GB2061074A - Improved visual display systems for computer generated images - Google Patents

Abstract

A computer-generated displayed image for a flight-simulator having a rectangular raster-scanned display on screen 101 has a surface detail generator providing a display of textured surfaces in perspective during simulated flight. The surface detail generator comprising a perspective transformation computer (scanner 108) and a surface detail store (memory 111) is organised as a pipeline processor to compute in real time the perspective transformation from the textured surface (ground) plane to the display plane by a scan of a trapezium area of the surface. A sky scene is added (113) in the part of the display above the simulated horizon. <IMAGE>

Description

1

SPECIFICATION

Improvements in or relating to visual display systems of the computer generated image type GB 2 061 074 A 1 Introduction to the description

This invention relates to real-time computer-generated image displays of three-dimensional scenes for ground-based flight simulation and is particularly concerned with the provision of textured surfaces.

Ground-based flight simulators are increasingly used forflight training. The simulator provides a dummy cockpitwith dummy controls and a flight computer which computes in real time the characteristics of real flight during an exercise. Forward of the dummy cockpit there is frequently provided a visual display of terrain overflown during the exercise. The present invention relates to such visual displays.

Electronically produced visual displays conventionally employ one or more cathode ray tubes or a television type projector which projects the display upon a forward projection screen which is viewed by the trainee pilot through the cockpit forward windows.

The method of image production may then be either calligraphic or raster scan.

Although an earlier method of image generation used a closed-circuit television camera moving over a scale model of terrain, the majority of ground-based flight simulators now manufactured use digital computer generated images (C.G.I.).

As stated, the display method may be either calligraphic or raster-scan. The calligraphic method lends itself particularly to the display of night scenes, which consist almost solely of a display of light points on the 20 simulated ground plane.

A typical night-only C.G.I. generator comprises a database holding digital data models of selected airports, stored on one or more floppy discs for example, a minicomputer for preliminary model processing and in the memory of which the currently-used airport model is held, a special- purpose transformation processor and a beam-penetration type display tube. Such a typical system is able to display a ground scene containing 6,000 25 light points and, in addition, construct surface involving up to 64 edges. Such a scene is, of course, computed and displayed in true perspective in real time during a flight exercise.

A limitation of calligraphic image display is that the time required to paint one frame of the image is a function of the complexity of the scene. Human eye sensitivity to image flicker demands a frame repetition rate of about 30 Hz. and this sets a practical limitation upon the scene complexity at present possible for a real-time display. A high-complexity daylight scene, involving for example the display not only of runway features, but also solid surfaces of surrounding terrain features and airport and neighbouring city buildings, demands a raster scan type display. 35 The first-known real- time C.G.I. image system depicting solid surfaces was able to provide a scene based 35 on up to 240 edges. An "edge", that is a line dividing two distinguishable surfaces, defined the visual environment for such a display. The edges were transformed into the display plane and incrementally generated by hardward edge generators. In the presentation of a three-dimensional scene in true perspective, hidden surfaces were eliminated by programming priorities among the edge generators. 40 Subsequent C.G.I. systems provided higher complexity scenes, including the display of curved surfaces. 40 These systems use the "polygon" to define the visual environment and can generate scenes involving a few hundred polygons. Such systems at present in development are likely to provide scenes of one order greater scene complexity, that is involving some few thousand polygons. However, scenes defined solely by edges or polygons may never be adequately realistic for flight training purposes. Although the scenes provided by available C.G.I. systems have proved valuable for training airline 45 pilots, particularly in take-off or landing manoeuvres, they are inadequate for many military operations.

The known techniques are unable to provide, economically and in real time, real istical ly-textu red surfaces in correct and changing perspective.

The object of the present invention is to provide a C.G.I. system capable of displaying textured plane surfaces.

Accordingly, the invention provides a visual display system of the computer generated image type, for a ground-based flight simulator, providing a rectangular raster scanned, perspective-transformed, pilot's visual display of a simulated textured surface, including a surface detail generator comprising a perspective transformation computer and a surface texture detail store, the perspective transformation computer being a pipeline calculator for computing in real time the perspective transformation from the simulated surface 55 plane to the display system display plane continuously during simulated flight, and correspondingly scanning the surface texture detail store to provide texture for each element of the said rectangular raster scanned pilot's visual display.

Short description of the drawings

In order that the invention may readily be carried into practice, relevant prior art will be referred to and one embodiment of the invention will be described in detail by way of example, both with reference to the accompanying drawings, of which:

Figures 1-8 relate to prior art and Figures 9-41 relate to the present invention; 65 and in which:

2 GB 2 061 074 A Figure 1 is a diagram showing the effect of differently shaped camera and display rasters; Figure 2 is a diagram illustrating the mapping of a display raster onto a different plane; Figure 3 is perspective and block schematic diagram showing apparatus for raster shaping with a photographic image; Figure 4 and Figure 5are diagrams illustrating undistorted scanning of a photographic image; Figure 6is a diagrammatic display showing defects in a flying-spot scanned image; Figure 7 is a block schematic diagram referred to in a description of raster shaping with an electronically-stored image; Figure 8 is a diagram defining levels of surface detail; Figure 9 is a block schematic diagram of the visual display system of the present invention; Figure 10 is a perspective diagram illustrating the principle of linear perspective; Figure 11 is an isometric diagram showing the geometry of perspective transformation; Figure 12 is a diagram defining the three sets of three-dimensional co- ordinates used; Figure 13 is a diagram defining the location of image points on the display plane raster; Figure 14 is a diagram showing the orientation of a defined plane with respectto rectangular axes; Figure 15 is a logic diagram showing the sequence of calculation steps in a pipeline processor; Figure 16 is a diagram explaining the progress of sequential calculations through a pipeline; Figure 17 is a logic diagram showing a parallel pipeline configuration; Figure 18 is a timing sequence and timing interface diagram for a parallel pipeline; and Figure 19 and Figure 20 show alternative methods to that of Figure 18, the method of Figure 19 being 20 preferred herein; Figure21 is a block diagram of a two-dimensional linearfunction generator; Figure22 is a block diagram of a pipelined multiplier; Figure23 is a diagram illustrating the process of two's complement non- restoring division; Figure24is a diagram showing one stage of a divider pipeline using the process of Figure 23; Figure25is a diagram explaining the arithmetic pipeline using the configuration of Figure 17; Figure26is a flowchart of the general purpose computer scanner control program; Figure27is perspective diagram illustrating the production of a television camera image of a plane surface; and Figure28is a diagram illustrating the corresponding process using an imaginary mapped aperture; 30 Figure29 explains thefilter effect of a mapped aperture in an accurate simulation; and Figure30 explains the modified filter effect of an approximated aperture; Figure 31 shows the relationships between the picture element grid, scene edges and the quantisation grid of a display; Figure 32 illustrates the process of sampling with matching grids, showing the relationship between the 35 sampling interval and the maximum image spatial frequencies; Figure 33 corresponds to the diagram of Figure 32 but shows a displaced sampling grid; Figure 34 shows the use of a fine image memory grid; Figure 35 is a diagram of surface resolution elements showing a sample spacing of five elements; Figure 36 is the corresponding diagram wherein two samples define the entire pattern in one of its 40 dimensions; Figure 37 shows the addressing of level zero, which contains 4096 samples; Figure 38 is a bloci(diagram showing the complete memory system; Figure 39 shows mapped raster lines forthree different angles of aircraft roll with zero pitch and heading angles; Figure 40 shows approximated level code mapping; Figure 41 is a block schematic diagram of a surface detail generator using the rolled-raster principle and providing separate stores forthe odd and the even fields; and

