Method and computer device for transforming a textured mesh of a design object into a textured mesh of a manufacturing object corresponding to the design object

Abstract

Method and computer device for transforming a textured mesh of a design object into a textured mesh of a manufacturing object corresponding to said design object. Method for determining a transformed textured mesh (M2) of a three-dimensional manufacturing object (O2) on the basis of an initial textured mesh (M1) of a three-dimensional design object (O1), the transformed textured mesh (M2) being intended to be used when printing a corresponding two-dimensional texture (T) on the manufacturing object (O2), an iterative process is performed in order to determine a set of affine transformations with personalized parameters, making it possible to minimize the value of an objective function comprising at least one term promoting a specific property, the determined set of affine transformations is then applied to the vertices of the initial textured mesh (M1) in order to obtain the transformed textured mesh (M2), said method being relatively simple to implement and particularly advantageous.

Description

Background Technology

[0001] The present invention relates to a method and computer apparatus for transforming a textured mesh of a design object into a textured mesh of a manufactured object corresponding to the design object.

[0002] Description of existing technology This invention relates more particularly to the field of texture mapping, which involves applying data from a two-dimensional texture to a three-dimensional object. Texture mapping can be used to print representations of colors, text, signage, images, artwork, etc., on a three-dimensional object. The three-dimensional object can be a large object (such as an airplane), for example, and has one or more curved surfaces. To manufacture the three-dimensional object, it is generally pre-designed via computer-aided design to associate the three-dimensional object with the two-dimensional texture.

[0003] However, generally speaking, the geometry of the manufactured object does not perfectly correspond to the geometry of the initially designed object, often exhibiting errors significantly greater than the required printing accuracy. For example, in the context of printing on aircraft, the manufactured aircraft typically has a shape different from the designed aircraft shape due to distortions, which are specifically attributed to the different distribution of forces between the aircraft in flight and the aircraft on the ground, and relative to manufacturing tolerances. It is necessary to account for such distortions in texture mapping.

[0004] According to existing technology, a mapping method is known that is based on matching the mosaic mesh of the manufactured object with the mosaic mesh of the design object in order to transfer the coordinates of the livery texture. The mosaic mesh of the manufactured object is constructed based on a (noisy) point cloud obtained via metrology. The result is a complex mosaic and a large mesh that potentially contains several times the number of vertices of the mesh of the design object. This makes it necessary (in order to obtain a sufficiently small mesh to be used in subsequent calculations of the raster image) to perform filtering at the appropriate time. This filtering is both complex (computationally intensive, difficult to perform adjustments, finding a trade-off between fidelity to the manufactured object and the number of vertices, etc.) and difficult to implement.

[0005] Additionally, implementing a rigid transformation (that is, applying the same transformation to all transformed points) to align with the point cloud is known in the art, which may generate problems with the fidelity of the reproduction of texture on the manufactured object relative to the design object, since not all points experience the same distortion between the design object and the manufactured object during manufacturing.

[0006] Therefore, a solution is needed that allows for the precise determination of the textured mesh of a manufactured object based on the textured mesh of the design object upon which the manufactured object is based, thus enabling faithful reproduction of the texture. Summary of the Invention

[0007] The object of this invention is to provide such a solution. For this purpose, the present invention relates to a method for determining a transformed textured mesh, called an initial textured mesh, of a three-dimensional manufactured object based on a textured mesh called an initial textured mesh of a three-dimensional design object, the manufactured object corresponding to the design object, the transformed textured mesh being intended for use when printing a corresponding two-dimensional texture on the manufactured object, the method being implemented by a computer device and comprising at least the following steps: - A receiving step for receiving a mesh representing a 3D design object and an associated 2D texture, as well as 3D points from a point cloud obtained on the manufactured object, the mesh and the associated 2D texture forming the initial textured mesh including vertices; and - Determine steps for determining a transformed textured mesh, taking into account at least some of the vertices and at least some of the 3D points.

[0008] According to the invention, the determining step implements an iterative process (or computation) to determine a set of affine transformations with personalized parameters, such that the value of an objective function can be minimized by taking into account the initial textured mesh and the 3D points taken into account from the point cloud. The objective function (specified below) includes at least one term that promotes a specific property involving the set of affine transformations. Therefore, the determined set of affine transformations is applied to the vertices taken into account by the initial textured mesh to obtain the transformed textured mesh.

