mathematics – Simple (quadratic) stat growth formula

I’m working on a fairly simple hobby project. It’s an RPG like game and am trying to figure out how to grow stats among different classes. I’ve read several posts about different ways to do this but haven’t quite found what I’m looking for. Usually it’s some sort of exponential growth formula. However I believe if I wanted different classes to scale differently using a formula like that I’d need to play with different formulas for each stat for each class. For instance I may want a tank to scale faster/higher HP than a mage.

In my mind, what I want to do is define a class by giving starting and ending stat values for each stat. So take HP as an example, at level 1 you start at 10 and at max level (say) 100 you end at 500. Another class may start at 10 and end at 350.

I believe what I want to do a quadratic growth curve so while it’s scaling on a curve it doesn’t start as slow as exponential and then ramp up so quickly. In my mind then if I can calculate quadratic growth between 0 and 1, I can multiply that by the total stat growth to get a value at any given level. Problem is I haven’t been able to find a formula to calculate quadratic growth between 2 numbers. Most formulas I’ve seen simply calculates a curve and you get what you get at level 5, 10. Yes you can tweak the growth curve to adjust the stats but to me it makes more sense to get a single growth curve (at this point) and be able to adjust the ending values at each level based on total growth.

mathematics – Triangle area selection using BVH raycasting

Let’s assume I’m already storing a BVH acceleration structure per mesh on my engine and I’d like start
making area selection like on many DCC tools out there, for instance, blender.

With blender you can do {rectangular, circle, lasso} selection to select faces and I’d like to understand the maths behind these algorithms. If I was using color picking techniques these sort of algorithms would be obvious but when using BVH+raycasting I’m still failing to understand the algo/maths behind it.

So, could you please explain the logic behind those? For instance, I assume rectangular selection should be easier to implement than circle/lasso, so how would you gather all screen projected triangles living inside the rectangular selection created by the mouse?

Probability Question Support! – Mathematics Stack Exchange

I am thinking about this question and I don’t really know how to tackle it.

The problem is:
The class has 30 students. If you want to call 5 students, each one is independent of the others and randomly with equal probability, what is the probability that none are repeated?

I am thinking as 30* 29 * 28 * 27*26 / 30^5, but I am not sure it is correct. Thank you so much!

discrete mathematics – Proving $aequiv b pmod m$ if $a bmod m = bbmod m$

I want to prove that for integers $a, b$ and positive integers $m$, that $a equiv bpmod m$ iff $a bmod m = bbmod m$

I’m on my tablet currently so I cannot type up my latex well. But I’ve been trying to do a direct proof using the fact that $b=mq+r$. I also tried using propositional logic, since this is a biconditional I tried proving the implications in both directions, but I’m still getting confused

engineering mathematics – Matrix dynamics to Kalman equations

Consider the system
$$begin{bmatrix}1 \ 1 \ 1 \1 end{bmatrix} begin{bmatrix}x_1 \ x_2 \ x_3 \ x_4 end{bmatrix} = begin{bmatrix} 3 \ 5 \ 4 \ 8 end{bmatrix}$$

Let $R$ be the errors in measurements $y$ and $P$
be the errors in the estimate of $hat{x}$. Assume that the uncertainty in measurements, $sigma^{2}$. Then, $R=begin{bmatrix}sigma^{2} & 0 & 0 & 0\ 0 & sigma^{2}& 0 & 0 \ 0 & 0 &sigma^{2}& 0 \ 0 & 0 & 0 & sigma^{2}end{bmatrix}$.

Now consider Linear Kalman filter equations

x_{k} &=F_{k-1} x_{k-1}+G_{k-1} u_{k-1}+q_{k-1} \
y_{k} &=A_{k} x_{k}+r_{k} \
q_{k} & sim Nleft(0, Q_{k}right) \
r_{k} & sim Nleft(0, R_{k}right) \

Assume a static model, with trivial dynamics $F = I$, so that $F_{k+1} = F_k$
and let’s assume again that the variable $x$ is directly observable, so that $A = I$, and $A_{k+1} = A_k$. Also, assume the uncertainty in both model, $F$, and observation, $A$, are both equal to $sigma^{2}$.

I’m trying to identify parameters of Kalman filter equations through this system. Since the model is static with trivial dynamics, I think $q_{k-1} = 0$. Can you please help me to identify other parameters?

mathematics – Rotate relative to set point in a specified direction in a 3D space

I know there’s a geometry formula to calculate the next point in rotation relative to another point in 2D but I’m working in 3D and I want to calculate the next position in specified direction as well. Think Spiderman or the Bloodstalkers from ARK. I’m working in a game engine that uses the basic {x = 1, y = 2, z = 1} for vectors. I’m pretty bad at math so I honestly can’t figure this out myself.

discrete mathematics – Logic, Proofs, and Mathematical Reasoning

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mathematics – How to decompose a 4×4 TRS transformation matrix with negative scale?

As the title says I need to decompose 4×4 TRS transformation matrices and extract the proper scale vectors and the proper rotation vectors (or rotation quaternions).

I know how to extract those information when the upper 3×3 matrix determinant is not negative. The problem is that those matrices can have that negative determinant and as far as I could understand, this negative determinant indicates a flip or mirrored transformation.

What do I have to do to extract the proper values for scale and rotation in those cases?

gm.general mathematics – Determine sample size when averaging over sensor data

I was not too sure where to post this if in either stackoverflow or mathoverflow. Im not too sure how to approach this problem.

I have a accelerometer which I use to calculate angles currently I’m averaging over 14 samples of data (the sensor samples at 1600Hz) and I see a lot variance in my measurements. If I keep my sensor at a stable angle it varies for each calculation around 2-4 degrees.

I thought this might be a statistics problem perhaps, I need to somehow find how many samples of data I should average over inorder to reach atleast +-1 degree accuracy

mathematical programming – Mathematics and Computer Science

I just got my master’s degree in mathematics, it was related to abstract algebra. I’m thinking about applying for a doc degree, however, I deeply want to study something with an “applied” appeal. Does anyone know a branch of computer science that can be done by math students but that can still be considered math? I hope my question makes sense.