3
votes
1answer
50 views

Sigmoid function with separate control of derivative at 0 and sharpness of bend.

For a physical relationship, $f(x)$, I'm trying to model, i have a fairly good determination of some of the boundaries, such that $ f(0) = 0$ $f'(0) = B$ $ \lim_{x\to\infty} f = A $ So far, what I ...
1
vote
1answer
163 views

How can I find which function corresponds to a set of data points?

Suppose I have a set of data points like this: 1;1 2;4 3;9 4;16 5;25 6;36 ... The first column is the input of the function and the second one is the result. I ...
0
votes
1answer
43 views

Rotation matrix for non-isometry transformation

Imagine that you have a sphere in $\mathbb{R}^3$ and a plane (that is parallel to the x,y plane) through the sphere. Now you want to have a clockwise rotation in the x/y plane that does the ...
3
votes
1answer
110 views

How can I add a curve to my otherwise linear values?

I have built an interactive map for the Web that transitions smoothly from lon/lat point to lon/lat point. The duration of the transition is calculated dynamically and depends on the distance between ...
2
votes
4answers
97 views

Function generation by input $y$ and $x$ values

I wonder if there are such tools, that can output function formulas that match input conditions. Lets say I will make input like that: $y=0, x=0$ $y=1, x=1$ $y=2, x=4$ and tool should ...
1
vote
2answers
376 views

Easing function, constant velocity then decelerate to zero

I'm trying to write an interpolator for a translate animation, and I'm stuck. The animation passes a single value to the function. This value maps a value representing the elapsed fraction of an ...
0
votes
1answer
154 views

How to determine a function from outputs

Given the following inputs and outputs to a function, how would I determine an algorithm to fit? ...
-4
votes
2answers
382 views

Please help to find function for given inputs and outputs [closed]

Can you help with finding the formula for these input and output values? When $n=1$: $f\left(1,1\right)= 0.0000000000$ When $n=2$: $f\left(1,2\right)= 0.0000000000$ $f\left(2,2\right)= ...
1
vote
1answer
633 views

How would I create a exponential ramp function from 0,0 to 1,1 with a single value to explain curvature?

I need an exponential function that will take linear input from 0,0 to 1,1 and give me back an exponential shaped curve such that changes in X near the 0 point result in small increases in Y, but each ...
0
votes
1answer
695 views

Find Y-Axis value from point on curve using X-Axis value

I think this maybe a basic question, but I'm not mathematically equipped to handle the details. The problem I have is that I will have a curve such as in the image below and I want to find the y-axis ...
0
votes
1answer
31 views

a mapping function is requested

I have $n$ data points in $d$-dimensional space, i.e $x_1,x_2,...x_n$ where $x_i\in R^d$. I want an interpolation function $f:R^d-> R$ on these data points to map them to $y_1,y_2,...,y_n$, where ...
1
vote
1answer
250 views

Using Lagrange's Interpolation Formula to show that boolean functions over finite fields are polynomials

Let $F_2$ be the set of all the functions from the finite field $GF(2^n)$ of $2^n$ elements to $GF(2)$. I am reading a textbook that proves that the elements of $F_2$ can be represented by ...
0
votes
1answer
351 views

Function to represent curve between two 2D points

I need a (simplest) function that interpolates values in range from predefined point $A$ to $B$ with rules: it must be smooth curve direction near $B$ must be the same as predefined $D$ vector ...
2
votes
3answers
797 views

Deriving an equation that satisfies many points

Say I have a collection of points, for example the following: (1, 167), (2, 11), (3, 255), etc Is it possible to construct an equation that satisfies all of ...
3
votes
2answers
634 views

Need a formula for a quadratic spline

I'm trying to reproduce some results from a paper and I need an explicit formula for a specific quadratic spline to do so. The problem is, I've only got a plot of it. The quadratic spline is from ...
1
vote
2answers
372 views

What mathematical function would do this: if $x = 0$ then $y = 0$ but if $x > 0$ then $y = 1$?

$x = 0$, $f(x) = 0$ $x = 1$, $f(x) = 1$ $x = 2$, $f(x) = 1$ $x = 3$, $f(x) = 1$ ... There have been so many times I could have used this at different programming problems but I always resorted to ...
1
vote
1answer
62 views

Proof that infinite functions can fit a table of numerical values

Suppose while conducting experiments, I measure a finite number of variables with some constants like temperature, etc. We get a table of finite number measurements (numerical values to some decimal ...
1
vote
1answer
904 views

Construct / find the simplest function based on data

Let's say I have these 7 natural numbers (all between 0 and 255): 255, 23, 45, 32, 87, 52, 146 How can I find a function F(x) that, once computed, gives me back ...
1
vote
1answer
311 views

Produce piecewise monotonic function with 3 points and their slope with MATLAB

I'm trying to reproduce the shape of an airfoil's camber line using the leading edge angle, the trailing edge angle, the chord and the max camber value. I cannot use a spline because it overshoots ...
2
votes
3answers
572 views

Interpolation to a power function

We have an experiment which have the variables $x$ and $y$. $x$ and $y$ can be measured into pair $(x_i,y_i)$. Now I'm finding a way to interpolate it into a power function $y=a+bx^c$. Which $a,b,c$ ...
1
vote
1answer
63 views

A function for forming a closing curve on all points on a 2D image

First of all, this is for image processing. The small circles above is on an image and are my list of points. The points are always in order from p1, p2, p3 to pn. And I am to create a curve that ...