GB2076570A - Random Number Generator - Google Patents

Abstract

A random number generator provides substantially-random numbers with a substantially- Gaussian probability distribution, and comprises a 24-bit shift register (22) forming a chain code generator, the numbers defined by each of four groups of six bits, being added in an adder (24). The generator (2) is applied to an airbrush simulator for an electronic graphic system (Fig. 1), in which it constitutes a dedicated- hardware peripheral to supply random numbers to a computer controller, these random numbers being used to modify which storage locations are addressed in response to the output of a two-dimension graphics tablet. <IMAGE>

Description

SPECIFICATION Method of and Apparatus for Random Number Generation and Electronics Graphic System Incorporating the Same This invention relates to a method of and apparatus for generating essentially random numbers with an approximately Gaussian probability distribution, and to an electronics graphic system incorporating such apparatus.

A graphic artist will often resort to using an "airbrush" to effect shading (e.g. in representing side-lit solids) or to soften the transitions between areas of different hue and/or brightness. In essence, the airbrush is a hand-held "atomiser" in which a stream of compressed air passes over a hole in a small vessel containing paint, picks up small droplets of paint, and emerges from the circular jet of the "brush" as an aerosol of paint in a conical spray. Because the droplets have random transverse velocities, the spray cone has a radial probability density function (p.d.f.) approaching a Gaussian, so more droplets fall on or near the spray cone axis than far off-axis.A microscopic "pointillism" results, with the density of paint spots on the artwork depending on the proximity of the airbrush to the artwork and the duration of its use (and, obviously, air pressure, jet size, paint viscosity, etc). Gradual transitions between colours or shading are achieved with a sweeping motion as with spray painting.

In a typical electronic graphics system, the artist's input is from a "graphics tablet". The artist's "brush" strokes are converted to a sequence of co-ordinates representing successive positions of his "brush" (a pick-up stylus) on the tablet surface. A central processor converts these co-ordinates into pixel addresses in a frame store and accesses those pixels according to the action required. For example, in drawing a line in AMBER the processor writes to successively addressed pixel locations in the frame store a word which represents the colour amber.

In order to simulate airbrush effects, the processor must write the appropriate word to random pixels surrounding the one which represents the present stylus position. To be convincing, not only must the spatial distribution of written pixels about the reference appear to be correct, but also a reasonable number of such pixels, must be written for every stylus position~ it should not be necessary to wait a long time to get the effect of a dense spray and the system should respond to practical speeds of sweeping the "brush" over the tablet.

Simply making pseudo-random numbers by software is invariably a slow process especially if the sequence is to have an adequately long repetition rate, and if a Gaussian-like p.d.f. is required.

The present invention assists in the reduction of at least some of these problems, and is defined in the appended claims.

The invention will now be described by way of example, with reference to the drawings, in which:~ Figure 1 is a general block diagram of an electronic graphics system; Figure 2 is a graph illustrating true and pseudo Gaussian probability functions; Figure 3 is a block diagram of a pseudo random number generator providing a Gaussian-like probability density function; and Figure 4 is a detailed circuit diagram of the random number generator.

Figure 1 shows the basic elements of an electronic graphics system enabling a graphic artist to draw a picture or illustration \which is electronically stored and is displayed as he draws it.

The system includes a sensitive graphics tablet 10 which has a surface across which a stylus can be drawn and which generates output signals representing in two co-ordinate form the instantaneous position at which the stylus is pressed on the tablet. The output of the tablet 10 is passed to a computer or controller unit 12, which, possibly after conducting certain checks on the data, stores the coordinate data in associated addresses of a digital frame-store 14.

This is done by storing a colour indicator signal at each storage location which corresponds to a spot of that colour on the picture.

The content of the frame store 14 is continuously scanned and applied through digitalto-analogue converter circuitry 16 to a visual display unit (VDU) 18 comprising a cathode ray tube. The converter circuitry 16 may comprise three digital-to-analogue converters providing three output signals respectively representing the red, green and blue components of the colour to be displayed. These signals can then be applied to the R, G and B inputs of a colour monitor. It will be appreciated, however, that the system can woe used for texturing monochrome artwork.

