Method and computing device for determining a set of raster images for a strip to be printed on an object

Abstract

A method and a computing device for determining a set of raster images for a strip to be printed on an object are disclosed. A method for determining a set of raster images for a strip to be printed on an object using a printing system comprising at least one robot provided with a printing tool intended to follow a set of trajectories, the method receives a mesh of the object, a texture map associated with the mesh and trajectories (TR1, TR2) to be followed by the robot, and it carries out a simulation of the printing process taking into account the aerodynamic effects on the printing jets by means of a computing device, and it determines the greyscales as a function of the splicing (R) between the strips (B1, B2) related to the trajectories (TR1, TR2), which makes it possible to obtain raster images that can generate high-quality prints even in the case of complex geometries and long projection distances.

Description

Technical Field

[0001] The present invention relates to a method and computing apparatus for determining a set of raster images for strips to be printed on an object. Background Technology

[0002] This invention is more specifically applicable to the field of texture mapping, which involves applying two-dimensional texture data to a three-dimensional object. Texture mapping can be used to print representations of colors, text, logos, images, artistic designs, etc., on an object. For example, the object can be large, such as an airplane, and can have one or more curved surfaces.

[0003] Printing is performed using a printing system known as "DTS printing" ("Direct-To-Shape printing"), which prints directly onto a shape. Typically, such a printing system includes at least one robot designed to follow a set of trajectories. The robot is equipped with multiple printheads, each of which is equipped with multiple 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, wherein each strip is obtained by a robot traversing a given trajectory.

[0005] Document EP 3208746 A1 describes a method for inkjet printing on three-dimensional objects. The printing method is specifically designed to enable printing on curved surfaces. However, the method described in this document does not address the problem of splicing between adjacent strips, i.e., partial overlap between two adjacent strips. This problem must therefore be solved on a two-dimensional image as a post-processing step in the generated image. However, such processing is only possible for simple splicing configurations.

[0006] Note that if obstacles affecting the robot's movement exist, such as antennas on the area of ​​the aircraft fuselage to be printed, then as a result of the presence of such obstacles and with the aim of reducing the unprinted area around one or more obstacles, it is generally expected that the area to be printed will be complexly divided into strips. The complexity involved in printing increases when the area to be printed is curved.

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

[0008] Therefore, there is a requirement to find a solution that allows for the accurate and relatively simple determination of the set of raster images for the strips to be printed on an object, taking into account all splicing situations between the strips and allowing for high-quality printing, especially regardless of any complex geometry. Summary of the Invention

[0009] The object of this invention is to provide such a solution. To this end, it relates to a method for determining a set of grid images for strips to be printed on an object, wherein printing must be carried out using a printing system comprising at least one robot designed to follow a set of trajectories, the robot being equipped with a plurality of print heads, each of which is equipped with a plurality of nozzles for printing the ejected material at a given ejection moment.

[0010] According to the present invention, the method includes at least the following sequential steps: - A receiving step for receiving the mesh of the object corresponding to the tessellation mesh formed by triangles, the texture map associated with the mesh, and the trajectory to be followed by the robot; and - Determine steps for determining the raster image set based on the mesh, the texture map, and the trajectory by: simulating the printing method considering the aerodynamic effects on the printed ejector; and determining grayscale as a function of the stitching between strips associated with the trajectory.

[0011] Therefore, with the present invention, the method allows for the precise and relatively simple determination of a set of raster images for strips to be printed on the manufactured object, taking into account all splicing between strips and allowing for high-quality printing regardless of complex geometry, and also allows for long jetting distances, as specified below.

[0012] In a preferred embodiment, the determining step includes the following successive sub-steps: - First sub-step, used to (digitally) simulate the printing method to determine the coordinates of the impact point of the potential droplet on the triangle of the grid and the identifier of the triangle for each trajectory, each nozzle of each printhead and each ejection moment; - The second sub-step is used to identify the stitching situation based on the trajectory in the triangles of the re-divided mesh, to apply the stitching code associated with each stitching situation, and to associate the stitching code with the texture mapping at the position corresponding to the coordinates of the re-divided triangle under consideration. - The third sub-step is used to analyze the texture mapping, which includes all splicing cases and splicing codes, and to associate each splicing case with the splicing gradient for each of the successive strips to be printed; - The fourth sub-step is used to determine the droplet to be used from the potential droplets, and to assign grayscale values ​​to each of the droplets to be used; and - A fifth sub-step, which is implemented for each trajectory and each printhead, wherein the fifth sub-step merges the grayscale assigned to each droplet to be used corresponding to the trajectory and the printhead into an initially empty raster image to obtain a raster image associated with the trajectory and the printhead, wherein the set of raster images includes raster images thus obtained for all trajectories and all printheads.

