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Vector Matrix Multiplier for Graphics Display

IP.com Disclosure Number: IPCOM000062598D
Original Publication Date: 1986-Dec-01
Included in the Prior Art Database: 2005-Mar-09
Document File: 3 page(s) / 47K

Publishing Venue

IBM

Related People

Jones, JW: AUTHOR

Abstract

In interactive graphics display system transformers may be expressed as matrices to simplify arithmetic calculations. Disclosed is a method for vector matrix multiplication to transform pictures into screen coordinates. Precomposed sums of elements are stored as a look-up table in RAM (random-access memory) to be used in high speed vector matrix multiply computation. TRANSFORMATION OPERATION Coordinate transformations for graphics operations are neatly represented by matrices (see Newman and Sproull, pages 491-501, McGraw- Hill Computer Science Series). These transformations refer to scaling, rotation, translation and projection to screen coordinates of objects described by a series of vectors or end points. The following shows a representation of the transformation of (X, Y, Z, W) to screen coordinates (Xs, Ys, Zs, Ws).

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Vector Matrix Multiplier for Graphics Display

In interactive graphics display system transformers may be expressed as matrices to simplify arithmetic calculations. Disclosed is a method for vector matrix multiplication to transform pictures into screen coordinates. Precomposed sums of elements are stored as a look-up table in RAM (random-access memory) to be used in high speed vector matrix multiply computation. TRANSFORMATION OPERATION Coordinate transformations for graphics operations are neatly represented by matrices (see Newman and Sproull, pages 491-501, McGraw- Hill Computer Science Series). These transformations refer to scaling, rotation, translation and projection to screen coordinates of objects described by a series of vectors or end points. The following shows a representation of the transformation of (X, Y, Z, W) to screen coordinates (Xs, Ys, Zs, Ws). Transformation matrix vector matrix multiply

(Image Omitted)

Transformation Column 1 to a vector Similarly the remaining three columns upon transformation give coefficients Ys, Zs and Ws. Note that the coordinate (X, Y, Z,
W) is common to all 4 ROW COLUMN products. It is also a fact that the elements of the matrix (all to a44) are fixed during the transformation of an entity(picture). Therefore, sixteen possible combinations of the sum of products of each column could be precalculated and saved in a suitable RAM. Note that only 8 combinations would be required for operating on three coefficients. The following figure represents the 16 combinations for the first column. Precalculated Transformation Column

(Image Omitted)

This is now similar to the well-understood shift and add multiplier, except that the selected partial sum of products is added to the accumulator instead of the multiplicand. Example: Assume 4-bit coordinates (10, 8, 3, 5) or (1010, 1000, 0011, 0101) in binary form and the following parameters for the column matrix. al1 = 35 = X(0023) a21 = 18 = X(0012) a31 = 10 = X(000A) a41 0 1 = X(0001), where X is hexadecimal notation. With these values, the calculation by the method described here is as follows: The precalculated transformation matrix is set up in the RAM as shown in the following figure. Precalculated Transformation Column

(Image Omitted)

Taking the...