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Software and hardware implementation of a 4*4 matrix for coordinate transforms on graphical displays

: Encarnacao, J.; Waldschmidt, K.; Giloi, W.; Saniter, J.; Strasser, W.

Elektronische Rechenanlagen 14 (1972), Nr.5, S.206-19
ISSN: 0013-5720
Fraunhofer HHI ()
computer graphics; geometry; matrix algebra; microprogramming; crt screen; software; hardware; implementation; 4 x 4 matrix; coordinate transforms; graphical displays; manipulation; pictures; homogeneous coordinates; rotation; scaling; translation; perspective

In the first part of this paper the relevant fundamentals of geometry for the manipulation and the display of pictures on the screen of a CRT are discussed. The usual coordinate transforms are stated first. Introducing homogeneous coordinates it is possible to use a single 4*4 matrix for the representation and computation of the rotation, scaling, translation and perspective transforms. This is very useful, because all the transforms can be computed using a single algorithm. Then different possibilities for the software implementation of the 4*4 matrix are shown, and their advantages and disadvantages are discussed. The second part of the paper presents in detail different possibilities of a hardware implementation of the 4*4 matrix, as well as the theory and construction of the computing elements which are set into operation.