FR2635874A1 - Device for the magnification of images - Google Patents

Abstract

Device for the magnification of television images, comprising a mirror 3 of concave type, directed towards the observer 5 and producing a magnified image 4 of the screen 2 of a television 1. The observer can move horizontally in a zone of + - 22.9 DEG . Variants furthermore provide an auxiliary optical device (mirror or lens) enabling the television to be placed in the usual vertical position.

Description

The present invention relates to the enlargement of images, such as those presented by television apparatuses. One or two mirrors are used for this purpose, which make it possible to obtain, from a real object, an enlarged image, with the possibility, for the observer, to move in a fairly large area while observing an image. correct, that is to say without giant deformation. In the rest of this text, we will call the observation zone "the zone where the observer can be to observe a correct image.

Known devices for enlarging television images are described in French patents Nos. 1,346,696, 1,379,018, 2,472,197, in US patent No. 3,418,426, and in French patent application No. 87 18005. In these known devices, a lens is used.
Fresnel to produce an enlarged virtual image of a real object which can be constituted by a television screen.

The disadvantages of the devices mentioned above are as follows - the observation area is very small (except for French patent No. 2,472,197); - the manufacture of large Fresnel lenses is a delicate operation, since it is especially necessary to obtain a good optical polish on a large complex surface - the cost of manufacture of large Fresnel lenses is relatively high - if the lens is not protected against dust, the latter comes to put in the hollow of the furrows. It interferes with vision and is difficult to remove.

 There are also other devices for obtaining large images from a video source: video projectors. These devices project an image created on the screen of a very bright cathode ray tube onto a screen. The current cost of these devices is much higher than the cost of conventional Fresnel lens devices or the device according to the present invention.

In the present application, and in the claims, we will call 'television' the apparatus which produces the image which one wishes to enlarge. We will call "source image * the initial image, produced by the television, and which one wishes to enlarge. The device according to the present invention also applies to the enlargement of images other than those produced by the screen of "a conventional television. We call these images images" comparable to "television images. The television" may be a conventional television, a plasma screen, a liquid crystal screen, or any other means producing images. We will speak of "angular enlargement" to designate the relationship between the angle at which an image (generally virtual) is seen by an observer and the angle at which the source image would be seen by the same observer if it were oriented. to him. We will say that a mirror "is directed towards" a given point if, from this point, an observer can see the reflecting surface of said mirror. Likewise, we will say that a screen is directed towards "a given point if, from this point, an observer can directly see the image produced by said screen. Similarly, we will say that the back of a television is" directed to "a given point if, from that point, an observer can see the rear of the television directly.

The device according to the present invention makes it possible to produce an enlarging effect analogous to that of Fresnel lenses, but eliminates the drawbacks mentioned above. It allows an angular enlargement of the order of 2 and more, does not present chromatic aberrations (because it works according to the laws of optical reflection, and not of refraction), except in its fourth embodiment, and is much easier to manufacture (because the dimensional tolerances are less strict than for Fresnel lenses). The mirrors which form part of the device according to the present invention can be mass produced by pressing a plastic material.

Figure 1 shows a first embodiment of the device for enlarging images according to the present invention.

FIG. 2 represents a second embodiment of the device according to the present invention.

Figure 3 shows a third embodiment of the device according to the present invention.

FIG. 4 represents, in profile view, variants of the first embodiment of the device according to the present invention.

FIG. 5 represents, in top view, variants of the first embodiment of the device according to the present invention.

FIG. 6a represents the coordinate system, seen from above, making it possible to define the positions of the mirror, of the screen and of the observer, as well as the shape of the surface of the mirror. We distinguish the center of coordinates O, the observer represented by point C, the axes of the x-coordinates x'Ox and the ordinates y'Oy, and two half-lines Ot and Ou, which represent the limits of the area of observation in which point C is located. These two half-lines, parallel to the xOy plane, each make an angle ss with the y'Oy axis. The dimension axis, z'Oz, is not shown in Figure 6a. It is placed perpendicular to the plane of Figure 6a, in a conventional manner. We thus have a coordinate system (O, x, y, z). In the present description, the coordinates will be expressed in meters.

Figure 6b shows the coordinate system in perspective. There are television 61, screen 62, mirror 63, observer 64.

FIG. 7 represents an implementation of the first embodiment of the device according to the present invention.

FIG. 8 represents a general diagram of the apparatus 6 of FIG. 1.

FIG. 9 represents a fourth embodiment of the device according to the present invention.

FIG. 10 represents a device allowing the assembly of a mirror made up of several parts.

A first embodiment of the present invention is shown in Figure 1 by way of illustration. We distinguish the television 1, the screen 2, a mirror 3 giving the screen 2 an image 4, the observer 5, an optional device 6 connected to the television 1 by a socket 7 which may be, for example, of the type "Scart". The mirror 3 is directed towards the observer 5. In this arrangement, the screen 2 is inclined relative to the horizontal by an angle a, and it is directed towards the mirror 3. The angle a can vary between OO and 900. The television set is kept in an inclined position by a cradle 9. The observer 5 is at a slightly higher height (5 k 10 cm) than that of the top of the television set 1. The bottom of the mirror 3 is a little lower (5 to 20 cm) than the top of the television 1. The back of the television 1 faces the observer 5: we will say that the screen 2 of the television 1 is directed on the opposite side to that of the observer 5 by compared to TV 1.

The cradle 9 must be able to receive any television whatsoever, and be able to give the screen 2 an angle a of 0 to 900. This cradle may include a pedestal mounted on ball casters, casters in contact with the ground, the pedestal being with variable inclination and comprising sliding tubular arms for enclosing the television, said arms being maintained at the desired elongation by locking screws. Said cradle should not obscure the TV remote control receiver.

Depending on whether the curvature of the mirror 3 is small or large in the horizontal direction, the image 4 that the observer sees has or does not have an inversion in the right-left direction. A weak curvature can be preferable if one wishes that the image seen seems to be distant and precisely located in space. If we take a greater curvature in the horizontal direction, the mirror 3 will cause an inversion of the image in the left-right direction, thus restoring the original orientation: the texts will be readable by the observer 5. We will say that the mirror then realizes a "self-inversion". But in this case, the image will be of real nature in the horizontal direction, and of virtual nature in the vertical direction. We will say that the image is of "mixed" nature. Hence the possibility of eye discomfort for the observer.

It may thus be necessary to prefer the weak curvature, for reasons of visual comfort. It is then necessary to remedy the drawback of the left-right inversion of the image. This can be achieved by installing a switch 10 on the television which reverses the direction of horizontal "line" scanning. This switch can, for example, act on the coils of horizontal deflection, by reversing the wires which end there. It can also act on the "lines" scanning amplifier to modify its operation, causing it to produce a signal opposite to the usual signal. It can also act on another part of the electronic assembly which controls the television, provided that the manufacturer of the television has provided for the presence of such a switch from the design of the television. It is the most economical solution.

Another solution to avoid the drawback of left-right inversion of the image is to provide a device 6 outside the television set, which modifies the video signal to apply left-right symmetry to the image; such a device can collect the video signal before it reaches the video power amplifier stages of the television set, and process it to send it back to said amplifier stages. The advantage of this solution using an external device 6 is to avoid the need for a physical modification inside the television. The video signal input / output jacks are used; these sockets are available on most current televisions. The device 6 can be provided with a socket 8 which reproduces the functions of the socket 7 for the devices which need to be connected to the television set 1 via the socket 7.

Another solution to avoid the inconvenience of left-right inversion consists in putting the television upside down, but always directed towards the mirror 3. The mirror 3 is then calculated to provide a self-inversion in the upward direction. bottom, not left-right. The visual disturbance is less, because the eye is sensitive to left-right movements in terms of distance evaluation, and much less to up-down movements. Instead of putting the TV upside down, which may be harmful to certain types of television not intended to operate in this position, you can reverse the direction of "line" scanning and that of "field" scanning using a switch such as switch 10, or install a external device such as device 6, but which processes the video signal to reverse the entire image, and no longer just the line k line image. This requires that the device 6 contains enough memory to store two video images. This type of device, processing entire video images, is conventional.

As an example, Tables 1 and 2 give the coordinates of the surface of the mirror 3, the first table for a slight curvature of the mirror in the horizontal direction, the second table for a strong curvature giving the effect of self- inversion. In these tables, the notation with decimal point, which separates the whole part from the decimal part of the values, is replaced by the notation with decimal point. To read one of these tables, we look for the desired value of x in the first row of numbers at the top of each table in the table, then we look for the desired value of z in the left column of the table; the value of x indicates a column, and the value of z indicates a row; at the intersection of said column and said row, we find the value of y (x, z).

Example: in Table 1, we look for the value of y for x-0.09 and z = 1.7706: we find, in Plate 1 of Table 1, the column where x = 0.09 (3rd column, not counting the column of z) and the line where zg1.7706 (4th line); at the intersection, we find y = 0.0228.

In both cases (table 1 and table 2), the device according to the present invention has symmetry with respect to the plane yOz, and the tables give the values of y as a function of x and z, but only for positive x. The screen of the television measures 39 cm x 50 cm, the average angular enlargement (as seen by the observer) is approximately 2; the coordinates of the observer are: (0; 3; 0.46). For the surface defined by table 1, the coordinates of the observer are: (0; 3; 0.46), the coordinates of the center of the base of the screen are: (0; 0.2; 0) and the angle a is 55. For the surface defined by table 2, the coordinates of the observer are: (0; 3; 0.48), the coordinates of the center of the base of the screen are: (0; 0.7; 0), and the angle a is equal to 600. Under these conditions, the angle ss in FIG. 6 is equal to 22.80 for the mirror according to Table 1 and Table 2. In addition, the observer can also move in the vertical direction ; the observation zone includes the "normal" position of the observer, as defined above, and extends in height, from this normal position, over a distance of 0.5 m for the mirror according to the table 1, and 0.2 m for the mirror according to table 2.

Said tables 1 and 2 give the ordinates yo of a set of points of the mirror, defined by their abscissa xo and their dimension zo, xo varying from 4.5 cm to 4.5 cm and zo varying from 3 cm to 3 cm. For a given table, it may be useful to know the y coordinate of an istermediate point M of the mirror, of abscissa x and of dimension z, when this point M does not appear in said table. To evaluate said ordinate y, conventional interpolation formulas can be used. As an example, we will study an interpolation method using Taylor's formula for a real function of two real variables: we will first look in the table for the point Mo (xo, zo) closest to the intermediate point M (x, z) sought. We will call Sx and Sz the steps of the table along x and z (here, we have 8x = 0.045 m and 8z = 0.03 m). Then, we can consider that y is a function of x and z, and that the partial derivatives of y with respect to x and z, at point Mo of the table found, can be estimated as follows - first derivative of y with respect to at x at point Mo (xo, zo):
dy y (xo + # x, zo) -y (xo, zo) - (xo, zo)
dx #x - first derivative of y with respect to z at the point Mo (xo, zo):
dy y (xo, zo + # z) -y (xo, zo)
- (xo, zo) =
dz - second derivative of y with respect to x at the point Mo (xo, zo) ::
d2y y (xo + # x, zo) + y (xo- # x, zo) -2 y (xo, zo) - (xo, zo) I ~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
dx2 (6x) 2 - second derivative of y with respect to z at the point Mo (xo, zo):
d2y y (xo, zo + # z) + y (xo, zo- # z) -2 y (xo, zo) - (xo, zo) "-
dz: (#z) - second derivative of y with respect to x and z at the point Mo (xo, zo):
4 y (xo, zo) 2 [y (xo, zo + # z) + y (xo + # x, zo) + y (xo, zo- # z) + y (xo- # x, zo) +
dy̑ + y (xo + # x, zo + # z) + y (xo + # x, zo- # z) + y (xo- # x, zo- # z) + y (xo- # x, zo + # z) - (xo, zo) = dxdz 4 #x #z
Now that we have a value for the different first and second derivatives of y at the point Mo (xo, zo), we will call Dx and Dz the deviations, in x and z, of the sought intermediate point M (x, z) compared at the point Mo (so, zo) known from the table. That is, we have: Dx = x-xo and Dz-z-zo.

Taylor's formula allows us to obtain an approximate value for the y-coordinate of said intermediate point
dy dy d2y (Dx) 2 y (x, z) wy (xo, zo) + - (xo, zo) Dx + - (xo, zo) Dz + - (xo, zo) - +
dx dz dxt 2
d2y (Dz) 2 d2y
+ - (xo, zo) - + - (xo, zo) Dx Dz (formula 1)
dz: 2 dxdz
Similarly, if we need the values of dy / dx or dy / dz at said intermediate point M (x, z), we can use the following formulas dy dy d: y d2y - (x, z) * - ( xo, zo) + - (xo, zo) Dx + - (xo, zo) Dz (formula 2) dx dx dx: dxdz dy dy d :: y d2y - (x, z) - - (xo, zo) + - (xo, zo) Dz + - (xo, zo) Dx (formula 3) dz dz dzZ dxdz
The errors which one commits by replacing y (x, z) or the partial derivatives first by the values obtained by the formulas 1, 2 and 3 above are estimated according to the derivatives of higher order (see bibliography) .

If the precision provided by these formulas is not sufficient, we can take into account the derivatives of order greater than 2 and proceed as indicated above, first by searching for the point in the nearest table, then by applying the formula of Taylor at orders greater than 2.

FIG. 8 represents a general diagram of the apparatus 6 of FIG. 1.

We will describe the internal organization of the device, then we will see what its operating principle is. The dotted lines indicate the path of a control signal; solid lines indicate the flow of video information coming from outside and processed by the device. The video signal enters via the wire 80, and arrives in a synchronization separator 81. This separator sends the synchronization signals "lines" 82 and the sunchronization signals "frames" 120 to a central control unit 83, and sends the signal video 84, free of synchronization signals, to a chrominance-luminance separator 85. This separator 85 sends the demodulated chrominance signals 86 to an analog-digital converter 87, and the luminance signals 88 to an analog-digital converter 89. The converter 87 transforms the analog chrominance signal 86 into a series of digital values 90 which are sent to a switch 91 having an input 92 and two outputs 93, 94. Similarly, the converter 89 transforms the analog luminance signal 88 into a sequence digital values 95 which are sent to a switch 96 k an input 97 and two outputs 98, 99. The converters 87 and 89, as well as the switches urs 91 and 96, work under control of the central control unit 83. The switch 91 transmits to one of its two outputs 93, 94 (according to orders from the unit 83) the information it receives in Likewise for the switch 96. A digital memory 100, 101, 102, 103 is connected to each of the outputs 93, 94, 98, 99. The information stored in the digital memories 100 and 101 is read and sent to the inputs 105 and 106 of a switch 104 having an output 107. Likewise, the information stored in the digital memories 102 and 103 is read and sent to the two inputs 109 and 110 of a switch 108 having an output 111. At output of the switch 104, the digital information is sent to a digital-analog converter 112, which restores an analog chrominance signal at its output 113. At the output of the switch 108, the digital information is sent to a digital converter -analog 114, which restores an analog luminance signal at its output 115. The synchronization signals have been removed by the separator 81, and it is necessary, at the output, to recreate them. To do this, a synchronization tick generator "lines" and "frames" 116 is used. A color reference signal generator 117 recreates the color reference signals at the start of the line. A mixer 118 modulates the chrominance information from the converter 112, and mixes it with the luminance, synchronization "lines" and "fields", and color reference information, respectively from the converter 114 and the generators 116 and 117, to recreate a full video signal at its output 119.

The central control unit 83 controls the triggering of the analog-digital conversions, the writes and readings in the memories 100, 101, 102, and 103, the switches operated by the switches 91, 96, 104, and 108, as well as the generation of synchronization and reference signals by the generators 116 and 117. When the beginning of a video line appears at input 80, the central unit 83 is informed by a synchronization signal "lines * at 82 The central unit then triggers a series of analog-digital conversions in the converters 87 and 89, and supplies the memories 100 and 102, via the switches 91 and 96. At the same time, the central unit 83 controls the reading of the memories 101 and 103, via switches 104 and 108, in the reverse order of the order in which the information was entered there. When the video line ends, at input 80, the control unit 83 switches the four switches 91, 96, 104, and 108: po ur the next input video line, memories 101 and 103 will be supplied, and memories 100 and 102 that will be read. There is thus obtained, at output, a complete video signal representing a video image having undergone a right-left symmetry.

A variant of the apparatus 6 described above can be constituted by using analog memories in place of digital memories. These analog memories must be read in the reverse order of the order in which the signals are entered. In this case, it is no longer necessary to use analog-to-digital and digital-to-analog converters; furthermore, the switches 91, 96, 104 and 108 must then be analog switches, and no longer digital switches.

For the rest, the general diagram and the operating principle of the apparatus 6 are unchanged.

A second embodiment of the device according to the present invention is represented in FIG. 2. There is a television 11, its screen 12, a first mirror 13, which we will call "auxiliary mirror", and a second mirror 14, which we will call " main mirror ". The mirror 13 gives the screen 12 an image 15, which is represented here as a virtual image. The mirror 14 gives the image 15 an image 16, which is represented here as a virtual image. Image 16 is seen by an observer 17. The mirror 14 is directed towards the observer 17. The mirror 13 is directed towards the mirror 14. The screen 12 is vertical, and is directed towards the observer 17. The bottom of the mirror 14 is at the height of the top of the television 11. The bottom of the mirror 13 is close to the bottom of the screen 12. The top of the mirror 13 is at a height close to that of the top of the television 11.

The observer 17 is u .: little (5 to 20 cm) above the top of the television 11.

The use of two mirrors 13 and 14 makes it possible to restore an image t the place ", that is to say having not undergone left-right or top-bottom symmetries. Thus, a text appearing on the screen 12 can be read by the observer 17 observing the image 16.

The mirror 13 is of a planar nature or not, and may for example be a convex spherical mirror. The mirror 14 is of a concave nature, and may for example be a concave spherical mirror.

