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What does the radius and normal information about an arc mean?

by Technical Evangelist on ‎02-18-2016 11:26 AM - edited on ‎04-06-2016 06:20 PM by Moderator (346 Views)

Question

What does the radius and normal information about an arc mean? How do I tell if the arc is greater or less than PI?

Answer

If the arc sweep angle is greater than PI, the radius in the blob will be positive. If the arc sweep angle is less than PI, the radius in the blob will be negative. Thus, when you want to work with the radius itself, you should always take the absolute value of the radius as found in the blob.

 

The normal vector is a vector perpendicular to the plane in which the arc lies (since our geometry is 3-D, we have to use some means of telling what 2-D plane contains the start, end, origin, points along arc segment, etc.). In typical situations where our geometry all has z values of zero (is effectively 2-D) and the coordinate system is right-handed, then you will see the normal vector pointing straight up (0,0,1).

 

Normal vector must have length equal 1.

 

When normal have for example (i, j, k) = (0, 0, 1), then the arc is counter-clockwise. (i, j, k) = (0, 0, -1), then the arc is clockwise.  If any other value is negative, the projection to x-y plane is elliptical arc.

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