I believe he was talking about generic programming (he coined the term), whether meant in the context of this talk about the STL, or ‘at large’, in the sense of: programming against a sort of interface that describes something that could fit all (and hopefully several) types (hence multi-sorted), … … provided they have some … Read more
Your expression should be ((x-1) + k) % k. This will properly wrap x=0 around to 11. In general, if you want to step back more than 1, you need to make sure that you add enough so that the first operand of the modulo operation is >= 0. Here is an implementation in C++: … Read more
c = Math.log(a)/Math.log(b)
Here’s a version without sqrt, though I’m not sure whether it is faster than a version which has only one sqrt (it may depend on the distribution of values). Here’s the math (how to remove both sqrts): ad = a2-a1 bd = b2-b1 a1+sqrt(b1) < a2+sqrt(b2) // subtract a1 sqrt(b1) < ad+sqrt(b2) // square it … Read more
Euler angles are more human understandable and also good for decomposing rotations into individual degrees of freedom (for kinematic joints and the like) but have disadvantages like ambiguity and gimbal lock. In practice I would prefer quaternions, as they are easier to compute with (for the computer, not for humans) and more efficient. You have … Read more
(Full disclosure: I am the lead developer of SymPy) The first thing you should understand is that SymPy and Sage are not quite the same thing. SymPy is a pure Python library, that does computer algebra. Sage is a collection of open source mathematical software. Sage tries to gather together all the major open source … Read more
@Dave was the first to post an answer to this (with working code), and his answer has been an invaluable source of shameless copy and pasting inspiration to me. This post began as an attempt to explain and refine @Dave’s answer, but it has since evolved into an answer of its own. My method is … Read more