Figure 42 is a diagram showing the form of the mapped raster with constant sample spacing along raster lines.

2 so Description of L-he prior art

For the correct representation of texture in a surface of a computed perspective image, that texture must be defined as a part of the geometrical database which defines the visual environment. It is then possible to subject the texture to the same transformations as are applied to the points, lines and polygons of the scene. 55 This process ensures that textures are firmly attached to their respective surfaces and exhibitthe same perspective variations both static and dynamic.

In contrast, methods have been proposed for applying texture to the transformed image, that is display plane texturing.

Display plane texturing can be used for certain effects. Thus, scintillation of sunlight from water surfaces 60 can be simulated simply by injecting random pulses in areas of the scene representing water. Another application is 't')r the simulaticr. of water droplets on sights or windshields fixed relatively to the observer, and therefore not subject to perspective change.

An approximation to correct texture perspective has been proposed, in which the proximity of texture elements is increased in the direction towards the displayed horizon. While some realism is added to the 65 R, j 3 GB 2 061 074 A 3 overall scene, this expedient is inadequate for manoeuvres where depth and slant perception are important. An always present limitation of display plane texturing is that the textures are not attached to their respective surfaces so that, with a changing scene, the effect is analagous to viewing the world through a patterned net curtain. 5 Texturing may alternatively be added to a C.G.I. display by defining the texture in terms of edges, similarly 5 to other features of the scene. For a real-time system, however, this method is impracticable because of the large number of edges needed. Display plane texturing is not effective or not economical except for limited effects and some alternative method must be used.

One such is the raster shaping principle of the present invention, as described herein.

This principle may be described as follows, in terms of a television system:

If the camera and display tube scanning rasters differ, the displayed image is distorted.

If the camera raster is shaped and the display tube raster has the normal format, the displayed image undergoes a transformation which is the inverse of that applied to the camera raster.

Figure 1 shows the effect of such raster shaping. The left diagram represents the viewed scene comprising 15 a square object on a rectangular field. The centre diagram shows trapezium shaping of the camera raster and the right diagram shows the inversely transformed displayed object. The effect extends further to two-dimensional distortion and even to curvi-linear distortion.

A particular case is inverse perspective distortion. If an inverse perspective transformation is applied to shape the camera raster, then the object is displayed in perspective.

Figure 2 explains the principle of such inverse perspective distortion. An observer at 0 views the plane S. In front of the observer is erected a display plane D, defined by a scanning raster R. In a simulation, an image in the plane D is required to be identical to the observer's view of the real-world plane S.

Considering the projection of the display raster R upon the plane S, as shown at T, the raster T distorted by projection represents the required inverse perspective distortion. Surface details on the plane S, explored by 25 the distorted raster R, would be displayed in the plane D in correct perspective.

This same principle is applied by the invention to synthetic image generation from stored image data representing the plane S, by using scanned sampling which is subject to inverse perspective distortion.

The implementation of this method involves the real-time calculation of the inverse perspective transformation continuously as the position and attitude of the observer and his display plane change with respect to the simulated plane viewed.

Figure 3 is a diagram, part perspective and part block schematic, showing a known application of the raster shaping method in a closed circuit television system.

In Figure 3, an object plane 1 carries a rectangular Figure 2, which is scanned by a flying spot scanner 3 by way of an associated lens system 4. The video signal is provided by a phototube 5, amplified by a video amplifier 6 and fed to a cathode ray display tube 7 to provide an image 8. A single synchronising pulse generator 9 serves both the flying spot scanner sweep generator 10 and the CRT sweep generator 11. The raster scan of the CRT 7 is a normal rectilinear scan. The raster scan of the flying spot scanner is a trapezium narrower at the top than at the bottom, as shown in Figure 1. The shape of the raster scan of the plane 1 is determined by a transformation generator 12 under control from distortion controls 13.

Because the flying spot scan. is a trapezium narrower at the top than at the bottom and because the raster scan of CR tube 7 is rectilinear, the rectangle 2 is transformed into a trepezium 8, which is the inverse of the flying spot scan and thus is wider at the top than at the bottom.

If the object plane 1 is a terrain view photograph of transparency, the CRT image 8 shows a perspective transformation which, if the distortion controls 13 are set as required, can effect the perspective transformation of Figure 2, where the plane 1 corresponds to the plane S and the image 8 is provided in the plane D.

Photographic image scanning in the manner of Figure 3 was subject to a serious problem, that of improper sampling.

W Figures 4 and 5 illustrate the requirements of correct sampling.

In Figure 4, parts of successive scan fines 15 are shown on the plane 1. The line 16 is shown perpendicular to the direction of line scan in the plane 1.

Figure 5 represents a section on the line 16 of Figure 4 showing the flying spot profiles 15.1, 15.2 and 15.3 of three successive lines of the raster scan 15. The scanning spot configuration in plane 1, profile in Figure 5, is chosen so that the maximum information from the image in plane 1 is extracted by the scan 15. Too narrow a spot profile give rise to aliasing in the frequency spectrum of the sampled image. Too wide a spot profile results in unnecessary video frequency reduction, that is image blurring.

Figure 6 represents a display resulting from perspective transformation by a system similar to that of Figure 3, where the display comprises the perspective transformed image of a runway 20 in the plane 1, 60 extending from the observer towards an horizon 22 separating the plane 1 from a sky area 21.

To provide the image of Figure 6, the photographic image scan rester is distorted to be wide at the horizon 22 and narrow in the foreground 24. In consequence, the reproduction in the displayed image is satisfactory only in the middle ground 23. The foreground 24 becomes blurred and in the background 25, the image breaks up.

Development of such a system with a variable image scanning spot size would present considerable 65 4 GB 2 061 074 A 4 electronic and optical problems. No such system has in fact been developed.

