Method and computer device for determining a set of raster images for strips to be printed on an object.

Abstract

Method and computer device for determining a set of raster images for strips to be printed on an object. The method for determining a set of raster images for strips to be printed on an object using a printing system comprising at least one robot equipped with a printing tool, which is intended to follow a set of trajectories, receives a mesh of the object, texture maps associated with this mesh and the trajectories (TR1, TR2) to be followed by the robot, and it performs, using a computer device, a simulation of a printing process taking into account aerodynamic effects on printing jets and it determines gray levels according to joining situations (R) between strips (B1, B2) relative to the trajectories (TR1, TR2), which makes it possible to obtain raster images capable of generating a high quality print even in the case of complex geometry and long projection distances.Figure for the abbreviation: Figure 5.

Description

Title of the invention: Method and computer device for determining a set of matrix images for strips to be printed on an object. technical field

[0001] The present invention relates to a method and a computer device for determining a set of matrix images for strips to be printed on an object. State of the art

[0002] The invention applies more particularly to the field of texture mapping, which consists of applying two-dimensional texture data to a three-dimensional object. Texture mapping can be used to imprint representations of colors, text, logos, images, artistic designs, etc., onto the object. This object can be large, such as an airplane, for example, and have one or more curved surfaces.

[0003] Printing is performed using a printing system that performs direct-to-shape printing (DTS). Generally, such a printing system includes at least one robot designed to follow a set of trajectories. The robot is equipped with a plurality of print heads, each fitted with a plurality of nozzles.

[0004] The present invention relates to a method for determining a set of raster images that can be used by such a printing system to print strips on a three-dimensional object, each strip being obtained by a passage of the robot along a given trajectory.

[0005] A method for printing a three-dimensional object using inkjet printing is known from document EP 3 208 746 A1. The printing method is defined to allow printing on a curved surface. However, the printing method described in this document does not address the problem of joining adjacent strips, i.e., the partial overlap between two adjacent strips. This problem must therefore be addressed in 2D images, as a post-processing step on the generated images. However, such processing is only possible for a simple joining configuration.

[0006] In particular, in the event of obstacles impacting the robot's movement, such as, for example, an antenna on a printing area of ​​an aircraft fuselage, a complex decomposition of the printing area into strips is generally planned, induced by this presence and by the objective of reducing the unprinted area around the or obstacles. Printing complexity increases when the area to be printed is curved.

[0007] Such a complex decomposition of the strips generates a wide variety of joining situations, some of which are difficult, or even impossible, to manage with 2D post-processing of the generated strips.

[0008] There is therefore a need to find a solution enabling the determination, in a precise and relatively simple way, of a set of matrix images for strips to be printed on an object, taking into account all situations of joining between the strips and enabling the provision of high-quality printing despite, in particular, a complex geometry. Description of the invention

[0009] The present invention aims to provide such a solution. To this end, it relates to a method for determining a set of matrix images for strips to be printed on an object (manufactured), the printing to be carried out using a printing system comprising at least one robot intended to follow a set of trajectories, said robot being equipped with a plurality of print heads, each of which is equipped with a plurality of nozzles for printing jets at given projection times.

[0010] According to the invention, said method comprises at least the following successive steps: - a reception step to receive a mesh of the object, corresponding to a tessellated mesh formed of triangles, texture maps associated with this mesh and said trajectories to be followed by the robot; and - a determination step to determine, from said mesh, said texture maps and said trajectories, said set of raster images, by carrying out a simulation of a printing process taking into account aerodynamic effects on the printing jets and by determining grey levels according to joining situations between bands relating to said trajectories.

[0011] Thus, thanks to the invention, the method makes it possible to determine, precisely and relatively simple, a set of raster images for strips to be printed on a manufactured object, taking into account all situations of joining between the strips and allowing to provide a high quality print despite a complex geometry and also long projection distances, as specified below.

