Background of the Invention Decoration of products with texts and images is commonly made in a wide variety of industries. However, decoration is mostly made in two dimensions, i. e. a two dimensional (2D) decoration such as a 2D image is applied on a flat surface of a product. Three dimensional (3D) decoration on three dimensionally distributed (3D) surfaces of products is yet not so common.

In industry, the today most commonly used methods for decoration in 3D of medium sized products such as consumer electronics or toys with texts and images are indirect in that a decoration is first printed on a film, whereafter the film is applied on a product so that the decoration adhers to the product. These methods have some disadvantages though, of being complex, slow and expensive.

Some methods for printing a decoration directly on a non-planar, 3D surface, without first printing the decoration onto a film, have been developed.

In US 5 831 641 is described a method for 3D printing with inkjet. The idea of this method is to print on a 3D surface of an object by using a positioning apparatus which functions to automatically maintain the surface of the object within a plan substantially parallell to and slightly spaced apart from the place within which the inkjet nozzles of the ink-jet plotter

reside. This is a straightforward printing method, but it requires advanced positioning mechanics if the shape of the surface is complicated.

US 2001/0019340 Al describes another method for 3D printing with inkjet. In this method, the surface of a printing object is divided into a plurality of target areas, each of which is then approximated by a 2D projective plane. An inkjet printhead then prints a projected part image on each target area while moving in parallell with the projective planes. This method decreases the need for positioning mechanics, but introduces the problem with image deterioration owing to the inclination of the object surface in relation to the projective planes and the printhead.

This image deterioration consists largely of image distortion, which is due to that the space between pixels of the image on the surface is increased because of the inclination. In other words, the image distortion is due to non-uniform stretching of the image when applied on the 3D surface.

US 5 931 166 A describes a method and an apparatus for decorating or coloring fingernails or toenails.

According to the method, a subject's fingernail is scanned to obtain an image and the image is transferred to a computer. The computer then maps out the fingernail surface and scales a selected image or design to fit on the fingernail. This information is then used by the computer to activate an inkjet assembly to print out the stored image on the fingernail surface. The mapping of the fingernail is to account for the depth and size of the fingernail and to accurately center a selected design. However, the depth of a fingernail or toenail surface is small, wherefore the aforementioned problem with image deterioration owing to the inclination of the object surface is not relevant for fingernail decoration.

Summary of the Invention An object of the present invention is to provide an alternative and improved method and device for contactless application of a 2D image on a 3D surface.

Another object of the present invention is to provide a method and a device for contactless application of an image on a 3D surface without noticeable image distortion.

A particular object of the present invention is to make it possible to achieve a similar result when contactlessly printing a 2D image on a 3D surface as when applying a stick-on label with the image on the surface, i. e. to achieve an image on a 3D surface which follows the shape of the surface without being outstretched.

For achieving at least some of these and other objects, a method as defined in claim 1, a system as defined in claim 16, a method as defined in claim 19, a method as defined in claim 22, a computer program as defined in claim 23, and a computer program as defined in claim 24 are provided. Preferred embodiments of the invention are defined in the dependent claims.

More particularly, according to the invention, a method for contactless application of a two dimensional (2D) image on a three dimensionally distributed (3D) surface, comprises starting from image information representing said 2D image, and information representing said 3D surface, transforming said image information into a compensated image information such that distortion in the form of non-uniform stretching of said 2D image on said 3D surface is reduced, and transfering said 2D image in accordance with said compensated image information to said 3D surface by means of contactless application.

As defined herein, a two dimensional (2D) image means an image which is distributed in one 2D plane only in the 3D space, i. e. a flat image. The number of

dimensions, two or three, is defined according to an orthogonal coordinate system. The 2D image may be of any type reaching from simple patterns, figures and/or texts to more complicated paintings, logotypes, photographs etc. and may have any number of colours.

"Contactless application"of an image is herein defined as non-impact application wherein the surface is not touched by the application means. The particles which form said coating are instead ejected from the application means into the open air and then hit the surface. Examples of contactless application are inkjet printing, air-brush and other spray-painting.

Said image information representing said 2D image may be in the form of a data file, e. g. a bitmap file, or other information structure from which information about the image may be extracted.

Said information representing said 3D surface may also be in the form of a data file or other information structure. This information may differ depending on where the method starts from. The information may comprise the 3D surface itself physically or virtually in a computer program. The information may comprise a test pattern representing the structure of the 3D surface physically or virtually, which test pattern will be described hereinafter. The information may also comprise the 3D surface or the test pattern elastically unfolded into a 2D plane. The test pattern may be compensated into a compensating test pattern, which also will be described hereinafter.