[0013] Advantageously, the first sub-step includes the following (sequential) operations: for each trajectory, for each nozzle of each printhead, and for each ejection moment: - Printed material is ejected from a plate perpendicular to the nozzle toward the grid; - Calculate the intersection points of the printed jets and the mesh; and - The impact point corresponding to the impact point of the potential droplet (or droplet chance) is calculated by applying an offset to the intersection in the printing direction in order to take into account the aerodynamic offset of the printed ejector (or droplet) during jetting.

[0014] Furthermore, advantageously, the second sub-step includes the following (sequential) operations: for each triangle of the object's mesh: - Divide the triangle further into sub-triangles with predetermined side lengths; and - For each sub-triangle: • Select all potential droplets that fall on the sub-triangle; • Identify splicing patterns as a function of the number and order of various trajectories; and • Place the splicing code in the added color layer corresponding to the splicing situation, and associate it with the texture map at the position indicated by the coordinates of the sub-triangle.

[0015] Advantageously, the triangle is iteratively divided into sub-triangles until the predetermined resolution is achieved.

[0016] Furthermore, advantageously, the third sub-step includes the following (sequential) operations: - Analyze the texture map, including all splicing cases; - Simplify the splicing scenarios to be considered; - Texture mapping related to segmentation and splicing codes; and - Associate each stitching case with the stitching gradient for each of the successive strips to be printed.

[0017] Furthermore, advantageously, the fourth sub-step comprises the following (sequential) operations: for each triangle of the object's mesh: - Divide the triangle into sub-triangles with predetermined side lengths; - Based on texture mapping, determine the average target color to be applied to the sub-triangles and the stitching gradient to be applied to each strip; and - For each strip, determine which droplets will be used from the potential droplets, and assign grayscale to each of the droplets to be used.

[0018] Furthermore, advantageously, the fifth sub-step includes the following (sequential) operations: for each track and each printhead: - Create an empty raster image with a pixel height equal to the number of nozzles in the printhead and a pixel width equal to the duration of the trajectory multiplied by the ejection frequency, or equal to the length of the trajectory; and - For each droplet associated with the trajectory and printhead, store the grayscale value in the raster image at the location corresponding to the nozzle and at the time of ejection, so as to obtain a raster image associated with that trajectory, that printhead or nozzle.

[0019] The present invention also relates to a computing device for determining a set of raster images for strips to be printed on an object, wherein printing must be carried out using a printing system comprising at least one robot designed to follow a set of trajectories, the robot being equipped with a plurality of print heads, each of the plurality of print heads being equipped with a plurality of nozzles for printing the ejected material at a given ejection moment.

[0020] According to the present invention, the device includes at least: - A receiving unit configured to receive a mesh of an object corresponding to a tessellated mesh formed by triangles, a texture map associated with that mesh, and the trajectory to be followed by the robot; and - A computing unit configured to determine the set of raster images based on the mesh, the texture mapping, and the trajectory by: using a simulation of a printing method that takes into account the aerodynamic effects on the printed ejector material and determining the grayscale as a function of the stitching between strips associated with the trajectory. Attached Figure Description

[0021] The accompanying figures will help to understand how the invention can be implemented. In these figures, the same reference numerals designate similar elements.

[0022] Figure 1 It is a block diagram of a method for determining a set of raster images for stripes to be printed on a manufactured object.

[0023] Figure 2 The schematic diagram illustrates the configuration for implementing Figure 1 The equipment for the method.

[0024] Figure 3 A portion of an object associated with a tessellated mesh is shown schematically.

[0025] Figure 4 This is a schematic diagram illustrating an example of a printing system capable of direct-to-shape printing.

[0026] Figure 5 The diagram illustrates the splicing process.

[0027] Figure 6 This is a schematic representation of determining the contact point when spraying from a nozzle. Detailed Implementation

[0028] Within the scope of this invention, it can be made by computing device 1 (e.g., such as in...) Figure 2 The method P implemented by the computing device shown in a specific embodiment (e.g., in...) Figure 1 The method shown in a specific embodiment is intended to determine the material to be printed on already manufactured (in Figure 3 (Partially shown) A set of raster images IM of stripes on object O.