[0009] In the context of this invention, the phrase "a set of affine transformations with individualized parameters" signifies that the different parameters of the transformation set are determined individually, and specifically, in principle, not all parameters are equal as in the case of rigid transformations. Therefore, this set of affine transformations with individualized parameters enables non-rigid transformations.

[0010] In a preferred embodiment, the determining step includes at least a sequence of the following consecutive sub-steps, which are iteratively implemented: - A first sub-step, for applying a set of affine transformations to the vertices considered in the initial textured mesh to obtain the vertices of the textured mesh referred to as the computed textured mesh, the set of affine transformations corresponding to a predetermined set of affine transformations during the first iteration and corresponding to a set of affine transformations determined in the previous iteration during each iteration in subsequent iterations; - The second sub-step is used to calculate the value of the objective function based on the vertices included in the initial textured mesh, the 3D points included in the point cloud, and the vertices of the calculated textured mesh; - The third sub-step is used to compare the calculated value of the objective function with a predetermined threshold, and is used to: • If the calculated value is less than the threshold, the determination step is stopped, taking into account that the transformed textured mesh corresponds to the textured mesh calculated in the first sub-step of the current iteration; and • If the calculated value is greater than or equal to the threshold, the determining step continues by implementing the fourth sub-step; and - The fourth sub-step is used to determine a new set of affine transformations based on the objective function and the set of affine transformations, which will be used in the first sub-step of the subsequent iteration.

[0011] Therefore, by means of the present invention, two meshes of similar type (with the same number of vertices) are provided, the first mesh corresponding to the tessellation of the object as designed, and the second mesh being created as a copy of the first mesh, the copy of the first mesh being formed to be adapted to the object as manufactured (defined by the acquired point cloud) using a non-rigid transformation, that is, a potentially different (affine) transformation for each vertex of the mesh.

[0012] For this purpose, the method uses a distortion model (i.e., the set of affine transformations) to model the non-rigid distortions of the manufactured object compared to the object drawn (or designed) in CAD (Computer-Aided Design) (e.g., due to gravity and manufacturing tolerances in the case of an aircraft). This causes slight displacements of the vertices of the created mesh without changing the overall structure of the mesh (the same number of vertices and polygons, the regularity of the polygons, etc.). Therefore, the method makes it relatively simple (without complex filtering) and accurate to determine the textured mesh of the manufactured object, which allows for the performance of reproduction taking into account the specific characteristics of the fuselage (windows, door frames, etc.).

[0013] Additionally, the method performs a non-rigid transformation of the second mesh to adjust the point cloud of the manufactured object using a set of transformations that can be adapted to ensure, in particular, that certain vertices correspond precisely to the desired positions, as specified below, and to maintain the proportions of certain portions of the texture.

[0014] Therefore, with the help of the present invention, it is not necessary to continue with complex mosaicking based on noisy point clouds and associated complex filtering, as in the aforementioned example in document US 10 198 860 B1.

[0015] Advantageously, if necessary, the determining step is stopped when a predetermined number of iterations is reached, and then the transformed textured mesh corresponds to the last calculated textured mesh.

[0016] In the context of this invention, the objective function includes at least one term, and preferably includes a plurality of terms specified below, each of which promotes a particular property involving the set of transformations.

[0017] Therefore, advantageously, the objective function includes at least one term that makes a certain vertex of the transformed textured mesh (precisely) correspond to a point called the target point of the manufactured object.

[0018] Furthermore, advantageously, the objective function includes at least one term that causes certain vertices of the transformed textured mesh to maintain a predetermined distance between them in order to maintain the proportion of a certain portion of the paint.

[0019] Furthermore, in one particular embodiment, the objective function includes at least one of the following terms: - Makes the transformed textured mesh fit the item of 3D points obtained on the manufactured object; - Terms that force smoothing distortions in transformations generated from a set of affine transformations; - Terms that make the transformation generated by the set of affine transformations approximate a rigid transformation.

[0020] In a preferred embodiment, the fourth sub-step includes the following consecutive operations: - Calculate the gradient of the objective function with respect to the set of affine transformations; - Determine the adjustment direction based on this gradient; and - Determine a new set of affine transformations along this adjustment direction.

[0021] Advantageously, the fourth sub-step uses a specialized nonlinear least squares solver.