Let h be the height of the screen 12, d the distance between the center of the screen 12 and the mirror 13, h 'the height of the image 15. the distance between the mirror 13 and the center of the image 15, f the focal length of the mirror 13. The calculations are conventional. We have
2 hrs
f - ------, which suffices to characterize the mirror 13.

h-h '
Likewise, let h "be the height of image 16, d" the distance between mirror 14 and the center of image 16. We have
2 hrs "
f "=, which suffices to characterize the mirror 14.

 h'-h 'Example: h0.39 m; d-0.4 m; h'-O, 3 m; of-O, 3 m; h "-2h; d" = l m.

 We have: f-2.6 m and f "= 1.25 m.

This second embodiment has several advantages over the first embodiment: - it is no longer necessary to tilt the television, so it is no longer necessary to provide a cradle for holding the device, which would come complicate the whole and increase the cost - the restoration of the right-left orientation of the enlarged image is done without external device or intervention on the TV, and it is possible to preserve the virtual nature of the image seen, therefore good visual comfort.

This second embodiment has several drawbacks compared to the first embodiment - two mirrors are used instead of one, therefore the positioning is more delicate, since it is necessary to correctly position two mirrors one relative to the other, and compared to the television - the cost is increased with regard to the mirrors - the size of the device is greater, due to the presence of the mirror 13 - when the image 15 is an image of a virtual nature , it is farther from the mirror 14 than is the screen 2 from the mirror 3 in the first embodiment, which results in a less extensive observation area for the dimensions of the mirror 14 similar to that of the mirror 3.

A third embodiment of the device according to the present invention is shown in FIG. 3. We distinguish the television set 21, the screen 22, a first mirror 26, a second mirror 24, of concave nature, giving the screen 22 an image. represented here as a virtual image 25, and an observer 23. We will call the mirror 26 "auxiliary mirror" and the mirror 24 "main mirror". The mirror 26 is directed towards the screen 22 and to the mirror 24, and the mirror 24 is directed towards the observer 23. The rear of the television set 21 is directed towards the observer 23. In this arrangement, the screen 22 is vertical.

The mirror 26 can be calculated either so as to reverse the image 22 in the left-right direction and in the up-down direction, or so as to reverse only in the left-right direction, or so as to do nothing invert (in the latter case, the image provided by the screen 22 must be inverted by electronic means (such as the apparatus 6).

When the auxiliary mirror 26 reverses the image in the left-right direction, an image 25 is obtained which no longer has the left-right inversion proper to the mirror without self-inversion of the first embodiment (that with low curvature ). However, in the case where the mirror 26 provides an image of a real or mixed nature, there is a risk of some visual discomfort, for the same reasons as during the auto-inversion.

This third embodiment has an advantage over the second form: the assembly of the two mirrors 26 and 24 can constitute a single object, hence a simpler manufacture and a reduction in the positioning problems of the two mirrors one compared to each other when in use.

The advantages and disadvantages of this third embodiment compared to the first are the same as those of the second embodiment compared to the first.

A fourth embodiment of the present invention is shown in Figure 9 by way of illustration. We distinguish the television 131, the screen 132, a lens 133, which we will call "auxiliary lens", a mirror 134, and an observer 135. The screen 132 is inclined at an angle 'relative to the horizontal, and is directed towards the mirror 134. The angle 'can vary from 0 to 900. The mirror 134 is directed towards the observer 135. The auxiliary lens 133 is placed between the screen 132 and the mirror 134. The rear of the television 131 is directed towards the observer 135. The lens 133 can be a conventional lens or a Fresnel lens, and give the screen 132 a virtual, real or mixed image. As this lens is not very large ( about 80 cm wide), it is less delicate and less expensive to manufacture than the large Fresnel lenses used in the prior art. In a variant of the fourth embodiment of the present invention, it is possible to add to the lens 133 another optical system, such as a prism (conventional prism or Fresnel prism), the assembly formed by said lens and said system. optics forming what we will call an "auxiliary optical device". In another variant to the fourth embodiment of the present invention, it is also possible to replace said lens with another optical device, which we will call "auxiliary optical device", such as a prism.

In the case where the image provided by the lens 133 is virtual, it is located behind the screen 132 of the television 131, at a distance which depends on the magnification of the lens 133 and on the distance from this lens to the screen 132. The magnification of the lens can be, for example, 1.4. As the virtual image is already magnified relative to the screen, the mirror 134 no longer needs to achieve an angular enlargement of 2, but only of approximately 1.5. There would therefore be less distortion when the observer 135 moves.

In the case where the image provided by the lens 133 is real, it is located between said lens and the mirror 134. As it is closer to the mirror 134 than a virtual image would be, an observation area can be obtained larger than with a virtual image.

In the case where the image provided by the lens 133 is mixed, the advantage is to carry out using the lens 133 the left-right inversion necessary to restore the appearance of the original image presented by screen 132.

The first embodiment, with a single mirror, can undergo variants, represented in FIG. 4 (side view) and in FIG. 5 (top view). In FIG. 4, it can be seen that the distance between the screen and the bottom of the mirror 37 can vary: the screen can be both in the vicinity (31) of the mirror 37 and far (32) from said mirror; it can even be located farther (33) from the mirror 37 than the observer 36. Thus, the screen can be placed behind (33) the observer, above the observer. Similarly, the screen can be placed higher (34, 35) than the mirror 37. In FIG. 5, it can be seen that the screen can also be placed not only opposite (52) of the mirror 51, but also at its right (53) or to its left (54), "right" and "left being understood as seen by observer 55, represented by point C.

For each different arrangement, the calculations of the mirror result in a different form of said mirror. It should be noted that the further the screen is from the mirror, the less the image distorts when the observer moves, and that when the screen is far from the mirror, the image moves more for the same movement of the observer, and the surface defects of the mirror are more visible.

One can calculate (by conventional calculations) a mirror or a lens of one of the embodiments presented above so as to enlarge in a particular way the image presented by the screen of the television set: one makes so that the enlargement is greater in the horizontal direction than in the vertical direction. It is thus possible to carry out an image desanamorphosis, for films recorded in anamorphosis and reproduced as such on the television screen. We apply the same principle as for films called "big screen" in the cinema, where the image is compressed in the horizontal direction, on the film, and where the projectionist inserts a special lens to restore the full width of the image on the projection screen. For the first embodiment of the device according to the present invention, it is necessary to change the single mirror, that is to say the mirror 3 (see FIG. 1), to pass from a normal image to an image that needs to be desanamorphosed. For the second and third embodiments of the device according to the present invention, it suffices to change the auxiliary mirror, that is to say the mirror 13 (respectively 26), leaving the mirror 14 (respectively 24) fixed. For the fourth embodiment of the device according to the present invention, it suffices to change the auxiliary lens, that is to say the lens 133. For rendering anamorphic images on a television screen, it is necessary to have a source video giving an anamorphic image, thus exploiting the entire surface of the video screen. When watching a "big screen" movie in the usual way, part of the video screen remains black. With the desanamorphosis by the device according to the present invention, better vertical definition and better brightness are obtained.

The use of future panoramic television screens (length / width ratio close to 2) will always be possible with the same devices as those described in the present application.

FIG. 7 represents an implementation of the first embodiment of the device according to the present invention. There are a television set 71, a mirror 73, a matt black sunshade composed of two vertical parts 75 and 76, two loudspeakers 72 and 74, placed on either side of the mirror 73, an audio amplifier 79, and the observer represented by point C. The sun visor may further comprise a horizontal part fixed to the horizontal upper edge of the mirror 73. The sun visor is intended to prevent stray lights from coming to be reflected on the mirror 73 The loudspeakers 72 and 74 serve to produce a stereophonic sound, or, at least, a sound giving a space effect in relation to the size of the image seen by the observer.

Provision may be made, If the original sound is not stereophonic, to simulate the stereophony using a conventional device called "pseudo-stereophony", which processes the monophonic signal to produce two signals which are out of phase or having components at different frequencies, or to which reverberation effects are added, these two signals each being sent to one of the two loudspeakers 72 and 74. It is also possible to provide two other loudspeakers 77 and 78, to achieve quadraphony. The speakers 77 and 78 will be powered either directly by a quadraphonic signal, or by a device producing a pseudo-quadraphonic from a stereophonic or monophonic signal. We can also arrange the television 71, the mirror 73, the screen -sun 75, 76, amplifier 79, and the two loudspeakers 72 and 74, in the same piece of furniture forming a streamlined assembly, thus constituting an integrated audiovisual system, in compliance with the constraints and requirements for good rendering acoustic. This integrated system may also contain various audio-visual and communication devices: audio cassette player, video recorder, compact disc player, videodisc, digital optical disc player, digital compact disc player, modem, converter video switchboards, decoders, etc.

FIG. 10 represents a casing device which can be useful when it is desired to transport a large mirror according to the present invention. This involves cutting the mirror into two or more parts, which are connected together when the said mirror is put in place. There is a first part 150 and a second part 151 of the mirror, a "U" shaped edge 152, a "LD" shaped edge 153, a clip 154, a clip 155, a screw 156, and a nut 157. The shapes profiled edges 152 and 153 run all along the edges of the mirror which are opposite one another. The fasteners 154 and 155 are arranged at regular intervals along said profiled parts. When the "L" profile comes fit into the "U" profile, the two parts 150 and 151 of the mirror form a surface which appears continuous to an observer located a few meters from the mirror. The screw 156 and the nut 157 serve to hold together one on the other, via the fasteners 154 and 155, the two parts 150 and 151. The length and thickness of the profiled regions in "U" and "L" are such that after fitting, the different parts of the mirror are sufficiently united with one another so that there is continuity between them in the opt sense ic (continuity of tangent vectors on the surface of the mirror). The fasteners 154 and 155 may be either glued or fixed on ribs on the back of the mirror, ribs serving to reinforce the structure of said mirror, both in the horizontal direction (horizontal ribs) and in the vertical direction (vertical ribs).

--- PAINTINGS --
Values x of z 0.0000 0.0450 0.0900 0.1350 0.1800 0.2250 0.2700 0.3150 1.8606 0.1073 0.1079 0.1094 0.1121 0.1158 0.1205 0.1263 0.1331 1.8306 0.0777 0.0783 0.0799 0.0878 0.02 0.02 0.02 0.07 1.7406 -0.0067 -0.0062 -0.0047 -0.0021 0.0014 0.0059 0.0115 0.0180 1.7106 -0.0336 -0.0330 -0.0315 -0.0290 -0.0255 -0.0210 -0.0155 -0.0090 1.6806 -0.0598 -0.0592 -0.0577 -0.0553 -0.0518 -0.0473 -0.0419 -0.0355 1.6506 -0.0853 -0.0848 -0.0833 -0.0809 -0.0774 -0.0730 -0.0676 -0.0612 1.6206 -0.1103 -0.1098 -0.1083 -0.1059 -0.1025 -0.0981 -0.0927 -0.0864 1.5906 -0.1347 -0.1342 -0.1327 -0.1303 -0.1269 -0.1226 -0.1172 -0.1110 1.5606 0.1585 -0.1580 -0.1566 -0.1541 -0.1508 -0.1465 -0.1412 -0.1350 1.5306 -0.1818 -0.1813 -0.1798 -0.1774 -0.1741 -0.1698 -0.1645 -0.1584 1.5006 -0.2045 -0.2040 -0.2025 -0.2002 -0.1968 -0.1926 -0.1874 -0.1812 1.4706 -0.2266 -0.2261 -0.2247 -0.2223 -0.2190 -0.2148 -0.2096 -0.2035 1.4406 -0.2483 -0.2478 -0.2464 -0.2440 -0.2407 -0.2365 -0.2314 -0.2253 1.4106 -0.2694 -0.2689 -0.2675 -0.2651 -0.2619 -0.2577 -0.2526 -0.2465 1.3806 -0.2900 -0.2895 0.2881 -0.2858 -0.2825 -0.2783 -0.2733 -0.2672 1.3506 -0.3101 -0.3096 -0.3082 -0.3059 -0.3027 -0.2985 -0.2934 -0.2875 1.3206 -0.3297 -0.3292 -0.3278 -0.3255 -0.3223 -0.3182 -0.3131 -0.3072 1.2906 -0.3488 -0.388 -0.3470 -0.3447 -0.3415 -0.3373 -0.3323 -0.3264 1.2606 -0.3675 -0.3670 -0.3656 -0.3633 -0.3601 -0.3560 -0.3510 -0.3451 1.2306 -0.3856 -0.3852 -0.3838 -0.3815 -0.3783 -0.3742 -0.3693 -0.40 0.4029 -0.4015 -0.3992 -0.3961 -0.3920 -0.3870 -0.3812 1.1706 -0.4206 -0.4201 -0.4188 -0.4165 -0.4133 -0.4093 -0.4043 -0.3985 1.1406 -0.4374 -0.4369 -0.4356 -0.4333 -0.4301 -0.4261 -0.4211 -0.4153 1.1105 -0.4533 -0.4519 -0.4497 -0.4465 -0.4425 -0.4375 -0.4317 1.0806 -0.4697 -0.4692 -0.4678 -0.4656 -0.4624 -0.4584 -0.4535 -0.4477 1.0506 -0.4851 -0.4846 -0.4833 -0.481 0 -0.4779 -0.4739 -0.4690 -0.4632 1.0206 -0.5002 -0.4997 -0.4983 -0.4961 -0.4929 -0.4889 -0.4840 -0.4782 0.9906 -0.5148 -0.5143 -0.5129 -0.5107 -0.5076 -0.5035 -0.4986 -0.4929 0.9606 -0.5289 -0.5285 -0.5285 -0.5249 -0.5217 -0.5177 -0.5128 -0.5070 0.9306 -0.5427 -0.5422 -0.5409 -0.5386 -0.5355 -0.5315 -0.5266 -0.5208 0.9006 -0.5560 -0.5555 -0.5542 -0.5520 -0.5488 -0.5448 -0.5399 -0.5342 0.8706 -0.5689 0.5671 -0.5649 -0.5617 -0.5577 -0.5528 -0.5471 0.8406 -0.5814 -0.5810 -0.5796 -0.5774 -0.5742 -0.5702 -0.5653 -0.5596 0.8106 -0.5935 -0.5930 -0.5917 -0.5895 -0.5863 -0.5823 -0.5774 -0.5716 0.7806 -0.607 -0.6034 -0.6011 -0.5980 -0.5940 -0.5891 -0.5833 0.7506 -0.6165 -0.6160 -0.6146 -0.6124 -0.6093 -0.6053 -0.6004 -0.5946 0.7206 -0.6273 -0.6269 -0.6255 -0.6233 -0.6201 -0.6161 -0.6112 -0.6054 0.6906 -0.6378 - 0.6373 -0.6360 -0.6337 -0.6306 -0.6266 -0.6217 -0.6159 0.6606 -0.6479 -0.6474 -0.6460 -0.6438 -0.6406 -0.6366 -0.6317 -0.6259 0.6306 -0.6575 -0.6570 -0.6557 -0.6534 -0.6 503 -0.6463 -0.6413 -0.6356 0.6006 -0.6668 -0.6663 -0.6649 -0.6627 -0.6595 -0.6555 -0.6506 -0.6448 0.5706 -0.6756 -0.6751 -0.6738 -0.6715 -0.6684 -0.6644 -0.6594 -0.6536 0.5406 -0.6841 -0.6836 -0.6822 -0.6768 -0.6728 -0.6679 -0.6621 0.5106 -0.6921 -0.6917 -0.6903 -0.6880 -0.6849 -0.6808 -0.6759 -0.6701 0.4806 -0.6998 -0.6993 -0.6980 -0.6957 -0.6925 -0.6885 -0.6836 -0.6777 0.4506 -0.7071 -0.7066 -0.7066 0.7030 -0.6998 -0.6957 -0.6908 -0.6849 0.4206 -0.7139 -0.7134 -0.7121 -0.7098 -0.7066 -0.7026 -0.6976 -0.6918 0.3906 -0.7204 -0.7199 -0.7185 -0.7163 -0.7131 -0.7090 -0.7041 -0.6982 0.3606 -0.7264 -0.7264 -0.7223 -0.7192 -0.7151 -0.7101 -0.7042 0.3306 -0.7321 -0.7316 -0.7303 -0.7280 -0.7248 -0.7207 -0.7157 -0.7099 0.3006 -0.7374 -0.7369 -0.7355 -0.7332 -0.7300 -0.7260 -0.7210 -0.7151 0.2706 -0.7422 0.7404 -0.7381 -0.7349 -0.7308 -0.7258 -0.7199
Table 1: values of y as a function of x and z. Plate 1 of 4.

