A knowledge of arc relationships is required when working with curves in AutoCAD design and programming.

GDD in AutoCAD

Definitions[edit | edit source]

r=radius

delta=included angle

tan(angle)=sin(angle)/cos(angle)

Units[edit | edit source]

delta in radians

=delta in degrees*pi/180
=delta in degrees/57.2957786666 approx.

delta in degrees

=delta in radians*180/pi
=delta in radians*57.2957786666 approx.

Relationships[edit | edit source]

For all these relationships, angles are in radians. Angle 2 is the angle of triangle 123 at Point 2

Arc length=r*delta

Chord=r*tan(delta/2)

Bulge=tan(delta/4)

=b/(chord/2)
=2b/chord

Tangent

=r*tan(delta/2)
=r*sin(delta/2)/cos(delta/2)

Delta

=4*arctan(bulge)

R

=chord/(2*sin(delta/2)))
=arc length/delta

Angle 2 (even when point 2 is not at midpoint of arc)

=(2*pi-delta)/2
=pi-(angle1+angle3)
=arcsin(chord/(2*R))
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