The principle of perspective transformation applies equally to an electronically-stored image as to a photographically-stored image.

Figure 7 is a diagram showing the basic elements of a known wholly electronic system. In Figure 7, a synchronising pulse generator 9 controls both a perspective transformation computer 26 and the display 5 means 28. A surface detail store 27 is sampled under control of the transformation computer 26. Position and attitude of eyepoint data are supplied to the transformation computer at 30, so that the co-ordinates of sampling points are defined at 31.

The inverse perspective transformation is computed at 26 to provide an output of sampling point position defined either as two analogue voltages or as two digital numbers. The store 27 is addressed accordingly and a corresponding output signal defining the brightness and colour of the surface image at the defined sampling point is fed to modulate the display scan at 28.

The first such system known was the NASA surface generator developed in 1964 for the space program by the General Electric Company. The output of the transformation computer 26 was two digital numbers representing the sample point computed at a rate of 5 MHz.

In this system, the surface detail store of---maptable" was implemented as a purely synthetic logically-defined pattern. By using only the lower order bits of the sampling vectors, it was possible to create a repetitive pattern covering an entire surface, the so-called -contact analog".

The map table was structured as a four level hierarchy, with each level defined as an 8 x 8 matrix providing a one-bit output designating one of two possible colours.

Complex networks of patterns were obtained by logically combining the outputs of the map levels, each of which contributed to the textural design over repetitive regions of defined size. These regions are structured so that patterns corresponding to the several levels are nested within one another.

Figure 8 shows the principle applied. In Figure 8, the axes 32,33 define the X axis and Y axis of the map plane 34. Areas 35,36,37 and 38 respectively show map areas corresponding to level 1, level 2, level 3 and 25 level 4, each level defining an area one-quarter the area of the previous level.

Such a hierarchy of pattern levels made possible transitions from one level of detail to another by deleting the contribution from the map whose cells approached the raster cell structure. The display results of this system, while showing numerous sampling defects, was nevertheless a very satisfactory state of art at the time.

More recently, in patent application No. 7913058 there is described a system for providing simple surface detail for cloud systems overflown. That specification describes visual display apparatus for a ground-based craft flight simulator including a flight computer, comprising raster scan type display means for viewing by a trainee pilot observer synthetic image generating means for supplying to the display means a signal representing an image of sky, horizon and simulated patterned surface extending to the horizon, said 35 patterned surface being displayed in true perspective in accordance with the simulated altitude and position in space of the craft simulated and a general purpose programmable computer connected to interface the said flight computer and the said synthetic image generating means, said synthetic image generating means, said synthetic image generating means comprising a digital store for holding a single pattern cycle of a repetitive pattern for patterning the said patterned surface in one dimension thereof, a perspective computerfor computing the track of a ray from the observer's eye, through the scanning spot of the display means, in its instantaneous position, and to a point of intersection of said simulated patterned surface, a computing element for providing a signal output for the display means representative of a variable brightness portion of sky and switch means for selectively supplying to the display means either the signal representative of the patterned surface or the signal representative of the variable brightness portion of sky, 45 continuously during the raster scan of the display means.

No proposals have been published for the application of the shaped imagescanning raster technique to digitally-stored half-tone images, such as would be required for realistically textured terrain or target displays.

Description of the example

A specific embodiment of the invention will now be described firstly with reference to Figure 9, which is a block schematic diagram showing a complete surface texture generator for ground plane display. The block schematic elements of Figure 9 are then described and explained in greater detail with reference to Figures 10-41.

In Figure 9, a trainee pilot 100, seated in the dummy cockpit of a groundbased flight simulator, has a visual display provided before him on a back-projection screen 101 and has dummy flight controls represented by a control column 102. Control setting data is fed by line 103 to a flight simulation computer 104 in the usual manner. Aircraft position and attitude data is supplied twenty times per second from the flight simulation computer 104, by way of line 105 to a general purpose computer 106.

The visual display image on the screen 101 is produced by a television type projector 119 fed with a video signal on line 118. The raster scan of the projected image is controlled by a synchronising pulse generator 120 which provides line and frame synchronising pulses to the projector 119 on line 122.

Set-up data is sent from the general purpose computer 106 to the surface scanner 108 by way of line 107 once for each display field.

z i P, GB 2 061 074 A 5 The surface scanner 108 is a pipelined scanner more particularly described with reference to Figure 19.

The values of xp and y,, defined according to equations (1) and (2) later herein are supplied for each display field from the surface scanner 108 to the texture memory 111 by way of lines 109 and 110, respectively, and synchronising pulses are supplied to the surface scanner 108 from the pulse generator 120 byway of line 121.

The texture memory 111 is arranged in the manner described with reference to Figure 38, later herein, and the texture detail accessed by the input co-ordinates is supplied as a digital number by way of line 112 to a switch 113.

It will be appreciated that the ground plane surface texture information, with which the present invention is particularly concerned, relates to that part of the displayed image which lies below the simulated horizon.10 In the display exemplified upon the screen 101 in Figure 9, there is shown a runway of the ground plane and sky above the horizon. For completeness of the visual display system of Figure 9, there is included a sky generator 114 which provides an alternative digital input to switch 113 by way of line 115. The switch 113 selects either ground plane or sky information, from line 112 or line 115 respectively, during each line scan at the ground/sky transition defined by the horizon. This transition is effected in known manner as is described 15 in Patent Application No. 7913058, referred to earlier.

The selected output from switch 113 is supplied by line 116 to a digitalanalogue converter 117 and the analogue video signal is supplied by line 118 to the projector 119, as already stated.

In order to provide a surface detail generator according to Figure 9 in hardware, the two main sub-systems need to be designed. The first is the perspective transformation computer, or surface detail scanner, 108 and 20 the second is the surface detail store, or texture memory, 111.

An explanation and description of the surface scanner 108 will be given first.

Before doing so, however, it is necessary to define the objectives of perspective transformation and the co-ordinates and the mathematical terms used in the description.

Figure 10 is a perspective diagram showing a solid real-world object 40 viewed directly by an observer 0. 25 An image 41 is displayed in the intermediate display plane 28 which is the visual equivalent of the object 40, that is the eye of the observer 0 cannot in any way distinguish the image 41 from the object 40. As shown, the image 41 is subject to a perspective transformation with respect to the object 40.

Figure 11 is a three-dimensional diagram showing the geometry of such perspective transformation from an object plane 42 onto the display plane 28.

Figure 12 is a three-dimensional diagram showing the relationship of three sets of three-dimensional co-ordinates relating respectively to a fixed real-world origin, the simulated aircraft origin and the observer's eye origin. A point P on a display plane is defined in position relatively to the three sets of co-ordinates.

