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# Graphics Display Arcs by Enveloping

IP.com Disclosure Number: IPCOM000060370D
Original Publication Date: 1986-Mar-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 2 page(s) / 63K

IBM

## Related People

Silverwood, EA: AUTHOR

## Abstract

On a graphics display an arc is drawn by forming an envelope with a series of lines. Starting from an imaginary circumscribing square whose side equals arc radius, the end coordinates of lines across the square, external to the arc and tangential to the arc are calculated from a stored tangent table. When these lines are drawn on a graphics display, an envelope of a quadrant of the arc is formed with vignetting external to the arc. A solid quadrant-producing program flow follows: 1.Decide which quadrant to do first. 2. Define the imaginary circumscribing square whose side equals quadrant arc radius. 3. Define either corner of the square which touches the arc, as the starting point (one of two). 4. Make the x/y boundaries the two sides of the square outside the circle. 5.

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Graphics Display Arcs by Enveloping

On a graphics display an arc is drawn by forming an envelope with a series of lines. Starting from an imaginary circumscribing square whose side equals arc radius, the end coordinates of lines across the square, external to the arc and tangential to the arc are calculated from a stored tangent table. When these lines are drawn on a graphics display, an envelope of a quadrant of the arc is formed with vignetting external to the arc. A solid quadrant-producing program flow follows: 1.Decide which quadrant to do first. 2. Define the imaginary circumscribing square whose side equals quadrant arc radius. 3. Define either corner of the square which touches the arc, as the starting point (one of two). 4. Make the x/y boundaries the two sides of the square outside the circle. 5. Graduate these boundaries using tangent look-up table values between 0 and 45 degrees (i.e., values between 0 and 1). Since the 0 (zero) value represents the point touching the circle and the 1 (one) value the next corner, some simple arithmetic must be done to derive the actual x/y values which are the end coordinates of lines to be drawn. The key factor is the non-linear nature of successive graduations and not the scale used. Typically, for, say, the vertical side, use the y value multiplied by the tangent increments, to give the starting y coordinate for each line. The x coordinate is, of course, constant for each tangent starting on the vertical side. The...