2 += (prev - (*i)) * (prev - (...

C# Math class question

I need to calculate Tanh-1 in C# (and Sinh-1 and Cosh-1) I did not found it in Math library.. Any suggestions ? EDIT: Tanh not Tan !! ...

Solving a math problem/expression, which is a string, in PHP

The user can enter a math problem (expression) like 5 + 654, 6 ^ 24, 2!, sqrt(543), log(54), sin 5, sin(50). After some reformatting (e.g. change sin 5 into sin(5)), and doing an eval, PHP gives me the right result: $problem = "5 + 5324"; eval("$result = " . $problem); echo $problem . " = " . $result; However, this is quite unsafe: /...

sin v/s sinf fucntion in C

Hi Guys, I am trying to use sinf function in my C Program and it does give me undefined reference under MSVC 6.0 but sin works fine. This make me curious to find the difference between sin and sinf. What is the logical difference between sin and sinf(). How can I implement my own sinf functionality? ...

Find the sum of consecutive whole numbers w/o using loop in JavaScript

I'm looking for a method to do calculations like: function sumIntegerUpTo(number) { return 1+2+3+...+number; } If you pass number as 5 function should return the sum of 1+2+3+4+5. I'm wondering if it's possible to do without loops. ...

How do I find the most complex convex polygon enclosing a set of points?

I have a list of (about 200-300) 2d points. I know needs to find the polygon that encloses all of them. The polygon has to be convex, and it should be as complex as possible (i.e. not a rectangular bounding box). It should find this in as low as possible time, but there are no restrictions on memory. You may answer in pseudocode or any ...

Axis Rotation Question

By using left hand rule, I rotate one object left and right using y axis, and rotate up/down using x axis. After first object is rotated to the right, the up/down rotation should be using z axis. However, when I try to rotate using z axis, after the first rotation, it has the same effect when I rotate using y axis. Anyone has any ideas...