1
vote
1answer
29 views

re-arranging polynomial (newton interpolation)

How does: $$ f(x_2)= f(x_0)+\frac{f(x_1)-f(x_0)}{x_1-x_0}(x_2-x_0)+a_2(x_2-x_0)(x_2-x_1)\tag1 $$ rearrange to: $$ a_2 = \frac{\frac{f(x_2)-f(x_1)}{x_2-x_1}-\frac{f(x_1)-f(x_0)}{x_1-x_0}}{x_2-x_0} ...
0
votes
2answers
45 views

How can I find the gradient of this function? $f(r,t)=r^3\cos(t).$

$$f(r,t)=r^3\cos(t).$$ Is it not like this: $<3r^2,-\sin(t)>$
2
votes
2answers
53 views

Converting data to a specified range

I am trying to convert data to a particular range of 0-10. Actual Data may vary from - 50000 - 26214400. I have broken this down in to 4 parts as follows - ...
3
votes
1answer
186 views

Curve through four points — simple algebra??

The motivation for this is Bezier curves. But, if you don't know what these are, you can skip down to the last paragraph, where the problem is described in purely algebraic terms. Suppose I want to ...
1
vote
0answers
74 views

What are the constants in the relationship between point density and median point distance?

Given $\rho$ particles uniformly distributed on a plane within a unit square ($\rho > 1$), each particle has another particle that is closest to it; the median of those nearest distances is called ...
2
votes
1answer
105 views

A Question About Linear Interpolation

So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
1
vote
3answers
983 views

Smooth transition between two lines (2d)

I have function that is defined as $$ Y = \frac{1}{15} x \longrightarrow {\rm if}\qquad 0 \leq x \leq 30 $$ $$ Y = \frac{1}{70} x + \frac{11}{7} \longrightarrow {\rm if}\qquad x > 30 $$ The ...