LWPOLYLINE bulge to ARC

[Fahr]

Hello people,

I'm struggling with the following; I built a DXF parser/drawer in C++ which works fine, except for the bulges (42) in LWPOLYLINEs. I tried to convert this bulge to an ARC, but I can't figure it out. All the samples online are in Lisp and I don't quite read Lisp...
Can someone please explain in normal mathematical terminology how to convert an LWPOLYLINE bulge into an ARC? I have the coordinates of the starting and ending point and the bulge value and I'd like to turn this into an ARC with a center point, radius, start angle and end angle.
Any help is most appreciated!

Thanks,
- Fahr

 

[borgunit]

This may help...

http://www.afralisp.com/lisp/Bulges1.htm

"Everybody is ignorant, only on different subjects." — Will Rogers

 

[IFRs]

I always wondered that myself. I had tried to figure it out myself but was never sucessful. Thanks borgunit. (Resistance is futile)

 

[Fahr]

I already found that site, borgunit, but it describes all the procedures in LISP using many default AutoCAD functions which I can't just implement in C.
The story may provide some mathematical geniuses with enough info on deriving the formula, but I am no such genius... I'm really looking for a formula or formulas taking the 3 known parameters and spitting out the needed info for a normal ARC...

- Fahr

 

[IFRs]

Fahr - "The bulge is the tangent of 1/4 of the included angle for the arc between the selected vertex and the next vertex in the polyline's vertex list. A negative bulge value indicates that the arc goes clockwise from the selected vertex to the next vertex. A bulge of 0 indicates a straight segment, and a bulge of 1 is a semicircle." You should be able to implement that in C.

 

[Fahr]

IFRs - I read it and I understand it. However, I need more than just that. For now I am just working on turning it into the full circle and then further. I have the following;

double chord = sqrt(pow(abs(P1.x - P2.x), 2) + pow(abs(P1.y - P2.y), 2));
double s = chord / 2 * bulge;
double radius = (pow(chord / 2, 2) + pow(s, 2)) / (2 * s);

So, I have the radius, yay me. I can't figure out the center point, however...

- Fahr