Cathode ray oscilloscope displays curves or contours of complex shapes corresponding to sets of x,y coordinates. It requires few storage facilities and produces a rapid display of complex curves with a fewer number of commands than previous systems

Dertouzous, M. L.

Graham, H. L.

English

NASA Technical Reports Server

August 1969	 Brief 69-10247 
r 
L	 NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Simplified System Displays Complex Curves Corresponding to Input Data 
'v u.-	 Storage 
I Storage I 
In	 Program 
Command	
,	 Curvature	 geInformation Data
put	
Generator
Information	 i Storage 
Bea m- i nt ensity 
	
I Storage
Oscilloscope 
D/A	 I s-Coordinates 
	
Converter / Network
	 x(t) 
INo.1	 ________ 
	
Network	 Y  
No. 2 
Beam	 y-Coordinates 
Figure 1 
A relatively simple, inexpensive system has been 
devised to display curves or contours of complex 
shapes. The curves are displayed on a cathode ray 
oscilloscope and represent very good approximations 
of actual plots corresponding to sets of x,y coordinates. 
The new system requires comparatively few storage 
facilities and produces a rapid display of a highly com-
plex curve with a fewer number of commands than 
are required in any previously known systems. The 
latter characteristic is especially significant when the 
system is used with on-line computers, particularly 
those which are to be time-shared by many users. 
The system, Figure 1, digitally stores the informa-
tion from a command program generator which speci-
fies (I) the initial and final coordinate positions of each 
of several curve segments comprising the complex 
contour, (2) the curvature of each segment between 
the initial and final coordinate points, and (3) the
initial and final slopes of the segments. For display 
on a cathode ray tube, beam intensity information is 
also needed to indicate the times when the beam is 
either on or off. Once the command information has 
been stored, the system rapidly synthesizes the overall 
complex contour by sequentially reproducing each 
segment of the contour. To reproduce each segment, 
the initial and final coordinate information for that 
segment is converted from a digital to an analog form. 
This conversion provides a step-function input signal 
which is applied to a pair of networks (No. 1 and No. 2). 
These networks generate specified analog output 
signals in response to the step-function input signals. 
The parameters of the networks are determined by the 
digital curvature and slope information stored from the 
command program generator. The output signals from 
the networks, representing time-varying x and y func-
tions (i.e., x(t) and y(t), respectively), are then fed to 
(continued overleaf) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
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a suitable display device, such as the X and Y input 
terminals of a cathode ray oscilloscope tube, where the 
specific curve segment is displayed. The input step-
function and network-parameter values are then 
sequentially changed to reproduce the succeeding 
segments until the overall contour has been repro-
duced and displayed on the oscilloscope. 
The command program can be generated by any 
known technique, such as, for example, through the 
use of a software program translator capable of accept-
ing input data and producing a suitable command 
program for the display system. The networks (No. I 
and No. 2) for generating the sequence of desired 
curve segments are designed to produce a large 
family of waveforms having different slopes and curva-
tures in response to the step-function inputs. Various 
network configurations may be devised for this pur-
pose. 
Figure 2 represents an automobile silhouette re-
produced by the display system. Reproduction of 
this complex contour required only 30 curve seg-
ments (and fewer than 100 sets of commands). This 
number of segments can be contrasted with the use of 
several hundred points which would be necessary for 
a piece-wise linear approximation by a point-by-point 
plot of the same drawing. 
The type of display presented by this system should 
be most advantageous in cases where standard parts,.
or curve segments, are repeatedly used. In such cases, 
the commands required to reproduce the segments 
need only be formulated once and can be repeatedly 
used. The system has also proven useful even in cases 
where a particular curve had to be reproduced only 
once. 
Note: 
No further documentation is available. Inquiries 
may be directed to: 
Technology Utilization Officer 
Headquarters 
National Aeronautics and Space 
Administration 
Washington, D.C. 20546 
Reference: B69-10247 
Patent status: 
Title to this invention has been waived, under the 
provisions of the National Aeronautics and Space Act 
[42 U.S.C. 2457 (f)], to the Massachusetts Institute 
of Technology, Cambridge, Massachusetts 02139. 
Source: M. L. Dertouzous and H. L. Graham of 
Massachusetts Institute of Technology 
under contract to 
NASA Headquarters 
(HQN- 10073)
S 
. 
V
A	 P 
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Figure 2 
Brief 69-10247	 Category 01


Simplified system displays complex curves corresponding to input data

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