[0012] In a preferred embodiment, the determination step comprises the following successive substeps: - a first sub-step to simulate (digitally) the printing process in order to determine, for each trajectory, each nozzle of each print head printing and each projection instant, the coordinates of an impact point of a potential drop on a triangle of said mesh and the identification of said triangle; - a second sub-step to identify, in subdivided triangles of the mesh, a joining situation from said trajectories, to apply a joining code relative to each joining situation and to associate the joining code with the texture map at the location corresponding to the coordinates of the subdivided triangle considered; - a third sub-step to analyze the texture maps including all the joining situations and joining codes and to associate with each joining situation a joining gradient for each of the successive bands to be printed; - a fourth sub-step to determine, among the potential drops, which drops will be used, and to assign a grey level to each of the drops that will be used; and - a fifth sub-step implemented for each trajectory and for each print head, this fifth sub-step incorporating, for each drop that will be used corresponding to this trajectory and this print head, the level of grey assigned to it, in an initially empty matrix image so as to obtain the matrix image associated with this trajectory and this print head, said set of matrix images comprising the matrix images thus obtained for all trajectories and for all print heads.

[0013] Advantageously, the first substep comprises the following (successive) operations, for each trajectory, each nozzle of each print head and each projection instant: - projection of a print jet from the nozzle perpendicular to a nozzle plate towards the mesh; - Calculation of the point of intersection of the print jet with the mesh; and - calculation of the impact point corresponding to the impact point of a potential drop (or drop opportunity), by applying a deviation on the intersection point in a printing direction to take into account an aerodynamic deviation of the printing jet (or drop) during projection.

[0014] Furthermore, advantageously, the second substep comprises the following (successive) operations for each triangle of the object's mesh: - subdivision of the triangle into subtriangles having a predetermined side length; and - for each sub-triangle: • selection of all potential drops falling on this sub-triangle; • identification of the connection situation based on the number and order of the different trajectories; and • implementation of the blending code in an added color layer corresponding to the blending situation and association with the texture map at the location indicated by the sub-triangle coordinates.

[0015] Advantageously, the subdivision of the triangle into sub-triangles is carried out iteratively until a predetermined solution is obtained.

[0016] Moreover, advantageously, the third sub-step comprises the following (successive) operations: - analysis of the texture map containing all the connection situations; - simplification of the connection situations taken into account; - segmentation of the texture map in relation to the joining codes; and - association, at each joining situation, of the joining gradient for each of the successive bands to be printed.

[0017] Moreover, advantageously, the fourth substep comprises the following (successive) operations, for each triangle of the object's mesh: - subdivision of the triangle into sub-triangles having a predetermined side length; - determination from the texture map of an average target color to be applied to the sub-triangle and the blending gradient to be applied to each band; and - for each band, determination among the potential drops, of the drops that will be used and assignment to each of the drops that will be used a level of grey.

[0018] Furthermore, advantageously, the fifth substep comprises the following (successive) operations, for each trajectory and each print head: - creation of the empty matrix image which includes a height in pixels equal to the number of nozzles of the print head and a width in pixels equal to the duration of the trajectory multiplied by the ejection frequency or to the length of the trajectory; and - for each drop relative to the trajectory and the print head, storage in the matrix image of the gray level at the position corresponding to the nozzle and the projection time so as to obtain the matrix image associated with this trajectory, this print head or the nozzle.

[0019] The present invention also relates to a computer device for determining a set of matrix images for strips to be printed on an object, the printing to be carried out using a printing system comprising at least one robot intended to follow a set of trajectories, said robot being provided with a plurality of print heads, each of which is equipped with a plurality of nozzles for printing jets at given projection times.

[0020] According to the invention, the device comprises at least: - a receiving unit configured to receive a mesh of the object, corresponding to a tessellated mesh formed of triangles, texture maps associated with this mesh, and the trajectories to be followed by the robot; and - a computing unit configured to determine, from said mesh, said texture maps and said trajectories, said set of raster images, using a simulation of a printing process taking into account aerodynamic effects on the printing jets and a determination of grey levels according to joining situations between bands relating to said trajectories. Brief description of the figures

[0021] The accompanying figures will clearly illustrate how the invention can be implemented. In these figures, identical reference numerals designate similar elements.

[0022] The [Fig. 1] is the block diagram of a method for determining a set of matrix images for strips to be printed on a manufactured object.

[0023] Figure [Fig.2] schematically shows a device configured to implement the process of Figure [Fig.1].

[0024] Fig. 3 schematically shows part of an object to which a tessellated mesh is associated.

[0025] Fig. 4 is the block diagram of an example of a printing system capable of implementing direct printing on form.

[0026] Fig. 5 schematically illustrates a connection situation.

