Linear interpolation operator

Details Linear interpolation operator Linear interpolation operator

1994-11-17

2004-02-10

Malzahn, David H. (Department: 2124)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reissue Patent

active

RE038427

ABSTRACT:

BACKGROUND OF THE INVENTION
The instant invention relates to a linear interpolation operator, that is, a calculation device permitting, if one considers that a value y is a linear function of x and if one knows the values of y (y
1
and y
2
) corresponding to two specific values of x (x
1
and x
2
), to calculate the value of y corresponding to any given value of x included within the interval [X
1
, x
2
].
Such a linear interpolation operator is especially implemented in the field of synthesis graphic devices of bi- or tri-dimensional images for line plotting, Gouraud smoothing, Phong smoothing, S-plines, ray tracing and more generally for signal digital processing.
In mathematical form, a linear interpolation is written as follows:
y=y
1
+(x−x
1
)(y
2
−y
1
)/(x
2
−x
1
)   (1)
On the other hand, the object of the instant invention is to resolve calculations of the type
y=(aA+bB)/(a+b) and A*B/C.
According to the prior art, all those calculations require the use of calculation devices, softwares or hardwares, using a computation time period equal to that of about three multiplications (generally, the division duration is substantially equal to that of two multiplications).
SUMMARY OF THE INVENTION
An object of the instant invention is to provide for a linear interpolation operator permitting to carry out the abovementioned calculations (and analog and derived calculations) within a period of time equal to that of one multiplication.
In order to achieve this purpose, the instant invention provides for a linear interpolation operator so as to determine the value y of a function x when one knows the value y
1
corresponding to x
1
, and a value y
2
corresponding to x
2
(x
2
<x
1
), comprising first calculation means for (x
m
+x
M
)/2, (with x
m
<x
M
, initial value of x
m
=x
1
, initial value of x
M
=x
2
); second calculation means of (y
m
+y
M
)/2, (initial value of y
m
=y
1
, and initial value of y
M
=y
2
); comparison means of x with (x
m
+x
M
)/2 for determining which one of the intervals [x
m
,(x
m
+x
M
)/2], [(x
m
+x
M
)/2, x
M
] comprises x and for feeding back the limits of the selected interval into the first calculation means and the interval limits corresponding in y into the second calculation means; and output means supplying as the wished value y the output of the second calculation means after a determined number of cycles.
Thus, according to the instant invention, successive multiplication operations are replaced by operations of the logic type, the number of which is roughly equal to that of one operation. Moreover, the hardware constituting the operator is substantially simplified with respect to the devices according to the prior art.
Moreover, it will be noted that the operator according to the instant invention is liable to be implemented in various ways, for example by a software or by various types of wired devices.


REFERENCES:
patent: 3789203 (1974-01-01), Catherall et al.
patent: 3943343 (1976-03-01), Irie
patent: 4001565 (1977-01-01), Kawai
patent: RE30132 (1979-10-01), Irie

Affiliated with

Also associated with

Rating

Linear interpolation operator does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Linear interpolation operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear interpolation operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-3351942