I am working with a line which has the following information.
[
{x: 384, y: 360, percentage: '0%'},
{x: 460.79998779296875, y: 360, percentage: '10%'},
{x: 537.5999755859375, y: 360, percentage: '20%'},
{x: 614.4000244140625, y: 360, percentage: '30%'},
{x: 691.2000122070312, y: 360, percentage: '40%'},
{x: 768, y: 360, percentage: '50%'},
{x: 844.7999877929688, y: 360, percentage: '60%'},
{x: 921.5999755859375, y: 360, percentage: '70%'},
{x: 998.4000244140625, y: 360, percentage: '80%'},
{x: 1075.199951171875, y: 360, percentage: '90%'},
{x: 1152, y: 360, percentage: '100%'}
]
The line starts at (384,360) and ends at (1152,360). Between 0% to 100% I calculated 9 intervals with 10% gap to calculate x and y coordinates at the respective percentage, by line parameterization, such as
@ 10% -> (1152-384)*0.1+384 = 76.8+384 = 460.80
@ 20% -> (1152-384)*0.2+384 = 76.8+384 = 537.60
Graphically, it looks like this
With this information, if I convert this line to a circle, how do I find the coordinate of each of these (x,y) interval coordinates on the circle?
The center coordinate of the circle is x coordinate @0%, y coordinate @0%+radius=> (384,360+circumference/2π)=>(384,482.231).
I am not a mathematician, apologies I don't know how to provide mathematical notations here.
So you have a line segment between the points: $$ P_1=(384,360)\\ P_2=(1152,360) $$ hence having length $1152-384=768$. You want this to be transformed to become circumference of a circle, hence having radius: $$ r=\frac{768}{2\pi} $$ Finally, you want a given point between $P_1$ and $P_2$ to be mapped to the corresponding point on the circle. You have already parametrized the line with a function having: $$ f(0)=P_1\\ f(1)=P_2 $$ namely: $$ f(t)=P_1+t\cdot(P_2-P_1)=(384+t\cdot768,360) $$ The circle has center: $$ C=P_1+(0,r)=\left(384,360+\tfrac{768}{2\pi}\right)\approx(384,482.23) $$ The correspondingly parametrized version of the circle will then be (written as a vector for better readability): $$ \begin{align} g(t) &= C+r\cdot\langle\sin(t\cdot 2\pi),-\cos(t\cdot 2\pi)\rangle\\ \quad\\ &= \begin{bmatrix} 384+\tfrac{768}{2\pi}\cdot\sin(t\cdot 2\pi)\\ \quad\\ 360+\tfrac{768}{2\pi}\cdot\left(1-\cos(t\cdot 2\pi)\right) \end{bmatrix} \end{align} $$
Your coordinate system has $y$-axis upside down, I think, but here is a dynamic GeoGebra-applet showing how it works:
Link to GeoGebra-applet