A 2D image printed contactlessly from one direction on a 3D surface will be more or less distorted on all those parts of the surface that are inclined in relation to the printhead. According to the present invention, this distortion may be eliminated by compensating the image for the distortion before applying it on the surface. The image is herein via said compensated image information transformed into a compensated state in which

the image is distorted so to say in"reversed directions" as compared to the distortion resulting by the shape of the surface. Hence, when the compensated image is applied on the surface, the image will be"un-distorted"by the shape of the surface.

As mentioned above, a particular object of the present invention is to make it possible to achieve a similar result when contactlessly printing a 2D image on a 3D surface as when applying a stick-on label with the image on the surface. However, the present invention has an advantage compared to the stick-on label. When a stick-on label is to be applied on a double curvature surface, it will be crinkled. With the invention, such crinkling does not occur.

Said transformation of said image information into a compensated image information may be achieved in many different ways. A straightforward way to make the compensation is to use an iterative"trial-and-error" method, wherein the image information again and again is first manually transformed and then applied on the surface, until there is no distortion of the image on the surface. The manual transformation may for example be made using one of many known digital image processing programs.

The application of the transformed image information on the surface may, in each iterative step, either be made"for real", whereafter the image is cleaned off the surface or the surface is replaced by another equal surface, or be made by simulation in a simulation program.

According to one preferred embodiment of the invention, the transformation of said two dimensional image into the compensated state is achieved in another way, which is more efficient than the above described "trial-and-error"method. In this embodiment, the method further comprises the following:

retrieving said information representing said 3D surface by applying a 2D test pattern on a test surface having equal shape as said 3D surface, determining the distortion of said 2D test pattern on said test surface, creating a 2D compensating pattern by compensating said test pattern for said distortion, wherein said information representing said 3D surface comprises said 2D compensating pattern.

Determining and compensating for the distortion of an image may be quite difficult even if the subject of the image is simple. An advantage with this embodiment is that said test pattern may be designed so that it is easy to determine the distortion of it and thereafter to compensate it for the distortion.

Another advantage with this embodiment is that said compensating pattern, created from the distorted test pattern, may be used for different images. Hence, once said compensating pattern is created, it may be used to deform all possible different two dimensional images to be applied on a surface equal to the one for which the compensating pattern is created.

According to another embodiment of the invention, said transformation of said image information into a compensated image information further comprises deforming said image information so that it conforms to said 2D compensating pattern.

According to another embodiment of the invention, said transformation of said image information is made such that distortion in the form of non-uniform stretching of said 2D image on said 3D surface is reduced.

According to another embodiment of the invention, said determination of the distortion of said 2D test pattern comprises reading said distortion of said 2D test pattern from said test surface. By reading the

distortion, for example into a computer unit by means of a vision system, the distortion may be determined by means of a computer program.

According to another embodiment, said determination of the distortion of said 2D test pattern further comprises determining the deviation in a 2D plane of a distorted coordinate of a 3D test pattern, elastically unfolded into said 2D plane, from a corresponding coordinate of said 2D test pattern, wherein said 3D test pattern is the result of said 2D test pattern being applied on said test surface.

A paper which is folded into a 3D shape may be unfolded again into a flat state, i. e. into a 2D plane.

During this unfolding, the relative distances along the paper surface between different coordinates points of it are not changed. When on the other hand a double curvature surface, like e. g. a sphere or a cone, shall be unfolded into a 2D plane, the relative distances between coordinate points of this surface must be changed during the unfolding. This change of the relative coordinate distances may be compared to the inflation of a balloon, where for example a figure on the balloon is elastically outstretched. Therefore, the term"elastically unfolded" is used herein.

By elastically unfolding the 3D test pattern into a 2D plane, the position in this plane of a distorted coordinate of the 3D test pattern may be compared to the position of the corresponding non-distorted coordinate of the original test pattern.

According to yet another embodiment of the invention, said creation of a 2D compensating pattern further comprises moving said corresponding coordinate of said 2D test pattern in a direction in said 2D plane which is opposite to the direction from said coordinate towards said distorted coordinate. In this way,"over- compensation"of the 2D image for the distortion may be achieved by means of said compensating pattern. This

over-compensation is made in opposite directions compared to the directions of the distortion.

