 Video display control system |
| It is therefore an object of the present invention to provide a video display control system in ... |
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| Graphics display device |
| This invention has been accomplished in order to overcome these problems noted above, and an object ... |
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| Projection exposure apparatus and projection exposure method |
| We claim: 1. A projection exposure apparatus comprising a stage for holding an exposure ... |
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| Data compression/expansion circuit for facsimile apparatus |
| It is an object of the present invention to provide a new and improved data compression/expansion ... |
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| Radar video processor |
| The present invention provides for apparatus which processes applied digital radar video signals ... |
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| Method for processing video signals in a digital image transformer |
| An object of the invention is then to define, for a digital image transformer, the conditions and ... |
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| Associative memory architecture |
| OF THE PREFERRED EMBODIMENTS In FIG. 1, a functional schematic drawing of the associative memory ... |
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| Two-dimensional kernel generator for transversal filters |
| In the present invention, image processing is performed at speeds comparable to those achieved in ... |
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| Digital processor system with conditional carry and status function in arithmetic unit |
| OF SPECIFIC EMBODIMENT Hand-held Electronic Calculator System Referring to FIG. 1, a typical small ... |
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Approximation system
| Details |
Inventors: Samuels, Howard R.;
Assignee: Analog Devices, Inc. (Norwood, MA)
Primary Examiner: Harkcom; Gary V.
Assistant Examiner: Shaw; Dale M.
Attorney, Agent or Firm: Wolf, Greenfield & Sacks
A system for generating a continuous piece-wise linear approximating function that approximately corresponds to a predetermined function over a preselected domain, the approximating function having a selected number of linear segments, the approximating function at the endpoints of the domain falling on the predetermined function. The system first selects an initial error limit, then identifies the points which define the segments. In defining the segments, the system begins at a low endpoint, extends a test segment from the low point to a high endpoint on the predetermined function, and then tests the error between the test segment and the predetermined function at each point. If the error is less than the error limit, the system selects a new higher point on the predetermined function as the new high endpoint, and repeats the operation until the test segment error between it and the predetermined function by at most the error limit. The system then extends the test segment until the error is, at most, the error limit. After determining all but the last segment, the system tests the last segment to determine whether each point is within the selected error of the approximating function. The system then adjusts the error and repeats the procedure until a termination criterion is satisfied. |
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DETAILED DESCRIPTION The invention provides a new and improved method and system for generating a continuous piece-wise linear function which approximately corresponds to a predetermined monotonically increasing or decreasing nonlinear function, so that the approximating function generated by means of the invention has a minimum of error, in relation to the number of linear segments used in the generated function, from the predetermined function over the function's entire domain of interest.
In brief summary, the invention iteratively generates a piece-wise linear function having a preselected number of linear segments which approximates the predetermined function to within a predetermined error band along the predetermined function's domain.
If, with the selected error band, the system is able to find the selected number of linear segments which approximates the function, the system reduces the error band and repeats the procedure.
Initially, the system divides the domain of the function into a selected number of divisions, determines the value of the predetermined function at each of the endpoints of the divisions, and selects an initial maximum error defining the initial error band.
During each iteration, the system first locates the endpoints of the segments except for the last or high-order segment.
During this process, the system iteratively determines the error between the predetermined function and line segments drawn from a low point to the function at the endpoint of each successive division.
If the system is in the first segment, the low point of the segment is the function at the low end of the domain; otherwise, the low point of the segment is the high end of the previously-determined segment.
This process continues until the error is, at most, the selected maximum error.
When a line segment is located having the maximum error, the system then extends the line segment, division by division, maintaining a constant slope, until the error between the segment and the function is again at most the selected maximum error, which point corresponds to the high endpoint of this segment and the low endpoint of the next segment
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