How to calculate start angle and end angle in ARC for DXF file ?

[Anonymous]

I am writing a software to generate simple 3D model from point cloud, output of which is also to be exported as DXF. Got struck with the 3D ARC generation in DXF format.

I have three 3D points (P1<x1,y1,z1> ; P2<x2,y2,z2> ; P3<x3,y3,z3>) with which I have to generate ARC and store it in DXF format. So far I am able to generate coordinates for Center (Code : 10,20,30 ), Radius (Code : 40), Extrusion Vector (Code: 210, 220, 230). But not able to find or develop mathematics for start angle and end angle for arc (Code: 50, 51).

Please help me to understand the mathematics behind generating Start and End Angle for ARC.

P.S. I am very new to CAD world.

Thanks,

Yash 

[cadffm]

ARC DXF

http://help.autodesk.com/view/ACD/2021/ENU/?guid=GUID-0B14D8F1-0EBA-44BF-9108-57D8CE614BC8

50 is start-angle (of a full circle, angle 0 is in east direction in your ocs/210,220,230)

51 is end-angle

between 50 and 51 you see the ARC, both values are stored es radian, so PI is a half circle.

An ARC from 1.57079.. (/ pi 2)

to 3.141592... (pi)

is drawn from North to West (1/4 circle)

[Anonymous]

Thanks for the reply, But my question is exactly this, with three 3D coordinates how to calculate values for start angle and end angle (Code 50, 51). I want to know the mathematics behind this.

[ChrisRS]

I know that this is an old post.

3D Arcs are not AutoCAD entities. Thus, they are not supported in DXF.

Mathematically an ellipse is a conic section viewed perpendicular to the cutting plane. The ellipse's projection is circular when viewed along the cone's axis. 

In that context, with respect to a plane perpendicular to the conic axis, a partial segment of an ellipse would be a 3D arc. These do not exist as AutoCAD entities.

Civil 3D Feature Lines can include 3D arcs. When converted to AutoCAD 3D Polylines, the circular arc sections are approximated by short straight-line segments. (Tessellation.)