According to yet another embodiment, said creation of a compensating pattern further comprises moving said corresponding coordinate of said 2D test pattern a distance which is equal in magnitude to said deviation in said 2D plane of said distorted coordinate from said corresponding coordinate of said 2D test pattern. If this embodiment is combined with the one previously mentioned, i. e. moving said corresponding coordinate in a direction opposite to the direction of the distortion, the transformation of the 2D image may completely cancel the effect of the distortion.

In another embodiment of the invention, said 2D test pattern is designed for machine reading. This makes it possible to automatize the reading of the test pattern.

In another embodiment, said 2D test pattern comprises coordinate points arranged in a bar pattern.

The coordinates may easily be read from a bar pattern as cartesian coordinates, and the resolution of a bar pattern may easily be changed for different resolutions of images.

In yet another embodiment, the resolution of said 2D test pattern is adapted to the shape of said 3D surface.

If the inclination of the surface is large in relation to e. g. the moving plane of a printhead for applying the image, the resolution of the test pattern may need to be higher.

In another embodiment, said deforming of said 2D image is made by means of an interpolation method. There are several known mathematical interpolation methods that may be used to quickly transform the image so that it conforms to said 2D compensating pattern.

In a specific embodiment, said deforming of said 2D image is made by means of spline interpolation. With spline interpolation, continuos deformation of the 2D image may be achieved.

According to another embodiment of the invention, said 2D image is applied in the form of electrically charged particles on said 3D surface. In this way, common printing technique may be used for the application of the 2D image on the surface.

According to another embodiment, said electrically charged particles are in the form of viscous droplets.

The viscosity may for example be in interval 5 to 25 cP.

Well known inkjet technologies may then be used.

According to another embodiment, said application of said 2D image on said 3D surface further comprises guiding each of said electrically charged particles individually to a predetermined position on said 3D surface by means of an adjustable electric field having flux lines with a longitudinal direction extending through said 3D surface.

"Predetermined position on said surface"is herein defined as a position within a particular target area on said surface, wherein the target arean is determined in advance and constitutes as small part area of the surface as allowed by the particle size and the precision of the used equipment.

The particles are thus guided to the surface by means of the electric field in such a way that they follow flux lines of the electric field in their path to said surface. More particularly, the particles strive for travelling in the direction of flux lines of the electric field. Since the flux lines have a longitudinal direction extending through the surface onto which said 2D image is to be applied, the particles will be attracted to the surface and form said image on the surface.

By guiding particles to the surface by means of an electric field in order to apply the 2D image on the 3D surface, another type of image deterioration may be reduced. This other type of image deterioration, which is also due to the inclination of the surface in relation to the printhead, consists of blurring of the image as a

result of the particles being thinly spread out on the surface because of the inclination. Herein, this type of image deterioration is called image"degradation".

Since the flux lines of an electric field may extend approximately perpendicular in relation to the three dimensionally distributed surface, despite that the surface is inclined in relation to the printhead, the particles may impinge on the surface approximately perpendicularly so that they are not thinly spread out on the surface causing image degradation.

According to the invention, a system for contactless application of a 2D image on a 3D surface comprises means for transforming, from image information representing said 2D image and information representing said 3D surface, said image information into a compensated image information such that distortion in the form of non-uniform stretching of said 2D image on said 3D surface is reduced, and means for transfering said 2D image in accordance with said compensated image information to said 3D surface by means of contactless application.

According to one embodiment of the invention, the system further comprises means for applying a 2D test pattern on a test surface having equal shape as said 3D surface, means for determining the distortion of said 2D test pattern on said test surface, means for creating a 2D compensating pattern by compensation of said 2D test pattern for said distortion, and means for deforming said 2D image so that it conforms to said 2D compensating pattern.

According to another embodiment of the invention, said means for transfering said 2D image to said 3D surface further comprises means for ejecting electrically charged particles,

an electrode for forming an electric field between the electrode and said means for ejecting said particles, wherein said electric field has flux lines with a longitudinal direction extending through said 3D surface in order to guide said particles to said 3D surface so that they form said 2D image.

According to the invention, a method for managing image information comprises starting from image information representing a 2D image and information representing a 3D surface, transforming said image information into a compensated image information for transfer of said 2D image to said 3D surface by means of contactless application, wherein said act of transforming said image information is made such that distortion in the form of non-uniform stretching of said 2D image on said 3D surface is reduced.