[0027] Fig. 6 is a schematic representation illustrating the determination of a point of contact during a projection from a nozzle. Detailed description

[0028] Within the framework of the present invention, a method P (for example such as that shown in a particular embodiment in [Fig.1]) which is capable of being implemented by a computer device 1 (for example such as that shown in a particular embodiment in [Fig.2]), is intended to determine a set E of matrix images IM (“raster images” in English) for strips to be printed on an object O (partially shown in [Fig.3]) which has been manufactured.

[0029] These raster images (IM) are defined within the framework of texture mapping, which consists of applying data from a two-dimensional (or 2D) texture to a three-dimensional (or 3D) object such as object O. Texture mapping can be used to add representations to the object, including colors, text, logos, images, artistic designs, etc.

[0030] In the context of the present invention, for the sake of simplicity, the term "object" means any device, machine or other mechanical element or part thereof A device, machine, or other mechanical element whose surface or part of a surface is capable of receiving such an impression. This could notably be the fuselage of an aircraft on which the characteristic markings (logos, colors, etc.) of the airline that will operate the aircraft will be printed.

[0031] IM matrix images are intended to be used for direct-to-shape printing of the "DTS Printing" type, which is a technology allowing printing directly onto the three-dimensional surface of an object, regardless of its shape.

[0032] Direct printing will be implemented using a printing system 8, for example such as that shown schematically in [Fig. 4]. This printing system 8 comprises at least one robot 9 designed to follow a set of trajectories TR. Within the scope of the present invention, the robot can be configured to perform any type of movement (linear movement, rotary movement, complex articulation, etc.) and can correspond, for example, to a robotic arm or a Cartesian gantry.

[0033] The robot 9 includes at one free end a printing end-effector 10. This printing end-effector 10 is provided with a plurality of print heads 11, for example, four print heads, in a non-limiting example, for each of the primary colors cyan, magenta, yellow, and black. Each of these print heads 11 is equipped with a plurality of nozzles 12, for example, more than a thousand nozzles, to generate print jets (i.e., projections of ink droplets) at given projection times.

[0034] The printing system 8 also includes a control unit 13 intended in particular to control the movement of the robot 9, generally a robotic arm, and the prints made by the printing tool 10. The set E of the matrix images IM determined by the computer device 1 can, for example, be provided to the control unit 13 of the printing system 8, for the purpose of printing.

[0035] During printing, the printing tool 10 of the robot 9 is moved each time (i.e., with each pass) along a path TR to print a strip each time, such as the strips B1 and B2 shown for illustration in [Fig. 5]. Each printed strip B1, B2 represents a part of the livery, i.e., the print to be produced.

[0036] The process P and the computer device 1 are specifically designed to take into account situations of joining (“stitching”) of such strips, i.e. of superimpositions of directly adjacent strips.

[0037] Fig. 5 shows very schematically a connection situation R (illustrated by hatching locating the overlap area) between the band Bl represented in thick lines and the band B2 represented in dashes.

[0038] Due to the presence of one or more potential obstacles on an area of ​​the object to be printed, for example an aircraft antenna, and the need to reduce the unprinted area around the obstacle(s), a complex decomposition of the strips (having various shapes and / or sizes and / or orientations) is generally planned to maximize the printable area despite the limited accessibility of the printing tool 10.

[0039] This complex decomposition of the strips generates a wide variety of joining situations, some of which are difficult or even impossible to manage with 2D post-processing of the generated strips.

[0040] By way of illustration, a plurality of different connection situations may arise, due in particular to: - strips of different shapes (for example, straight or curved strips), different sizes and / or different orientations; and / or - for curved strips, different printing areas for each color; and / or - partial overprinting on previously printed strips (curved or straight), with or without a previously applied join; and / or - beginnings and / or ends of tapes, possibly linked to other tapes, and this in particular in different ways.

[0041] These different joining situations therefore include different types of joining (i.e. areas (of overlap of at least two strips) which have different shapes and sizes).