[0029] These raster images (IMs) are defined in the context of texture mapping, which involves applying two-dimensional (or 2D) texture data to three-dimensional (or 3D) objects, such as object O. Texture mapping can be used to add representations to objects, especially colors, text, logos, images, and artistic designs.

[0030] Within the scope of this invention, for simplicity, the term "object" refers to any appliance, machine, or other mechanical element, or a portion thereof, whose surface or a portion thereof is capable of receiving such printing. This may particularly relate to the fuselage of an aircraft on which the unique markings (logos, colors, etc.) of the airline operating the aircraft are to be printed.

[0031] Raster image IM is designed for use in "DTS printing" (Direct to Shape Printing) technology, which allows direct printing on the three-dimensional surface of an object, regardless of its shape.

[0032] Will use, for example, in Figure 4 The printing system 8, schematically shown, enables direct printing. This printing system 8 includes at least one robot 9 designed to follow a set of trajectories TR. Within the scope of this invention, the robot can be configured to perform any type of movement (linear movement, rotational movement, complex connections, etc.) and can correspond, for example, to a robotic arm or a Cartesian table.

[0033] Robot 9 includes a printing tool 10 (“printer end manipulator”) at its free end. The printing tool 10 is equipped with a plurality of printheads 11, for example, four printheads in a non-limiting example for each of the primary colors cyan, magenta, yellow, and black. Each of these printheads 11 is equipped with a plurality of nozzles 12, for example, more than one thousand nozzles, for generating printed ejecta (i.e., ink droplet ejection) at a given ejection moment.

[0034] The printing system 8 also includes a control unit 13, which is specifically designed to control the movement of the robot 9 (typically a robotic arm) and the printing produced by the printing tool 10. The set E of raster images IM determined by the computing device 1 can, for example, be supplied to the control unit 13 of the printing system 8 for printing.

[0035] During printing, the printing tool 10 of robot 9 moves along the trajectory TR each time (i.e., for each pass) so that each time a strip is printed, such as in Figure 5 The strips B1 and B2 are shown in the illustration. Each printed strip B1, B2 represents a portion of the logo (i.e., the print to be produced).

[0036] The purpose of method P and computing device 1 is specifically to consider the splicing of strips, i.e., any overlap between directly adjacent strips.

[0037] Figure 5 The stitching R between strip B1 (represented by a thick line) and strip B2 (represented by a dashed line) is shown schematically.

[0038] Due to the presence of one or more potential obstacles (such as aircraft antennas) on the area of ​​the object to be printed and the need to reduce the unprinted area around one or more obstacles, complex divisions of strips (with varying shapes and / or sizes and / or orientations) are typically provided to maximize the printable area, regardless of the restricted accessibility of the printing tool 10.

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

[0040] By way of explanation, several different splicing situations can be attributed in particular to the following: - The strips come in different shapes (e.g., straight or curved), different sizes, and / or different orientations; and / or - For curved strips, different areas need to be printed for each color; and / or - In the case of having or not having any previously implemented stitching, partially overlap printing on previously printed strips (curved or straight); and / or - The start and / or end of a strip can optionally be linked to other strips, in particular in different ways.

[0041] These different splicing situations therefore include different types of splicing (i.e., areas that present different shapes and sizes (where at least two strips overlap)).

[0042] As indicated above, a significant objective of method P is to manage such splicing cases. To this end, as in Figure 1 As shown in the diagram, the method P specifically includes the following steps implemented by computing device 1: - By computing device 1 ( Figure 2 The receiving unit 2 (RECEPT) implements the receiving step S1, which is used to receive at least: • The mesh M of the manufactured object O, as shown in Figure 4 As illustrated schematically in the middle section, it corresponds to a standard tessellation grid formed by triangles; • The standard (two-dimensional) texture map CT associated with this mesh M. These texture maps are of HD (i.e., high resolution) type; and • The trajectory TR, the printing tool 10 of robot 9 must follow in order to print various strips; - The determination step S2, implemented by the computing unit 4 (COMP) of computing device 1, is used to determine the set E of raster images IM based on the mesh M, the texture map CT, and the trajectory TR, as specified below. Specifically, the determination step S2 considers a (digital) simulation of the printing method to account for the aerodynamic effects of the printed ejector material, and determines the grayscale as the stitching situation R between strips related to the trajectory TR. Figure 5 The function of ); and - Transmission step S3, implemented by the transmission unit 3 (TRANSM) of computing device 1, is used to transmit the set E of raster images IM to a user device (not shown), such as the computer or control unit of printing system 8 (e.g., ...). Figure 4 Control unit 13).