Figure 13 defines the location of that point P on the raster in the display plane 28.

The function of the surface scanner is to provide continuous real-time solutions to the two equations: 35 X = Xd-H (cosesinel sins tankcos stany}) cos-fcosstank +sinstan-y}sintp P sin@+{cosstany - sinstanA} 'cosO YP =Yo-H (cose+sing (sins tan A- c o so tan-r})sinot{costanA+sin 0 tany}costo (2) sin fl,,{cos t a ny-s In tan A}c osO These equations relate the position of the surface sampling point (x,, y, ) to the viewer's attitude defined by % 0 and (p, his displacement from the surface origin (X, Y., H) and the position of the display scanning spot, defined by tank and tan,,,. As can be seen from Figure 13, tan k and tan y are the actual rectangular 5D co-ordinates of the scanning spot on the display plane 28, and thus vary linearly when a rectangular scan is 50 used. The scanner must compute a value forx, and y, for every value of tan k and tan y between the limits of the display in the display plane 28, in synchronism with the scan of the display device.

The structure and properties of the perspective transformation itself, as represented by Equations (1) and (2), will be examined.

The two transformation equations (1) and (2) must be computed for every value of tank and tany, that is 55 for every picture element of every display frame.

For a 625 line 50 Hz system with square picture elements, tan k changes at a rate of 15 MHz and tan y at a rate of 15.625 kHz.

6 GB 2 061 074 A 6 The television type display standard selected determines the required perspective transformation computation rate. The form of the computation required is given by the two equations following:

X =XO-H { axAXtanA (3) 5 p c+d tanX} YP = YO-H{ c+d tanO 10 Considering first those parts which change at picture element rate, that is those parts which are functions of tan X, it is seen that tan k is proportional to the horizontal distance of an elementfrom the centre of a raster line. It is in fact equal to this distance on the unit display, as shown in Figure 13. Thus, both the numerators and denominators of equations (3) and (4) are linearfunctions of this distance, which itself is known at equal steps along a line. The values of a,, a, and c are likewise linear functions of tan y, which is proportional to the vertical distance of a line from the screen centre. A two-dimensional representation of one of these functions in equation (3) or (4) F, is given in Figure 14, in which the slope of the plane is given in thetan X direction by FX 20 and in the tan V direction by F,. This is consistent with the geometrical interpretation of Figure 11, where the three linear functions of equations (3) and (4) represent the distance of the scanning spot from the eye point in the three ground axes X, Y and Z. Referring to Figure 14, the (tank,tany) plane can be identified with the display plane 28 and the values of F with one of the three distances.

X m 7 GB 2 061 074 A 7 In general, the values of F,, F?. and F, change for each display frame, thus defining a new two-dimensional linear function. These functions may 6e computed in an incremental manner, thus:

Ax (A /Y) = AX(-aoi0) + m A X AAt an A+ nAxy at any --- (5) 5 A Y (A, Y) = AY (-ao,Bo) m AYAatatIA. nAyY tan Y --- (6) 10 15 9 (AM= a (-cto,Po)+mBA atank + nB-, Atan-r where numerator of Eqn. (3) (or Eqn. 1) A,(k,,1) numerator of Eqn. (4) (or Eqn. 2) 25 B (k, i,) denominator of these equations m picture element number (m=1,2,3 30 n line number (n=1,2,3.

A tan X elemental increment of tank Lta nl line increment of tany 35 Axk) Ayk) A, AV, B slopes in k direction 13k 40 Axy) Ay,1) Ax, AV, B slopes in y direction By 45 In the most direct implementation the desired resultsxp and y, may becomputed by performing the divisions A,/B and Ay/B, the multiplications by H and the subtractions from X. and Y. all at picture element rate.

In order to achieve the required computation rate, a form of parallel computing is used. In an efficient parallel processor, that is, one in which the arithmetic elements are never idle, the time needed to compute 50 Eqn. (3) or Eqn. (4) is easily found. The input parameters to this calculation are the performance characteristics of the circuit technology used and of the arithmetic algorithms chosen.

The types of arithmetic algorithms which may be considered are limited by the form of system architecture - the pipeline - which is chosen.

In conventional computation, a first set of data is inputted and propagates through the logic until the 55 answer is provided. At any instant, only a small part of the logic is in use. Consequently, the system capacity is low and the system has low efficiency.

When the total computation can be divided into a large number of subcomputations, a pipelined processor may be used. Each sub-computation occupies a separate stage of the processor, in sequence, with a memory between each stage. The first data input propagates through all the sequential stages but, as each 60 stage is vacated, new data may follow, so that every stage is occupied simultaneously, performing its own sub-computation and storing its own answer in its own memory. Although the throughput delay is the sum of the sub-computation periods, the computation rate is set by the sub- computation period, because a new final answer becomes available after each period.

The system has been described in the technical literature, for example T. G. Hallen and MJ. Flynn, 65 8 GB 2 061 074 A -Pipelining of arithmetic functions-, IEEE Trans. Comput. vol. C-21, pp. 880-886, Aug. 1972, and J. Deverell -Pipeline Iterative Arithmetic Arrays- , IEEE Trans. Comput. pp. 317-322, March 1975.

The pipeline form of parallel processing has here been chosen mainly for its ease of implementation and flexibility. No complex control logic is necessary and the structure of the computation is -built in". The surface memory sub-system is also conveniently organised as a pipeline, so that a completely homogeneous system has been constructed.

Pipelining is effective in a system where the minimum system computation rate is a constraint, as it is in the present surface scanner. A calculation is pipelined by splitting it into steps, each of which is performed by a logic network in one time period, (66 213 ns for a 15 MHz clock frequency). At the end of each calculation step, the result is resynchronised with the clock in a synchronisation register. Figure 15 shows the form of a pipelined system, while Figure 16 illustrates the progress of an n-step calculation through such a pipeline. It is to be noted thatthe time for one complete calculation is n clock cycles, and that new results emerge every cycle. It is of interestthat pipelines may be operated in parallel and may be split and merged, as shown in Figure 17, to fitthe particular calculation.