Using this inventive method, it is possible for a service provider to provide pre-transformed image information for application of 2D images on specific products by users of these products.

According to another embodiment of the invention, the method further comprises retrieving said information representing said 3D surface by applying a 2D test pattern on a test surface having equal shape as said 3D surface, determining the distortion of said 2D test pattern on said test surface, creating a 2D compensating pattern by compensating said 2D test pattern for said distortion, wherein said information representing said 3D surface comprises said 2D compensating pattern.

According to another embodiment, said transformation of said image information into a compensated image information further comprises

deforming said image information so that it conforms to said 2D compensating pattern.

According to the invention, a method of preparing transformation of image information representing a 2D image for contactless application of the 2D image on a 3D surface, comprises applying a 2D test pattern on a test surface having equal shape as said 3D surface, determining the distortion of said 2D test pattern on said test surface, creating a 2D compensating pattern by compensating said 2D test pattern for said distortion, and providing means for deforming said image information so that it conforms to said 2D compensating pattern.

Using this inventive method, it is possible for a service provider to provide means for deforming 2D images to users of one or more specific products. Thereby a user of such a specific product may transform any 2D image for application on this product.

According to the invention, a computer program directly loadable into the internal memory of a computer device comprises software code portions performing input of image information representing a 2D image to be contactlessly applied on a 3D surface, input of a 2D test pattern which has been distorted by being applied on a test surface having equal shape as said 3D surface, determination of the distortion of said 2D test pattern by comparing it to a non-distorted, original 2D test pattern, creation of a 2D compensating pattern by compensating said original 2D test pattern for said distortion, deformation of said image information so that it conforms to said 2D compensating pattern, and output of said deformed image information.

According to the invention, a computer program directly loadable into the internal memory of a computer device comprises software code portions performing input of image information representing a 2D image to be applied on a 3D surface, input of a 2D compensating pattern for compensation of said image information for distortion resulting from application of said 2D image on said 3D surface, deformation of said image information so that it conforms to said 2D compensating pattern, and output of said deformed image information.

Brief Description of the Drawings The present invention will now be described in more detail with reference to the accompanying drawings, in which Fig. 1 is a schematic view of one embodiment of a system according to the invention; Fig. 2 is a schematic view of another embodiment of a system according to the invention ; Fig. 3 is schematic flow chart showing the steps of an embodiment of a method according to the invention; Fig. 4 illustrates a simple test pattern according to one embodiment of the invention; Figs 5.1 to 5.3 are a schematic perspective view, cross-sectional side view and top plan view, respectively, of an object with a simple 3D surface to be printed; Figs 6.1 and 6.2 are a schematic cross-sectional side view and top plan view, respectively, of the object shown in Figs 5.1 to 5.3 with the test pattern shown in Fig. 4 printed on it; Fig. 7.1 is the same view as shown in Fig. 6.1, but illustrates also elastic unfolding of the printed test pattern to a 2D plane; Fig. 7.2 is an illustration of the printed test pattern elastically unfolded in the 2D plane;

Fig. 8.1 shows a comparison between the original test pattern in Fig. 4 and the printed and elastically unfolded test pattern in Fig. 7.2 ; Fig. 8.2 shows compensation of the test pattern for the distortion due to the three dimensional shape of the object surface.

Detailed Description of Preferred Embodiments Fig. 1 shows an embodiment of a system according to the invention. The system comprises a computing device, here in the form of a personal computer (PC) 1, and a means, here in the form of an inkjet printer 2 connected to the PC 1, for applying a two dimensional (2D) test pattern on a three dimensionally distributed (3D) surface 5. Further, the system comprises means for determining the distortion of said test pattern on said 3D surface 5.

This means is here in the form of a video camera 3 with a frame grabber card which may be connected to the PC 1.

The device also comprises one or more mirrors 4 for elastically unfolding, into a two dimensional plane, the test pattern printed on the 3D surface 5.

The means for applying the 2D test pattern on the 3D surface 5 may be any type of device for contactless application of an image on a surface. Examples of such a device are, in addition to the inkjet printer, air-brush and spray-painting devices.

The means for determining the distortion of said test pattern on said 3D surface 5 may also be some other type of vision or image processing system. For example a digital camera with high resolution may be used instead of the video camera with frame grabber card. The purpose of this means is to be able to compare deviations of the printed test pattern in relation to the original test pattern. If necessary in order to cover all parts of the 3D surface, two or more video cameras or digital cameras may also be used.