[0042] As indicated above, the purpose of process P is, in particular, to manage such connection situations. To this end, said process P comprises, as shown in [Fig. 1], in particular the following steps, implemented by the computer device 1: - a reception step S1 implemented by a reception unit 2 (RECEPT for "reception unit" in English) of the computer device 1 ([Fig.2]), to receive at least: • a mesh M of the manufactured object O, as partially and schematically illustrated in [Fig.4], corresponding to a usual tessellated mesh, formed of triangles; • standard CT (two-dimensional) texture maps, associated with this M mesh. These texture maps are HD (high resolution); and • the TR trajectories which must be followed by the printing tool 10 of the robot 9 to print the different strips; - a determination step S2 implemented by a computing unit 4 (COMP) of the computer system 1, to determine the set E of matrix images IM, from said mesh M, of said maps CT texture and said TR trajectories, in the manner specified below. In particular, the determination step S2 performs a (numerical) simulation of a printing process taking into account aerodynamic effects on printing jets and determines gray levels as a function of R blending situations ([Fig. 5]) between bands related to the TR trajectories; and - a transmission step implemented by a transmission unit 3 (TRANSM for "transmission unit" in English) of the computer device 1, to transmit this set E of matrix images IM to a user device (not shown), for example a computer or a control unit of the printing system 8 (such as the control unit 13 of [Fig.4]).

[0043] As shown in [Fig.1], the determination step S2 comprises a sequence SE of successive substeps S2A to S2E.

[0044] The determination step S2 includes, first of all, the substep S2A which is implemented by a calculation element 4A of the calculation unit 4, to simulate (digitally) a printing process.

[0045] To carry out this printing simulation, the calculation element 4A determines data for each trajectory TR, for each nozzle 12 of each print head 11 and for each projection instant (i.e. a precise instant when a print jet is generated from the nozzle 12), namely the coordinates of an impact point of a potential droplet (specified below) on a triangle of the mesh M and the identification of this triangle.

[0046] This data is integrated into a table T. This table T is preferably stored in a memory of the computer device 1, for example in a memory 5 ([Fig.2]) or in a memory (not shown) of the computing unit 4.

[0047] To perform this simulation of the printing process, the calculation element 4A implements the following operations: - it selects and orders the TR trajectories of the printing tool 10 of the robot 9 to cover the livery; - it creates the empty table T, to store the data later; and - for each TR trajectory, for each projection instant (corresponding to a time step of the trajectory, sampled with the projection frequency performed by the print heads 11): • It positions the printing tool 10 at a corresponding (6D-type) position relative to the tessellated mesh M of the object O. This (6D-type) position designates the location and orientation of the printing tool 10 in (three-dimensional) space according to six degrees of freedom (with three translational degrees of freedom and three rotational degrees of freedom); and • for each nozzle 12 of each print head 11 at each projection instant, it implements a series of operations.

[0048] This sequence of operations comprises the following (successive) operations (therefore for each nozzle 12 of each print head 11 at each projection instant): - projection of a print jet 14 from the nozzle 12 perpendicularly to a plate 12A of the nozzle 12 towards the mesh M of the object, as schematically illustrated in [Fig. 6]. The nozzle 12 is located at a distance D from the mesh which is, for example, greater than 5 mm (in the case of "DTS Printing" type printing) so that the print jet becomes sensitive to aerodynamic effects, as specified below; - Calculation of the intersection point PI of the printing jet 14 with the mesh M; and - Calculation of the impact point P2 corresponding to the impact point of a potential droplet (or droplet opportunity), by applying a deviation (illustrated by an arrow G in [Fig. 5]) to the intersection point PI. This deviation to go from the intersection point PI to the impact point P2 is carried out along a printing direction F (i.e. the direction of movement of the printing tool 10) to take into account an aerodynamic deviation (i.e. a deviation due to aerodynamic effects) of the droplet (or the printing jet) during projection.

[0049] Then, the calculation element 4A adds a new row to table T in which are stored the trajectory reference, the projection time, the print head reference 11 (which corresponds to a color), the nozzle reference 12, the reference of the (impacted) triangle of the mesh M, and the coordinate of the impact point P2 on this triangle. For the purposes of the present invention, the term "reference" of an element means any type of information that allows that element to be identified.

[0050] The process P thus makes it possible to take into account and compensate for aerodynamic effects in the placement of the drops. These aerodynamic effects are due in particular to: - at a large projection distance D ([Fig.6]), for example greater than 5 mm, in the case of direct printing on a "DTS Printing" type form, which induces a significant transverse airflow, likely to deflect the effective movement of the droplets, compared to a straight printing jet 14; and - aerodynamic turbulence which can be generated between the nozzles 12 when several of them, close to each other, carry out projections for a short period of time.

[0051] The determination step S2 then includes the substep S2B implemented (after the substep S2A) by a calculation element 4B of the calculation unit 4, to classify the connection situations (between the bands).