Values Values of x
de z 0.3600 0.4050 0.4500 0.4950 0.5400 0.5850 0.6300 0.6750
1.8606 0.1409 0.1498 0.1598 0.1707 0.1828 0.1959 0.2100 0.2252
1.8306 0.1110 0.1198 0.1296 0.1405 0.1524 0.1653 0.1793 0.1943
1.8006 0.0818 0.0905 0.1002 0.1110 0.1228 0.1356 0.1494 0.1642
1.7706 0.0533 0.0620 0.0716 0.0822 0.0939 0.1065 0.1202 0.1349
1.7406 0.0255 0.0341 0.0436 0.0541 0.0657 0.0782 0.0917 0.1062
1.7106 -0.0016 0.0069 0.0163 0.0267 0.0382 0.0506 0.0640 0.0784
1.6806 -0.0281 -0.0197 -0.0103 0.0000 0.0113 0.0236 0.0369 0.0511
1.6506 -0.0539 -0.0456 -0.0363 -0.0261 -0.0148 -0.0027 0.0105 0.0246
1.6206 -0.0791 -0.0709 -0.0617 -0.0515 -0.0404 -0.0283 -0.0153 -0.0013
1.5906 -0.1037 -0.0956 -0.0864 -0.0764 -0.0653 -0.0533 -0.0404 -0.0265
1.5606 -0.1278 -0.1197 -0.1106 -0.1006 -0.0896 -0.0777 -0.0649 -0.0511
1.5306 -0.1512 -0.1432 -0.1342 -0.1242 -0.1134 -0.1016 -0.0888 -0.0751
1.5006 -0.1741 -0.1661 -0.1572 -0.1473 -0.1365 -0.1248 -0.1121 -0.0985
1.4706 -0.1965 -0.1885 -0.1796 -0.1698 -0.1591 -0.1474 -0.1349 -0.1214
1.4406 -0.2183 -0.2104 -0.2015 -0.1918 -0.1811 -0.1695 -0.1570 -0.1436
1.4106 -0.2396 -0.2317 -0.2229 -0.2132 -0.2026 -0.1911 -0.1787 -0.1653
1.3806 -0.2603 -0.2525 -0.2438 -0.2341 -0.2236 -0.2121 -0.1998 -0.1865
1.3506 -0.2806 -0.2728 -0.2641 -0.2545 -0.2440 -0.2326 -0.2203 -0.2071
1.3206 -0.3003 -0.2926 -0.2839 -0.2744 -0.2639 -0.2526 -0.2403 -0.2272
1.2906 -0.3196 -0.3118 -0.3032 -0.2937 -0.2833 -0.2720 -0.2598 -0.2467
1.2606 -0.3383 -0.3306 -0.3220 -0.3126 -0.3022 -0.2909 -0.2788 -0.2658
1.2306 -0.3566 -0.3489 -0.3404 -0.3309 -0.3206 -0.3094 -0.2973 -0.2843
1.2006 -0.3744 -0.3668 -0.3582 -0.3488 -0.3385 -0.3273 -0.3153 -0.3024
1.1706 -0.3917 -0.3841 -0.3756 -0.3662 -0.3560 -0.3448 -0.3328 -0.3199
1.1406 -0.4086 -0.4010 -0.3925 -0.3832 -0.3729 -0.3618 -0.3498 -0.3370
1.1106 -0.4250 -0.4174 -0.4090 -0.3996 -0.3894 -0.3783 -0.3664 -0.3536
1.0806 -0.4410 -0.4334 -0.4250 -0.4156 -0.4054 -0.3944 -0.3825 -0.3697
1.0506 -0.4565 -0.4489 -0.4405 -0.4312 -0.4210 -0.4100 -0.3981 -0.3853
1.0206 -0.4716 -0.4640 -0.4556 -0.4463 -0.4361 -0.4251 -0.4132 -0.4004
0.9906 -0.4862 -0.4787 -0.4702 -0.4610 -0.4508 -0.4398 -0.4279 -0.4152
0.9606 -0.5004 -0.4929 -0.4845 -0.4752 -0.4650 -0.4540 -0.4421 -0.4294
0.9306 -0.5142 -0.5066 -0.4982 -0.4890 -0.4788 -0.4678 -0.4559 -0.4432
0.9006 -0.5275 -0.5200 -0.5116 -0.5023 -0.4922 -0.4812 -0.4693 -0.4566
0.8706 -0.5404 -0.5329 -0.5245 -0.5152 -0.5051 -0.4941 -0.4822 -0.4695
0.8406 -0.5529 -0.5454 -0.5370 -0.5277 -0.5176 -0.5066 -0.4947 -0.4819
0.8106 -0.5650 -0.5575 -0.5491 -0.5398 -0.5296 -0.5186 -0.5067 -0.4940
0.7806 -0.5767 -0.5691 -0.5607 -0.5514 -0.5413 -0.5303 -0.5184 -0.5056
0.7506 -0.5879 -0.5804 -0.5720 -0.5627 -0.5525 -0.5415 -0.5296 -0.5168
0.7206 -0.5988 -0.5912 -0.5828 -0.5735 -0.5633 -0.5523 -0.5404 -0.5276
0.6906 -0.6092 -0.6017 -0.5932 -0.5839 -0.5738 -0.5627 -0.5508 -0.5380
0.6606 -0.6192 -0.6117 -0.6033 -0.5939 -0.5838 -0.5727 -0.5608 -0.5480
0.6306 -0.6289 -0.6213 -0.6129 -0.6036 -0.5934 -0.5823 -0.5704 -0.5575
0.6006 -0.6381 -0.6305 -0.6221 -0.6128 -0.6026 -0.59l5 -0.5795 -0.5667
0.5706 -0.6469 -0.6393 -0.6309 -0.6216 -0.6113 -0.6002 -0.5883 -0.5754
0.5406 -0.6553 -0.6478 -0.6393 -0.6299 -0.6197 -0.6086 -0.5966 -0.5838
0.5106 -0.6634 -0.6558 -0.6473 -0.6379 -0.6277 -0.6166 -0.6046 -0.5917
0.4806 -0.6710 -0.6 (34 -0.6549 -0.6455 -0.6353 -0.6241 -0.6121 -0.5992
0.4506 -0.6782 -0.6706 -0.6621 -0.6527 s0.6424 -0.6313 -0.6193 -0.6063
0.4206 -0.6850 -0.6774 -0.6689 -0.6595 -0.6492 -0.6380 -0.6260 -0.6131
0.3906 -0.6915 -0.6838 -0.6753 -0.6659 -0.6556 -0.6444 -0.6323 -0.6194
0.3606 -0.6975 -0.6898 -0.6813 -0.6719 -0.6616 -0.6504 -0.6383 -0.6253
0.3306 -0.7031 -0.6954 -0.6869 -0.6774 -0.6671 -0.6559 -0.6438 -0.6308
0.3006 -0.7083 -0.7006 -0.6921 -0.6826 -0.6723 -0.6610 -0.6489 -0.6359
0.2706 -0.7131 -0.7054 -0.6969 -0.6874 -0.6770 -0.6658 -0.6536 -0.6406
Table 1: values of y as a function of x and z. Plate 2 of 4.

Values Values of x
de z 0.7200 0.7650 0.8100 0.8550 0.9000 0.9450 0.9900 1.0350
1.8606 0.2415 0.2588 0.2772 0.2966 0.3172 0.3388 0.3615 0.3852
1.8306 0.2104 0.2275 0.2457 0.2649 0.2851 0.3065 0.3288 0.3523
1.8006 0.1801 0.1970 0.2149 0.2339 0.2539 0.2750 0.2971 0.3202
1.7706 0.1506 0.1673 0.1850 0.2038 0.2236 0.2444 0.2662 0.2890
1.7406 0.1218 0.1383 0.1559 0.1744 0.1940 0.2145 0.2361 0.2586
1.7106 0.0937 0.1101 0.1275 0.1458 0.1651 0.1855 0.2068 0.2291
1.6806 0.0664 0.0826 0.0998 0.1179 0.1371 0.1572 0.1783 0.2003
1.6506 0.0397 0.0558 0.0728 0.0908 0.1097 0.1297 0.1505 0.1723
1.6206 0.0137 0.0296 0.0465 0.0643 0.0831 0.1028 0.1235 0.1451
1.5906 -0.0117 0.0041 0.0208 0.0385 0.0571 0.0767 0.0972 0.1186
1.5606 --0.0364 -0.0207 -0.0042 0.0134 0.0318 0.0512 0.0715 0.0927
1.5306 -0.0605 -0.0450 -0.0285 -0.0111 0.0072 0.0264 0.0466 0.0676
1.5006 -0.0840 -0.0686 -0.0523 -0.0350 -0.0168 0.0023 0.0222 0.0431
1.4706 -0.1070 -0.0916 -0.0754 -0.0583 -0.0402 -0.0213 -0.0014 0.0193
1.4406 -0.1293 -0.1141 -0.0980 -0.0809 -0.0630 -0.0442 -0.0245 -0.0039
1.4106 -0.1511 -0.1360 -0.1199 -0.1030 -0.0852 -0.0665 -0.0469 -0.0265
1.3806 -0.1723 -0.1573 -0.1413 -0.1245 -0.1068 -0.0882 -0.0687 -0.0484
1.3506 -0.1930 -0.1780 -0.1622 -0.1454 -0.1278 -0.1093 -0.0900 -0.0698
1.3206 -0.2132 -0.1983 -0.1825 -0.1658 -0.1483 -0.1299 -0.1107 -0.0906
1.2906 -0.2328 -0.2180 -0.2022 -0.1857 -0.1682 -0.1499 -0.1307 -0.1108
1.2606 -0.2519 -0.2371 -0.2215 -0.2050 -0.1876 -0.1694 -0.1503 -0.1304
1.2306 -0.2705 -0.2558 -0.2402 -0.2237 -0.2064 -0.1883 -0.1693 -0.1494
1.2006 -0.2886 -0.2739 -0.2584 -0.2420 -0.2247 -0.2066 -0.1877 -0.1679
1.1706 -0.3062 -0.2915 -0.2760 -0.2597 -0.2425 -0.2245 -0.2056 -0.1859
1.1406 -0.3232 -0.3087 -0.2932 -0.2769 -0.2598 -0.2418 -0.2229 -0.2033
1.1106 -0.3399 -0.3253 -0.3099 -0.2936 -0.2765 -0.2586 -0.2398 -0.2202
1.0806 -0.3560 -0.3415 -0.3261 -0.3099 -0.2928 -0.2749 -0.2561 -0.2366
1.0506 -0.3716 -0.3571 -0.3418 -0.3256 -0.3085 -0.2906 -0.2719 -0.2524
1.0206 -0.3868 -0.3723 -0.3570 -0.3408 -0.3238 -0.3059 -0.2872 -0.2677
0.9906 -0.4015 -0.3871 -0.3717 -0.3556 -0.3386 -0.3207 -0.3020 -0.2825
0.9606 -0.4158 -0.4013 -0.3860 -0.3699 -0.3528 -0.3350 -0.3163 -0.2968
0.9306 -0.4296 -0.4151 -0.3998 -0.3837 -0.3667 -0.3488 -0.3301 -0.3107
0.9006 -0.4430 -0.4285 -0.4132 -0.3970 -0.3800 -0.3622 -0.3435 -0.3240
0.8706 -0.4559 -0.4414 -0.4261 -0.4099 -0.3929 -0.3750 -0.3563 -0.3368
0.8406 -0.4683 -0.4539 -0.4385 -0.4224 -0.4053 -0.3875 -0.3688 -0.3492
0.8106 -0.4804 -0.4659 -0.4506 -0.4344 -0.4174 -0.3995 -0.3808 -0.3612
0.7806 -0.4920 -0.4775 -0.4622 -0.4460 -0.4289 -0.4110 -0.3923 -0.3727
0.7506 --0.5032 -0.4887 -0.4734 -0.4572 -0.4401 -0.4222 -0.4034 -0.3838
0.7206 -0.5140 -0.4995 -0.4841 -0.4679 -0.4508 -0.4329 -0.4141 -0.3945
0.6906 -0.5244 -0.5098 -0.4945 -0.4782 -0.4611 -0.4432 -0.4244 -0.4047
0.6606 -0.5343 -0.5198 -0.5044 -0.4881 -0.4710 -0.4530 -0.4342 -0.4145
0.6306 -0.5439 -0.5293 -0.5139 -0.4976 -0.4805 -0.4624 -0.4436 -0.4239
0.6006 -0.5530 -0.5384 -0.5230 -0.5067 -0.4895 -0.4715 -0.4526 -0.4328
0.5706 -0.5617 -0.5471 -0.5317 -0.5153 -0.4981 -0.4801 -0.4612 -0.4414
0.5406 -0.5700 -0.5554 -0.5399 -0.5236 -0.5064 -0.4883 -0.4693 -0.4495
0.5106 -0.5779 -0.5633 -0.5478 -0.5314 -0.5142 -0.4960 -0.4771 -0.4572
O.4806 -0.5854 -0.5708 -0.5553 -0.5389 -0.5216 -0.5034 -0.4844 -0.4645
0.4506 -0.5925 -0.5779 -0.5623 -0.5459 -0.5286 -0.5104 -0.4913 -0.4714
0.4206 -0.5992 -0.5845 -0.5690 -0.5525 -0.5352 -0.5170 -0.4979 -0.4779
0.3906 -0.6055 -0.5908 -0.5752 -0.5587 -0.5414 -0.5231 -0.5040 -0.4840
0.3606 -0.6114 -0.5967 -0.5811 -0.5645 -0.5471 -0.5289 -0.5097 -0.4897
0.3306 -0.6169 -0.6021 -0.5865 -0.5700 -0.5525 -0.5342 -0.5150 -0.4950
0.3006 -0.6220 -0.6072 -0.5915 -0.5750 -0.5575 -0.5392 -0.5200 -0.4999
0.2706 -0.6267 -0.6119 -0.5962 -0.5796 -0.5621 -0.5437 -0.5245 -0.5044
Table 1: values of y as a function of x and z. Plate 3 of 4.

Values Values of x
de z 1.0800 1.1250 1.1700 1.2150 1.2600 1.3050 1.3500 1.3950
1.8606 0.4101 0.4359 0.4628 0.4908 0.5197 0.5494 0.5801 0.6113
1.8306 0.3767 0.4022 0.4287 0.4562 0.4846 0.5139 0.5440 0.5747
1.8006 0.3443 0.3694 0.3956 0.4226 0.4506 0.4794 0.5090 0.5392
1.7706 0.3128 0.3376 0.3634 0.3900 0.4176 0.4460 0.4751 0.5049
1.7406 0.2821 0.3066 0.3320 0.3584 0.3856 0.4135 0.4423 0.4715
1.7106 0.2523 0.2765 0.3016 0.3276 0.3545 0.3821 0.4104 0.4392
1.6806 0.2233 0.2472 0.2720 0.2977 0.3242 0.3515 0.3794 0.4079
1.6506 0.1951 0.2187 0.2433 0.2687 0.2948 0.3218 0.3494 0.3775
1.6206 0.1676 0.1910 0.2153 0.2404 0.2663 0.2929 0.3202 0.3480
1.5906 0.1409 0.1640 0.1881 0.2129 0.2386 0.2649 0.2919 0.3193
1.5606 0.1148 0.1378 0.1616 0.1862 0.2116 0.2377 0.2643 0.2915
1.5306 0.0895 0.1122 0.1358 0.1602 0.1854 0.2112 0.2376 0.2645
1.5006 0.0648 0.0874 0.1108 0.1350 0.1599 0.1855 0.2117 0.2384
1.4706 0.0408 0.0632 0.0865 0.1104 0.1352 0.1605 0.1865 0.2129
1.4406 0.0175 0.0397 0.0628 0.0866 0.1111 0.1363 0.1621 0.1883
1.4106 -0.0052 0.0169 0.0398 0.0634 0.0878 0.1128 0.1383 0.1643
1.3806 -0.0273 -0.0053 0.0174 0.0409 0.0651 0.0899 0.1153 0.1411
1.3506 -0.0488 -0.0270 -0.0043 0.0190 0.0431 0.0677 0.0930 0.1187
1.3206 -0.0697 -0.0480 -0.0255 -0.0022 0.0217 0.0462 0.0713 0.0968
1.2906 -0.0899 -0.0683 -0.0460 -0.0229 0.0009 0.0253 0.0503 0.0757
1.2606 -0.1097 -0.0881 -0.0659 -0.0429 -0.0192 0.0051 0.0300 0.0553
1.2306 -0.1288 -0.1074 -0.0852 -0.0623 -0.0387 -0.0145 0.0103 0.0355
1.2006 -0.1474 -0.1260 -0.1039 -0.0811 -0.0576 -0.0335 -0.0088 0.0163
1.1706 -0.1654 -0.1441 -0.1221 -0.0993 -0.0759 -0.0518 -0.0272 -0.0022
1.1406 -0.1829 -0.1616 -0.1397 -0.1170 -0.0936 -0.0696 -0.0451 -0.0201
1.1106 -0.1998 -0.1786 -0.1567 -0.1340 -0.1107 -0.0868 -0.0623 -0.0373
1.0806 -0.2162 -0.1951 -0.1732 -0.15b5 -0.1273 -0.1033 -0.0789 -0.0540
1.0506 -0.2321 -0.2109 -0.1891 -0.1665 -0.1432 -0.1193 -0.0949 -0.0700
1.0206 -0.2474 -0.2263 -0.2045 -0.1819 -0.1587 -0.1348 -0.1103 -0.0855
0.9906 -0.2622 -0.2411 -0.2193 -0.1968 -0.1735 -0.1496 -0.1252 -0.1003
0.9606 -0.2765 -0.2555 -0.2336 -0.2111 -0.1878 -0.1639 -0.1395 -0.1145
0.9306 -0.2904 -0.2693 -0.2474 -0.2249 -0.2016 -0.1777 -0.1532 -0.1282
0.9006 -0.3037 -0.2826 -0.2607 -0.2381 -0.2148 -0.1909 -0.1664 -0.1413
0.8706 -0.3165 -0.2954 -0.2735 -0.2509 -0.2276 -0.2036 -0.1790 -0.1539
0.8406 -0.3289 -0.3078 -0.2859 -0.2632 -0.2398 -0.2158 -0.1912 -0.1661
0.8106 -0.3409 -0.3197 -0.2978 -0.2751 -0.2517 -0.2276 -0.2029 -0.1777
0.7806 -0.3524 -0.3312 -0.3092 -0.2865 -0.2630 -0.2389 -0.2142 -0.1889
0.7506 -0.3634 -0.3422 -0.3202 -0.2974 -0.2739 -0.2498 -0.2250 -0.1997
0.7206 -0.3740 -0.3528 -0.3308 -0.3080 -0.2844 -0.2602 -0.2353 -0.2099
0.6906 -0.3842 -0.3630 -0.3409 -0.3180 -0.2944 -0.2702 -0.2452 -0.2198
0.6606 -0.3940 -0.3727 -0.3506 -0.3277 -0.3040 -0.2797 -0.2547 -0.2291
0.6306 -0.4033 -0.3820 -0.3598 -0.3369 -0.3132 -0.2888 -0.2637 -0.2381
0.6006 -0.4123 -0.3909 -0.3687 -0.3457 -0.3219 -0.2975 -0.2723 -0.2466
0.5706 -0.4208 -0.3993 -0.3771 -0.3540 -0.3302 -0.3057 -0.2805 -0.2547
0.5406 -0.4289 -0.4074 -0.3851 -0.3620 -0.3381 -0.3135 -0.2883 -0.2624
0.5106 -0.4365 -0.4150 -0.3927 -0.3695 -0.3456 -0.3209 -0.2956 -0.2696
0.4806 -0.4438 -0.4222 -0.3998 -0.3766 -0.3527 -0.3279 -0.3025 -0.2765
0.4506 -0.4507 -0.4290 -0.4066 -0.3833 -0.3593 -0.3345 -0.3090 -0.2829
0.A206 -0.4571 -0.4354 -0.4130 -0.3897 -0.3656 -4.3407 -0.3152 -0.2890
0.s306 -0.4632 -0.4415 -0.4189 -0.3956 -0.3714 -0.3465 -0.3209 -0.2946
0.3606 -0.4688 -0.4471 -0.4245 -0.4011 -0.3769 -0.3519 -0.3262 -0.2998
0.3306 -0.4740 -0.4523 -0.4296 -0.4062 -0.3819 -0.3569 -0.3311 -0.3047
0.3006 -0.4789 -0.4571 -0.4344 -0.4109 -0.3866 -0.3615 -0.3357 -0.3092
0.2706 -0.4834 -0.4615 -0.4388 -0.4152 -0.3909 -0.3657 -0.3399 -0.3133
Table 1: values of y as a function of x and z. Plate 4 of 4.