The solution of Equations (3) and (4) can be organised in differentways. Figure 18 shows the most obvious way, while Figures 19 and 20 show more economical methods. The choice between the method of Figure 19 or Figure 20 depends on the relative costs of the pipelined multipliers and dividers, which again depends on the number of bits required. Scaling and accuracy considerations define this. The function generator resolutions can be determined by examinining their effect on the displayed horizon, whose location is given as the locus of points where B=O. The smallest resolvable roll angle is approximately tan-' (l/800), given by 20 the size of the picture element grid. With pitch set to zero, B(?,,y) = coso tany sin(p tank .... (8) For the incremental generation of this function (according to Equation (7)) the magnitudes of BX and By are 25 approximately tan (l/800) Atank (or tan (11800) Atany, since Atank = Atany) which is between 29 and 2 -20 As the maximum absolute value of B is 1.16, 22 bits are required for the B function generation. The same type of argument is applied for the pitch and heading angles by use of the Band A,, or Ay functions respectively. In practice, 22 bits are found to be sufficient in all cases. However, 24 bits are used for the function generators, since arithmetic circuit blocks generally come in four-bit units. With the 20 bits used for 30 the representation of x, and y, all arithmetic units were designed for 24 bit wide inputs, four bits being unused at the outputs to allow for rounding errors.

The choice between the arrangements of Figures 18 and 19 can now be made. The arrangement of Figure 19 has been chosen, as two fewer circuit cards are needed.

The arithmetic units include:

a) a 24 bit two-dimensional linear function generator, b) a 24 bit pipe] ined multiplier, and c) a 24 bit pipelined divider.

The purpose of a function generator is to produce values of the function F, according to the formula:

F(k,,1) = F(-rjj),,) + mFX Atany + nFy iLtany ... (9) 8 r, Figure 21 shows in block diagram form how such a function can be computed. This process is further described in Patent Application No. 7913058 referred to earlier herein.

The pipelined multiplier, shown in Figure 22, is based on the Texas Instruments 74LS261. This device, which operates on a modified form of Booth's algorithm in which multiplier bits are examined three at a time, is used in the recommended configuration.

No special logic is needed to handle negative operands and the whole multiplier produces a correct two's complement result. The partial product bits generated are combined in an addertree using 74H183 carry-save adders. Two sets of pipeline registers are required, one afterthe multiplication and one in the addertree.

Division is performed bythe non-restoring algorithm. Figure 23 shows a graph forthe example: (-318 112) calculated by this method. The non-restoring method adds or subtracts powers of the divisor so as to reduce the absolute magnitude of the partial dividend and for a proper division the remainder has a magnitude less than that of the divisor, and may have the opposite sign. In this case, the quotient should be 55 further corrected, but as this adds an error only in the least significant place it is ignored.

The algorithm is easily implemented as a pipeline; one stage is shown in Figure 24. Each calculation is performed by an adder/subtractor controlled by the exclusive - OR of the most significant bits of the partial dividend and divisor. After each addition/subtraction the shifttakes place through the discarding of the partial dividend most significant bit and the substitution of a new partial dividend bit in the least significant 60 position. After each stage in the division the quotientlunused dividend register contains one more quotient bit and one less unused dividend bit until atthe end it contains only quotient bits. The final stage of the division is the quotient correction which converts the +1, -1 coded number into two's complement.

All adder/subtractors in the divider are Texas Instruments 74S181 arithmeticllogic units with Intel 3003 look-ahead carry units.

h.

9 GB 2 061 074 A 9 The pipeline diagram forthe whole transformation calculation can now be drawn following the scheme of Figure 17, this is given in Figure 25. It is to be noted thatthe A, and Ayfunction generators are fed modified initial conditions, A, (-ct., P.) and A, because of their position in the pipeline. Figure 25 also shows the scaling of all operands.

The three function generators, each with three inputs, are interfaced to a general purpose computer by its 5 1/0 bus. Transfers of data between the computer and the function generators occur whenever an output instruction containing one of the nine function generator addresses is executed. These transfers occur during display blanking periods. The computer program must therefore have some means of determining when these periods occur. This is achieved by use of the computer input/output flag system. A flag consists of a filp-flop which can be set by an external signal. The state of this flip-flop can be sensed by the computer 10 (using input and conditional branch instructions) and it can be reset (using an output instruction).

Two flags are used for synchronisation of the program with the display raster, the odd-field flag and the even-field flag. The odd-field flag is set at the start of the odd-field blanking period and the even-field flag is set at the start of the even-field blanking period. The computer must be idle at the end of an odd or even field and thus able to continuously test the two flags. When one of these flags has been set, the program updates 15 the function generators with data computed during the previous field, and clears the flag. Computations of the set-up data forthe next field may now proceed using the latest available input data. This computation must end before the end of the current field.

The flowchart of Figure 26 shows how the program is organised. It is to be noted that, during the even field, the odd field set up conditions are calculated and vice-versa. New data defining the eye point attitude 20 and position is read every field.

The second sub-system of the surface detail generator of Figure 9, that is the surface texture memory 111, will now be described.

The surface memory accepts as input the vector (x,, yp) at a rate of 15 MHz representing the position of the surface intersection, and delivers as output a video signal which may be sent directly to the display device, 25 after digitalianalogue conversion. The design problem is totally that of aliasing control.

Figure 27 and Figure 28 are two perspective diagrams representing the process of viewing a textured plane surface in perspective. Figure 27 represents viewing by a television camera. Figure 27 shows a textured plane 46 viewed by a camera along the axis 47. The camera image plane is shown at 48. Figure 28 shows the textured plane 46 viewed along the line 47 and the plane 48 represents the display plane.

Considering the television camera image production process of Figure 27, on any position of the television raster scan, a ray may be drawn from the centre of projection (the imagined eyepoint) to the surface 46, where it intersects at point A. The action of the camera optical system and scanning beam may be combined by imagining an "aperture" with a distribution similar to that of Figure 27. The effect of the aperture is to integrate information from surrounding parts of the brightness distribution on the image plane into a single 35 value which is tile video signal for that point of the raster scan. In a well-adjusted camera, the extent of this aperture will be such that the maximum possible amount of information will be extracted from the scene. In other words, the pre-sampling filter is correct. Too small an aperture produces aliasing, whereas too large an aperture causes unnecessary blurring. The image, therefore, corresponding to point A is made up from the brightnesses of a region of the surface in the neighbourhood of A. The further A is from the image plane the 40 greater the size of this neighbourhood will be and the less detailed the image.

Figure 28 shows an alternative way of viewing this process, one less related to the physical process. Here the aperture is mapped onto the surface 46 itself. The video signal corresponding to point B of the scan is made up of those elements of the surface failing under the mapped aperture. In signal processing terms, a two-dimensional filter is applied to the brightness distribution of the surface. The shape and extent of this 45 filter is a function of the distance and tilt of the surface and is in general asymmetrical.

A direct implementation of this process is impossible, due to the huge memory access and computing problems that would arise. The parallel access of texture values at a 15 MHz rate and their combination in a variable two-dimensional filter is not considered practical.

