Aizatulin

Your subset should have id = 1 and the other points id != 1 (-1 for example). As I've mentioned before, this is just an example. You can rename this attribute if you want, but make sure to do this in python node aswell. With this method the parameters depends only on the least square fit (so the focus does).

This is just an option/example (related to your first picutre). If you don't want to use all points you can filter by id. By default you can use all but usually a curve with degree 2 won't fit good (higher degree has better chance for better fit). If you know you have a specific subset of points you want to use , you can set the id for this subset to 1.

You can define which points are filtered out. You will get different results with different ids. You know how to calculate the focus? As hint: If your parabola is y = a*x^2 + b*x + c the derivative is y' = 2*a*x + b. What will happen, if the derivative is 0 (base) and 1 (reflection at this point is from vertical to horizontal (45°)).

The focus is determined by the parameters of the parabola

set i@id = 1 for all points (set_id_example - node) and move the end-points of curve 2 along the x-axis.

the fit is already good, so raising the degree will only have little effect.

The id is used to select the points, which are used for the fit. If you want to use all points just set i@id = 1 in a wrangle. You can use cubic or higher degrees aswell just change degree in python node to 3,4,... . Every x-value has y-value in points set, since the values are extracted from the curve @P = (P.x, P.y, P.z), where P.x ~ x, P.y ~ y and P.z = 0

I haven't tried multiple y, but it sounds, that the fits are indepentent from each other. So if y has k components, it will perform k different fits for the same x, where each fit represents a function 1D -> 1D. You can invert a function if there is no y-value with multiple x values. For examples a parabola y=x^2 for y=1 there are two x-values with y=1: x=1 and x=-1, so you can't invert this function.

Afaik this type of fitting only works for (1D) polynomial functions [like y = a*x^2 + b*x + c [which is degree 2] -> [a,b,c] will be calculated]. The "id" attribute is if you want to select a subset of points (not all points), so you can filter the "id" points. You cannot generally invert a function (or what do you mean with flip/invert?).

Hi, you can use (for example) python -> numpy -> polyfit to perform a least square fit. The result will be a parameter set for a polynomial function. For degree = 2 it will be a parabola. This method will work, if you have a defined (sub)set of points which are in the x,y plane. But the parabola is not a closed curve, since it is a function from x to y. fit_curve.hipnc

Ok I'm not sure what you mean with radius. Perhaps you can provide us with (your) definition of a parabola. For me it is something that you map (float)values to squared values. What is your goal? Are you trying to fit an existing curve with a parabola?

Hi, here are two possibilities (not the only ones) to calculate a parabola curve from a planar curve. The first method uses the relative ptnum and the second uses the distance of the point to zero. parabola.hipnc

Hi, just if interested here is wrangle solution using the primuv() function and polyframe. From polyframe you get "N" and "up" for a local Rotation Matrix and from the curve itself you get the postion "P" for every u-value (not just limited to the discrete points), since primuv interpolates the values inbetween. transform_along_curve.hipnc

Hi, here is a simple example, where you have control over the length using a ramp. helix.hipnc

Hi, very rough ideas based on your example: if you construct the surface by a curve you can use a width attribute along the curve, which determines the local width of the river. This attribute can be used to control the speed. Another attribute can be the curve's derivative (call it D, which is a vector). the y-component of this derivative determines the gradient, which should also influence the speed. Use something like abs(D.y) / length(D) to get the relative amount to be multiplied with the maximum force.