Values Values of x
of z 0.0000 0.0450 0.0900 0.1350 0.1800 0.2250 0.2700 0.3150
1.8268 -0.1641 -0.1633 -0.1611 -0.1575 -0.1524 -0.1459 -0.1379 -0.1283
1.7968 -0.1862 -0.1854 -0.1832 -0.1796 -0.1746 -0.1681 -0.1602 -0.1507
1.7668 -0.2078 -0.2070 -0.2048 -0.2013 -0.1963 -0.1899 -0.1820 -0.1726
1.7368 -0.2289 -0.2281 -0.2259 -0.2224 -0.2175 -0.2111 -0.2033 -0.1940
1.7068 -0.2495 -0.2487 -0.2466 -0.2431 -0.2382 -0.2319 -0.2241 -0.2149
1.6768 -0.2697 -0.2689 -0.2668 -0.2633 -0.2585 -0.2522 -0.2445 -0.2354
1.6468 -0.2894 -0.2887 -0.2866 -0.2831 -0.2783 -0.2721 -0.2644 -0.2554
1.6168 -0.3087 -0.3080 -0.3059 -0.3025 -0.2977 -0.2915 -0.2839 -0.2749
1.5868 -0.3276 -0.3268 -0.3248 -0.3214 -0.3166 -0.3105 -0.3029 -0.2940
1.5568 -0.3460 -0.3453 -0.3432 -0.3399 -0.3351 -0.3290 -0.3215 -0.3127
1.5268 -0.3640 -0.3633 -0.3613 -0.3579 -0.3532 -0.3472 -0.3397 -0.3309
1.4968 -0.3817 -0.3809 -0.3789 -0.3756 -0.3709 -0.3649 -0.3575 -0.3487
1.4668 -0.3989 -0.3981 -0.3961 -0.3928 -0.3881 -0.3822 -0.3748 -0.3661
1.4368 -0.4157 -0.4149 -0.4129 -0.4096 -0.4050 -0.3990 -0.3917 -0.3831
1.4068 -0.4321 -0.4313 -0.4293 -0.4261 -0.4215 -0.4155 -0.4083 -0.3996
1.3768 -0.4481 -0.4473 -0.4454 -0.4421 -0.4375 -0.4316 -0.4244 -0.4158
1.3468 -0.4637 -0.4630 -0.4610 -0.4578 -0.4532 -0.4474 -0.4402 -0.4316
1.3168 -0.4790 -0.4782 -0.4763 -0.4730 -0.4685 -0.4627 -0.4555 -0.4470
1.2868 -0.4938 -0.4931 -0.4912 -0.4880 -0.4834 -0.4776 -0.4705 -0.4620
1.2568 -0.5083 -0.5076 -0.5057 -0.5025 -0.4980 -0.4922 -0.4851 -0.4767
1.2268 -0.5225 -0.5218 -0.5198 -0.5166 -0.5122 -0.5064 -0.4993 -0.4909
1.1968 -0.5363 -0.5355 -0.5336 -0.5304 -0.5260 -0.5202 -0.5132 -0.5048
1.1668 -0.5497 -0.5490 -0.5471 -0.5439 -0.5395 -0.5337 -0.5267 -0.5184
1.1368 -0.5627 -0.5620 -0.5601 -0.5570 -0.5526 -0.5468 -0.5398 -0.5315
1.1068 -0.5755 -0.5748 -0.5729 -0.5697 -0.5653 -0.5596 -0.5526 -0.5443
1.0768 -0.5878 -0.5871 -0.5852 -0.5821 -0.5777 -0.5720 -0.5651 -0.5568
1.0468 -0.5999 -0.5992 -0.5973 -0.5941 -0.5898 -0.5841 -0.5772 -0.5689
1.0168 -0.6115 -0.6109 -0.6090 -0.6058 -0.6015 -0.5958 -0.5889 -0.5807
0.9868 -0.6229 -0.6222 -0.6203 -0.6172 -0.6128 -0.6072 -0.6003 -0.5921
0.9568 -0.6339 -0.6332 -0.6314 -0.6283 -0.6239 -0.6183 -0.6114 -0.6032
0.9268 -0.6447 -0.6440 -0.6421 -0.6390 -0.6346 -0.6290 -0.6222 -0.6140
0.8968 -0.6550 -0.6543 -0.6524 -0.6493 -0.6450 -0.6394 -0.6325 -0.6243
0.8668 -0.6650 -0.6643 -0.6624 -0.6593 -0.6550 -0.6494 -0.6425 -0.6344
0.8368 -0.6746 -0.6739 -0.6721 -0.6690 -0.6647 -0.6591 -0.6522 -0.6441
0.8068 -0.6840 -0.6833 -0.6815 -0.6784 -0.6740 -0.6685 -0.6616 -0.6535
0.7768 -0.6930 -0.6924 -0.6905 -0.6874 -0.6831 -0.6775 -0.6707 -0.6626
0.7468 -0.7018 -0.7011 -0.6992 -0.6961 -0.6918 -0.6863 -0.6794 -0.6713
0.7168 -0.7102 -0.7095 -0.7076 -0.7046 -0.7002 -0.6947 -0.6879 -0.6798
0.6868 -0.7183 -0.7176 -0.7157 -0.7126 -0.7083 -0.7028 -0.6960 -0.6879
0.6568 -0.7260 -0.7254 -0.7235 -0.7204 -0.7161 -0.7106 -0.7037 -0.6956
0.6268 -0.7335 -0.7328 -0.7310 -0.7279 -0.7236 -0.7180 -0.7112 -0.7031
0.5968 -0.7406 -0.7400 -0.7381 -0.7350 -0.7307 -0.7252 -0.7183 -0.7103
0.5668 -0.7475 -0.7468 -0.7449 -0.7419 -0.7375 -0.7320 -0.7252 -0.7171
0.5368 -0.7540 -0.7533 -0.7515 -0.7484 -0.7441 -0.7385 -0.7317 -0.7236
0.5068 -0.7602 -0.7595 -0.7577 -0.7546 -0.7503 -0.7447 -0.7379 -0.7298
0.4768 -0.7661 -0.7654 -0.7636 -0.7605 -0.7562 -0.7506 -0.7438 -0.7357
0.4468 -0.7717 -0.7710 -0.7692 -0.7661 -0.7617 -0.7562 -0.7493 -0.7412
0.4168 -0.7770 -0.7763 -0.7744 -0.7713 -0.7670 -O.'ïL4 -0.7546 -0.7465
0.3868 -0.7820 -0.7813 -0.7794 -0.7763 -0.7720 -0.7664 -0.7595 -0.7514
0.3568 -0.7866 -0.7859 -0.7841 -0.7810 -0.7766 -0.7710 -0.7642 -0.7560
0.3268 -0.7910 -0.7903 -0.7884 -0.7853 -0.7810 -0.7754 -0.7685 -0.7603
0.2968 -0.7950 -0.7943 -0.7925 -0.7894 -0.7850 -0.7794 -0.7725 -0.7643
0.2668 -0.7988 -0.7981 -0.7962 -0.7931 -0.7887 -0.7831 -0.7762 -0.7680
0.2368 -0.8022 -0.8015 -0.7996 -0.7965 -0.7921 -0.7865 -0.7796 -0.7714
Table 2: values of y as a function of x and z. Plate 1 of 4.

Values Values of X
de z 0.3600 0.4050 0.4500 0.4950 0.5400 0.5850 0.6300 0.6750
1.8268 -0.1172 -0.1046 -0.0903 -0.0743 -0.0567 -0.0373 -0.0161 0.0070
1.7968 -0.1397 -0.1272 -0.1130 -0.0973 -0.0798 -0.0606 -0.0396 -0.0167
1.7668 -0.1617 -0.1493 -0.1353 -0.1196 -0.1023 -0.0833 -0.0625 -0.0399
1.7368 -0.1832 -0.1709 -0.1570 -0.1415 -0.1244 -0.1055 -0.0849 -0.0625
1.7068 -0.2042 -0.1920 -0.1782 -0.1629 -0.1459 -0.1272 -0.1068 -0.0845
1.6768 -0.2247 -0.2126 -0.1990 -0.1837 -0.1669 -0.1484 -0.1281 -0.1061
1.6468 -0.2448 -0.2328 -0.2193 -0.2041 -0.1874 -0.1690 -0.1490 -0.1271
1.6168 -0.2644 -0.2525 -0.2391 -0.2241 -0.2075 -0.1892 -0.1693 -0.1476
1.5868 -0.2836 -0.2717 -0.2584 -0.2435 -0.2270 -0.2090 -0.1892 -0.1677
1.5568 -0.3023 -0.2906 -0.2773 -0.2625 -0.2462 -0.2282 -0.2086 -0.1873
1.5268 -0.3206 -0.3089 -0.2958 -0.2811 -0.2649 -0.2470 -0.2275 -0.2063
1.4968 -0.3385 -0.3269 -0.3138 -0.2992 -0.2831 -0.2653 -0.2460 -0.2249
1.4668 -0.3559 -0.3444 -0.3314 -0.3169 -0.3009 -0.2832 -0.2640 -0.2431
1.4368 -0.3730 -0.3615 -0.3486 -0.3341 -0.3182 -0.3007 -0.2816 -0.2608
1.4068 -0.3896 -0.3782 -0.3653 -0.3510 -0.3352 -0.3177 -0.2988 -0.2781
1.3768 -0.4059 -0.3945 -0.3817 -0.3674 -0.3517 -0.3344 -0.3155 -0.2949
1.3468 -0.4217 -0.4104 -0.3977 -0.3835 -0.3678 -0.3506 -0.3318 -0.3113
1.3168 -0.4371 -0.4259 -0.4132 -0.3991 -0.3835 -0.3664 -0.3476 -0.3273
1.2868 -0.4522 -0.4410 -0.4284 -0.4143 -0.3988 -0.3817 -0.3631 -0.3429
1.2568 -0.4669 -0.4557 -0.4432 -0.4292 -0.4137 -0.3967 -0.3782 -0.3581
1.2268 -0.4812 -0.4701 -0.4576 -0.4436 -0.4282 -0.4113 -0.3929 -0.3728
1.1968 -0.4951 -0.4840 -0.4716 -0.4577 -0.4424 -0.4255 -0.4072 -0.3872
1.1668 -0.5087 -0.4977 -0.4852 -0.4714 -0.4561 -0.4394 -0.4211 -0.4012
1.1368 -0.5219 -0.5109 -0.4985 -0.4847 -0.4695 -0.4528 -0.4346 -0.4148
1.1068 -0.5347 -0.5238 -0.5114 -0.4977 -0.4825 -0.4659 -0.4477 -0.4280
1.0768 -0.5472 -0.5363 -0.5240 -0.5103 -0.4952 -0.4786 -0.4605 -0.4408
1.0468 -0.5594 -0.5485 -0.5362 -0.5225 -0.5075 -0.4909 -0.4728 -0.4532
1.0168 -0.5711 -0.5603 -0.5481 -0.5344 -0.5194 -0.5029 -0.4849 -0.4653
0.9868 -0.5826 -0.5718 -0.5596 -0.5460 -0.5310 -0.5145 -0.4965 -0.4770
0.9568 -0.5937 -0.5829 -0.5707 -0.5572 -0.5422 -0.5258 -0.5078 -0.4884
0.9268 -0.6045 -0.5937 -0.5816 -0.5681 -0.5531 -0.5367 -0.5188 -0.4994
0.8968 -0.6149 -0.6041 -0.5920 -0.5785 -0.5636 -0.5472 -0.5294 -0.5100
0.8668 -0.6249 -0.6142 -0.6021 -0.5886 -0.5737 -0.5574 -0.5396 -0.5202
0.8368 -0.6347 -0.6239 -0.6119 -0.5984 -0.5835 -0.5672 -0.5494 -0.5301
0.8068 -0.6441 -0.6334 -0.6213 -0.6078 -0.5930 -0.5767 -0.5589 -0.5396
0.7768 -0.6532 -0.6425 -0.6304 -0.6170 -0.6021 -0.5859 -0.5681 -0.5489
0.7468 -0.6619 -0.6512 -0.6392 -0.6258 -0.6109 -0.5947 -0.5770 -0.5577
0.7168 -0.6704 -0.6597 -0.6476 -0.6342 -0.6194 -0.6032 -0.5855 -0.5662
0.6868 -0.6785 -0.6678 -0.6557 -0.6423 -0.6276 -0.6113 -0.5936 -0.5744
0.6568 -0.6863 -0.6756 -0.6635 -0.6501 -0.6354 -0.6191 -0.6014 -0.5822
0.6268 -0.6937 -0.6830 -0.6710 -0.6576 -0.6428 -0.6266 -0.6089 -0.5897
0.5968 -0.7009 -0.6902 -0.6782 -0.6648 -0.6500 -0.6338 -0.6161 -0.5968
0.5668 -0.7077 -0.6970 -0.6850 -0.6716 -0.6568 -0.6406 -0.6229 -0.6037
0.5368 -0.7142 -0.7035 -0.6915 -0.6781 -0.6633 -0.6470 -0.6293 -0.6101
0.5068 -0.7204 -0.7097 -0.6976 -0.6842 -0.6694 -0.6532 -0.6355 -0.6162
0.4768 -0.7263 -0.7155 -0.7035 -0.6901 -0.6753 -0.6590 -0.6413 -0.6220
0.4468 -0.7318 -0.7211 -0.7090 -0.6956 -0.6808 -0.6645 -0.6468 -o.6275
0.4168 -0.7371 -0.7263 -0.7142 -0.7008 -0.6860 -0.6697 -0.6519 -0.6326
0.3868 -0.7420 -0.7312 -0.7191 -0.7057 -0.6908 -0.6745 -0.6567 -0.6374
0.3568 -0.7466 -0.7358 -0.7237 -0.7102 -0.6953 -0.6790 -0.6612 -0.6419
0.3268 -0.7509 -0.7401 -0.7280 -0.7145 -0.6995 -0.6832 -0.6654 -0.6460
0.2968 -0.7548 -0.7440 -0.7319 -0.7184 -0.7034 -0.6870 -0.6692 -0.6498
0.2668 -0.7585 -0.7477 -0.7355 -0.7220 -0.7070 -0.6906 -0.6727 -0.6532
0.2368 -0.7618 -0.7510 -0.7388 -0.7252 -0.7102 -0.6938 -0.6758 -0.6563
Table 2: values of y as a function of x and z. Plate 2 of 4.