The first simplifying assumption is in the use of a two-dimensionally symmetrical mapped aperture. This is 50 subjectively justifiable, as the greatest distortion of the aperture occurs when the displayed detail is the least. With this assumption, off-line and predefined, rather than online, filtering is possible. The additional memory required for holding pre-filtered textures requires less board space than a filter required to operate at 15 MHz. Memory architecture can also be considerably simplified, as only one sample has to be read every 66 2/3 n s.

GB 2 061 074 A The second problem is that of filter selection; the determination in real time of what degree of texture filtering is needed. One possibility is to use the distance from the eyepointto the surface. This distance is given by:

5 d t a n2A. t,,n2, A10) Sing - tosoftosstanT- sinotanA} The value of d may be approximated to:

H ... (11) B (X,V) 15 with a maximum error of about 14% at the corners of the display. This quantity is available "for free" in the arithmetic pipeline of Figure 20. The use of this value must be rejected however, as no simple relation exists between the mapped aperture dimension and the range.

Since the approach to the filter design is based on aliasing control, the distance between intersections is a useful and easily obtainable measure.

The memory system is based on the hierarchy principle, as previously described, but now the hierarchy levels are real images computed by a variable two-dimensional filter. The system provides a variable number of levels so that the choice of the optimum number can be made subjectively.

The texture memory system design is based on the two following assumptions:

a) The filter applied to the texture is symmetrical and undistorted, and b) The selection of which filtered version of the texture to map is a picture element-by-picture element decision based on the distance between successive samples.

Both of these assumptions introduce approximations, but bring about local geometrical errors only. The 30 main sampling grid is computed exactly and aliasing can be completely controlled. The effect of the first assumption is to apply a greater degree of filtering than would apply in an exact simulation. In this, as has been mentioned previously, the mapped aperture is elongated in the direction of the line of sight for all cases except that of viewing in a direction normal to the surface. The filtering effect is thus greater in the line of sight direction than at right angles. However, since it is assumed that the filter has the same filtering effect in 35 both directions, a greater degree of filtering must be applied across the line of sight in orderto avoid aliasing along the line of sight. Figures 29 and 30 illustrate this effect. The elongation of the real mapped aperture increases as the line of sighttouches the plane at smaller angles, as occurs at points nearto those corresponding to the displayed horizon. However, as the total degree of filtering (detail reduction) becomes greater atthese points, the effect of this overfiltering becomes less noticeable. The question of aperture 40 elongation and its effects is considered in more detail later he'rein.

The second assumption above is also related to aperture elongation, for the definition of the "clistance between samples" must be decided. As can be seen in Figures 29 and 30, the distance between successive samples along a mapped raster line, a, is notthe same as the distance between mapped lines, b. A definition of the -distance between samples- is also considered later herein.

Much work has been done recently on the aliasing problem in digital television image synthesis. The known studies are summarised below, as they have an important influence on the design of the texture memory system.

Television image formation can be considered as a three-dimensional sampling process, the three dimensions being the two linear dimensions of the image and time. The sampling aspects of television are 50 well understood and the theory can be profitably applied to television- based computer generated imagery.

By studying the operation of a television camera system in terms of sampling theory and then comparing synthetic image generation, the reasons for aliasing in the latter systems can be understood. It is also possible to devise methods for the reduction of aliasing in computed images through this knowledge of television systems.

The classic theory of television image generation derives the spectrum of the television camera output signal by an analysis of the scanning process and the form of sampling used in a television system. The effect of the scanning aperture on aliasing can be considered therefrom. Considering image synthesis in the light of television theory, it is possible to conclude that computed images are analogous to non-band-limited scenes sampled without the use of a pre-sampling filter. Aliasing may be reduced by sampling at a higher 60 frequency and synthesising a pre-sampling filter. Experience has shown that a sampling frequency four times higher in both the vertical and horizontal dimensions produces satisfactory results when using a 625-line projected display in a simulator.

Figure 31 represents the sampling grid of a discretised display together with some scene details in their exact positions as would be computed by a polygon-based image generator of infinite resolution. Since only 65 11 GB 2 061 074 A 11 one value of brightness and colour can exist overthe area of a picture element, some method of mapping the computed image onto the element grid must be employed.

In early image generators the brightness and colour of a picture element was taken to be that of the scene surface visible at the centre of the element, so that for example, in Figure 31, element (3,3) would be assigned the value B,. This method resulted in edges portrayed with stepped boundaries, and a slight positional change in a computed edge might result in a displayed change in position of one picture element. Distracting effects such as these were accepted in the first image generators, but solutions to these problems have since been found. The method used is to synthesise each. displayed picture element from a number of "sub-elements" which in effect, sample the scene on a finer grid. Element (4,10) in Figure 31 shows the sample points when 16 sub-elements are used. The brightness and colour values computed for each sub-element are combined in a two-dimensional filterto yield the final element to be displayed. The cut-off frequency of this filter must be equal to the maximum spatial frequency which can be represented on the display grid. This is given by sampling theory and is shown by the two sine wave cycles portrayed in Figure 31.

In simple systems, sub-elements lying within one element are added with equal weights, (the "area time 15 colour rule"), while in more complex systems, sub-elements lying in adjacent elements may be used as well.

All currently manufactured raster-scan computer image generators for simulation now incorporate some form of anti-aliasing.

It is noted that some so-called solutions to the aliasing problem are not in fact cures, but merely treatment of the symptoms. "Edge smoothing" and post-filtering of an image with aliasing errors can only produce 20 acceptable results at the cost of a reduction in the resolution of the displayed image. In other words, elements are treated as sub-elements in a gross filter.

Consider, now, the sampling of an image stored in a memory. For simplicity it will be assumed thatthe image is defined on a grid identical to that of the display picture element grid. Figure 32 shows the stored image with the display sampling grid superimposed. There is thus an exact correspondence between stored 25 and displayed images. For a correct representation of the image, before storage, its spatial frequency content must be such that no higher spatial frequencies than those show in in the figure exist. This is achieved by application of the usual pre-sampling filter.

Now assume that the stored image is displaced with respect to the sampling grid, as shown in Figure 33, as would occur with scene or observer movement. The displacement represented is one-quarter of an element in both vertical and horizontal dimensions. The sampling points all lie within the same boundaries on the memory grid and thus the displayed image is identical to that existing before the displacement. No image change will occur until a displacement of one-half of an element has occurred in either direction. A further change of one element spacing is then required until the next change occurs. A smooth movement of the computed image thus produces abrupt changes in the displayed image.