[0052] More specifically, in substep S2B, the calculation element 4B identifies, in subdivided triangles of the mesh M, a connection situation from the trajectories TR, then it applies a connection code relative to each connection situation (i.e. a code which makes it possible to identify the type of connection among the different possible types) and it associates the connection code with the texture map CT, at the location corresponding to the coordinates of the subdivided triangle considered.

[0053] To do this, in substep S2B, the calculation element 4B performs a plurality of operations for each triangle of the mesh M of the object O.

[0054] The calculation element 4B first subdivides the triangle under consideration into subtriangles, which are in turn subdivided, and so on, iteratively, until a suitable size is obtained for the subtriangles. To do this, preferably, each triangle, and then each subtriangle, is subdivided (iteratively) into four subtriangles, and this continues until the subtriangles (preferably equilateral) have a side length that is less than a predetermined value (representing a desired resolution), for example, 500 pm.

[0055] Then, for each subtriangle (obtained by such subdivisions), the calculation element 4B performs the following sequence of (successive) operations: - it selects from the table T all the potential drops falling on this sub-triangle; - it identifies the connection situation based on the number and order of the different trajectories; and - it sets up the join code in an added color layer, corresponding to the join situation, and it associates the join code with the CT texture map at the location indicated by the sub-triangle coordinates (for example by storing the join code identifying the join situation in a dedicated additional "color" layer of the CT texture map).

[0056] The determination step S2 then includes the substep S2C implemented (after substep S2B) by a calculation element 4C of the calculation unit 4, to incorporate blending gradients into the texture map CT.

[0057] More specifically, in substep S2C, the calculation element 4C analyzes the CT texture maps (as completed in substep S2B) including the join situations and the join codes, and associates to each join situation a join gradient (or pattern) for each of the successive strips to be printed, each of the strips being associated with one of the TR trajectories.

[0058] For a given point (to be printed at a seam) that must receive a given total volume of color (ink), the seam gradient defines the percentage of this total volume for each of the bands participating in the seam. For example, if the point is located at a seam of two bands, a given percentage of the color (by example 80%, corresponding to the blend gradient of the first band) is deposited at this point to form the first band and the remainder (20% in this example, corresponding to the blend gradient of the second band) is deposited at this point to form the second band.

[0059] To do this, in substep S2C, the calculation element 4C performs the following operations: - it analyzes the CT texture map containing all the joining situations; - it simplifies the connection situations where possible. For example, a connection situation between four different trajectories can be considered as a connection situation with only three trajectories, if we consider that one of the four trajectories does not contribute to this area; - it segments the CT texture map with respect to the joining codes; and - it associates with each joining situation the joining gradient (or pattern) for each of the successive bands to be printed (i.e. for each of the successive passes).

[0060] The determination step S2 then includes the substep S2D implemented (after the substep S2C) by a 4D calculation element of the calculation unit 4, to determine, among the potential drops, the drops that will be used, and to assign to each of the drops that will be used a level of grey which is stored in the table T.

[0061] To do this, in substep S2D, the 4D calculation element performs a plurality of operations for each triangle of the mesh M of the object O.

[0062] The 4D calculation element first subdivides the triangle into subtriangles, which are in turn subdivided, and so on, iteratively, until a suitable size is obtained for the subtriangles. To do this, preferably, each triangle, and then each subtriangle, is subdivided (iteratively) into four subtriangles, until the subtriangles (preferably equilateral) have a side length that is less than a predetermined value (representing a desired resolution), for example, 500 pm.

[0063] The 4D calculation element then performs the following (successive) operations: - it determines, for each sub-triangle, where applicable, from the CT texture map, an average target color to be applied to the sub-triangle and the blending gradient to be applied to each band; and - for each band (i.e. each passage corresponding to a trajectory), it determines, among the potential drops, the drops that will be used, and it assigns to each of the drops that will be used a level of grey.

[0064] To do this, it performs an optimization to obtain homogeneity and accuracy of colors on the sub-triangle, based on the diameter of the (printed) points and the ICC profile (for "International Color Consortium") which defines how colors should be reproduced to ensure consistent and accurate color management. The ICC profile can be received at the SI reception stage and / or stored in a memory of the computer device 1 (for example, in memory 5).

[0065] The grey level thus determined is then stored in the table T.