Values Values of x
de z 0.7200 0.7650 0.8100 0.8550 0.9000 0.9450 0.9900 1.0350
1.8268 0.0322 0.0594 0.0888 0.1205 0.1547 0.1915 0.2311 0.2738
1.7968 0.0082 0.0350 0.0642 0.0955 0.1292 0.1657 0.2048 0.2469
1.7668 -0.0152 0.0114 0.0402 0.0712 0.1046 0.1406 0.1792 0.2208
1.7368 -0.0381 -0.0117 0.0168 0.0475 0.0805 0.1161 0.1543 0.1954
1.7068 -0.0604 -0.0343 -0.0061 0.0243 0.0571 0.0922 0.1301 0.1707
1.6768 -0.0822 -0.0563 -0.0283 0.0017 0.0341 0.0690 0.1064 0.1466
1.6468 -0.1034 -0.0778 -0.0500 -0.0202 0.0118 0.0464 0.0834 0.1232
1.6168 -0.1241 -0.0987 -0.0712 -0.0417 -0.0099 0.0243 0.0610 0.1004
1.5868 -0.1443 -0.1191 -0.0919 -0.0626 -0.0310 0.0028 0.0392 0.0783
1.5568 -0.1641 -0.1391 -0.1120 -0.0830 -0.0517 -0.0181 0.0179 0.0566
1.5268 -0.1833 -0.1585 -0.1317 -0.1028 -0.0718 -0.0385 -0.0028 0.0356
1.4968 -0.2021 -0.1774 -0.1508 -0.1222 -0.0914 -0.0583 -0.0229 0.0152
1.4668 -0.2204 -0.1959 -0.1695 -0.1410 -0.1105 -0.0777 -0.0425 -0.0047
1.4368 -0.2383 -0.2139 -0.1876 -0.1594 -0.1291 -0.0965 -0.0615 -0.0241
1.4068 -0.2557 -0.2315 -0.2054 -0.1773 -0.1472 -0.1148 -0.0802 -0.0429
1.3768 -0.2726 -0.2486 -0.2226 -0.1948 -0.1648 -0.1327 -0.0982 -0.0612
1.3468 -0.2892 -0.2653 -0.2395 -0.2117 -0.1820 -0.1500 -0.1158 -0.0791
1.3168 -0.3053 -0.2815 -0.2558 -0.2283 -0.1987 -0.1669 -0.1329 -0.0964
1.2868 -0.3210 -0.2973 -0.2718 -0.2444 -0.2149 -0.1833 -0.1495 -0.1132
1.2568 -0.3362 -0.3127 -0.2873 -0.2600 -0.2307 -0.1993 -0.1657 -0.1296
1.2268 -0.3511 -0.3276 -0.3024 -0.2752 -0.2461 -0.2148 -0.1813 -0.1455
1.1968 -0.3656 -0.3422 -0.3170 -0.2900 -0.2610 -0.2299 -0.1966 -0.1609
1.1668 -0.3796 -0.3564 -0.3313 -0.3044 -0.2755 -0.2445 -0.2114 -0.1759
1.1368 -0.3933 -0.3701 -0.3452 -0.3184 -0.2896 -0.2588 -0.2257 -0.1904
1.1068 -0.4066 -0.3835 -0.3586 -0.3319 -0.3033 -0.2725 -0.2397 -0.2044
1.0768 -0.4195 -0.3964 -0.3717 -0.3451 -0.3165 -0.2859 -0.2532 -0.2181
1.0468 -0.4320 -0.4090 -0.3843 -0.3578 -0.3294 -0.2989 -0.2662 -0.2313
1.0168 -0.4441 -0.4213 -0.3966 -0.3702 -0.3418 -0.3114 -0.2789 -0.2441
0.9868 -0.4559 -0.4331 -0.4085 -0.3822 -0.3539 -0.3236 -0.2912 -0.2565
0.9568 -0.4673 -0.4446 -0.4201 -0.3938 -0.3656 -0.3354 -0.3030 -0.2684
0.9268 -0.4784 -0.4557 -0.4313 -0.4050 -0.3769 -0.3468 -0.3145 -0.2800
0.8968 -0.4890 -0.4664 -0.4420 -0.4158 -0.3878 -0.3577 -0.3255 -0.2911
0.8668 -0.4993 -0.4767 -0.4523 -0.4262 -0.3982 -0.3682 -0.3361 -0.3018
0.8368 -0.5092 -0.4866 -0.4623 -0.4363 -0.4083 -0.3784 -0.3463 -0.3121
0.8068 -0.5188 -0.4962 -0.4720 -0.4460 -0.4180 -0.3882 -0.3562 -0.3220
0.7768 -0.5280 -0.5055 -0.4813 -0.4553 -0.4274 -0.3976 -0.3656 -0.3315
0.7468 -0.5369 -0.5144 -0.4902 -0.4642 -0.4364 -0.4066 -0.3747 -0.3406
0.7168 -0.5454 -0.5229 -0.4988 -0.4728 -0.4450 -0.4153 -0.3834 -0.3494
0.6868 -0.5536 -0.5311 -0.5070 -0.4811 -0.4533 -0.4235 -0.3917 -0.3577
0.6568 -0.5614 -0.5390 -0.5149 -0.4890 -0.4612 -0.4315 -0.3997 -0.3657
0.6268 -0.5689 -0.5465 -0.5224 -0.4965 -0.4687 -0.4390 -0.4072 -0.3732
0.5968 -0.5761 -0.5536 -0.5295 -0.5036 -0.4759 -0.4462 -0.4144 -0.3804
0.5668 -0.5829 -0.5604 -0.5363 -0.5104 -0.4827 -0.4530 -0.4212 -0.3872
0.5368 -0.5893 -0.5669 -0.5428 -0.5169 -0.4891 -0.4594 -0.4276 -0.3937
0.5068 -0.5954 -0.5730 -0.5489 -0.5230 -0.4952 -0.4655 -0.4337 -0.3997
0.4768 -0.6012 -0.5788 -0.5546 -0.5287 -0.5009 -0.4712 -0.4394 -0.4054
0.4468 -0.6067 -0.5842 -0.5600 -0.5341 -0.5063 -0.4765 -0.4447 -0.4107
0.4168 -0.6118 -0.5893 -0.5651 -0.5391 -0.5113 -0.4815 -0.4496 -0.4156
0.3868 -0.6165 -0.5940 -0.5698 -0.5438 -0.5159 -0.4861 -0.4542 -0.4201
0.3568 -0.6209 -0.5984 -0.5741 -0.5481 -0.5202 -0.4903 -0.4584 -0.4242
0.3268 -0.6250-0.6024 -0.5781 -0.5520 -0.5241 -0.4942 -0.4622 -0.4280
0.2968 -0.6288 -0.6061 -0.5818 -0.5556 -0.5276 -0.4977 -0.4656 -0.4314
0.2668 -0.6322 -0.6095 -0.5851 -0.5589 -0.5308 -0.5008 -0.4687 -0.4344
0.2368 -0.6352 -0.6125 -0.5880 -0.5618 -0.5336 -0.5036 -0.4714 -0.4370
Table 2: values of y as a function of x and z. Plate 3 of 4.

Values Values of x
de z 1.0800 1.1250 1.1700 1.2150 1.2600 1.3050 1.3500 1.3950
1.8268 0.3197 0.3690 0.4222 0.4796 0.5414 0.6081 0.6800 0.7576
1.7968 0.2921 0.3408 0.3934 0.4498 0.5108 0.5764 0.6471 0.7236
1.7668 0.2655 0.3135 0.3654 0.4210 0.4812 0.5458 0.6155 0.6908
1.7368 0.2396 0.2871 0.3382 0.3932 0.4525 0.5163 0.5850 0.6592
1.7068 0.2144 0.2613 0.3118 0.3661 0.4246 0.4876 0.5554 0.6285
1.6768 0.1898 0.2361 0.2861 0.3397 0.3975 0.4596 0.5265 0.5988
1.6468 0.1659 0.2118 0.2612 0.3142 0.3713 0.4327 0.4988 0.5701
1.6168 0.1427 0.1881 0.2370 0.2894 0.3459 0.4066 0.4719 0.5424
1.5868 0.1201 0.1651 0.2134 0.2654 0.3212 0.3813 0.4459 0.5155
1.5568 0.0981 0.1426 0.1905 0.2419 0.2972 0.3566 0.4204 0.4894
1.5268 0.0767 0.1209 0.1683 0.2192 0.2739 0.3327 0.3960 0.4642
1.4968 0.0560 0.0997 0.1467 0.1971 0.2514 0.3096 0.3723 0.4397
1.4668 0.0358 0.0791 0.1257 0.1757 0.2295 0.2872 0.3493 0.4161
1.4368 0.0161 0.0592 0.1054 0.1549 0.2082 0.2654 0.3270 0.3932
1.4068 -0.0031 0.0396 0.0855 0.1346 0.1875 0.2442 0.3052 0.3709
1.3768 -0.0217 0.0207 0.0663 0.1150 0.1675 0.2237 0.2842 0.3494
1.3468 -0.0397 0.0024 0.0476 0.0960 0.1480 0.2039 0.2639 0.3285
1.3168 -0.0573 -0.0154 0.0294 0.0775 0.1292 0.1846 0.2442 0.3083
1.2868 -0.0744 -0.0328 0.0118 0.0595 0.1109 0.1659 0.2250 0.2887
1.2568 -0.0910 -0.0497 -0.0053 0.0422 0.0932 0.1478 0.2066 0.2698
1.2268 -0.1071 -0.0660 -0.0219 0.0253 0.0760 0.1303 0.1887 0.2515
1.1968 -0.1227 -0.0818 -0.0380 0.0090 0.0593 0.1134 0.1714 0.2338
1.1668 -0.1379 -0.0972 -0.0536 -0.0069 0.0432 0.0969 0.1546 0.2166
1.1368 -0.1525 -0.1121 -0.0687 -0.0222 0.0276 0.0810 0.1384 0.2001
1.1068 -0.1668 -0.1265 -0.0833 -0.0371 0.0125 0.0657 0.1227 0.1841
1.0768 -0.1806 -0.1404 -0.0974 -0.0514 -0.0021 0.0508 0.1076 0.1687
1.0468 -0.1939 -0.1539 -0.1111 -0.0653 -0.0162 0.0365 0.0930 0.1538
1.0168 -0.2069 -0.1670 -0.1244 -0.0788 -0.0298 0.0226 0.0789 0.1394
0.9868 -0.2194 -0.1797 -0.1372 -0.0917 -0.0430 0.0093 0.0653 0.1256
0.9568 -0.2314 -0.1919 -0.1495 -0.1042 -0.0557 -0.0036 0.0522 0.1122
0.9268 -0.2432 -0.2037 -0.1615 -0.1164 -0.0680 -0.0161 0.0395 0.0993
0.8968 -0.2543 -0.2150 -0.1729 -0.1279 -0.0796 -0.0279 0.0275 0.0871
0.8668 -0.2651 -0.2258 -0.1839 -0.1390 -0.0908 -0.0393 0.0160 0.0754
0.8368 -0.2754 -0.2363 -0.1944 -0.1496 -0.1016 -0.0502 0.0049 0.0641
0.8068 -0.2854 -0.2464 -0.2046 -0.1599 -0.1120 -0.0607 -0.0057 0.0533
0.7768 -0.2950 -0.2560 -0.2143 -0.1697 -0.1219 -0.0708 -0.0159 0.0430
0.7468 -0.3042 -0.2653 -0.2236 -0.1791 -0.1314 -0.0804 -0.0256 0.0331
0.7168 -0.3130 -0.2741 -0.2325 -0.1881 -0.1405 -0.0895 -0.0349 0.0238
0.6868 -0.3214 -0.2825 -0.2410 -0.1966 -0.1491 -0.0982 -0.0436 0.0149
0.6568 -0.3294 -0.2905 -0.2491 -0.2047 -0.1573 -0.1064 -0.0520 0.0065
0.6268 -0.3370 -0.2982 -0.2567 -0.2124 -0.1650 -0.1142 -0.0598 -0.0015
0.5968 -0.3442 -0.3054 -0.2640 -0.2197 -0.1723 -0.1216 -0.0672 -0.0089
0.5668 -0.3510 -0.3122 -0.2708 -0.2266 -0.1792 -0.1285 -0.0742 -0.0160
0.5368 -0.3574 -0.3187 -0.2772 -0.2330 -0.1857 -0.1350 -0.0807 -0.0225
0.5068 -0.3634 -0.3247 -0.2833 -0.2390 -0.1917 -0.1410 -0.0868 -0.0286
0.4768 -0.3691 -0.3303 -0.2889 -0.2446 -0.1973 -0.1466 -0.0924 -0.0342
0.4468 -0.3743 -0.3356 -0.2941 -0.2498 -0.2025 -0.1518 -0.0975 -0.0394
0.4168 -0.3792 -0.3404 -0.2989 -0.2546 -0.2072 -0.1565 -0.1023 -0.0441
0.3868 -0.3837 -0.3448 -0.3033 -0.2590 -0.2116 -0.1608 -0.1065 -0.0483
0.3568 -0.3878 -0.3489 -0.3073 -0.2629 -0.2155 -0.1647 -0.1103 -0.0521
0.3268 -0.3915 -0.3525 -0.3109 -0.2664 -0.2189 -0.1681 -0.1137 -0.0554
0.2968 -0.3948 -0.3558 -0.3141 -0.2696 -0.2220 -0.1711 -0.1166 -0.0583
0.2668 -0.3978 -0.3586 -0.3169 -0.2723 -0.2246 -0.1736 -0.1191 -0.0607
0.2368 -0.4003 -0.3611 -0.3192 -0.2745 -0.2268 -0.1757 -0.1210 -0.0626
Table 2: values of y as a function of x and z. Plate 4 of 4.

 --- BIBLIOGRAPHY "Treaty of special mathematics" by G. Cagnac, E. Ramis, J Commeau in particular volume 2, "Analysis". Publisher Masson et Cie, France, 1967.

--- TECHNICAL ANNEX -
Computer simulation showing what the observer sees by looking at the mirror according to Tables 1 and 2, when he moves in the observation area.

Claims (25)