To match the performance of such a sampled memory system to image generators with anti-aliasing which do not exhibit this element-to-element jumping of scene components, the number of stored image samples must be increased by a factor of 16, the number of sub-elements in each element of the polygon-based system. A smooth movement of the computed image then produces displayed image changes which change four times more often in any linear dimension, thus producing a closer approximation to smooth movement. The stored image must still be prefiltered to the same degree, except that there are now eight rather than two samples per spatial cycle at maximum spatial frequency. Figure 34 shows the two new grids and the maximum spatial frequency which can be stored. This arrangement is now exactly analogous to the polygon system with anti-aliasing. As far as rotation of the computed image is concerned, the same argument applies. The same approximation to smooth rotation is used as in polygon 45 systems with sub-element sampling.

The design of a texture memory system can now be considered using this data and the two assumptions previously referred to.

At the closest possible eye-surface distance one sub-element, as defined above, maps into a surface element of about 2 inches square. For smooth motion, the eye must not be allowed to approach the 50 simulated surface any closer. If the surface is viewed normally at this minimum eye-surface distance, then the situation depicted in Figure 34 applies.

A memory containing a pattern stored in this manner and filtered to the degree shown could thus constitute the top level of a memory hierarchy, designed to be sampled every four surface elements. This level is called level 0 and is produced from the basic texture pattern by applying a symmetrical two-dimensional filter with cut-off spatial frequencies iTI4 with respect to the fine grid.

Consider the case now where sample points are five surface resolution elements apart. With normal viewing, this corresponds to an eye-surface distance of 514 of that producing the four surface element spacing. Figure 35 shows the dimensions of the memory required for this spacing, where each element has 5/4 the linear dimension of a surface resolution element. The new memory grid, the top right-hand one in Figure 35, maps onto the display exactly as the level 0 grid shown in Figure 34. The degree of prefiltering required for tils level to prevent aliasing requires a low-pass filter with cut-off frequencies n/4 with respect to the larger mapped sub-element grid, or n/5 with respect to the resolution element grid. Ideally, the total amount of storage required for this level of detail would be 4/5 x 4/5 = 0.64 of that required for level 0.

However, this amount is not achievable in practice.

1 12 GB 2 061 074 A 12 Level 2, pre-filtered for a sample spacing of 6 resolution elements, would require 4/6 x 4/6 = 0.44 of the storage, level 3 4/7 x 417 = 0.33, and so on. The final level in the hierarchy will contain only one sample, representing the average brightness of the whole textured area. The next- to-last level, shown in Figure 36 needs to contain 64 samples and corresponds to the situation where 4 mapped display elements cover the 5 entire pattern. These last levels will exist whatever the initial texture pattern size.

In the implementation a texture pattern size of 64 x 64 = 4096 surface resolution elements has been chosen as the largest practical size in a practical system, considering the programmable read-only memories with suitable access times available at the present time.

1 Z.

S' 1; fl 13 GB 2 061074 A 13 With this pattern size, the following Table sets outthe theoretical and practical memory size forthe number of levels needed, 29 levels in this case.

Storage Quantities Sample Theoretical Practical Level Spacing memory size memory size Address bits used 0 4 4096 64x64=4096 X5X4X3X2X1XOY5Y4Y3Y2Y1YO 1 5 2621 4096 2 6 1820 4096 3 7 1337 4096 4 8 1024 32x32=1024 X4X3X2XIXOY4Y3Y2Y1YO 9 809 1024 6 10 655 1024 7 11 542 1024 8 12 455 1024 9 13 388 1024 14 334 1024 11 15 291 1024 12 16 256 16x16=256 X3X2X1XOY3Y2YIYO 13 17 227 256 14 18 202 256 19 182 256 16 20 164 256 17 21 149 256 18 22 135 256 19 23 124 256 24 114 256 21 25 105 256 22 26 97 256 23 27 90 256 24 28 84 256 29 78 256 26 30 73 256 27 31 68 256 28 32 64 1 none Total 16,584 28,673 Expansion ratio: 4.05 7 14 GB 2 061 074 A 14 Memory addressing difficulties preventthe optimum use of memory capacity. The texture memory is addressed by two vectors, x, and y, changing at picture element rate, which representthe mapped sub-element positions. Figure 37 shows how level 0, which contains 4096 samples, would be addressed. (XO and Y,, are the least significant bits of the X and Y vectors and represent one surface resolution element).

Level 1 ideally requires 2621 samples which have to be mapped onto the same address bits used by level 0.

This mapping is feasible using either look-up tables or arithmetic circuitry, and a memory could be constructed to hold the required number of samples.

The practical solution is to simplify the addressing atthe expense of storage economy. For level 1, for example, 4096 samples are used and addressed in the same manner as level 0. The above Table shows how the complete hierarchy is stored and the addressing used. The memory expansion factor is 7 for the case of a 10 4096 sample pattern, as opposed to 4 for the optimum memory use scheme. The simplification in addressing hardware far outweights the increased memory requirement. Prefiltered images can be computed by application of a suitable two- dimension low-pass filter.

The final design decision is how the memory hierarchy level selection is to operate. The earlier discussion is based on the assumption that the sample spacing is known. In general, as can be seen in Figure 29, the sample spacing is different in thex and y directions and the square sampling grid is a special case. To prevent aliasing, the largest distance, b in Figure 29, is used. In the example given, this distance is that between samples on adjacent lines, but it can equally well be that between adjacent elements on the same line.

Computation of the distance between samples on the same line is simple andonly the previous value of 20 (x,,y,) needs to be stored. On the other hand, computation of the distance between samples on adjacent lines requires the storage of one whole line's worth of (x,,y,)'s. This amounts to approximately 800 x 24 x 2 bits of storage in high speed memory. While this is practical, it would require an extra circuit card. The simpler solution of computing the distance between samples adjacent in time and providing a correction for aperture elongation is considered to be adequate.

This correction factor is applied by use of a level code mapping memory. This memory converts the computed sample spacing into a texture memory level code, which is a number in the range 0 to 28, according to a table loaded from the general purpose computer once per field.

The whole set of texture memories are addressed in parallel using the x, and y, bits shown in the foregoing Table. Monolithic Memories 6353-1 integrated circuit programmable read-only memories are 30 used.

Figure 38 is the block diagram of the complete texture memory system described above, which generates the image of a complete textured ground plane.

The final, eight-bit wide sequence of digital texture vaues is fed to a horizon switch identical to that builtfor the cloudlsky generator. Here a sky signal is combined to form a final image which is set to the video digital-analogue converter and fed to the display monitor.

A sample spacing correction must be computed and loaded to the level code mapping memory each field to ensure correct operation in all attitudes. It is not practical to compute this exactly, but an acceptable approximation can be made. Figure 39 shows the mapped raster lines for three angles of roll; it is immediately apparent that the computed sample spacing is only correct when =90'. The error may be simply computed by considering the mapped raster as a continuous function and comparing the rates of change of x and y in the tan k (along lines) and tany (across lines) directions.

