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# Chord-Size Determination

IP.com Disclosure Number: IPCOM000047002D
Original Publication Date: 1983-Sep-01
Included in the Prior Art Database: 2005-Feb-07
Document File: 2 page(s) / 35K

IBM

Nye, DD: AUTHOR

## Abstract

Described is an algorithm for determining the optimum chord size to use when representing circular arcs with straight line estimations. In any system where curves are approximated by straight lines, i.e., chords, a compromise between the number of chords used and the aesthetic appearance of the result must be determined. The use of more chords than necessary uses computer time inefficiently, but too few chords produces a poor display. The same number of chords for all size circles or arcs is a poor decision because small circles can be displayed with fewer chords than large circles without appearing distorted. The disclosed algorithm determines the number of chords on the basis of the height of a segment of a circle as a function of the radius.

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Chord-Size Determination

Described is an algorithm for determining the optimum chord size to use when representing circular arcs with straight line estimations. In any system where curves are approximated by straight lines, i.e., chords, a compromise between the number of chords used and the aesthetic appearance of the result must be determined. The use of more chords than necessary uses computer time inefficiently, but too few chords produces a poor display. The same number of chords for all size circles or arcs is a poor decision because small circles can be displayed with fewer chords than large circles without appearing distorted. The disclosed algorithm determines the number of chords on the basis of the height of a segment of a circle as a function of the radius. (The height of a segment is the maximum distance between the chord and the circle circumference.) The relationship is logarithmic- exponential. In the figure, if X is the square root of R- squared minus (R-D)-squared, then the angle P is the arctangent of X/(R-D) and the angle 0 is 2*r, i.e., two times theta. The sector height, D, is chosen by D = K*exp(1.7 log R) where the logarithm is taken to the base 10. The result is an approximation of a circle that uses as few sides as possible consistent with a good appearance. The value of K depends on the units of measurement of R and has a value of 0.0341 when R is measured in millimeters. With an R value of 1 mm, the number of chords is found to be 12,...