[0043] As in Figure 1 As shown in the diagram, determining step S2 comprises a sequence SE of successive sub-steps S2A to S2E.

[0044] The initial step S2 includes a sub-step S2A implemented by the computing element 4A of the computing unit 4 for simulating the printing method (in a digital manner).

[0045] To perform this printing simulation, the computing element 4A determines data for each trajectory TR, each nozzle 12 of each printhead 11, and each ejection moment (i.e., the specific moment when printed ejection is generated from the nozzle 12), namely the coordinates of the potential droplet impact point on the triangle of the grid M (as specified below) and the identifier of the triangle.

[0046] This data is integrated into table T. Table T is preferably stored in the memory of computing device 1, such as memory 5. Figure 2 In, or in the memory (not shown) of computing unit 4.

[0047] To implement this simulation of the printing method, computational element 4A performs the following operations: - It selects and sorts the trajectory TR of the printing tool 10 of robot 9 in order to cover the logo; - It creates an empty table T for subsequent data storage; and - For each trajectory TR, for each ejection moment (sampled at the ejection frequency performed by printhead 11 corresponding to the time step of the trajectory): • It positions the printing tool 10 at a corresponding (6D type) location associated with the tessellation mesh M of the object O. This (6D type) location specifies the position and orientation of the printing tool 10 in (3D) space according to six degrees of freedom (three for translation and three for rotation); and • For each nozzle 12 of each printhead 11 at each injection moment, the operation sequence is implemented.

[0048] The sequence of operations includes the following (sequential) operations (therefore for each nozzle 12 of each printhead 11 at each ejection moment): - Printed material 14 is ejected from the plate 12A perpendicular to the nozzle 12 towards the grid M of the object, as shown in... Figure 6 As illustrated schematically. Nozzle 12 is located at a certain distance D from the grid, for example greater than 5 mm (in the case of "DTS Printing" type printing), so that the printed jet becomes sensitive to aerodynamic effects, as specified below; - Calculate the intersection point P1 between the printed jet 14 and the grid M; and - By applying an offset to the intersection point P1 (by...) Figure 5(See arrow G in the diagram), calculate the impact point P2 corresponding to the impact point of the potential droplet (or droplet chance). Perform this offset in the printing direction F (i.e. the direction of movement of the printing tool 10) to move from the intersection P1 to the impact point P2 in order to take into account the aerodynamic offset of the droplet (or printed ejection) during ejection (i.e., the offset attributed to aerodynamic effects).

[0049] Then, the computing element 4A adds a new row to table T, which stores the trajectory reference, the ejection time, the reference of the printhead 11 (corresponding to the color), the reference of the nozzle 12, the reference of the (impacted) triangle of the grid M, and the coordinates of the impact point P2 on the triangle. Within the scope of this invention, the term "reference" for an element is understood to mean any type of indication that allows the element to be identified.

[0050] Method P thus allows for the consideration and compensation of aerodynamic effects during droplet placement. These aerodynamic effects are specifically attributed to: - In the case of direct printing of the "DTS Printing" type, the significant jetting distance D ( Figure 6 For example, greater than 5 mm, this induces significant lateral airflow, which is likely to deflect the actual movement of the droplets compared to a straight printed jet 14; and - Aerodynamic turbulence may be generated between nozzles 12 when several nozzles 12 close to each other spray within a short period of time.

[0051] The determination step S2 then includes a sub-step S2B implemented by the computing element 4B of the computing unit 4 (after sub-step S2A) for classifying the splicing situation (between strips).

[0052] More specifically, in substep S2B, computation element 4B identifies stitching cases based on trajectory TR in the re-divided triangles of mesh M, then applies a stitching code associated with each stitching case (i.e., a code that allows identification of the type of stitching from a variety of possible types), and associates the stitching code with the texture map CT at the position corresponding to the coordinates of the re-divided triangle under consideration.

[0053] Therefore, in sub-step S2B, computational element 4B performs multiple operations for each triangle of the mesh M of object O.

