## Direct way of computing clockwise angle between 2 vectors

2D case Just like the dot product is proportional to the cosine of the angle, the determinant is proprortional to its sine. So you can compute the angle like this: The orientation of this angle matches that of the coordinate system. In a left-handed coordinate system, i.e. x pointing right and y down as is … Read more

## Mathematica matrix diagonalization

What you need to do is normalize the answer you get. There is a function called Normalize, which can be used like this:

## Function to determine if two numbers are nearly equal when rounded to n significant decimal digits

There is a function assert_approx_equal in numpy.testing (source here) which may be a good starting point.

## How to determine if a point is in a 2D triangle?

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:

## Finding square root without using sqrt function?

There is a better algorithm, which needs at most 6 iterations to converge to maximum precision for double numbers: Algorithm starts with 1 as first approximation for square root value. Then, on each step, it improves next approximation by taking average between current value y and x/y. If y = sqrt(x), it will be the same. If y > sqrt(x), then x/y < sqrt(x) by about the same … Read more

## Rotating a Vector in 3D Space

If you want to rotate a vector you should construct what is known as a rotation matrix. Rotation in 2D Say you want to rotate a vector or a point by θ, then trigonometry states that the new coordinates are To demo this, let’s take the cardinal axes X and Y; when we rotate the X-axis 90° counter-clockwise, … Read more

## What’s the difference between “mod” and “remainder”?

My friend said that there are differences between “mod” and “remainder”. If so, what are those differences in C and C++? Does ‘%’ mean either “mod” or “rem” in C?

## Calculate Average Java

Your last line should probably be something like: Mind my calculations, but you get the idea.

## Is there a math nCr function in python? [duplicate]

The following program calculates nCr in an efficient manner (compared to calculating factorials etc.) As of Python 3.8, binomial coefficients are available in the standard library as math.comb:

## Is there a standard sign function (signum, sgn) in C/C++?

I want a function that returns -1 for negative numbers and +1 for positive numbers. http://en.wikipedia.org/wiki/Sign_function It’s easy enough to write my own, but it seems like something that ought to be in a standard library somewhere. Edit: Specifically, I was looking for a function working on floats.