How to generate a random point within a circle of radius R: r = R * sqrt(random()) theta = random() * 2 * PI (Assuming random() gives a value between 0 and 1 uniformly) If you want to convert this to Cartesian coordinates, you can do x = centerX + r * cos(theta) y = … Read more
Cantor pairing function is really one of the better ones out there considering its simple, fast and space efficient, but there is something even better published at Wolfram by Matthew Szudzik, here. The limitation of Cantor pairing function (relatively) is that the range of encoded results doesn’t always stay within the limits of a 2N … Read more
Exponentiation by squaring. int ipow(int base, int exp) { int result = 1; for (;;) { if (exp & 1) result *= base; exp >>= 1; if (!exp) break; base *= base; } return result; } This is the standard method for doing modular exponentiation for huge numbers in asymmetric cryptography.
In GNU libm, the implementation of sin is system-dependent. Therefore you can find the implementation, for each platform, somewhere in the appropriate subdirectory of sysdeps. One directory includes an implementation in C, contributed by IBM. Since October 2011, this is the code that actually runs when you call sin() on a typical x86-64 Linux system. … Read more
It’s doing integer division. You can use to_f to force things into floating-point mode: 9.to_f / 5 #=> 1.8 9 / 5.to_f #=> 1.8 This also works if your values are variables instead of literals. Converting one value to a float is sufficient to coerce the whole expression to floating point arithmetic.
Decimal numbers can be represented exactly, if you have enough space – just not by floating binary point numbers. If you use a floating decimal point type (e.g. System.Decimal in .NET) then plenty of values which can’t be represented exactly in binary floating point can be exactly represented. Let’s look at it another way – … Read more
You could use… Math.trunc() (truncate fractional part, also see below) Math.floor() (round down) Math.ceil() (round up) Math.round() (round to nearest integer) …dependent on how you wanted to remove the decimal. Math.trunc() isn’t supported on all platforms yet (namely IE), but you could easily use a polyfill in the meantime. Another method of truncating the fractional … Read more
In general, the simplest (and quite optimal) algorithm is checking on which side of the half-plane created by the edges the point is. Here’s some high quality info in this topic on GameDev, including performance issues. And here’s some code to get you started: float sign (fPoint p1, fPoint p2, fPoint p3) { return (p1.x … Read more
Some of the suggested methods will fail in the case of a non-convex polygon, such as a crescent. Here’s a simple one that will work with non-convex polygons (it’ll even work with a self-intersecting polygon like a figure-eight, telling you whether it’s mostly clockwise). Sum over the edges, (x2 − x1)(y2 + y1). If the … Read more
For positive numbers where you want to find the ceiling (q) of x when divided by y. unsigned int x, y, q; To round up … q = (x + y – 1) / y; or (avoiding overflow in x+y) q = 1 + ((x – 1) / y); // if x != 0