Implementing rotation matrix constraints in Analog VLSI

Abstract

We describe an algorithm for continuously producing a 3x3 rotation matrix from 9 changing input values that form an approximate rotation matrix, and we describe the implementation of that constraint in analog VLSI circuits. This constraint is useful when some source (e.g., sensors, a modeling system, other analog VLSI circuits), produces a potentially “imperfect” matrix, to be used as a rotation. The 9 values are continuously adjusted over time to find the “nearest” true rotation matrix, based on a leastsquares metric. The constraint solution is implemented in analog VLSI circuitry; with appropriate design methodology [Kirk 93], adaptive analog VLSI is a fast, accurate, and low-power computational medium. The implementation is potentially interesting to the graphics community because there is an opportunity to apply adaptive analog VLSI to many other graphics problems. CR