[0022] In one particular embodiment, the method includes: - Computational steps for determining the initial set of affine transformations; and / or - Calculation steps used to determine the target point of the manufactured object; and / or - A computational step for determining at least one region of a two-dimensional texture, wherein the scale of the region must be maintained.

[0023] The present invention also relates to a computer device for determining, based on a textured mesh called an initial textured mesh of a three-dimensional manufacturing object, the manufacturing object corresponding to the design object, the transformed textured mesh being intended for use when printing a corresponding two-dimensional texture on the manufacturing object, the computer device comprising at least: - A receiving unit configured to receive a mesh representing a 3D design object and an associated 2D texture, as well as 3D points from a point cloud acquired on the manufactured object, the mesh and the associated 2D texture forming the initial textured mesh including vertices; and - A computing unit configured to take into account at least some of the vertices and at least some of the three-dimensional points to determine a transformed textured mesh.

[0024] According to the invention, the computing unit includes computing elements configured to perform iterative processing (or computation) to determine a set of affine transformations with personalized parameters, such that the value of an objective function can be minimized by taking into account the initial textured mesh and the 3D points taken into account from the point cloud. The objective function includes at least one term that promotes a specific property involving the set of affine transformations. Therefore, the determined set of affine transformations is applied to the vertices taken into account by the initial textured mesh to obtain the transformed textured mesh. Attached Figure Description

[0025] The accompanying drawings will make it easy to understand how the invention can be implemented. In these drawings, the same reference numerals denote similar elements.

[0026] Figure 1 This is a block diagram of a method for transforming a textured mesh of a design object into a textured mesh of a manufacturing object corresponding to the design object.

[0027] Figure 2 The schematic diagram illustrates the configuration to implement Figure 1 The equipment for the method.

[0028] Figure 3 The diagram schematically shows a portion of the design object and the same portion of the manufactured object, allowing for clear highlighting. Figure 1 The characteristics of the method. Detailed Implementation

[0029] In the context of this invention, it is possible to use a computer device 1 (e.g., such as in...) Figure 2 The method P implemented (e.g., such as in a specific embodiment depicted) is described. Figure 1 The one depicted in a particular embodiment is intended to form the textured mesh specified below.

[0030] This textured mesh is used for texture mapping, which involves applying data from a two-dimensional (or 2D) texture to a three-dimensional (or 3D) object. Texture mapping can be used to add representations of, in particular, colors, text, signage, images, artistic drawings, etc., to three-dimensional objects.

[0031] The resulting textured meshes are particularly used in conventional printing systems (not depicted) for direct-to-texture (DTS) printing, a printing technique that allows printing directly onto the three-dimensional surface of an object, regardless of its shape or texture. These textured meshes, in particular, enable the determination of raster images that can be used by the printing system.

[0032] In the context of this invention, for the sake of simplicity, "object" means any machine or other mechanical element, or a part of such a machine or other mechanical element, whose surface or a portion thereof is capable of receiving such printing. It can be, in particular, the outer surface of an aircraft, on which characteristic markings (symbols, colors, etc.) and technical markings (identifiers for doors and panels, instructions for ground personnel, etc.) of the airline that will operate the aircraft will be printed.

[0033] To create a three-dimensional object, it is typically designed in advance using computer-aided design. This three-dimensional object is associated with a two-dimensional texture, which defines the representation to be applied to the designed object.

[0034] Figure 3 A two-dimensional texture T is depicted in an illustrative manner. This texture T is defined for a design object O1 that is depicted in a segmented manner (partially), and it is intended to be applied to a manufacturing object O2 that is also depicted in a segmented manner (partially).

[0035] Manufacturing object O2 corresponds to design object O1; that is, manufacturing object O2 is manufactured based on design object O1. However, generally, the geometry of manufacturing object O2 does not perfectly correspond to the geometry of the initial design object O1, such as... Figure 2 The errors shown typically have a significant margin of error greater than the required printing accuracy, which may be less than 1 millimeter or even drop to tens of micrometers. For example, in the case of aircraft, the manufactured aircraft generally has a shape that differs from the designed aircraft shape due to distortion, which is specifically attributed to gravity (up to several centimeters) and manufacturing tolerances (up to several millimeters).

[0036] like Figure 3 As depicted, the manufactured object O2 is defined by a point cloud NP. The three-dimensional points Pm from this point cloud NP are typically determined (or measured or acquired) by a metrology system, such as by photogrammetry (which uses photographs), by using a laser scanner, or by profilometry (which measures the topography of a surface). In the case of large three-dimensional objects, such as a part of an aircraft fuselage, the number of three-dimensional points can be very high, approximately one million or even one billion points.