--- CLAIMS - 1) Device for enlarging television or similar images, characterized in that it comprises a mirror (3) of concave nature, directed towards an observer (5), and producing an enlarged image (4) of the screen (2) of a television set (1). 2) Device according to claim 1, characterized in that it further comprises an auxiliary mirror (13, 26) directed both towards the screen (12, 22) and towards the main mirror (14, 24). 3) Device according to claim 1, characterized in that it further comprises an auxiliary optical device such as lens (133) etlou prism placed between the screen (132) and the mirror (134). 4) Device according to claim 1, characterized in that the screen (2) of the television (1) is directed on the side opposite to that of the observer (5) relative to the television (1). 5) Device according to claim 1, characterized in that the screen (2) of the television (1) is further arranged so that the upper part of the image is located lower in space than the lower part of the image, that is to say that the television is placed "upside down". 6) Device according to claim 2, characterized in that - the screen (12) is in a conventional vertical position, and directed towards the observer (17); - The auxiliary mirror (13) is arranged between the screen (12) and the observer (17). 7) Device according to claim 2, characterized in that - the screen (22) of the television (21) is directed on the side opposite to that of the observer (23) relative to the television (21) - the screen (22 ) is placed between the auxiliary mirror (26) and the observer (23). 8) Device according to claim 1, characterized in that the television set (1) is provided with a switch (10) making it possible to reverse the direction of scanning "lines" to reverse in the left-right direction the image produced by the screen (2). 9) Device according to claim 1, characterized in that the television set (I) is provided with a switch (10) making it possible to reverse the direction of scanning "lines * and that of scanning" fields "to reverse in the left-right direction and in the up-down direction the image produced by the screen (2). 10) Device according to claim 1, characterized in that the enlargement produced by the mirror (3) is greater in the horizontal direction than in the vertical direction, in order to achieve a desanamorphosis of an anamorphic image provided by the screen (2). 11) Device according to claim 2, characterized in that the enlargement produced by the auxiliary mirror (13, 26) is greater in the horizontal direction than in the vertical direction, in order to achieve a de-anamorphosis of an anamorphic image provided by the screen (12, 22). 12) Device according to claim 3, characterized in that the enlargement produced by the auxiliary lens (133) is greater in the horizontal direction than in the vertical direction, in order to achieve a de-anamorphosis of an anamorphic image provided by the screen (132). 13) Device according to claim 1, characterized in that it comprises an apparatus (6) processing the video signal before this signal reaches the power video amplifier stages of the television set (1), so as to apply to the image supplied by the screen (2) has a left-right symmetry. 14) Device according to claim 13, characterized in that the apparatus (6) comprises a synchronization separator (81) sending its information as an output to a control unit (83) which controls - a synchronization generator (116), - a reference signal generator (117), - switches (91, 96, 104, 108) which make it possible to introduce and read information alternately in different memories (100, 101, 102, 103) the chrominance signals, of luminance and synchronization being finally mixed by a mixer (118). 15) Device according to claim 14, characterized in that the apparatus (6) makes it possible to store a video line while producing as output the preceding video line reversed in the left-right direction. 16) Device according to claim 1, characterized in that it comprises an apparatus (6) processing the video signal before this signal reaches the power video amplifier stages of the television set (1), so as to apply to the image supplied by the screen (2) a left-right symmetry and a top-bottom symmetry. 17) Device according to claim 16, characterized in that the apparatus (6) makes it possible to store a video image while producing as output the previous video image reversed in the left-right direction and in the up-down direction. 18) Device according to claim 1, characterized in that the coordinates of the surface of the mirror (3) are given by the following table 1, with - coordinates of the observer: (0.0000; 3.0000; 0.4604) - coordinates of the center of the bottom source image  (0.0000; 0.2000; 0.0000) - Tilt angle of the television (angle a>: 55,000.  Table 1: values of y as a function of x and z. Plate 1 of 4.  0.2706 -0.7422 -0.7417 -0.7404 -0.7381 -0.7349 -0.7308 -0.7258 -0.7199  0.3006 -0.7374 -0.7369 -0.7355 -0.7332 -0.7300 -0.7260 -0.7210 -0.7151  0.3306 -0.7321 -0.7316 -0.7303 -0.7280 -0.7248 -0.7207 -0.7157 -0.7099  0.3606 -0.7264 -0.7260 -0.7246 -0.7223 -0.7192 -0.7151 -0.7101 -0.7042  0.3906 -0.7204 -0.7199 -0.7185 -0.7163 -0.7131 -0.7090 -0.7041 -0.6982  0.4206 -0.7139 -0.7134 -0.7121 -0.7098 -0.7066 -0.7026 -0.6976 -0.6918  0.4506 -0.7071 -0.7066 -0.7052 -0.7030 -0.6998 -0.6957 -0.6908 -0.6849  0.4806 -0.6998 -0.6993 -0.6980 -0.6957 -0.6925 -0.6885 -0.6836 -0.6777  0.5106 -0.6921 -0.6917 -0.6903 -0.6880 -0.6849 -0.6808 -0.6759 -0.6701  0.5406 -0.6841 -0.6836 -0.6822 -0.6800 -0.6768 -0.6728 -0.6679 -0.6621  0.5706 -0.6756 -0.6751 -0.6738 -0.6715 -0.6684 -0.6644 -0.6594 -0.6536  0.6006 -0.6668 -0.6663 -0.6649 -0.6627 -0.6595 -0.6555 -0.6506 -0.6448  0.6306 -0.6575 -0.6570 -0.6557 -0.6534 -0.6503 -0.6463 -0.6413 -0.6356  0.6606 -0.6479 -0.6474 -0.6460 -0.6438 -0.6406 -0.6366 -0.6317 -0.6259  0.6906 -0.6378 -0.6373 -0.6360 -0.6337 -0.6306 -0.6266 -0.6217 -0.6159  0.7206 -0.6273 -0.6269 -0.6255 -0.6233 -0.6201 -0.6161 -0.6112 -0.6054  0.7506 -0.6165 -0.6160 -0.6146 -0.6124 -0.6093 -0.6053 -0.6004 -0.5946  0.7806 -0.6052 -0.6047 -0.6034 -0.6011 -0.5980 -0.5940 -0.5891 -0.5833  0.8106 -0.5935 -0.5930 -0.5917 -0.5895 -0.5863 -0.5823 -0.5774 -0.5716  0.8406 -0.5814 -0.5810 -0.5796 -0.5774 -0.5742 -0.5702 -0.5653 -0.5596  0.8706 -0.5689 -0.5685 -0.5671 -0.5649 -0.5617 -0.5577 -0.5528 -0.5471  0.9006 -0.5560 -0.5555 -0.5542 -0.5520 -0.5488 -0.5448 -0.5399 -0.5342  0.9306 -0.5427 -0.5422 -0.5409 -0.5386 -0.5355 -0.5315 -0.5266 -0.5208  0.9606 -0.5289 -0.5285 -0.5271 -0.5249 -0.5217 -0.5177 -0.5128 -0.5070  0.9906 -0.5148 -0.5143 -0.5129 -0.5107 -0.5076 -0.5035 -0.4986 -0.4929  1.0206 -0.5002 -0.4997 -0.4983 -0.4961 -0.4929 -0.4889 -0.4840 -0.4782  1.0506 -0.4851 -0.4846 -0.4833 -0.4810 -0.4779 -0.4739 -0.4690 -0.4632  1.0806 -0.4697 -0.4692 -0.4678 -0.4656 -0.4624 -0.4584 -0.4535 -0.4477  1.1106 -0.4538 -0.4533 -0.4519 -0.4497 -0.4465 -0.4425 -0.4375 -0.4317  1.1406 -0.4374 -0.4369 -0.4356 -0.4333 -0.4301 -0.4261 -0.4211 -0.4153  1.1706 -0.4206 -0.4201 -0.4188 -0.4165 -0.4133 -0.4093 -0.4043 -0.3985  1.2006 -0.4034 -0.4029 -0.4015 -0.3992 -0.3961 -0.3920 -0.3870 -0.3812  1.2306 -0.3856 -0.3852 -0.3838 -0.3815 -0.3783 -0.3742 -0.3693 -0.3634  1.2606 -0.3675 -0.3670 -0.3656 -0.3633 -0.3601 -0.3560 -0.3510 -0.3451  1.2906 -0.3488 -0.3483 -0.3470 -0.3447 -0.3415 -0.3373 -0.3323 -0.3264  1.3206 -0.3297 -0.3292 -0.3278 -0.3255 -0.3223 -0.3182 -0.3131 -0.3072  1.3506 -0.3101 -0.3096 -0.3082 -0.3059 -0.3027 -0.2985 -0.2934 -0.2875  1.3806 -0.2900 -0.2895 -0.2881 -0.2858 -0.2825 -0.2783 -0.2733 -0.2672  1.4106 -0.2694 -0.2689 -0.2675 -0.2651 -0.2619 -0.2577 -0.2526 -0.2465  1.4406 -0.2483 -0.2478 -0.2464 -0.2440 -0.2407 -0.2365 -0.2314 -0.2253  1.4706 -0.2266 -0.2261 -0.2247 -0.2223 -0.2190 -0.2148 -0.2096 -0.2035  1.5006 -0.2045 -0.2040 -0.2025 -0.2002 -0.1968 -0.1926 -0.1874 -0.1812  1.5306 -0.1818 -0.1813 -0.1798 -0.1774 -0.1741 -0.1698 -0.1645 -0.1584  1.5606 -0.1585 -0.1580 -0.1566 -0.1541 -0.1508 -0.1465 -0.1412 -0.1350  1.5906 -0.1347 -0.1342 -0.1327 -0.1303 -0.1269 -0.1226 -0.1172 -0.1110  1.6206 -0.1103 -0.1098 -0.1083 -0.1059 -0.1025 -0.0981 -0.0927 -0.0864  1.6506 -0.0853 -0.0848 -0.0833 -0.0809 -0.0774 -0.0730 -0.0676 -0.0612  1.6806 -0.0598 -0.0592 -0.0577 -0.0553 -0.0518 -0.0473 -0.0419 -0.0355  1.7106 -0.0336 -0.0330 -0.0315 -0.0290 -0.0255 -0.0210 -0.0155 -0.0090  1.7406 -0.0067 -0.0062 -0.0047 -0.0021 0.0014 0.0059 0.0115 0.0180  1.7706 0.0207 0.0213 0.0228 0.0254 0.0290 0.0335 0.0391 0.0457  1.8006 0.0489 0.0495 0.0510 0.0536 0.0572 0.0618 0.0675 0.0741  1.8306 0.0777 0.0783 0.0799 0.0825 0.0861 0.0908 0.0965 0.1032  1.8606 0.1073 0.1079 0.1094 0.1121 0.1158 0.1205 0.1263 0.1331 Values Values of a. o.oooo 0.0450 0.0900 0.1350 0.180u 0.2250 0.2700 0.3150  Table 1: values of y as a function of x and z. Plate 2 of 4.  0.2706 -0.7131 -0.7054 -0.6969 -0.6874 -0.6770 -0.6658 -0.6536 -0.6406  0.3006 -0.7083 -0.7006 -0.6921 -0.6826 -0.6723 -0.6610 -0.6489 -0.6359  0.3306 -0.7031 -0.6954 -0.6869 -0.6774 -0.6671 -0.6559 -0.6438 -0.6308  0.3606 -0.6975 -0.6898 -0.6813 -0.6719 -0.6616 -0.6504 -0.6383 -0.6253  0.3906 -0.6915 -0.6838 -0.6753 -0.6659 -0.6556 -0.6444 -0.6323 -0.6194  0.4206 -0.6850 -0.6774 -0.6689 -0.6595 -0.6492 -0.6380 -0.6260 -0.6131  0.4506 -0.6782 -0.6706 -0.6621 -0.6527 -0.6424 -0.6313 -0.6193 -0.6063  0.4806 -0.6710 -0.6634 -0.6549 -0.6455 -0.F353 -0.6241 -0.6121 -0.5992  0.5106 -0.6634 -0.6558 -0.6473 -0.6379 -0.6277 -0.6166 -0.6046 -0.5917  0.5406 -0.6553 -0.6478 -0.6393 -0.6299 -0.6197 -0.6086 -0.5966 -0.5838  0.5706 -0.6469 -0.6393 -0.6309 -0.6216 -0.6113 -0.6002 -0.5883 -0.5754  0.6006 -0.6381 -0.6305 -0.6221 -0.6128 -0.6026 -0.5915 -0.5795 -0.5667  0.6306 -0.6289 -0.6213 -0.6129 -0.6036 -0.5934 -0.5823 -0.5704 -0.5575  0.6606 -0.6192 -0.6117 -0.6033 -0.5939 -0.5838 -0.5727 -0.5608 -0.5480  0.6906 -0.6092 -0.6017 -0.5932 -0.5839 -0.5738 -0.5627 -0.5508 -0.5380  0.7206 -0.5988 -0.5912 -0.5828 -0.5735 -0.5633 -0.5523 -0.5404 -0.5276  0.7506 -0.5879 -0.5804 -0.5720 -0.5627 -0.5525 -0.5415 -0.5296 -0.5168  0.7806 -0.5767 -0.5691 -0.5607 -0.5514 -0.5413 -0.5303 -0.5184 -0.5056  0.8106 -0.5650 -0.5575 -0.5491 -0.5398 -0.5296 -0.5186 -0.5067 -0.4940  0.8406 -0.5529 -0.5454 -0.5370 -0.5277 -0.5176 -0.5066 -0.4947 -0.4819  0.8706 -0.5404 -0.5329 -0.5245 -0.5152 -0.5051 -0.4941 -0.4822 -0.4695  0.9006 -0.5275 -0.5200 -0.5116 -0.5023 -0.4922 -0.4812 -0.4693 -0.4566  0.9306 -0.5142 -0.5066 -0.4982 -0.4890 -0.4788 -0.4678 -0.4559 -0.4432  0.9606 -0.5004 -0.4929 -0.4845 -0.4752 -0.4650 -0.4540 -0.4421 -0.4294  0.9906 -0.4862 -0.4787 -0.4702 -0.4610 -0.4508 -0.4398 -0.4279 -0.4152  1.0206 -0.4716 -0.4640 -0.4556 -0.4463 -0.4361 -0.4251 -0.4132 -0.4004  1.0506 -0.4565 -0.4489 -0.4405 -0.4312 -0.4210 -0.4100 -0.3981 -0.3853  1.0806 -0.4410 -0.4334 -0.4250 -0.4156 -0.4054 -0.3944 -0.3825 -0.3697  1.1106 -0.4250 -0.4174 -0.4090 -0.3996 -0.3894 -0.3783 -0.3664 -0.3536  1.1406 -0.4086 -0.4010 -0.3925 -0.3832 -0.3729 -0.3618 -0.3498 -0.3370  1.1706 -0.3917 -0.3841 -0.3756 -0.3662 -0.3560 -0.3448 -0.3328 -0.3199  1.2006 -0.3744 -0.3668 -0.3582 -0.3488 -0.3385 -0.3273 -0.3153 -0.3024  1.2306 -0.3566 -0.3489 -0.3404 -0.3309 -0.3206 -0.3094 -0.2973 -0.2843  1.2606 -0.3383 -0.3306 -0.3220 -0.3126 -0.3022 -0.2909 -0.2788 -0.2658  1.2906 -0.3196 -0.3118 -0.3032 -0.2937 -0.2833 -0.2720 -0.2598 -0.2467  1.3206 -0.3003 -0.2926 -0.2839 -0.2744 -0.2639 -0.2526 -0.2403 -0.2272  1.3506 -0.2806 -0.2728 -0.2641 -0.2545 -0.2440 -0.2326 -0.2203 -0.2071  1.3806 -0.2603 -0.2525 -0.2438 -0.2341 -0.2236 -0.2121 -0.1998 -0.1865  1.4106 0.2396 -0.2317 -0.2229 -0.2132 -0.2026 -0.1911 -0.1787 -0.1653  1.4406 -0.2183 -0.2104 -0.2015 -0.1918 -0.1811 -0.1695 -0.1570 -0.1436  1.4706 -0.1965 -0.1885 -0.1796 -0.1698 -0.1591 -0.1474 -0.1349 -0.1214  1.5006 -0.1741 -0.1661 -0.1572 -0.1473 -0.1365 -0.1248 -0.1121 -0.0985  1.5306 -0.1512 -0.1432 -0.1342 -0.1242 -0.1134 -0.1016 -0.0888 -0.0751  1.5606 -0.1278 -0.1197 -0.1106 -0.1006 -0.0896 -0.0777 -0.0649 -0.0511  1.5906 -0.1037 -0.0956 -0.0864 -0.0764 -0.0653 -0.0533 -0.0404 -0.0265  1.6206 -0.0791 -0.0709 -0.0617 -0.0515 -0.0404 -0.0283 -0.0153 -0.0013  1.6506 -0.0539 -0.0456 -0.0363 -0.0261 -0.0148 -0.0027 0.0105 0.0246  1.6806 -0.0281 -0.0197 -0.0103 0.0000 0.0113 0.0236 0.0369 0.0511  1.7106 -0.0016 0.0069 0.0163 0.0267 0.0382 0.0506 0.0640 0.0784  1.7406 0.0255 0.0341 0.0436 0.0541 0.0657 0.0782 0.0917 0.1062  1.7706 0.0533 0.0620 0.0716 0.0822 0.0939 0.1065 0.1202 0.1349  1.8006 0.0818 0.0905 0.1002 0.1110 0.1228 0.1356 0.1494 0.1642  1.8306 0.1110 0.1198 0.1296 0.1405 0.1524 0.1653 0.1793 0.1943  1.8606 0.1409 0.1498 0.1598 0.1707 0.1828 0.1959 0.2100 0.2252  de z 0.3600 0.4050 0.4500 0.4950 0.5400 0.5850 0.6300 0.6750 Values Values of x  Table 1: values of y as a function of x and z. Plate 3 of 4.  