math

问题 Here's what I mean: if you found all possible 2-element combinations of [1,2,3,4], you would get [1,2], [1,3],[1,4],[2,3],[2,4] and [3,4] What I want is groups of combinations that don't overlap and include all elements. So for example [[1,2],[3,4]] is an example of one "group", because the elements in both combinations do not overlap, and all possible elements are used. [[1,3],[2,4]] is an example of another "group" By the way, I'm aware that itertools will allow me to print combinations

问题 A user will define a line on screen which will have, when drawn, a given thickness ( or width ). I now need to be able to determine the coordinates of a bounding rectangle around this. I have the coordinates A and B, along with the line thickness (W). How can I calculate the coordinates A1, A2, B1 and B2. I searched but was unable to find a question corresponding to this already asked. 回答1: Dx= Xb - Xa Dy= Yb - Ya D= sqrt(Dx * Dx + Dy * Dy) Dx= 0.5 * W * Dx / D Dy= 0.5 * W * Dy / D This

问题 A user will define a line on screen which will have, when drawn, a given thickness ( or width ). I now need to be able to determine the coordinates of a bounding rectangle around this. I have the coordinates A and B, along with the line thickness (W). How can I calculate the coordinates A1, A2, B1 and B2. I searched but was unable to find a question corresponding to this already asked. 回答1: Dx= Xb - Xa Dy= Yb - Ya D= sqrt(Dx * Dx + Dy * Dy) Dx= 0.5 * W * Dx / D Dy= 0.5 * W * Dy / D This

问题 I have 2 objects (i'll refer to them as target and interceptor ). I know the target's current location and velocity. I know the interceptor's current location and speed it can travel. From that, what I now need to know is : Is interception possible ie same location at same point in time. What vector would the interceptor need to travel on How much time will the interception take i.e target @ (120,40) with a V(5,2) per second and interceptor @ (80,80) that can travels with a speed of 10 per

问题 Why is there a W term in a lot of 3D API's Vector class (i.e. Vector4(x, y, z, w) ) ? Are there math operations that absolutely require the W term? 回答1: This is a special representation of a point in 3D space, called homogeneous coordinates . They are just another way to describe a point in 3D space. They are used a lot in 3D graphics because they have a few advantages: they make some formulas simpler, and they allow you to represent a "point at infinity" (or "line at infinity" etc. depending

问题 I have spent the last 5 hours searching for an answer. Even though I have found many answers they have not helped in any way. What I am basically looking for is a mathematical, arithmetic only representation of the bitwise XOR operator for any 32bit unsigned integers. Even though this sounds really simple, nobody (at least it seems so) has managed to find an answer to this question. I hope we can brainstorm, and find a solution together. Thanks. 回答1: XOR any numerical input a + b - ab(1 + a +

问题 I'm looking for a better algorithm than one I found on stackoverflow to handle 4096 byte numbers, i'm hitting a maximum recursion depth. Code from stackoverlow post, i copy/pasted it but lost the original link: def linear_congruence(a, b, m): if b == 0: return 0 if a < 0: a = -a b = -b b %= m while a > m: a -= m return (m * linear_congruence(m, -b, a) + b) // a This works fine for smaller numbers, for example: In [167]: pow_mod(8261, 63, 4033) 63 1 8261 4033 31 195 1728 4033 15 2221 1564 4033

问题 Recently, I saw this question which asks how you can divide integers with ceil rounding (towards positive infinity). Unfortunately the answers either don't work for signed integers or have problems with underflows and overflows. For instance, the accepted answer has this solution: q = 1 + ((x - 1) / y); When x is zero, there is an underflow to ~0 and the the result is incorrect. How can you implement ceil rounding correctly for signed and unsigned integers and how do you implement other

问题 Recently, I saw this question which asks how you can divide integers with ceil rounding (towards positive infinity). Unfortunately the answers either don't work for signed integers or have problems with underflows and overflows. For instance, the accepted answer has this solution: q = 1 + ((x - 1) / y); When x is zero, there is an underflow to ~0 and the the result is incorrect. How can you implement ceil rounding correctly for signed and unsigned integers and how do you implement other

问题 I'm creating a little game in Javascript, and I have trees that can hold a certain amount of max experience, and each tree have a varied amount of branches that also needs to be leveled up with experience, and they should total to the tree max experience. If it was that easy, I would just divide them equally, like max / branches , but since it's for a game, I need to make a formula where the first branch needs no experience, and then each branch experience needed steadily increase (while