[0054] The computing element 4B initially subdivides the considered triangle into sub-triangles, which are then iteratively subdivided, and so on, until the desired appropriate size is obtained for the sub-triangles. For this purpose, preferably, each triangle, and then each sub-triangle, is (iteratively) subdivided into four sub-triangles, and this continues until the sub-triangles (which are preferably equilateral) have a side length less than a predetermined value (e.g., 500 µm) (representing the desired resolution).

[0055] Then, for each sub-triangle (obtained through such re-division), computational element 4B performs the following (sequential) sequence of operations: - It selects all potential droplets falling on the sub-triangle from table T; - It identifies the splicing pattern as a function of the number and order of various trajectories; and - It implements a splicing code corresponding to the splicing situation in the added color layer, and it (for example by storing the splicing code that identifies the splicing situation in an additional dedicated "color" layer of the texture map CT) associates the splicing code with the texture map CT at the position indicated by the coordinates of the sub-triangle.

[0056] The determination step S2 then includes a sub-step S2C implemented by the computation element 4C of the computation unit 4 (after sub-step S2B) to merge the stitched gradient into the texture map CT.

[0057] More specifically, in substep S2C, the computation element 4C analysis includes the splicing case and the texture mapping CT of the splicing code (completed in substep S2B), and associates the splicing gradient (or pattern) with each splicing case for each of the successive strips to be printed, wherein each of the strips is associated with one of the trajectories TR.

[0058] For a given point (to be printed near the stitching) that receives a given total volume of color (ink), the stitching gradient defines a percentage of that total volume for each of the strips involved in the stitching. For example, if the point is located at the stitching point of two strips, a given percentage of color (e.g., 80% corresponding to the stitching gradient of the first strip) is deposited as it passes through the point to form the first strip, and the remaining portion (20% corresponding to the stitching gradient of the second strip in this example) is deposited as it passes through the point to form the second strip.

[0059] Therefore, in sub-step S2C, computational element 4C performs the following operations: - Its analysis includes texture mapping (CT) for all stitching cases; - If possible, simplify the stitching case. For example, when considering that one of the four trajectories does not contribute to the region, the stitching case between the four different trajectories can be considered as a stitching case with only three trajectories; - Its segmentation and splicing code-related texture mapping CT; and - It associates each stitching case with the stitching gradient (or pattern) for each of the successive strips to be printed (i.e., for each of the successive passes).

[0060] The determination step S2 then includes a sub-step S2D implemented by the computing element 4D of the computing unit 4 (after sub-step S2C) to determine the droplets to be used from the potential droplets, and to store the grayscale of each assignment in the droplets to be used in table T.

[0061] Therefore, in sub-step S2D, computational element 4D performs multiple operations for each triangle of the mesh M of object O.

[0062] The computational element 4D initially subdivides the triangle into sub-triangles, which are then iteratively subdivided, and so on, until the desired appropriate size is obtained for the sub-triangles. For this purpose, preferably, each triangle, and then each sub-triangle, is (iteratively) subdivided into four sub-triangles, and this continues until the sub-triangles (which are preferably equilateral) have a side length less than a predetermined value (e.g., 500µm) (representing the desired resolution).

[0063] Calculate the 4D of the element and then perform the following (sequential) operations: - For each sub-triangle, where applicable, it determines the average target color to be applied to the sub-triangle and the stitching gradient to be applied to each strip based on texture mapping (CT); and - For each strip (i.e. each pass corresponding to the trajectory), it determines which droplets will be used from the potential droplets and assigns grayscale to each of the droplets to be used.

[0064] To this end, an optimization method is implemented to achieve color consistency and accuracy on the sub-triangle based on the diameter of the (printed) points and the constraints on how colors should be reproduced to ensure consistent and accurate color management according to the ICC (International Color Consortium) profile. The ICC profile may be received during receiving step S1 and / or may be stored in the memory of computing device 1 (e.g., in memory 5).

[0065] Therefore, the determined grayscale is then stored in table T.

[0066] Finally, the determination step S2 also includes a sub-step S2E implemented by the computing element 4E of the computing unit 4 (after sub-step S2D) for determining the raster image IM for each trajectory TR and for each printhead 11 (i.e. for each pair including one of the initially received trajectories TR and one of the printheads 11 of the printing system 8).

[0067] For all pairs of trajectories and printheads (in substep S2E), the raster images IM obtained are formed into a set E of raster images IM.

[0068] Therefore, in sub-step S2E, for each droplet in table T corresponding to the trajectory TR and the print head 11, the computing element 4E merges (in sub-step S2D) the grayscale assigned to it into the initially empty 2D raster image so as to obtain a 2D raster image associated with the trajectory TR and the print head 11 after considering all the corresponding droplets.