First, note that the mapped raster shape is independent of X, YO, H and ip. If ip is made zero, as in Figure 39, the surface x and y axes are aligned as shown and a suitable correction factor can be defined. This is given by the ratio:

This ratio can beshownto be.

c X a Y a (tan -r) / (tanA) -cos 0 sin6 coso + tanycos - _05) Since the correction factor has to apply to a complete field, the tan y factor is approximated by using a constant value. Figure 40 shows the effect of this constant correction factor, which replaces the exact, curved

5b level code mapping functions with straight lines. The value of tany is determined empirically by setting O=(p=0 and adjusting the level code mapping until no aliasing is visible. Use of this value in the general 60 correction factor produces acceptable results for all attitudes.

The Surface Detail Generator described above is suitable for integration into a polygon-based raster scan image generator. Selected surfaces defined as "textured" have their single luminance value modulated by the Surface Detail Generator output.

The system described is capable of transforming texture for a single surface in any one frame. A 4 i GB 2 061 074 A is modification, however, would allow the transformation processor to be re- loaded during aline blanking interval to allow a different plane to be defined. A change in the transformation along a line would also be possible if delaying stages were added to the pipeline so that all inputs referred to the same time instant. The pipeline would of course have to be loaded with the correct number of elements before the surface change 5 was desired due to the computation delay, see Figure 25.

A problem arises at the boundary of a textured polygon due to the way abasing is handled at edges in most image generators. To correctly represent the transition, values of the texture luminance have to be known to a resolution finer than one picture element. This is not possible, as the transformation computer can only produce one sample per element. However, since the texture is only modulating an overall luminance value, 10 the filtered edge retains its correct appearance.

Recent advances in high-speed semiconductor memories make possible the construction of a texture generator with a smaller high-speed computing requirement. This may be achieved using the known "rolled rasterprinciple. Figure 41 shows such a system in block diagram form.

The texture memory is accessed by vectors x, and y, computed according to Equations (1) and (2), that is 15 with l)=0.

Xp. Xo - H (cos B --sin6 tanY) cosf - tan-)-sink? sin + tany cos c.... 17) Yp = Yo - H (cose -sine tanz()-sinw "ar.)-cosf (18) which can be re-written as:

sine + tanY cose XP - XO H Ec + Fx tan').-) (19) 25 9 J YP = YO H Ey + Fy tan-.X-) (20) 30 Considering those parts which change at picture element rate, that is those parts which are functions of tan X, and noting, as previously described, that tan X is proportional to the distance along a scan line from the centre of that scan line, then equations (19) and (20) can be solved at picture element rate with two adders 129 controlled by an address counter 128, Figure 41.

The multiplications and divisions required may be performed on a line-byline basis in the general purpose computer 106 supplied with simulated attitude and position information on the input line 105. The output of the texture memory 111 is read into one half, 131 or 132, of the frame store constructed from high speed semiconductor memories. The distance between samples is constant along any line and between lines, as is shown in Figure 42. Both of these distances are available for any line in the general purpose computer 106 40 which may then determine which is the greater and select the texture memory level accordingly. No problem of sample spacing correction exists. While one half, 131 or 132, of the frame store is being loaded, the other half, 132 or 131, respectively, is sending its contents to the display along output line 112. Roll is introduced at this point by a simple linear address mapping 130. In other words, the partially transformed texture is read out in lines at an angle of (p to those on which it was written. The address map 130 requires two high speed 45 adders for implementation. The whole system thus requires a frame store, a general purpose computer and a small amount amount of high speed arithmetic circuitry. This represents a considerable saving over the original design if 16K or larger memories are used for the frame store. The disadvantage of this alternative is that only surfaces with the same roll angle with respect to the observer can be transformed in the same ro frame.

16 GB 2 061074 A

Claims (9)

16 1. A visual display system of the computer generated image type, fora ground-based flight simulator, providing a rectangular raster scanned, perspective-transformed, pilot's visual display of a simulated textured surface, including a surface detail generator comprising a perspective transformation computer and a surface texture detail store, the perspective transformation computer being a pipelined calculator for computing in real time the perspective transformation from the display system display plane to the simulated flight, and correspondingly scanning the surface texture detail store to provide texture for each element of the said rectangular raster scanned pilot's visual display.

2. A visual display system as claimed in Claim 1, in which the line and frame constants of the rectangular 1() raster scanned display are first determined, and the pipeline calculator continuously computes the following two equations:

is X =XO-H ( ax+bxtank p c+d tanA Yp Y0 -H { c+d tanO wherein: 25 x,, y, define the simulated surface sampling point; X, Yo define the origins of the simulated surface; H defines the pilot's eye displacement from the simulated surface; 1 defines the horizontal angle of instantaneous displacement of the scanning spot from the pilot's line of view during level flight; and a, b, c, d are constants. 30

3. A visual display system as claimed in Claim 1 or Claim 2, in which the surface texture detail store holds 30 digital information corresponding to the surface texture of said simulated surface, the digital information being filtered correspondingly to a preferred scanning aperture diameter, whereby aliasing of the raster scanned display is avoided.

4. A visual display system as claimed in Claim 1 or Claim 2, in which the surface texture detail store holds digital information corresponding to the surface texture of the said simulated surface, the digital information 35 being separately filtered correspondingly to a plurality of different scanning aperture sizes, the separate filtered information being stored in separate locations of the said surface texture detail store, said information being retrieved selectively to provide filtered information corresponding to a preferred scanning aperture size as determined by the projection of the display plane scanning aperture onto the simulated surface.

5. A visual display system as claimed in anyone of the preceding claims, in which the perspective transformation computer is reloaded with input data during line blanking intervals for the purpose of computing the perspective transform for more than a single simulated surface in any frame.

6. A visual display system as claimed in anyone of Claims 1-4, in which the pipelined perspective transformation computer includes input means providing for the loading of data corresponding to a change 45 of surface perspective transformation in the course of a line scan and at least one delaying stage to ensure that all inputs refer to a single instant of time of computation.

7. A visual display system as claimed in anyone of Claims 1-4, in which the surface texture detail store includes first and second frame stores for storing surface texture information for consecutive frames of the visual display, the said frame stores being loaded alternately, the one outputting its contents while the other 56 is being loaded.

8. A visual display system as claimed in Claim 1, constructed substantially as described herein with reference to Figure 9 of the accompanying drawings.

9. A visual display system as claimed in Claim 7, constructed substantially as described herein with reference to Figure 41 of the accompanying drawings.

---(3.) -- - - M Printed for Her Majesty's Stationery Office. by Croydon Printing Company Limited, Croydon, Surrey. 1981. Published by The Patent Office, 25 Southampton Buildings, London, WC2A lAY. from which copies may be obtained.

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