Why are ARC coordinates wrong?

[mozman]

It's the OCS

• The ARC and other 2D entities are located in the Object Coordinate System OCS.
• The OCS is used to place 2D entities in 3D space.
• A description of the OCS can be found here.
• The OCS is defined by the extrusion vector and an elevation value.
• The default OCS is defined by an extrusion vector of (0, 0, 1), that means the extrusion vector is aligned to the WCS z-axis and the OCS is coincident with the WCS, in simpler words: OCS coordinates are WCS coordinates.
• Always compare 3D vectors by the isclose() method of the Vec3 class:

from ezdxf.math import Z_AXIS
 
if not Z_AXIS.isclose(arc.dxf.extrusion):
    # this entity has not WCS coordinates
    ...

When should you care about OCS coordinates?

When the extrusion vector Arc.dxf.extrusion is (0, 0, -1) you are dealing with an inverted OCS.

• Even pure 2D drawings can contain inverted OCS as a result of mirror operations.
• ezdxf has a special module called upright to flip inverted OCS and align them with the WCS.

from ezdxf import upright
  
upright.upright(entity)  # or
upright.upright_all(msp)  # to apply the function to all entities in a collection

• The function can be called on any entity, even multiple times, without raising an error - only inverted OCS will be flipped.
• The extrusion vector should be (0, 0, 1) now and the OCS is aligned with the WCS.
• Text based entity types can not be flipped!

In all other cases you have to convert OCS coordinates to WCS coordinates:

ocs = arc.ocs()
wcs_center = ocs.to_wcs(arc.dxf.center)  # center.z defines the elevation

• The start- and end angles of the arc are counter-clockwise oriented around the OCS z-axis (extrusion vector) and starting at the OCS x-axis defined by the Arbitrary Axis Algorithm.
• A point on ARC calculation is done in OCS coordinates and converted to WCS coordinates:

import math
from ezdxf.math import Vec3

radius = arc.dxf.radius
center = Vec3(arc.dxf.center)  # center.z defines the elevation
angle = arc.dxf.start_angle  # in degrees
ocs_point = center + Vec3.from_deg_angle(angle, radius)
ocs = arc.ocs()
wcs_point = ocs.to_wcs(ocs_point)

Using a Path object

A different solution is to convert linear entities (Line, ARC, LWPOLYLINE, ...) to a Path object:

from ezdxf import path

p = path.make_path(arc)

• ARC and ELLIPSE entities are approximated by multiple cubic Bézier-curves, which
  are close enough for display rendering.
• A Path has WCS coordinates and can be flattened into points (vertices).

Documentation

• Object Coordinate System
  • DXF Reference
  • Arbitrary Axis Algorithm
• Tutorial for OCS/UCS Usage
• OCS Class
• Path Class
• Vec3 Class