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# Coordinate Transformations for Vector Graphics on a Printer

IP.com Disclosure Number: IPCOM000038596D
Original Publication Date: 1987-Feb-01
Included in the Prior Art Database: 2005-Jan-31
Document File: 1 page(s) / 12K

IBM

## Related People

Makowka, CD: AUTHOR

## Abstract

Input to an APA (all-points addressable) graphic printer typically requires that the input vector graphic coordinates be scaled or transformed to graphic device coordinates consistent with the internal coordinate space supported by the particular APA hardware. The present transformation algorithm performs this scaling function with simple integer arithmetic. The problem is to transform a graphics coordinate (Xs,Ys) to a device coordinate (Xp,Yp) with all terms expressed in integers within a limited range, i.e., valid 16 binary bit integers, as in a typical known printer. The required transformation equations are developed from the following information. 1. (Xsc,Ysc) = the known center of the region of interest in graphic coordinate space. 2.

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Coordinate Transformations for Vector Graphics on a Printer

Input to an APA (all-points addressable) graphic printer typically requires that the input vector graphic coordinates be scaled or transformed to graphic device coordinates consistent with the internal coordinate space supported by the particular APA hardware. The present transformation algorithm performs this scaling function with simple integer arithmetic. The problem is to transform a graphics coordinate (Xs,Ys) to a device coordinate (Xp,Yp) with all terms expressed in integers within a limited range, i.e., valid 16 binary bit integers, as in a typical known printer. The required transformation equations are developed from the following information. 1. (Xsc,Ysc) = the known center of the region of interest in graphic coordinate space. 2. S = the known scaling factor by which the graphic coordinates are to be magnified or reduced. 3. (Xpc,Ypc) = the desired center point of the picture on the printed page. It is seen that the required transformations are effected by the following equations. In the case of magnification (where * denotes multiplication) Xp = Xpc + (Xs - Xsc) * S,

Yp = Ypc - (Ys - Ysc) * S, and in the case of reduction (where / denotes division) Xp = Xpc + (Xs - Xsc) / S,

Yp = Ypc - (Ys - Ysc) / S. (The difference in sign between the Xp and Yp equations provides transformation from the right-handed coordinate system of the application to the internal left-handed coordinate system of a par...