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Fast Parallel DIVISION for Graphics Display Coordinates

IP.com Disclosure Number: IPCOM000038422D
Original Publication Date: 1987-Jan-01
Included in the Prior Art Database: 2005-Jan-31
Document File: 2 page(s) / 49K

Publishing Venue

IBM

Related People

Jones, JW: AUTHOR

Abstract

In an interactive graphics display system with homogeneous coordinates X, Y, Z, W of a vector it is required to project or map X, Y, Z onto the W plane. This entails dividing each of X, Y, Z by W. Each division uses a known non-restoring division algorithm but with a common control of division W. For background information, see Principles of Interactive Graphics by Newman and Sproull, Second Edition, in the McGraw-Hull Computer Science Series, pages 491-499. The method is designed to divide the four coordinates (X, Y, Z, W) of the vector by the W component. The resultant W component is therefore equal to unity. The other three vector components are the values X/W, Y/W and Z/W, respectively.

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Fast Parallel DIVISION for Graphics Display Coordinates

In an interactive graphics display system with homogeneous coordinates X, Y, Z, W of a vector it is required to project or map X, Y, Z onto the W plane. This entails dividing each of X, Y, Z by W. Each division uses a known non-restoring division algorithm but with a common control of division W. For background information, see Principles of Interactive Graphics by Newman and Sproull, Second Edition, in the McGraw-Hull Computer Science Series, pages 491-499. The method is designed to divide the four coordinates (X, Y, Z, W) of the vector by the W component. The resultant W component is therefore equal to unity. The other three vector components are the values X/W, Y/W and Z/W, respectively. The division algorithm operates on all four values simultaneously by adding or subtracting a fraction of their original value to as to make W converge to unity. This operation is used to operate on graphic coordinates (homogeneous coordinates) system for projecting onto the W plane. DIVISION The controlling result is W, and the iterative process to make it converge to 1 is given by Wn = Wn-1 +/- W*2**-n. The add/subtract operation is governed by the magnitude of the result; i.e., if Wn is > 1, then the next operation is subtraction, otherwise, it is addition.

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The add/subtract operation is the same for the other three element components. Thus Xn = Xn-1 +/- X*2**-n, Yn = Yn-1 +/- Y*2**-n and Zn = 1 +/- Z*2**-n, the arithmetic operation being the same as that used for W. The relative magnitudes are therefore maintained. OPERATING ON THE W COMPONENT The sign of the result must follow the rules of division. Therefore, it makes sense to determine this at the start of the operation by making the controllin...