In accordance with this invention the computer 12 comprises or is provided with a dedicated hardware psuedo-random number generator 20 of a type which provides random numbers with an approximately Gaussian probability density function. The generator operates on the principle that the p.d.f. of the sum of a large number of independent random variables approaches a Gaussian curve, regardless of the p.d.f. of the component variables. It is therefore possible to produce a random variable with an approximately Gaussian p.d.f. by summing sufficient independent random variables generated by any desired method. Figure 2 shows the p.d.f. of a pseudo Gaussian comprising the sum of only 4 uniformly distributed independent random variables each ranging from~1 to approximately + 1 (actually + 127/128), against the true Gaussian curve with the same variance.Although the probability of the mean is lower than for the true Gaussian, the shape and spatial extent of the p.d.f. is very similar. Furthermore, an advantage, especially for digital signal processing, is that the pseudo-Gaussian has limits to signal magnitude; in Figure 2 there is zero probability of the sum being greater in magnitude than 4. Naturally, taking more variables for the sum leads to a result closer to the Gaussian.

Figure 3 shows in schematic form hardware used to generate pseudo-random numbers with a pseudo-Gaussian probability distribution. A 24-bit m sequence generator 22 of the feedback type is used, with the 24 stages providing between them four six-bit random numbers. These numbers are produced simultaneously and continuously, and are summed in an adder 24, the most significant bit of the sum being inverted. This will produce a 2's complement 8-bit resultant, with zero mean and ranging between~1 and +127/128.

In use in the system of Figure 1, the generator 20 is accessed by the computer 12 when a random number is required in response to a request for airbrush techniques. When this happens the instantaneous output of adder 24 is latched in a latch 26 and returned to the computer as data. The latching takes place without interrupting the m sequence register 22, and enables the computer 12 to read the latched number over several system clock periods. When airbrush technique simulation is required, the computer adds a pair of random numbers to the individual pair of x, y coordinates of the reference address from the tablet 10 and uses these as new address pairs. Thus, for a reference or data input (x, y), access is made in the frame store to (x+Ax, y+Ay) where Ax and by are the random numbers.

This operation is repeated at a rate or for a time period sufficient to give a predetermined mean spot density.

Typically the computer 12 in Figure 1 may be a 8085A based microcomputer. A maximum "airbrush width" of 256 pixels (picture elements), approximately one-third of the picture width and 4/9th of the picture height, is ample for most purposes, so the system illustrated provides 8-bit random numbers with a p.d.f. the continuous form of which corresponds to the pseudo-Gaussian of Figure 2.

Because the m sequence register 22 in Figure 3 works with system clock pulses, every 24 clock pulses (representing 2, 3 or 4 instruction periods only) a completely independent set of pseudorandom values are presented for access. A single IN instruction occupies the 8085 microprocessor for 10 clock cycles alone, and this is used to access the random number generator. As subsequent additional processing will be done with the input data value, successive accesses to the generator in practical cases will be more than 24 system clock pulses apart and will result in independent values being read. Additionally, the long sequence length (224-1) and the variable period between accesses will ensure a proper spread of values.

When used to implement a graphics airbrush, the visual effect is convincing and easy to control and the speed of operation high. The technique can be extended for greater accuracy by the addition of more uniform values either by software addition of successive outputs from the present circuit, or by providing more values to add within the hardware. If independent values are to be obtained, the increase of register length must be balanced against access time, the practical delay in clock pulses between successive accesses to the generator; it may prove necessary to run several separate generators with different sequence lengths.

It will be appreciated that the 24 bit m sequence register 22 can be replaced by a register of different size, i.e. one providing r words each of p bits. There are then r.p register stages, and the adder output word contains (p+log2r) bits.

Figure 4 is a more detailed block diagram of the generator. The diagram indicates the relevant integrated circuit component numbers and these details are not therefore repeated here. The input/output or I/O address 13D accesses the pseudo-Gaussian p.d.f. values. In addition an address 12D accesses a uniform p.d.f. random number formed from 8 parallel bits from the m sequence register which are separately latched. A counter circuit detects the stable "all-zeroes" state in the shift register and in the presence of all zeroes stuffs a one into the feedback loop to avoid lock-up.

Claims (4)

Claims

1. A method of generating substantially random numbers with a substantially Gaussian probability distribution, comprising generating a plurality of essentially-independent random or pseudo-random numbers, and combining the numbers thus generated to provide an output.

2. Apparatus for use in the method of claim 1, comprising one or more psuedo-random chain code generators, and means for adding the numbers represented by a plurality of groups of generator stages to provide a substantially random output number having a substantially Gaussian probability distribution.

3. An electronic graphic system comprising a two-dimensional input device, a store capable of providing locations corresponding to individual elemental areas of the input device, control means for entering data into the store in response to the output of the input device, and a dedicated- handwave generator coupled to the control means and adapted to provide substantially random numbers with a substantially Gaussian probability distribution to modify the storage locations which are addressed by the control means so as to simulate an air-brush technique.

4. A system according to claim 3, in which the generator comprises apparatus according to claim 2.