[0066] Finally, the determination step S2 also includes the substep S2E implemented (after the substep S2D) by a computing element 4E of the computing unit 4, to determine a matrix image IM, for each trajectory TR and for each print head 11, that is to say for each pair comprising one of the trajectories TR initially received and one of the print heads 11 of the printing system 8.

[0067] The matrix images IM, which are obtained (in substep S2E) for all pairs consisting of a trajectory and a print head, form the set E of matrix images IM.

[0068] To do this, in substep S2E, the calculation element 4E incorporates, for each drop of the table T corresponding to this trajectory TR and to this print head 11, the level of grey which was assigned to it (in substep S2D), in an initially empty 2D matrix image so as to obtain the 2D matrix image associated with this trajectory TR and to this print head 11 after taking into account all the corresponding drops.

[0069] More specifically, in substep S2E, the calculation element performs the following 4D operations for each trajectory TR and each print head 11: - it creates the empty 2D raster image IM which has a height in pixels equal to the number of nozzles 12 of the print head 11 and a width in pixels equal to the duration of the trajectory TR multiplied by the projection frequency (performed from the print head 11) or to the length of the trajectory; and - for each drop of the table T corresponding to the trajectory TR and the print head 11 considered, it stores in the matrix image IM the grey level at the position corresponding to the nozzle 12 and at the time of projection, so as to obtain the matrix image IM associated with this trajectory TR and this print head 11.

[0070] Therefore, for a number N of trajectories TR and a number M of print heads 11, the set E comprises NxM matrix images IMnm, m being between 1 and N and m being between 1 and M.

[0071] All the aforementioned processing, sub-steps and operations are implemented digitally by the computer device 1. No physical processing is carried out.

[0072] Said computer device 1 may also include, as shown in the [Fig.2]: - at least one memory, such as memory 5 (MEM for "Memory" in English), capable of storing data used for data processing and calculations performed by the computing elements of the computer device 1, such as, for example, array T; and - a human-machine interface 6 (HMI for "Human-Machine Interface" in English) allowing an operator to provide data to the computer device 1, such as for example the predetermined value concerning the lengths of the sides of the subdivided triangles, which is used in substeps S2B and S2D.

[0073] In addition, the receiving unit 2 and the transmitting unit 3 can be part of a common communication system 7 allowing the computer device 1 to communicate with devices external to the computer device 1, by a wired or wireless link.

[0074] The various calculation elements and / or calculation units of the computer device 1 can correspond to any type of processor capable of implementing the corresponding processing and calculations.

[0075] The process P and the computer device 1, as described above, thus make it possible to create matrix images for all the strips to be printed along the robot's trajectories, taking into account all the situations of joining between the strips and providing high-quality printing despite complex geometry and long projection distances.

[0076] More specifically, they thus allow, in particular: - to achieve very high precision in droplet positioning, resulting in better color management and, consequently, color consistency and a sharper, more faithful print reproduction; and - by taking into account the (3D) joins, to manage complex join situations, which in particular allows to extend the area that can be printed (around obstacles), without generating visual defects.

Claims

Demands

1. A method for determining a set of raster images for strips to be printed on an object, the printing to be carried out using a printing system (8) comprising at least one robot (9) intended to follow a set of trajectories (TRI, TR2), said robot (9) being provided with a plurality of print heads (11) each of which is equipped with a plurality of nozzles (12) for printing jets at given projection times, characterized in that it comprises at least the following successive steps: - a reception step (SI) to receive a mesh (M) of the object (0), corresponding to a tessellated mesh formed of triangles, the texture maps associated with this mesh (M) and said trajectories (TRI, TR2) to be followed by the robot (9);and - a determination step (S2) to determine, from said mesh (M), said texture maps and said trajectories (TRI, TR2), said set of raster images, by carrying out a simulation of a printing process taking into account aerodynamic effects on the printing jets (14) and by determining grey levels according to joining situations (R) between bands (B1, B2) relating to said trajectories (TRI, TR2).;