The computing device, here the PC 1, is equipped with software, or in some other embodiment hardware, according to the invention for performing a method according to the invention, which method will be described later on herein.

Fig. 2 shows another embodiment of a system according to the invention which comprises a special inventive means for applying the 2D test pattern on the 3D surface 5. This means comprises a printhead, here an inkjet printhead 2.1 with an ejection nozzle 2.2, and an electrode 2.3 for forming an adjustable electric field between the electrode 2.3 and the printhead 2.1. The ejection nozzle 2.2 is arranged to eject electrically charged particles, here electrically charged ink droplets, towards the surface 5 onto which an image is to be printed.

As in Fig. 1, the device further comprises a video camera 3 with a frame grabber card, a PC 1 to which both the printhead 2.1 and the video camera 3 may be connected, and one or more mirrors (not shown) for elastically unfolding a test pattern printed on the surface 5.

The electric field is established as a result of a difference in electric potential between the printhead 2.1 and the electrode 2.3. In Fig. 2, this is illustrated by a potential V1 of the printhead 2.1 and another different potential V2 of the electrode 2.3.

When the 3D surface 5 of an object is to be coated by a 2D image, the electric field is applied over the surface 5 so that flux lines of the electric field cross the surface 5. In most cases, this means that the electrode 2.3 is placed behind the surface 5 in relation to the printhead 2.1. The ejection nozzle 2.2 of the printhead 2.1 then ejects the electrically charged ink droplets towards the surface 5. The ink droplets, being attracted by the electrode 2.3, strive for travelling in the direction of flux lines of the electric field. Since

the flux lines cross the surface 5, the ink droplets will impinge on the surface 5 and together form the image.

Thus, the ink droplets are guided to the surface 5 by means of the electric field.

As mentioned earlier herein, the embodiment shown in Fig. 2 has the advantage that it may reduce degradation of the image due to inclination of the surface 5 in relation to the printhead 2.1.

Fig. 3 shows the steps a to h of an embodiment of a method according to the invention. This method is largely implemented in the form of a software computer program in the PC 1 shown in Figs 1 and 2.

In the first step a of the method shown in Fig. 3, a 2D test pattern is printed on the 3D surface 5 by means of the inkjet printer 2. The size and resolution of the 2D test pattern may be adapted to the size and shape of the 3D surface. The 3D surface 5 may either be the 3D surface onto which a 2D image is to be printed later, or be a 3D test surface which shape is equal to the shape of a 3D surface onto which the 2D image is to be printed. If the 2D test pattern and the image are to be printed on the same 3D surface 5, the 2D test pattern may be printed in such ink that may be cleaned off the 3D surface 5 before the image is printed.

For illustration, a simple 2D test pattern is shown in Fig. 4. This 2D test pattern comprises black coordinate points arranged in a bar pattern. The 2D test pattern may look different, but is preferably designed for machine reading and so simple that distortion of it may be determined automatically.

In Figs 5.1 to 5.3 is shown an object with a simply shaped 3D surface which corresponds to the shape of the 3D surface 5. In Figs 6.1 and 6.2 the test pattern of Fig. 4 is shown printed on the 3D surface of the object shown in Figs 5.1 to 5.3.

In the next step b shown in Fig. 3, the printed test pattern is read from the 3D surface 5 into the computer

program by means of the video camera 3 with the frame grabber card. The printed test pattern is at this step digitalized and saved in the PC 1, e. g. in the form of a bitmap image.

In order to determine the distortion of the printed (3D) test pattern, due to the inclination of the 3D surface 5, compared to the original 2D test pattern (as the one shown in Fig. 4), the printed test pattern is elastically unfolded to a two dimensional plane before the reading. This is illustrated in Fig. 7.1. The 2D plane is perpendicular to the ejection direction of the printhead. As described above,"elastic unfolding"means unfolding where the relative distances between coordinate points, in this case coordinate points of the printed test pattern, may be changed during the unfolding.

This elastic unfolding of the printed test pattern is here achieved by means of mirrors 4 which are positioned in an angle of approximately 45° in relation to said 2D plane in such way as shown in Fig. 1. The printed test pattern is read by the video camera 3 partly directly from the 3D surface 5 and partly from the mirrors 4. The parts of the 3D surface which are read directly from the 3D surface 5 are the ones most parallell to said 2D plane, here the 3D surface on the top of the object (shown in Figs 5.1 to 5.3), while the parts read via the mirrors 4 are the ones most inclined in relation to said 2D plane, here the 3D surface on the sides of the object.