[0069] More specifically, in sub-step S2E, the computational element 4D performs the following operations for each trajectory TR and each printhead 11: - It creates an empty raster image IM (2D) with a pixel height equal to the number of nozzles 12 of printhead 11 and a pixel width equal to the duration of trajectory TR multiplied by the jetting frequency (implemented from printhead 11) or the length of the trajectory; and - For each droplet in the table T corresponding to the trajectory TR and the considered printhead 11, the grayscale at the position corresponding to the nozzle 12 and at the time of ejection is stored in the raster image IM in order to obtain the raster image IM associated with the trajectory TR and the printhead 11.

[0070] Therefore, for the number of trajectory TRs N and the number of printheads M, the set E includes N x M raster images. , where n ranges between 1 and N, and m ranges between 1 and M.

[0071] All the aforementioned processes, sub-steps, and operations are implemented digitally by computing device 1. No physical processing is performed.

[0072] As in Figure 2 As shown in the diagram, the computing device 1 may also include: - At least one memory, such as memory 5 (MEM), capable of storing data for data processing and computation implemented by the computing elements of computing device 1, such as, for example, table T; and - Human-Machine Interface 6 (HMI) allows the operator to supply data to the computing device 1, such as predetermined values ​​of the lengths of the sides of the re-divided triangle used in sub-steps S2B and S2D.

[0073] Furthermore, the receiving unit 2 and the transmitting unit 3 can form part of a standard communication system 7 that allows the computing device 1 to communicate with devices outside the computing device 1 via wired or wireless connections.

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

[0075] As described above, method P and computing device 1 thus allow the creation of raster images for all strips to be printed along the robot's trajectory, taking into account all splicing situations between strips and providing high-quality printing, regardless of complex geometry and long jetting distance.

[0076] More specifically, they therefore especially allow: - Achieves very high precision in droplet positioning, thus allowing for better color management, and as a result, enabling color consistency and sharper, more accurate printing; and - By taking stitching (3D) into account, they allow for the management of complex stitching situations, which in particular allows for the expansion of printable areas (around obstacles) without generating visual defects.

Claims

1. A method for determining a set of raster images for strips to be printed on an object, wherein printing must be carried out using a printing system (8) comprising at least one robot (9) designed to follow a set of trajectories (TR1, TR2), the robot (9) being provided with a plurality of print heads (11), each of the plurality of print heads (11) being equipped with a plurality of nozzles (12) for printing the ejecta at a given ejection moment, the method (P) being implemented by a computing device (1) and comprising at least the following successive steps: - Receiving step (S1), for receiving the mesh (M) of the object (O) corresponding to the tessellated mesh formed by triangles, the texture map associated with the mesh (M), and the trajectory (TR1, TR2) to be followed by the robot (9); and - Determine step (S2) for determining the raster image set based on the grid (M), the texture map, and the trajectories (TR1, TR2) by: simulating the printing method considering the aerodynamic effects on the printed jet (14); and determining the grayscale as a function of the stitching (R) between strips (B1, B2) associated with the trajectories (TR1, TR2). Determine step (S2) includes at least the following sub-steps: - A second sub-step (S2B) is used to identify stitching cases (R) based on the trajectories (TR1, TR2) in the re-divided triangles of the mesh (M), to apply a stitching code associated with each stitching case (R), and to associate the stitching code with a texture map at a position corresponding to the coordinates of the considered re-divided triangle; and - The third sub-step (S2C) is used to analyze the texture mapping, which includes all splicing cases (R) and splicing codes, and to associate each splicing case (R) with the splicing gradient for each of the successive strips to be printed.

2. The method as described in claim 1, Its features are, The determination step (S2) also includes the following sub-steps: - First sub-step (S2A) is used to simulate the printing method in order to determine the coordinates of the impact point (P2) of the potential droplet on the triangle of the grid (M) and the identifier of the triangle for each trajectory (TR1, TR2), each nozzle (12) of each printhead (11) and each ejection moment; - The fourth sub-step (S2D) is used to determine the droplets to be used from the potential droplets and to assign grayscale to each droplet to be used; as well as - A fifth sub-step (S2E) is implemented for each trajectory (TR1, TR2) and each printhead (11), wherein the fifth sub-step (S2E) merges the grayscale assigned to each droplet that will be used for the trajectory (TR1, TR2) and the printhead (11) into an initially empty raster image to obtain a raster image associated with the trajectory (TR1, TR2) and the printhead (11), wherein the set of raster images includes raster images thus obtained for all trajectories (TR1, TR2) and all printheads (11).