[0037] The purpose of method P, implemented by computer device 1, is to determine the textured mesh of manufacturing object O2, called the transformed textured mesh M2, based on the textured mesh of design object O1, called the initial textured mesh M1.

[0038] The transformed textured mesh M2 is intended for printing the corresponding two-dimensional texture T on the manufactured object O2, particularly by being used to form a raster image.

[0039] For this purpose, such as Figure 1 The method P described herein specifically includes the following steps implemented by computer device 1: - By computer device 1 ( Figure 2 The receiving unit 2 (RECEPT) implements the receiving step S1, which is used to receive at least: • Represents the tessellation mesh and associated 2D texture T of the 3D design object O1, which together form an initial textured mesh M1 with N vertices; and • M three-dimensional points Pm from the point cloud NP obtained on the manufactured object O2, where M is an integer different from the integer N, and is generally greater than N; and - The determination step S2, implemented by the computing unit 4 (COMP1) of computer device 1, is used to determine the transformed textured mesh M2 based on at least some or all of the N vertices and at least some or all of the M three-dimensional points; and - Transmission step S3, implemented by transmission unit 3 (TRANSM) of computer device 1, is used to transmit the transformed textured mesh M2 to user equipment (not depicted), such as a computer, and in particular a computer for determining a raster image that can be used by a printing system.

[0040] In the remainder of this description, the following parameters are taken into account: These are the N vertices of the textured mesh M1 of the design object O1; These are M three-dimensional points from a point cloud NP obtained on a manufacturing object O2 (in... Figure 3 (referring to Pm in Chinese); and These are the corresponding positions of the N points of the transformed textured mesh M2, determined in step S2 of method P.

[0041] In step S2, all N vertices and all M 3D points can be used, but alternatively, only some of the N vertices and / or some of the M 3D points can be selected based on the desired location. Selection is important relative to these points because it is desirable to avoid offsets relative to the theoretical locations determined in the CAD file.

[0042] In the following description, all N vertices and all M 3D points are taken into account and used in the determination steps.

[0043] like Figure 1 As described, determining step S2 includes a sequence of successive sub-steps SE from sub-step S2A to sub-step S2D. This suite SE is implemented iteratively.

[0044] The determination step S2 first includes a sub-step S2A implemented by the computational element 4A of the computational unit 4, used to determine the affine transformation set. The affine transformation is applied to the N vertices of the initial textured mesh M1 to obtain the N vertices of the textured mesh M3, which is called the computed textured mesh M3. This set of affine transformations is as follows: - During the first iteration, this corresponds to a set of affine transformations known as the initial set of affine transformations; this initial set of affine transformations can be as simple as, for example, a set of rigid transformations, in which all rigid transformations are identical and correspond to the optimal adjustment of vertices on the point cloud; and - During each iteration in subsequent iterations, it corresponds to the set of affine transformations determined (directly) at the previous iteration.

[0045] To compute the non-rigid transformation, method P is applied at each point of the textured mesh M1. Using potentially different affine transformations It is written as follows: ,in and , It is an affine transformation. and The twelve components have no prior constraints (unlike rigid transformations, where...). It will be a rotation matrix.

[0046] This set of transformations is therefore called "a set of transformations with personalized parameters".

[0047] Then, step S2 is determined to include a sub-step S2B implemented by computational element 4B of computational unit 4, for calculating the value V1 of objective function E based on N vertices of the initial textured mesh M1, M 3D points from the point cloud NP, and N vertices of the computed textured mesh M3 (computed in sub-step S2A). Objective function E includes at least one term that promotes a specific property involving the set of affine transformations, as specified below.

[0048] Then, step S2 includes a sub-step S2C implemented by the computing element 4C of the computing unit 4, for comparing the calculated value V1 of the objective function E (calculated in sub-step S2B) with a predetermined threshold V2 of the objective function E, and for: - If the calculated value V1 is less than the threshold V2, then stop determining step S2, taking into account that the transformed textured mesh M2 corresponds to the textured mesh M3 calculated in the sub-step S2A of the current iteration; and - If the calculated value V1 is greater than or equal to the threshold V2, then the determination step S2 is continued by implementing sub-step S2D.

