Draw arc within polyline using bulge in THREE.JS

Question

I'm reading in a cad file from a dxf and I need to be able to draw an arc between two arbitrary points with a bulge value. I'm using THREE.Line to draw segments of the arc.

This page describes some of the necessary calculations in lisp but doesn't explain the center-point calculation very well. I also don't know what angle function does in the example code (Maybe the angle between two points using 0,0 as an origin?). Here is the code there:

;; Bulge to Arc  -  Lee Mac
;; p1 - start vertex
;; p2 - end vertex
;; b  - bulge
;; Returns: (<center> <start angle> <end angle> <radius>)

(defun LM:Bulge->Arc ( p1 p2 b / a c r )
    (setq a (* 2 (atan b))
          r (/ (distance p1 p2) 2 (sin a))
          c (polar p1 (+ (- (/ pi 2) a) (angle p1 p2)) r)
    )
    (if (minusp b)
        (list c (angle c p2) (angle c p1) (abs r))
        (list c (angle c p1) (angle c p2) (abs r))
    )
)

I understand how a (ie theta) and r (radius) are calculated, but I don't understand the center-point calculation and I need it (I think) to figure the segments for my arc. Can anyone help explain the math and/or provide some javascript code?

Answer 1

A coworker was able to figure out what to do here:

In the lisp code, the angle a (aka theta) was just simplified to 2atan(b) as opposed to 4atan(b) because later we only need half the angle for some calculations of the center point c and radius r, not the whole angle.

The lisp angle function finds the angle of a vector (in this case, p1 -> p2) where 0 is the positive x axis, pi / 2 is positive y axis, and so forth. That angle of that chord, plus the angle between the cord and vector p1 -> c, which is (pi - pi/2 - a), gives us enough to do a polar coordinate calculation to find the coordinates of the center point c.