William E Swanson

Daniel R Emmons

A cross product calculator to multiply mathematical representations of a pair of vectors in order to calculate a resultant vector, which resultant vector is aligned normal to the plane in which the pair of vectors is located. The present cross product calculator has application to a real time computer generated imagery or graphics system having the capability to provide reliable color shading of a three dimensional object moving across the screen of a video display. The resultant normal vector provided by the cross product calculator is indicative of the orientation of the object relative to a source of supply of incident light. Storage apparatus and control hardware are included to provide accurate, normalized equivalents of the mathematical representations of the pair of vectors which are multiplied together to derive the cross product thereof. More particularly, a plurality of multiple bit data strings, representing intermediate products of the pair of vectors, are reduced in size without suffering a corresponding loss of information content, so that the resultant cross product (i.e. normal vector) can be calculated with increased speed and minimized data storage requirements.

Cross product calculator with normalized output

A matrix multiplier having application to a real time computer-generated imagery or graphics system, wherein the output of the multiplier is normalized to increase both the accuracy and speed by which a three dimensional object can be displayed on a video stream. The output of the matrix multiplier is typically a plurality of multiple (e.g. 32 or more) bit serial data screen. Each data stream is normalized to itself and to each of the other of the plurality of data streams which form the product of the matrix multiplication. That is, a particular segment (e.g. 16 bits) of each data stream is selected for continued processing in order to efficiently and accurately define an object in three dimensional space. The selection of each data stream segment is dependent upon the bit pattern thereof and, more particularly, upon the occurance of a pair of successive bits of opposite polarity relative to one another. Accordingly, in the event that many streams of data contain respective bit patterns wherein a large number of the most significant bits are all of the same polarity, the data streams are normalized or shifted by an identical number of bit positions, wherein some of the most significant bits thereof are discarded while the lesser significant bits are retained. Thus, the data streams are scaled to provide representative data words of both reduced size and maximized precision.

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San Diego, CA, United States of America

William E Swanson