0.2706 -0.6267 -0.6119 -0.5962 -0.5796 -0.5621 -0.5437 -0.5245 -0.5044  0.3006 -0.6220 -0.6072 -0.5915 -0.5750 -0.5575 -0.5392 -0.5200 -0.4999  0.3306 -0.6169 -0.6021 -0.5865 -0.5700 -0.5525 -0.5342 -0.5150 -0.4950  0.3606 -0.6114 -0.5967 -0.5811 -0.5645 -0.5471 -0.5289 -0.5097 -0.4897  0.3906 -0.6055 -0.5908 -0.5752 -0.5587 -0.5414 -0.5231 -0.5040 -0.4840  0.4206 -0.5992 -0.5845 -0.5690 -0.5525 -0.5352 -0.5170 -0.4979 -0.4779  0.4506 -0.5925 -0.5779 -0.5623 -0.5459 -0.5286 -0.5104 -0.4913 -0.4714  0.4806 -0.5854 -0.57Oo -0.5553 -0.5389 -0.5216 -0.5034 -0.4844 -0.4645  0.5106 -0.5779 -0.5633 -0.5478 -0.5314 -0.5142 -0.4960 -0.4771 -0.4572  0.5406 -0.5700 -0.5554 -0.5399 -0.5236 -0.5064 -0.4883 -0.4693 -0.4495  0.5706 -0.5617 -0.5471 -0.5317 -0.5153 -0.981 -0.4801 -0.4612 -0.4414  0.6006 -0.5530 -0.5384 -0.5230 -0.5067 -0.4895 -0.4715 -0.4526 -0.4328  0.6306 -0.5439 -0.5293 -0.5139 -0.4976 -0.4805 -0.4624 -0.4436 -0.4239  0.6606 -0.5343 -0.5198 -0.5044 -0.4881 -0.4710 -0.4530 -0.4342 -0.4145  0.6906 -0.5244 -0.5098 -0.4945 -0.4782 -0.4611 -0.4432 -0.4244 -0.4047  0.7206 -0.5140 -0.4995 -0.4841 -0.4679 -0.4508 -0.4329 -0.4141 -0.3945  0.7506 -0.5032 -0.4887 -0.4734 -0.4572 -0.4401 -0.4222 -0.4034 -0.3838  0.7806 -0.4920 -0.4775 -0.4622 -0.4460 -0.4289 -0.4110 -0.3923 -0.3727  0.8106 -0.4804 -0.4659 -0.4506 -0.4344 -0.4174 -0.3995 -0.3808 -0.3612  0.8406 -0.4683 -0.4539 -0.4385 -0.4224 -0.4053 -0.3875 -0.3688 -0.3492  0.8706 -0.4559 -0.4414 -0.4261 -0.4099 -0.3929 -0.3750 -0.3563 -0.3368  0.9006 -0.4430 -0.4285 -0.4132 -0.3970 -0.3800 -0.3622 -0.3435 -0.3240  0.9306 -0.4296 -0.4151 -0.3998 -0.3837 -0.3667 -0.3488 -0.3301 -0.3107  0.9606 -0.4158 -0.4013 -0.3860 -0.3699 -0.3528 -0.3350 -0.3163 -0.2968  0.9906 -0.4015 -0.3871 -0.3717 -0.3556 -0.3386 -0.3207 -0.3020 -0.2825  1.0206 -0.3868 -0.3723 -0.3570 -0.3408 -0.3238 -0.3059 -0.2872 -0.2677  1.0506 -0.3716 -0.3571 -0.3418 -0.3256 -0.3085 -0.2906 -0.2719 -0.2524  1.0806 -0.3560 -0.3415 -0.3261 -0.3099 -0.2928 -0.2749 -0.2561 -0.2366  1.1106 -0.3399 -0.3253 -0.3099 -0.2936 -0.2765 -0.2586 -0.2398 -0.2202  1.1406 -0.3232 -0.3087 -0.2932 -0.2769 -0.2598 -0.2418 -0.2229 -0.2033  1.1706 -0.3062 -0.2915 -0.2760 -0.2597 -0.2425 -0.2245 -0.2056 -0.1859  1.2006 -0.2886 -0.2739 -0.2584 -0.2420 -0.2247 -0.2066 -0.1877 -0.1679  1.2306 -0.2705 -0.2558 -0.2402 -0.2237 -0.2064 -0.1883 -0.1693 -0.1494  1.2606 -0.2519 -0.2371 -0.2215 -0.2050 -0.1876 -0.1694 -0.1503 -0.1304  1.2906 -0.2328 -0.2180 -0.2022 -0.1857 -0.1682 -0.1499 -0.1307 -0.1108  1.3206 -0.2132 -0.1983 -0.1825 -0.1658 -0.1483 -0.1299 -0.1107 -0.0906  1.3506 -0.1930 -0.1780 -0.1622 -0.1454 -0.1278 -0.1093 -0.0900 -0.0698  1.3806 -0.1723 -0.1573 -0.1413 -0.1245 -0.1068 -0.0882 -0.0687 -0.0484  1.4106 -0.1511 -0.1360 -0.1199 -0.1030 -0.0852 -0.0665 -0.0469 -0.0265  1.4406 -0.1293 -0.1141 -0.0980 -0.0809 -0.0630 -0.0442 -0.0245 -0.0039  1.4706 -0.1070 -0.0916 -0.0754 -0.0583 -0.0402 -0.0213 -0.0014 0.0193  1.5006 -0.0840 -0.0686 -0.0523 -0.0350 -0.0168 0.0023 0.0222 0.0431  1.5306 -0.0605 -0.0450 -0.0285 -0.0111 0.0072 0.0264 0.0466 0.0676  1.5606 -0.0364 -0.0207 -0.0042 0.0134 0.0318 0.0512 0.0715 0.0927  1.5906 -0.0117 0.0041 0.0208 0.0385 0.0571 0.0767 0.0972 0.1186  1.6206 0.0137 0.0296 0.0465 0.0643 0.0831 0.1028 0.1235 0.1451  1.6506 0.0397 0.0558 0.0728 0.0908 0.1097 0.1297 0.1505 0.1723  1.6806 0.0664 0.0826 0.0998 0.1179 0.1371 0.1572 0.1783 0.2003  1.7106 0.0937 0.1101 0.1275 0.1458 0.1651 0.1855 0.2068 0.2291  1.7406 0.1218 0.1383 0.1559 0.1744 0.1940 0.2145 0.2361 0.2586  1.7706 0.1506 0.1673 0.1850 0.2038 0.2236 0.2444 0.2662 0.2890  1.8006 0.1801 0.1970 0.2149 0.2339 0.2539 0.2750 0.2971 0.3202  1.8306 0.2104 0.2275 0.2457 0.2649 0.2851 0.3065 0.3288 0.3523  1.8606 0.2415 0.2588 0.2772 0.2966 0.3172 0.3388 0.3615 0.3852  from z. 0.7200 0.7650 0.8100 0.8550 0.9000 0.9450 0.9900 1.0350 Values Values of x Table 1: values of y as a function of x and z. Plate 4 of 4.  0.2706 -0.4834 -0.4615 -0.4388 -0.4152 -0.3909 -0.3657 -0.3399 -0.3133  0.3006 -0.4789 -0.4571 -0.4344 -0.4109 -0.3866 -0.3615 -0.3357 -0.3092  0.3306 -0.4740 -0.4523 -0.4296 -0.4062 -0.3819 -0.3569 -0.3311 -0.3047  0.3606 -0.4688 -0.4471 -0.4245 -0.4011 -0.3769 -0.3519 -0.3262 -0.2998  0.3906 -0.4632 -0.4415 -0.4189 -0.3956 -0.3714 -0.3465 -0.3209 -0.2946  0.4206 -0.4571 -0.4354 -0.4130 -0.3897 -0.3656 -0.3407 -0.3152 -0.2890  0.4506 -0.4507 -0.4290 -0.4066 -0.3833 -0.3593 -0.3345 -0.3090 -0.2829  0.4806 -0.4438 -0.4222 -0.3998 -0.3766 -0.3527 -0.3279 -0.3025 -0.2765  0.5106 -0.4365 -0.4150 -0.3927 -0.3695 -0.3456 -0.3209 -0.2956 -0.2696  0.5406 -0.4289 -0.4074 -0.3851 -0.3620 -0.3381 -0.3135 -0.2883 -0.2624  0.5706 -0.4208 -0.3993 -0.3771 -0.3540 -0.3302 -0.3057 -0.2805 -0.2547  0.6006 -0.4123 -0.3909 -0.3687 -0.3457 -0.3219 -0.2975 -0.2723 -0.2466  0.6306 -0.4033 -0.3820 -0.3598 -0.3369 -0.3132 -0.2888 -0.2637 -0.2381  0.6606 -0.3940 -0.3727 -0.3506 -0.3277 -0.3040 -0.2797 -0.2547 -0.2291  0.6906 -0.3842 -0.3630 -0.3409 -0.3180 -0.2944 -0.2702 -0.2452 -0.2198  0.7206 -0.3740 -0.3528 -0.3308 -0.3080 -0.2844 -0.2602 -0.2353 -0.2099  0.7506 -0.3634 -0.3422 -0.3202 -0.2974 -0.2739 -0.2498 -0.2250 -0.1997  0.7806 -0.3524 -0.3312 -0.3092 -0.2865 -0.2630 -0.2389 -0.2142 -0.1889  0.8106 -0.3409 -0.3197 -0.2978 -0.2751 -0.2517 -0.2276 -0.2029 -0.1777  0.8406 -0.3289 -0.3078 -0.2859 -0.2632 -0.2398 -0.2158 -0.1912 -0.1661  0.8706 -0.3165 -0.2954 -0.2735 -0.2509 -0.2276 -0.2036 -0.1790 -0.1539  0.9006 -0.3037 -0.2826 -0.2607 -0.2381 -0.2148 -0.1909 -0.1664 -0.1413  0.9306 -0.2904 -0.2693 -0.2474 -0.2249 -0.2016 -0.1777 -0.1532 -0.1282  0.9606 -0.2765 -0.2555 -0.2336 -0.2111 -0.1878 -0.1639 -0.1395 -0.1145  0.9906 -0.2622 -0.2411 -0.2193 -0.1968 -0.1735 -0.1496 -0.1252 -0.1003  1.0206 -0.2474 -0.2263 -0.2045 -0.1819 -0.1587 -0.1348 -0.1103 -0.0855  1.0506 -0.2321 -0.2109 -0.1891 -0.1665 -0.1432 -0.1193 -0.0949 -0.0700  1.0806 -0.2162 -0.1951 -0.1732 -0.1505 -0.1273 -0.1033 -0.0789 -0.0540  1.1106 -0.1998 -0.1786 -0.1567 -0.13hO -0.1107 -0.0868 -0.0623 -0.0373  1.1406 -0.1829 -0.1616 -0.1397 -0.1170 -0.0936 -0.0696 -0.0451 -0.0201  1.1706 -0.1654 -0.1441 -0.1221 -0.0993 -0.0759 -0.0518 -0.0272 -0.0022  1.2006 -0.1474 -0.1260 -0.1039 -0.0811 -0.0576 -0.0335 -0.0088 0.0163  1.2306 -0.1288 -0.1074 -0.0852 -0.0623 -0.0387 -0.0145 0.0103 0.0355  1.2606 -0.1097 -0.0881 -0.0659 -0.0429 -0.0192 0.0051 0.0300 0.0553  1.2906 -0.0899 -0.0683 -0.0460 -0.0229 0.0009 0.0253 0.0503 0.0757  1.3206 -0.0697 -0.0480 -0.0255 -0.0022 0.0217 0.0462 0.0713 0.0968  1.3506 -0.0488 -0.0270 -0.0043 0.0190 0.0431 0.0677 0.0930 0.1187  1.3806 -0.0273 -0.0053 0.0174 0.0409 0.0651 0.0899 0.1153 0.1411  1.4106 -0.0052 0.0169 0.0398 0.0634 0.0878 0.1128 0.1383 0.1643  1.4406 0.0175 0.0397 0.0628 0.0866 0.1111 0.1363 0.1621 0.1883  1.4706 0.0408 0.0632 0.0865 0.1104 0.1352 0.1605 0.1865 0.2129  1.5006 0.0648 0.0874 0.1108 0.1350 0.1599 0.1855 0.2117 0.2384  1.5306 0.0895 0.1122 0.1358 0.1602 0.1854 0.2112 0.2376 0.2645  1.5606 0.1148 0.1378 0.1616 0.1862 0.2116 0.2377 0.2643 0.2915  1.5906 0.1409 0.1640 0.1881 0.2129 0.2386 0.2649 0.2919 0.3193  1.6206 0.1676 0.1910 0.2153 0.2404 0.2663 0.2929 0.3202 0.3480  1.6506 0.1951 0.2187 0.2433 0.2687 0.2948 0.3218 0.3494 0.3775  1.6806 0.2233 0.2472 0.2720 0.2977 0.3242 0.3515 0.3794 0.4079  1.7106 0.2523 0.2765 0.3016 0.3276 0.3545 0.3821 0.4104 0.4392  1.7406 0.2821 0.3066 0.3320 0.3584 0.3856 0.4135 0.4423 0.4715  1.7706 0.3128 0.3376 0.3634 0.3900 0.4176 0.4460 0.4751 0.5049  1.8006 0.3443 0.3694 0.3956 0.4226 0.4506 0.4794 0.5090 0.5392  1.8306 0.3767 0.4022 0.4287 0.4562 0.4846 0.5139 0.5440 0.5747  1.8606 0.4101 0.4359 0.4628 0.4908 0.5197 0.5494 0.5801 0.6113  de z 1.0800 1.1250 1.1700 1.2150 1.2600 1.3050 1.3500 1.3950 Values Values of x 19) Device according to claim 1, characterized in that the coordinates of the surface of the mirror (3) are given by the following table 2, with - coordinates of the observer: (0.0000; 3.0000; 0.4811) - coordinates of the center of the bottom source image  (0.0000; 0.7000; 0.0000) - tilt angle of the television (angle a): 60,000. Table 2: values of y as a function of x and z. Plate 1 of 4.  0.2368 -0.8022 -0.8015 -0.7996 -0.7965 -0.7921 -0.7865 -0.7796 -0.7714  0.2668 -0.7988 -0.7981 -0.7962 -0.7931 -0.7887 -0.7831 -0.7762 -0.7680  0.2968 -0.7950 -0.7943 -0.7925 -0.7894 -0.7850 -0.7794 -0.7725 -0.7643  0.3268 -0.7910 -0.7903 -0.7884 -0.7853 -0.7810 -0.7754 -0.7685 -0.7603  0.3568 -0.7866 -0.7859 -0.7841 -0.7810 -0.7766 -0.7710 -0.7642 -0.7560  0.3868 -0.7820 -0.7813 -0.7794 -0.7763 -0.7720 -0. <o64 -0.7595 -0.7514  0.4168 -0.7770 -0.7763 -0.7744 -0.7713 -0.7670 -0. 14 -0.7546 -0.7465  0.4468 -0.7717 -0.7710 -0.7692 -0.7661 -0.7617 -0.7562 -0.7493 -0.7412  0.4768 -0.7661 -0.7654 -0.7636 -0.7605 -0.7562 -0.7506 -0.7438 -0.7357  0.5068 -0.7602 -0.7595 -0.7577 -0.7546 -0.7503 -0.7447 -0.7379 -0.7298  0.5368 -0.7540 -0.7533 -0.7515 -0.7484 -0.7441 -0.7385 -0.7317 -0.7236  0.5668 -0.7475 -0.7468 -0.7449 -0.7419 -0.7375 -0.7320 -0.7252 -0.7171  0.5968 -0.7406 -0.7400 -0.7381 -0.7350 -0.7307 -0.7252 -0.7183 -0.7103  0.6268 -0.7335 -0.7328 -0.7310 -0.7279 -0.7236 -0.7180 -0.7112 -0.7031  0.6568 -0.7260 -0.7254 -0.7235 -0.7204 -0.7161 -0.7106 -0.7037 -0.6956  0.6868 -0.7183'-0.7176 -0.7157 -0.7126 -0.7083 -0.7028 -0.6960 -0.6879  0.7168 -0.7102 -0.7095 -0.7076 -0.7046 -0.7002 -0.6947 -0.6879 -0.6798  0.7468 -0.7018 -0.7011 -0.6992 -0.6961 -0.6918 -0.6863 -0.6794 -0.6713  0.7768 -0.6930 -0.6924 -0.6905 -0.6874 -0.6831 -0.6775 -0.6707 -0.6626  0.8068 -0.6840 -0.6833 -0.6815 -0.6784 -0.6740 -0.6685 -0.6616 -0.6535  0.8368 -0.6746 -0.6739 -0.6721 -0.6690 -0.6647 -0.6591 -0.6522 -0.6441  0.8668 -0.6650 -0.6643 -0.6624 -0.6593 -0.6550 -0.6494 -0.6425 -0.6344  0.8968 -0.6550 -0.6543 -0.6524 -0.6493 -0.6450 -0.6394 -0.6325 -0.6243  0.9268 -0.6447 -0.6440 -0.6421 -0.6390 -0.6346 -0.6290 -0.6222 -0.6140  0.9568 -0.6339 -0.6332 -0.6314 -0.6283 -0.6239 -0.6183 -0.6114 -0.6032  0.9868 -0.6229 -0.6222 -0.6203 -0.6172 -0.6128 -0.6072 -0.6003 -0.5921  1.0168 -0.6115 -0.6109 -0.6090 -0.6058 -0.6015 -0.5958 -0.5889 -0.5807  1.0468 -0.5999 -0.5992 -0.5973 -0.5941 -0.5898 -0.5841 -0.5772 -0.5689  1.0768 -0.5878 -0.5871 -0.5852 -0.5821 -0.5777 -0.5720 -0.5651 -0.5568  1.1068 -0.5755 -0.5748 -0.5729 -0.5697 -0.5653 -0.5596 -0.5526 -0.5443  1.1368 -0.5627 -0.5620 -0.5601 -0.5570 -0.5526 -0.5468 -0.5398 -0.5315  1.1668 -0.5497 -0.5490 -0.5471 -0.5439 -0.5395 -0.5337 -0.5267 -0.5184  1.1968 -0.5363 -0.5355 -0.5336 -0.5304 -0.5260 -0.5202 -0.5132 -0.5048  1.2268 -0.5225 -0.5218 -0.5198 -0.5166 -0.5122 -0.5064 -0.4993 -0.4909  1.2568 -0.5083 -0.5076 -0.5057 -0.5025 -0.4980 -0.4922 -0.4851 -0.4767  1.2868 -0.4938 -0.4931 -0.4912 -0.4880 -0.4834 -0.4776 -0.4705 -0.4620  1.3168 -0.4790 -0.4782 -0.4763 -0.4730 -0.4685 -0.4627 -0.4555 -0.4470  1.3468 -0.4637 -0.4630 -0.4610 -0.4578 -0.4532 -0.4474 -0.4402 -0.4316  1.3768 -0.4481 -0.4473 -0.4454 -0.4421 -0.4375 -0.4316 -0.4244 -0.4158  1.4068 -0.4321 -0.4313 -0.4293 -0.4261 -0.4215 -0.4155 -0.4083 -0.3996  1.4368 -0.4157 -0.4149 -0.4129 -0.4096 -0.4050 -0.3990 -0.3917 -0.3831  1.4668 -0.3989 -0.3981 -0.3961 -0.3928 -0.3881 -0.3822 -0.3748 -0.3661  1.4968 -0.3817 -0.3809 -0.3789 -0.3756 -0.3709 -0.3649 -0.3575 -0.3487  1.5268 -0.3640 -0.3633 -0.3613 -0.3579 -0.3532 -0.3472 -0.3397 -0.3309  1.5568 -0.3460 -0.3453 -0.3432 -0.3399 -0.3351 -0.3290 -0.3215 -0.3127  1.5868 -0.3276 -0.3268 -0.3248 -0.3214 -0.3166 -0.3105 -0.3029 -0.2940  1.6168 -0.3087 -0.3080 -0.3059 -0.3025 -0.2977 -0.2915 -0.2839 -0.2749  1.6468 -0.2894 -0.2887 -0.2866 -0.2831 -0.2783 -0.2721 -0.2644 -0.2554  1.6768 -0.2697 -0.2689 -0.2668 -0.2633 -0.2585 -0.2522 -0.2445 -0.2354  1.7068 -0.2495 -0.2487 -0.2466 -0.2431 -0.2382 -0.2319 -0.2241 -0.2149  1.7368 -0.2289 -0.2281 -0.2259 -0.2224 -0.2175 -0.2111 -0.2033 -0.1940  1.7668 -0.2078 -0.2070 -0.2048 -0.2013 -0.1963 -0.1899 -0.1820 -0.1726  1.7968 -0.1862 -0.1854 -0.1832 -0.1796 -0.1746 -0.1681 -0.1602 -0.1507  1.8268 -0.1641 -0.1633 -0.1611 -0.1575 -0.1524 -0.1459 -0.1379 -0.1283  of z 0.0000 0.0450 0.0900 0.1350 0.1800 0.2250 0.2700 0.3150 Values Values of x Table 2: values of y as a function of x and z. Plate 2 of 4.  