Question regarding Arc

Hi All,

Pls check the posted image.
How can i get that distance ??

But I suspect you already have this information :wink:


I want to make the arc of known length between two point using script.
So i will need the mid point of the arc. I need to find out that mid point
I dont know the radius of arc. I just know the length of arc i want to make.

You can approximate it by using this: but I don’t think you can calculate it exactly using just those two values?

My degree is in model making for film and TV not maths and geometry :wink:

The attached script draws an arc based on the endpoints of a chord and the arc length. Is that the sort of thing you’re after? I didn’t make the solver very robust, nor did I worry about which plane the arc is drawn in, so there are a few things to do.


Arc from 2pts and arc length.rvb (2.2 KB)

Perfect !!

Thank You radair3155

Ok, so if that fits your needs, I took a little closer look at things like stability issues and which plane the arc gets drawn in. The attached file updates a couple items and adds more notes on the equations used.

  1. The initial guess for theta sets the solver stability. It looks like the guess I made is stable, but by fitting three known points, I made a better and simpler initial guess function that should be completely stable.

  2. If one picks 3 points, that can specify both the plane in which to draw the arc and which side of the chord it’s drawn on. I don’t see a stock Rhino command for generating an orthogonal, planar coordinate system from three points, but it can be readily done with the vector functions.


Arc from 2pts and arc length 01.rvb (2.9 KB)

I took a hard look at the behavior of Newton’s method for the case that arc length nearly equals chord length. The function is vertically going to 0 which causes the method to fail. It’s a pretty minor failure, but there’s an easy fix.


Arc from 2pts and arc length 02.rvb (3.3 KB)