Actually, only surfaces which have flat sloping sides may be perfectly elastically unfolded into a 2D plane by means of flat mirrors. In order to elastically unfold the hemisphere-shaped surface 5 illustrated in the figures more perfectly, some other appropriate arrangement of mirrors may be used. For example, a cup- shaped mirror may be used in order to unfold all the sides at the same time, but this requires more of the following image processing in the computer program.

Alternatively, the surface 5 may be divided into part strips, which each is read via a bowed mirror or approximated by a flat sloping part strip and read via a flat mirror.

The use of mirrors for elastic unfolding is still applicable only on surfaces with relatively simple 3D shapes. If the shape of the surface is more complicated, the printed test pattern may first be scanned from the surface and then be modelled three dimensionally and elastically unfolded in a digital image processing program.

In step c, the parts of the printed test pattern which are read via the mirrors 4, i. e. the most inclined part surfaces, are mirrored back again by the computer program. The parts of the printed test pattern which are read in the mirrors 4 become mirrored in relation to the test pattern read directly from the 3D surface 5.

Therefore, these mirrored parts must be mirrored back again so that a correct two dimensional distorted test pattern is obtained. In Fig. 7.2 is shown the result of the elastic unfolding illustrated in Fig. 7.1. As described, this elastic unfolding includes mirroring in the mirrors 4 according to step b in Fig. 3 plus mirroring back again according to step c.

In step d, the coordinate deviation resulting from distortion is determined. As mentioned, the distortion is due to the inclination of the 3D surface 5 in relation to the printhead. When the embodiment shown in Fig. 2 is used, the distortion is also caused by the electric field. Irrespective of what has caused the distortion, it may be determined by determining the deviation of coordinates of the printed test pattern from corresponding coordinates of the original 2D test pattern.

This deviation determination is illustrated in Fig.

8.1, which shows a comparison between the original and the printed test pattern and a distance of deviation d

between an original and a printed point. In the computer program, the deviation may be determined in a x-and a y- direction separately.

In step e, a 2D compensating pattern is created, which compensates for the distortion and, more specifically, for the coordinate deviation. This is made by moving the position of each coordinate of the original test pattern the same distance as the magnitude of the coordinate deviation caused by the distortion, but in the opposite direction in said 2D plane compared to the distortion direction.

This is illustrated in Fig. 8.2, which shows how the coordinate point which was distorted a distance of deviation d is moved the same distance d but in the opposite direction (which is elucidated by the minus sign before the letter d in Fig. 8.2).

In the computer program, the coordinates of the original and the printed test pattern, as well as the determined coordinate deviations and the coordinates of the determined 2D compensating pattern, may be arranged in matrices.

In step f, an optional 2D image to be printed on the 3D surface 5 is input to the computer program. The image may be in the form of a bitmap image or some other appropriate data format.

In step g, the 2D image which was input in step f is deformed by means of an interpolation method in order to conform to the earlier determined compensating pattern.

In this embodiment, spline interpolation is used. Curves, or"splines", are herein generated by means of the coordinate points of the compensating pattern as control points. The pixels of the 2D image are then mapped to their new positions, in a compensated, deformed image, by connecting these positions to the generated splines. This is made in the x-direction and the y-direction separately. The colour of each pixel is determined by

interpolation of the colour, e. g. interpolation of RGB values, on nearby pixels.

Other interpolation methods which give the desired deformation of the image may also be used.

In the last step h, the deformed 2D image is printed on the surface 5. For conversion from an RGB to a CMYK colour space, known standard routines may be used.

Several known algorithms are also available for conversion from continuous to binear colour tones.

Once a compensating pattern has been determined for a specific surface by the steps a to e, any 2D image may be printed on equal surfaces by means of the steps f to h.

In an alternative embodiment of a method according to the invention, the printing of the test pattern is simulated in a PC or other computing device. All of the steps a to g in Fig. 3 are thus performed virtually inside the PC. This method is however more difficult to implement than the above described method with test printing on a real surface 5, especially if the distortion due to an electric field (see Fig. 2) should be determined.

In another alternative embodiment of a method according to the invention, the distortion is determined directly from the image to be printed on the surface.

Hence, no test pattern is needed in this embodiment, but the method is more difficult to implement if the image is complex.

It is to be understood that modifications of the above described systems and methods can be made by people skilled in the art without departing from the spirit and scope of the invention.