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From: jbn@glacier.STANFORD.EDU (John B. Nagle)
Newsgroups: comp.graphics
Subject: Re: AutoCAD question
Keywords: polylines, bulge, arc-information
Message-ID: <17515@glacier.STANFORD.EDU>
Date: 26 Jun 88 18:47:39 GMT
References: <4406@csli.STANFORD.EDU>
Reply-To: jbn@glacier.UUCP (John B. Nagle)
Organization: Stanford University
Lines: 26

In article <4406@csli.STANFORD.EDU> rustcat@csli.UUCP (Vallury Prabhakar) writes:
>Say, for example the two vertices are (x1, y1) and (x2, y2) with the value
>of the bulge being z.  I can calculate the value of the included angle 
>between the arc end-points by the above definition of the bulge.  Call this
>angle A.  So, now I have two end-points and an included angle defining an
>arc-segment.  It seems to me that this is not sufficient for uniquely
>defining a circular arc.  Some piece of information appears to be missing.

     There are two data items, the "bulge" (type 42) and the "curve fit
tangent direction" (type 50) used to define the curvature of polyline arcs in
AutoCAD.  

     Splines are not used in AutoCAD's curve fitting.  Fitted curves
are composed strictly of arcs, with the arcs tangent at the endpoints.
Between each pair of vertices defined by the user, there will be two
arc segments, with an additional vertex introduced by the curve fitter.
The description on page 376 of the AutoCAD 2.6 manual describes how
this data is expressed in the .DXF file.

     The major advantage of restricting curves to circular arcs is that
the space of arcs is closed under rotation, translation, and cutting.
Thus, one can rotate, translate, and cut a polyline, repeatedly if
desired.  This is harder with splines; the complexity of the representation
grows under such operations.

					John Nagle