trigonometry

How could I define trigonometric functions that take arguments in degrees instead of the usual radians, and compute correctly rounded results for these arguments? Multiplying the argument by M_PI/180.0 before passing it to the corresponding function in radians does not work, because M_PI/180.0 is not π/180. Section 5.5 of the Handbook of Floating-Point Arithmetic offers a method to compute the correctly rounded product of the argument by π/180, but some arguments will still be such that this product is close to the midpoint between two consecutive representable floats, and then applying even a

Test code: #include <cmath> #include <cstdio> const int N = 4096; const float PI = 3.1415926535897932384626; float cosine[N][N]; float sine[N][N]; int main() { printf("a\n"); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { cosine[i][j] = cos(i*j*2*PI/N); sine[i][j] = sin(-i*j*2*PI/N); } } printf("b\n"); } Here is the time: $ g++ main.cc -o main $ time ./main a b real 0m1.406s user 0m1.370s sys 0m0.030s After adding using namespace std; , the time is: $ g++ main.cc -o main $ time ./main a b real 0m8.743s user 0m8.680s sys 0m0.030s Compiler: $ g++ --version g++ (Ubuntu/Linaro 4.5.2

I'm struggling to find a rock solid solution to detecting collisions between a circle and a circle segment. Imagine a Field of View cone for a game enemy, with the circles representing objects of interest. The diagram at the bottom is something I drew to try and work out some possible cases, but i'm sure there are more. I understand how to quickly exlude extreme cases, I discard any targets that don't collide with the entire circle, and any cases where the center of the main circle is within the target circle are automatically true (E in the diagram). I'm struggling to find a good way to check

I have a point in a rectangle that I need to rotate an arbitrary degree and find the x y of the point. How can I do this using javascript. Below the x,y would be something like 1,3 and after I pass 90 into the method it will return 3,1. |-------------| | * | | | | | |-------------| _____ | *| | | | | | | | | _____ |-------------| | | | | | *| |-------------| _____ | | | | | | | | |* | _____ Basically I am looking for the guts to this method function Rotate(pointX,pointY,rectWidth,rectHeight,angle){ /*magic*/ return {newX:x,newY:y}; } This should do it: function Rotate(pointX, pointY, rectWidth

I know this is a recurring question, but I haven't really found a useful answer yet. I'm basically looking for a fast approximation of the function acos in C++, I'd like to know if I can significantly beat the standard one. But some of you might have insights on my specific problem: I'm writing a scientific program which I need to be very fast. The complexity of the main algorithm boils down to computing the following expression (many times with different parameters): sin( acos(t_1) + acos(t_2) + ... + acos(t_n) ) where the t_i are known real (double) numbers, and n is very small (like smaller