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# High Speed Arc Distinguisher

IP.com Disclosure Number: IPCOM000114724D
Original Publication Date: 1995-Jan-01
Included in the Prior Art Database: 2005-Mar-29
Document File: 4 page(s) / 63K

IBM

## Related People

Sakuragi, T: AUTHOR [+2]

## Abstract

Disclosed is a high speed method to judge whether a pixcel calculated with pixcel generator belongs to a given arc of circle/ellips or not. Only an addition and a subtruction are used in each judgement of a generated pixcel.

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This is the abbreviated version, containing approximately 74% of the total text.

High Speed Arc Distinguisher

Disclosed is a high speed method to judge whether a pixcel
calculated with pixcel generator belongs to a given arc of
circle/ellips or not.  Only an addition and a subtruction are used in
each judgement of a generated pixcel.

A pixcel of circle and ellips can be easily generated with
Bresenham algorithm.  Suppose V(Xv,Yv) are generated pixcel, S(Xs,Ys)
and E(Xe,Ye) are start point and end point of the arc respectively.
Then assume that all three vectors V, S and E belong to a same plane.

Inner product of S and E, i.e., S * E, becomes positive if the
anguler of S and E is within 0 degree to 180 degrees.  On the other
hand
the product becomes negative if the angular is within 180 degrees to
360 degrees.
Case 1 (0 degree - 180 degrees)

As shown in Fig. 1, following two inner products become
positive if vector V is in the anguler of S and E.

However, if vector V is outside of the anguler, the both or one
of two inner products become negative as shown in Fig. 2.  Since
increment of Xv and/or Yv equals 0, 1 or -1, above two equations for
each pixcel are calculated with addition or subtruction of Xs, Ys, Xe
and Ye to/from the inner products of previous calculated pixcel.
Case 2 (180 degrees - 360 degrees)

As shown in Fig. 3, the both or one of following two inner
products become positive if vector V is in the anguler of S and E.

However, if vector V is outside of the...