2. A method according to claim 1, characterized in that the determination step (S2) comprises the following successive substeps: - a first substep (S2A) to simulate the printing process so as to determine, for each trajectory (TRI, TR2), each nozzle (12) of each print head (11) and each projection instant, the coordinates of an impact point (P2) of a potential drop on a triangle of said mesh (M) and the identification of said triangle; - a second substep (S2B) to identify, in subdivided triangles of the mesh (M), a join situation (R) from said trajectories (TRI, TR2), to apply a join code relative to each join situation (R) and to associate the join code with the texture map at the location corresponding to the coordinates of the subdivided triangle considered; - a third sub-step (S2C) to analyze the texture maps including all the join situations (R) and the join codes and associate to each join situation (R) a join gradient for each of the successive bands to be printed; - a fourth substep (S2D) to determine, among the potential drops, the drops that will be used, and to assign to each of the drops that will be used a level of grey; and - a fifth substep (S2E) implemented for each trajectory (TRI, TR2) and for each print head (11), this fifth substep (S2E) incorporating, for each drop that will be used corresponding to this trajectory (TRI, TR2) and to this print head (11), the level of grey assigned to it, in an initially empty matrix image so as to obtain the matrix image associated with this trajectory (TRI, TR2) and to this print head (11), said set of matrix images comprising the matrix images thus obtained for all the trajectories (TRI, TR2) and for all the print heads (11).

3. Method according to claim 2, characterized in that the first sub-step (S2A) comprises the following operations, for each trajectory (TRI, TR2), each nozzle (12) of each print head (11) and each projection instant: - projection of a print jet (14) from the nozzle (12) perpendicular to a plate (12A) of the nozzle (12) towards the mesh (M); - calculation of the intersection point (PI) of the print jet (14) with the mesh (M); and - calculation of the impact point (P2) corresponding to the impact point of a potential drop, by applying a deviation on the intersection point (PI) in a printing direction (F) to take into account an aerodynamic deviation of the printing jet during projection.

4. A method according to any one of claims 2 and 3, characterized in that the second substep (S2B) comprises the following operations for each triangle of the mesh (M) of the object (O): - subdivision of the triangle into subtriangles having a predetermined side length; and - for each sub-triangle: • selection of all potential drops falling on this sub-triangle; • identification of the joining situation based on the number and order of the different trajectories (TRI, TR2); and • implementation of the joining code in an added color layer corresponding to the joining situation and association with the texture map at the location indicated by the coordinates of the sub-triangle.

5. A method according to any one of claims 2 to 4, characterized in that the third substep (S2C) comprises the following operations: - analysis of the texture map containing all the join situations (R); - simplification of the join situations (R) taken into account; - segmentation of the texture map with respect to the join codes; and - association, to each join situation (R), of the join gradient for each of the successive bands to be printed.

6. A method according to any one of claims 2 to 5, characterized in that the fourth substep (S2D) comprises the following operations, for each triangle of the mesh (M) of the object (0): - subdivision of the triangle into subtriangles having a predetermined side length; - determination from the texture map of an average target color to be applied to the subtriangle and the blending gradient to be applied to each band; and - for each band, determination among the potential drops, of the drops that will be used and assignment to each of the drops that will be used a level of grey.

7. A method according to any one of claims 2 to 6, characterized in that the fifth substep (S2E) comprises the following operations, for each trajectory (TRI, TR2) and each print head (11): - creation of the empty raster image which comprises a height in pixels equal to the number of nozzles (12) of the print head (11) and a width in pixels equal to the duration of the trajectory (TRI, TR2) multiplied by the ejection frequency or the length of the trajectory; and - for each drop relative to the trajectory (TRI, TR2) and to the print head (11), storage in the matrix image of the grey level at the position corresponding to the nozzle (12) and at the time of projection so as to obtain the matrix image associated with this trajectory (TRI, TR2) and to this print head (11).

8. A method according to any one of claims 4 and 6, characterized in that the subdivision of the triangle into sub-triangles is carried out iteratively until a predetermined resolution is obtained.

9. Computer device for determining a set of raster images for strips to be printed on an object, the printing to be carried out using a printing system (8) comprising at least one robot (9) intended to follow a set of trajectories (TRI, TR2), said robot (9) being provided with a plurality of print heads (11) each of which is equipped with a plurality of nozzles (12) for printing jets at given projection times, characterized in that it comprises at least: - a receiving unit (2) configured to receive a mesh (M) of the object (0), corresponding to a tessellated mesh formed of triangles, the texture maps associated with this mesh (M) and said trajectories (TRI, TR2) to be followed by the robot (9);and - a computing unit (4) configured to determine, from said mesh (M), said texture maps and said trajectories (TRI, TR2), said set of raster images, using a simulation of a printing process taking into account aerodynamic effects on the printing jets and a determination of grey levels as a function of joining situations (R) between bands (B1, B2) relating to said trajectories (TRI, TR2).;