0.2368 -0.7618 -0.7510 -0.7388 -0.7252 -0.7102 -0.6938 -0.6758 -0.6563  0.2668 -0.7585 -0.7477 -0.7355 -0.7220 -0.7070 -0.6906 -0.6727 -0.6532  0.2968 -0.7548 -0.7440 -0.7319 -0.7184 -0.7034 -0.6870 -0.6692 -0.6498  0.3268 -0.7509 -0.7401 -0.7280 -0.7145 -0.6995 -0.6832 -0.6654 -0.6460  0.3568 -0.7466 -0.7358 -0.7237 -0.7102 -0.6953 -0.6790 -0.6612 -0.6419  0.3868 -0.7420 -0.7312 -0.7191 -0.7057 -0.6908 -0.6745 -0.6567 -0.6374  0.4168 -0.7371 -0.7263 -0.7142 -0.7008 -0.6860 -0.6697 -0.6519 -0.6326  0.4468 -0.7318 -0.7211 -0.7090 -0.6956 -o.eqos -0.6645 -0.6468 -0.6275  0.4768 -0.7263 -0.7155 -0.7035 -0.6901 -0.6753 -0.6590 -0.6413 -0.6220  0.5068 -0.7204 -0.7097 -0.6976 -0.6842 -0.6694 -0.6532 -0.6355 -0.6162  0.5368 -0.7142 -0.7035 -0.6915 -0.6781 -0.6633 -0.6470 -0.6293 -0.6101  0.5668 -0.7077 -0.6970 -0.6850 -0.6716 -0.6568 -0.6406 -0.6229 -0.6037  0.5968 -0.7009 -0.6902 -0.6782 -0.6648 -0.6500 -0.6338 -0.6161 -0.5968  0.6268 -0.6937 -0.6830 -0.6710 -0.6576 -0.6428 -0.6266 -0.6089 -0.5897  0.6568 -0.6863 -0.6756 -0.6635 -0.6501 -0.6354 -0.6191 -0.6014 -0.5822  0.6868 -0.6785 -0.6678 -0.6557 -0.6423 -0.6276 -0.6113 -0.5936 -0.5744  0.7168 -0.6704 -0.6597 -0.6476 -0.6342 -0.6194 -0.6032 -0.5855 -0.5662  0.7468 -0.6619 -0.6512 -0.6392 -0.6258 -0.6109 -0.5947 -0.5770 -0.5577  0.7768 -0.6532 -0.6425 -0.6304 -0.6170 -0.6021 -0.5859 -0.5681 -0.5489  0.8068 -0.6441 -0.6334 -0.6213 -0.6078 -0.5930 -0.5767 -0.5589 -0.5396  0.8368 -0.6347 -0.6239 -0.6119 -0.5984 -0.5835 -0.5672 -0.5494 -0.5301  0.8668 -0.6249 -0.6142 -0.6021 -0.5886 -0.5737 -0.5574 -0.5396 -0.5202  0.8968 -0.6149 -0.6041 -0.5920 -0.5785 -0.5636 -0.5472 -0.5294 -0.5100  0.9268 -0.6045 -0.5937 -0.5816 -0.5681 -0.5531 -0.5367 -0.5188 -0.4994  0.9568 -0.5937 -0.5829 -0.5707 -0.5572 -0.5422 -0.5258 -0.5078 -0.4884  0.9868 -0.5826 -0.5718 -0.5596 -0.5460 -0.5310 -0.5145 -0.4965 -0.4770  1.0168 -0.5711 -0.5603 -0.5481 -0.5344 -0.5194 -0.5029 -0.4849 -0.4653  1.0468 -0.5594 -0.5485 -0.5362 -0.5225 -0.5075 -0.4909 -0.4728 -0.4532  1.0768 -0.5472 -0.5363 -0.5240 -0.51p3 -0.4952 -0.4786 -0.4605 -0.4408  1.1068 -0.5347 -0.5238 -0.5114 -0.4977 -0.4825 -0.4659 -0.4477 -0.4280  1.1368 -0.5219 -0.5109 -0.4985 -0.4847 -0.4695 -0.4528 -0.4346 -0.4148  1.1668 -0.5087 -0.4977 -0.4852 -0.4714 -0.4561 -0.4394 -0.4211 -0.4012  1.1968 -0.4951 -0.4840 -0.4716 -0.4577 -0.4424 -0.4255 -0.4072 -0.3872  1.2268 -0.4812 -0.4701 -0.4576 -0.4436 -0.4282 -0.4113 -0.3929 -0.3728  1.2568 -0.4669 -0.4557 -0.4432 -0.4292 -0.4137 -0.3967 -0.3782 -0.3581  1.2868 -0.4522 -0.4410 -0.4284 -0.4143 -0.3988 -0.3817 -0.3631 -0.3429  1.3168 -0.4371 -0.4259 -0.4132 -0.3991 -0.3835 -0.3664 -0.3476 -0.3273  1.3468 -0.4217 -0.4104 -0.3977 -0.3835 -0.3678 -0.3506 -0.3318 -0.3113  1.3768 -0.4059 -0.3945 -0.3817 -0.3674 -0.3517 -0.3344 -0.3155 -0.2949  1.4068 -0.3896 -0.3782 -0.3653 -0.3510 -0.3352 -0.3177 -0.2988 -0.2781  1.4368 -0.3730 -0.3615 -0.3486 -0.3341 -0.3182 -0.3007 -0.2816 -0.2608  1.4668 -0.3559 -0.3444 -0.3314 -0.3169 -0.3009 -0.2832 -0.2640 -0.2431  1.4968 -0.3385 -0.3269 -0.3138 -0.2992 -0.2831 -0.2653 -0.2460 -0.2249  1.5268 -0.3206 -0.3089 -0.2958 -0.2811 -0.2649 -0.2470 -0.2275 -0.2063  1.5568 -0.3023 -0.2906 -0.2773 -0.2625 -0.2462 -0.2282 -0.2086 -0.1873  1.5868 -0.2836 -0.2717 -0.2584 -0.2435 -0.2270 -0.2090 -0.1892 -0.1677  1.6168 -0.2644 -0.2525 -0.2391 -0.2241 -0.2075 -0.1892 -0.1693 -0.1476  1.6468 -0.2448 -0.2328 -0.2193 -0.2041 -0.1874 -0.1690 -0.1490 -0.1271  1.6768 -0.2247 -0.2126 -0.1990 -0.1837 -0.1669 -0.1484 -0.1281 -0.1061  1.7068 -0.2042 -0.1920 -0.1782 -0.1629 -0.1459 -0.1272 -0.1068 -0.0845  1.7368 -0.1832 -0.1709 -0.1570 -0.1415 -0.1244 -0.1055 -0.0849 -0.0625  1.7668 -0.1617 -0.1493 -0.1353 -0.1196 -0.1023 -0.0833 -0.0625 -0.0399  1.7968 -0.1397 -0.1272 -0.1130 -0.0973 -0.0798 -0.0606 -0.0396 -0.0167  1.8268 -0.1172 -0.1046 -0.0903 -0.0743 -0.0567 -0.0373 -0.0161 0.0070  de z 0.3600 0.4050 0.4500 0.4950 0.5400 0.5850 0.6300 0.6750 Values Values of x Table 2: values of y as a function of x and z. Plate 3 of 4.  0.2368 -0.6352 -0.6125 -0.5880 -0.5618 -0.5336 -0.5036 -0.4714 -0.4370  0.2668 -0.6322 -0.6095 -0.5851 -0.5589 -0.5308 -0.5008 -0.4687 -0.4344  0.2968 -0.6288 -0.6061 -0.5818 -0.5556 -0.5276 -0.4977 -0.4656 -0.4314  0.3268 -0.6250 -0.6024 -0.5781 -0.5520 -0.5241 -0.4942 -0.4622 -0.4280  0.3568 -0.6209 -0.5984 -0.5741 -0.5481 -0.5202 -0.4903 -0.4584 -0.4242  0.3868 -0.6165 -0.5940 -0.5698 -0.5438 -0.5159 -0.4861 -0.4542 -0.4201  0.4168 -0.6118 -0.5893 -0.5651 -0.5391 -0.5113 -0.4815 -0.4496 -0.4156  0.4468 -0.6067 -0.584t -0.5600 -0.5341 -0.5063 -0.4765 -0.4447 -0.4107  0.4768 -0.6012 -0.5788 -0.5546 -0.5287 -0.5009 -0.4712 -0.4394 -0.4054  0.5068 -0.5954 -0.5730 -0.5489 -0.5230 -0.4952 -0.4655 -0.4337 -0.3997  0.5368 -0.5893 -0.5669 -0.5428 -0.5169 -0.4891 -0.4594 -0.4276 -0.3937  0.5668 -0.5829 -0.5604 -0.5363 -0.5104 -0.4827 -0.4530 -0.4212 -0.3872  0.5968 -0.5761 -0.5536 -0.5295 -0.5036 -0.4759 -0.4462 -0.4144 -0.3804  0.6268 -0.5689 -0.5465 -0.5224 -0.4965 -0.4687 -0.4390 -0.4072 -0.3732  0.6568 -0.5614 -0.5390 -0.5149 -0.4890 -0.4612 -0.4315 -0.3997 -0.3657  0.6868 -0.5536 -0.5311 -0.5070 -0.4811 -0.4533 -0.4235 -0.3917 -0.3577  0.7168 -0.5454 -0.5229 -0.4988 -0.4728 -0.4450 -0.4153 -0.3834 -0.3494  0.7468 -0.5369 -0.5144 -0.4902 -0.4642 -0.4364 -0.4066 -0.3747 -0.3406  0.7768 -0.5280 -0.5055 -0.4813 -0.4553 -0.4274 -0.3976 -0.3656 -0.3315  0.8068 -0.5188 -0.4962 -0.4720 -0.4460 -0.4180 -0.3882 -0.3562 -0.3220  0.8368 -0.5092 -0.4866 -0.4623 -0.4363 -0.4083 -0.3784 -0.3463 -0.3121  0.8668 -0.4993 -0.4767 -0.4523 -0.4262 -0.3982 -0.3682 -0.3361 -0.3018  0.8968 -0.4890 -0.4664 -0.4420 -0.4158 -0.3878 -0.3577 -0.3255 -0.2911  0.9268 -0.4784 -0.4557 -0.4313 -0.4050 -0.3769 -0.3468 -0.3145 -0.2800  0.9568 -0.4673 -0.4446 -0.4201 -0.3938 -0.3656 -0.3354 -0.3030 -0.2684  0.9868 -0.4559 -0.4331 -0.4085 -0.3822 -0.3539 -0.3236 -0.2912 -0.2565  1.0168 -0.4441 -0.4213 -0.3966 -0.3702 -0.3418 -0.3114 -0.2789 -0.2441  1.0468 -0.4320 -0.4090 -0.3843 -0.3578 -0.3294 -0.2989 -0.2662 -0.2313  1.0768 -0.4195 -0.3964 -0.3717 -0.3451 -0.3165 -0.2859 -0.2532 -0.2181  1.1068 -0.4066 -0.3835 -0.3586 -0.3319 -0.3033 -0.2725 -0.2397 -0.2044  1.1368 -0.3933 -0.3701 -0.3452 -0.3184 -0.2896 -0.2588 -0.2257 -0.1904  1.1668 -0.3796 -0.3564 -0.3313 -0.3044 -0.2755 -0.2445 -0.2114 -0.1759  1.1968 -0.3656 -0.3422 -0.3170 -0.2900 -0.2610 -0.2299 -0.1966 -0.1609  1.2268 -0.3511 -0.3276 -0.3024 -0.2752 -0.2461 -0.2148 -0.1813 -0.1455  1.2568 -0.3362 -0.3127 -0.2873 -0.2600 -0.2307 -0.1993 -0.1657 -0.1296  1.2868 -0.3210 -0.2973 -0.2718 -0.2444 -0.2149 -0.1833 -0.1495 -0.1132  1.3168 -0.3053 -0.2815 -0.2558 -0.2283 -0.1987 -0.1669 -0.1329 -0.0964  1.3468 -0.2892 -0.2653 -0.2395 -0.2117 -0.1820 -0.1500 -0.1158 -0.0791  1.3768 -0.2726 -0.2486 -0.2226 -0.1948 -0.1648 -0.1327 -0.0982 -0.0612  1.4068 -0.2557 -0.2315 -0.2054 -0.1773 -0.1472 -0.1148 -0.0802 -0.0429  1.4368 -0.2383 -0.2139 -0.1876 -0.1594 -0.1291 -0.0965 -0.0615 -0.0241  1.4668 -0.2204 -0.1959 -0.1695 -0.1410 -0.1105 -0.0777 -0.0425 -0.0047  1.4968 -0.2021 -0.1774 -0.1508 -0.1222 -0.0914 -0.0583 -0.0229 0.0152  1.5268 -0.1833 -0.1585 -0.1317 -0.1028 -0.0718 -0.0385 -0.0028 0.0356  1.5568 -0.1641 -0.1391 -0.1120 -0.0830 -0.0517 -0.0181 0.0179 0.0566  1.5868 -0.1443 -0.1191 -0.0919 -0.0626 -0.0310 0.0028 0.0392 0.0783  1.6168 -0.1241 -0.0987 -0.0712 -0.0417 -0.0099 0.0243 0.0610 0.1004  1.6468 -0.1034 -0.0778 -0.0500 -0.0202 0.0118 0.0464 0.0834 0.1232  1.6768 -0.0822 -0.0563 -0.0283 0.0017 0.0341 0.0690 0.1064 0.1466  1.7068 -0.0604 -0.0343 -0.0061 0.0243 0.0571 0.0922 0.1301 0.1707  1.7368 -0.0381 -0.0117 0.0168 0.0475 0.0805 0.1161 0.1543 0.1954  1.7668 -0.0152 0.0114 0.0402 0.0712 0.1046 0.1406 0.1792 0.2208  1.7968 0.0082 0.0350 0.0642 0.0955 0.1292 0.1657 0.2048 0.2469  1.8268 0.0322 0.0594 0.0888 0.1205 0.1547 0.1915 0.2311 0.2738  de z 0.7200 0.7650 0.8100 0.8550 0.9000 0.9450 0.9900 1.0350 Values Values of x Table 2: values of y as a function of x and z. Plate 4 of 4.  0.2368 -0.4003 -0.3611 -0.3192 -0.2745 -0.2268 -0.1757 -0.1210 -0.0626  0.2668 -0.3978 -0.3586 -0.3169 -0.2723 -0.2246 -0.1736 -0.1191 -0.0607  0.2968 -0.3948 -0.3558 -0.3141 -0.2696 -0.2220 -0.1711 -0.1166 -0.0583  0.3268 -0.3915 -0.3525 -0.3109 -0.2664 -0.2189 -0.1681 -0.1137 -0.0554  0.3568 -0.3878 -0.3489 -0.3073 -0.2629 -0.2155 -0.1647 -0.1103 -0.0521  0.3868 -0.3837 -0.3448 -0.3033 -0.2590 -0.2116 -0.1608 -0.1065 -0.0483  0.4168 -0.3792 -0.3404 -0.2989 -0.2546 -0.2072 -0.1565 -0.1023 -0.0441  0.4468 -0.3743 -0.3356 -0.2941 -0.2498 -0.2025 -0.1518 -0.0975 -0.0394  0.4768 -0.3691 -0.3303 -0.2889 -0.2446 -0.1973 -0.1466 -0.0924 -0.0342  0.5068 -0.3634 -0.3247 -0.2833 -0.2390 -0.1917 -0.1410 -0.0868 -0.0286  0.5368 -0.3574 -0.3187 -0.2772 -0.2330 -0.1857 -0.1350 -0.0807 -0.0225  0.5668 -0.3510 -0.3122 -0.2708 -0.2266 -0.1792 -0.1285 -0.0742 -0.0160  0.5968 -0.3442 -0.3054 -0.2640 -0.2197 -0.1723 -0.1216 -0.0672 -0.0089  0.6268 -0.3370 -0.2982 -0.2567 -0.2124 -0.1650 -0.1114 -0.0598 -0.0015  0.6568 -0.3294 -0.2905 -0.2491 -0.2047 -0.1573 -0.1064 -0.0520 0.0065  0.6868 -0.3214 -0.2825 -0.2410 -0.1966 -0.1491 -0.0982 -0.0436 0.0149  0.7168 -0.3130 -0.2741 -0.2325 -0.1881 -0.1405 -0.0895 -0.0349 0.0238  0.7468 -0.3042 -0.2653 -0.2236 -0.1791 -0.1314 -0.0804 -0.0256 0.0331  0.7768 -0.2950 -0.2560 -0.2143 -0.1697 -0.1219 -0.0708 -0.0159 0.0430  0.8068 -0.2854 -0.2464 -0.2046 -0.1599 -0.1120 -0.0607 -0.0057 0.0533  0.8368 -0.2754 -0.2363 -0.1944 -0.1496 -0.1016 -0.0502 0.0049 0.0641  0.8668 -0.2651 -0.2258 -0.1839 -0.1390 -0.0908 -0.0393 0.0160 0.0754  0.8968 -0.2543 -0.2150 -0.1729 -0.1279 -0.0796 -0.0279 0.0275 0.0871  0.9268 -0.2432 -0.2037 -0.1615 -0.1164 -0.0680 -0.0161 0.0395 0.0993  0.9568 -0.2314 -0.1919 -0.1495 -0.1042 -0.0557 -0.0036 0.0522 0.1122  0.9868 -0.2194 -0.1797 -0.1372 -0.0917 -0.0430 0.0093 0.0653 0.1256  1.0168 -0.2069 -0.1670 -0.1244 -0.0788 -0.0298 0.0226 0.0789 0.1394  1.0468 -0.1939 -0.1539 -0.1111 -0.0653 -0.0162 0.0365 0.0930 0.1538  1.0768 -0.1806 -0.1404 -0.0974 -0.0514 -0.0021 0.0508 0.1076 0.1687  1.1068 -0.1668 -0.1265 -0.0833 -0.0371 0.0125 0.0657 0.1227 0.1841  1.1368 -0.1525 -0.1121 -0.0687 -0.0222 0.0276 0.0810 0.1384 0.2001  1.1668 -0.1379 -0.0972 -0.0536 -0.0069 0.0432 0.0969 0.1546 0.2166  1.1968 -0.1227 -0.0818 -0.0380 0.0090 0.0593 0.1134 0.1714 0.2338  1.2268 -0.1071 -0.0660 -0.0219 0.0253 0.0760 0.1303 0.1887 0.2515  1.2568 -0.0910 -0.0497 -0.0053 0.0422 0.0932 0.1478 0.2066 0.2698  1.2868 -0.0744 -0.0328 0.0118 0.0595 0.1109 0.1659 0.2250 0.2887  1.3168 -0.0573 -0.0154 0.0294 0.0775 0.1292 0.1846 0.2442 0.3083  1.3468 -0.0397 0.0024 0.0476 0.0960 0.1480 0.2039 0 ;; 2639 0.3285  1.3768 -0.0217 0.0207 0.0663 0.1150 0.1675 0.2237 0.2842 0.3494  1.4068 -0.0031 0.0396 0.0855 0.1346 0.1875 0.2442 0.3052 0.3709  1.4368 0.0161 0.0592 0.1054 0.1549 0.2082 0.2654 0.3270 0.3932  1.4668 0.0358 0.0791 0.1257 0.1757 0.2295 0.2872 0.3493 0.4161  1.4968 0.0560 0.0997 0.1467 0.1971 0.2514 0.3096 0.3723 0.4397  1.5268 0.0767 0.1209 0.1683 0.2192 0.2739 0.3327 0.3960 0.4642  1.5568 0.0981 0.1426 0.1905 0.2419 0.2972 0.3566 0.4204 0.4894  1.5868 0.1201 0.1651 0.2134 0.2654 0.3212 0.3813 0.4459 0.5155  1.6168 0.1427 0.1881 0.2370 0.2894 0.3459 0.4066 0.4719 0.5424  1.6468 0.1659 0.2118 0.2612 0.3142 0.3713 0.4327 0.4988 0.5701  1.6768 0.1898 0.2361 0.2861 0.3397 0.3975 0.4596 0.5265 0.5988  1.7068 0.2144 0.2613 0.3118 0.3661 0.4246 0.4876 0.5554 0.6285  1.7368 0.2396 0.2871 0.3382 0.3932 0.4525 0.5163 0.5850 0.6592  1.7668 0.2655 0.3135 0.3654 0.4210 0.4812 0.5458 0.6155 0.6908  1.7968 0.2921 0.3408 0.3934 0.4498 0.5108 0.5764 0.6471 0.7236  1.8268 0.3197 0.3690 0.4222 0.4796 0.5414 0.6081 0.6800 0.7576  de z 1.0800 1.1250 1.1700 1.2150 1.2600 1.3050 1.3500 1.3950 Values Values of x 20) Device according to claim 1, 2 or 3, characterized in that it comprises a sun visor (75, 76). 21) Device according to claim 1, 2 or 3, characterized in that it comprises one or more acoustic speakers (72, 74, 77, 78). 22) Device according to claim 1, characterized in that it comprises a mirror in two or more parts (150, 151), the connection between said parts being made by means of profiled edges (152, 153) fitting into each other others. 23) Device according to one of claims 1 to 22, characterized in that the images are produced both by the screen of a television set and by the screen of a video monitor, a plasma screen, a screen with liquid crystal, or by another image-producing device. 24) Device according to claim 1, characterized in that the mirror (3) has ribs on its back, intended to reinforce said mirror. 25) Device according to one of claims 1 to 24, characterized in that it comprises a cradle composed of a pedestal mounted on ball casters, casters in contact with the ground, the pedestal being of variable inclination and comprising sliding tubular arms for enclosing the television, said arms being maintained at the desired elongation by locking screws.