3. The method as described in claim 2, Its features are, The first sub-step (S2A) includes the following operations: for each trajectory (TR1, TR2), for each nozzle (12) of each printhead (11), and for each ejection moment: - Printed jets (14) are ejected from the nozzle (12) perpendicular to the plate (12A) toward the grid (M); - Calculate the intersection point (P1) between the printed jet (14) and the grid (M); and - The impact point (P2) corresponding to the potential droplet's impact point is calculated by applying an offset to the intersection point (P1) in the printing direction (F) to account for the aerodynamic offset of the printed ejection during jetting.

4. The method as described in any one of claims 2 and 3, Its features are, The second sub-step (S2B) includes the following operation: for each triangle of the mesh (M) of the object (O): - Divide the triangle further into sub-triangles with predetermined side lengths; and - For each sub-triangle: • Select all potential droplets that fall on the sub-triangle; • A function that identifies the splicing pattern as the number and order of various trajectories (TR1, TR2); and • Place the splicing code in the added color layer corresponding to the splicing situation, and associate it with the texture map at the position indicated by the coordinates of the sub-triangle.

5. The method as described in any one of claims 2 to 4, Its features are, The third sub-step (S2C) includes the following operations: - Analyze the texture map that includes all splicing cases (R); - Simplify the splicing scenarios to be considered (R); - Texture mapping related to segmentation and splicing codes; and - Associate each stitch case (R) with the stitch gradient for each of the successive strips to be printed.

6. The method as described in any one of claims 2 to 5, Its features are, The fourth sub-step (S2D) includes the following operations: for each triangle of the mesh (M) of the object (O): - Divide the triangle into sub-triangles with predetermined side lengths; - Based on texture mapping, determine the average target color to be applied to the sub-triangles and the stitching gradient to be applied to each strip; as well as - For each strip, determine which droplets will be used from the potential droplets, and assign grayscale to each of the droplets to be used.

7. The method as described in any one of claims 2 to 6, Its features are, The fifth sub-step (S2E) includes the following operations for each trajectory (TR1, TR2) and each printhead (11): - Create an empty raster image comprising a pixel height equal to the number of nozzles (12) of the printhead (11) and a pixel width equal to the duration of the trajectory (TR1, TR2) multiplied by the ejection frequency or the length of the trajectory; and - For each droplet associated with the trajectory (TR1, TR2) and the printhead (11), a grayscale value is stored in the raster image at the position corresponding to the nozzle (12) and at the time of ejection, so as to obtain a raster image associated with the trajectory (TR1, TR2) and the printhead (11).

8. The method as described in any one of claims 4 and 6, Its features are, The process iteratively divides the triangle into sub-triangles until the predetermined resolution is achieved.

9. A computing device for determining a set of raster images for strips to be printed on an object, wherein printing must be carried out using a printing system (8) comprising at least one robot (9) designed to follow a set of trajectories (TR1, TR2), the robot (9) being provided with a plurality of print heads (11), each of the plurality of print heads (11) being equipped with a plurality of nozzles (12) for printing the ejecta at a given ejection moment, the computing device (1) comprising at least: - A receiving unit (2) configured to receive a mesh (M) of an object (O) corresponding to a tessellated mesh formed by triangles, a texture map associated with the mesh (M), and the trajectories (TR1, TR2) to be followed by the robot (9); and - A computing unit (4) configured to determine the raster image set based on the grid (M), the texture map, and the trajectories (TR1, TR2) by: using a simulation of a printing method that considers the aerodynamic effects on the printed ejector and determining the grayscale as a function of the stitching (R) between stripes (B1, B2) associated with the trajectories (TR1, TR2), the computing unit (4) includes at least: • A computing element (4B) configured to identify stitching cases (R) based on the trajectories (TR1, TR2) in the re-divided triangles of the mesh (M), apply a stitching code associated with each stitching case (R), and associate the stitching code with a texture map at a position corresponding to the coordinates of the considered re-divided triangle; and • Computational element (4C) is configured to analyze the texture mapping, including all splicing cases (R) and splicing codes, and to associate each splicing case (R) with the splicing gradient for each of the successive strips to be printed.

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