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# Affine Transformation Method for Image Character Fonts

IP.com Disclosure Number: IPCOM000060182D
Original Publication Date: 1986-Mar-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 2 page(s) / 32K

IBM

## Related People

Miyazawa, A: AUTHOR

## Abstract

This article describes a method of affine transformation to expand, reduce and rotate image character fonts, in which a transformation matrix is decomposed into three matrices. Generally, the affine transformation on a two-dimensional plane is expressed as follows: (Image Omitted) By the above equation, a pel (picture element) originally located at (x, y) is moved to (x' y'). The following is a transformation matrix to rotate by s. (Image Omitted) According to the present method, the transformation matrix is decomposed into three matrices as follows: (Image Omitted) The first matrix A corresponds to a vertical inclination in which a horizontal line is inclined as shown in Fig. 1A. The second matrix B corresponds to a horizontal inclination in which a vertical line is inclined as shown in Fig. 1B.

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Affine Transformation Method for Image Character Fonts

This article describes a method of affine transformation to expand, reduce and rotate image character fonts, in which a transformation matrix is decomposed into three matrices. Generally, the affine transformation on a two-dimensional plane is expressed as follows:

(Image Omitted)

By the above equation, a pel (picture element) originally located at (x, y) is moved to (x' y'). The following is a transformation matrix to rotate by s.

(Image Omitted)

According to the present method, the transformation matrix is decomposed into three matrices as follows:

(Image Omitted)

The first matrix A corresponds to a vertical inclination in which a horizontal line is inclined as shown in Fig. 1A. The second matrix B corresponds to a horizontal inclination in which a vertical line is inclined as shown in Fig. 1B. The third matrix C corresponds to the expansion/reduction as shown in Fig. 1C. These matrices A, B and C may be implemented by line generators. For the matrix C, the implementation is described in IBM Technical Disclosure Bulletin 27, 7B, 4323- 4325 (December 1984). Note that the above decomposition means that the order of processing is the expansion/reduction of the horizontal inclination, and then the vertical inclination. According to this order, i.e., C T B T A, the matrices B and A can be processed simultaneously with the matrix C because the processing of B and A does not change the number of pels in an image....