[0049] Substep S2D is implemented by computational element 4D of computational unit 4 in order to determine a new set of affine transformations based on the objective function E and the current set of affine transformations, which is used in the subsequent iteration of substep S2A.

[0050] Therefore, step S2 is determined to perform an optimization operation, the purpose of which is to find (personalized) parameters of the affine transformation set that minimizes the objective function E.

[0051] Furthermore, in one particular embodiment, when a predetermined number of iterations is reached, the determination step S2 is stopped even if the calculated value V1 is not (yet) less than the threshold V2.

[0052] In this case, the transformed textured mesh M2 corresponds to the final calculated textured mesh M3 obtained in sub-step S2A.

[0053] In this particular embodiment, the sequence of successive sub-steps SE is thus iteratively implemented until one of the following conditions is met: a predetermined number of iterations is reached, or the calculated value V1 of the objective function E is less than a threshold V2.

[0054] Furthermore, in one particular embodiment, method P also includes a computational step S4 implemented by computational element 5 (COMP2) of computer device 1 for determining an initial affine transformation (used during the first iteration in substep S2A). This is not a single affine transformation, but a set of affine transformations, even though the same transformation will generally be chosen for all points, and this transformation will be a rigid transformation that will achieve optimal adjustment of N vertices with respect to M points from the point cloud.

[0055] In the first embodiment of this particular example, calculation step S4 determines the rigid transformation based on the ICP (Iterative Closest Point) algorithm and uses it as each point of the textured mesh M1. The initial affine transformation.

[0056] Furthermore, in the second embodiment of this particular example, the calculation step S4 estimates the initial affine transformation based on available data, such as approximate knowledge of the reference frame of the textured mesh of the design object O1 in the reference frame of the measurement system used to scan the manufacturing object O2.

[0057] As indicated above, the objective function E used in substep S2B includes at least one term that promotes a specific property involving the set of affine transformations.

[0058] Preferably, the objective function E includes a plurality of such terms, as specified below, with weighting coefficients associated with these terms in order to weight the relative effects of the different terms to be given.

[0059] The objective function E includes at least one position term. Position item The point that makes a certain vertex of the transformed textured mesh M2 approach the target point of the manufacturing object O2.

[0060] Therefore, this position item The purpose is to force a certain point to be close to a certain target point (or position). This is particularly suitable for situations where certain elements of a texture must be attached to a specific point of the manufacturing object O2, such as in the case of an airplane, attached to the outline of a window or door, and it is not desired that the representation be displaced.

[0061] In this case, method P preferably includes a calculation step S5 implemented by computing element 6 (COMP3) of computer device 1 for determining these target points. In this case, C indicates the set of vertices with positional constraints. ,and Indicates origin from point cloud The specific target point is determined in order to form a set. Each point of a part Correspondingly.

[0062] In a preferred embodiment, the position item Satisfy the following expression: in: - Therefore, it is a set of grid points with positional constraints; and - Therefore it is A specific target point. Typically, in the case of an aircraft, this might be a point on the outline of a door or window, or the outline of a specific decorative element that you wish to install correctly. For example, when making a safety mark around a hatch, the mark must be absolutely centered relative to the hatch to comply with positioning constraints.

[0063] In addition, the objective function E includes at least one term called shape preservation term. The item, the shape-preserving item This ensures that certain vertices of the transformed textured mesh M2 maintain a predetermined distance between them.

[0064] This is particularly suitable for situations where the paint job contains certain content (such as, for example, signage) and the proportions of that content must not be distorted.

[0065] In this case, method P preferably includes a calculation step S6 implemented by computing element 7 (COMP4) of computer device 1 for determining one or more regions of two-dimensional texture T, the proportions of which must be maintained. Defined as Each vertex The positive scalar weights, where when the vertex In the region of a two-dimensional texture T, To take strictly positive values, the proportion in this region must be maintained, and It is set to zero everywhere else.

[0066] This shape retention item The goal is to preserve the local shape, that is, to ensure that the distance metric is locally preserved around certain specific points.

[0067] For this purpose, shape retention item Penalize changes in the distance between these points and their neighbors.

[0068] Furthermore, in a preferred embodiment, the shape-retaining item Satisfy the following expression: in: - These are weights, which allow selection of areas in the paint scheme that must maintain their proportion (e.g., airline logos); and - This is for The vertices of its neighbors.

[0069] Location item and shape retention items This ensures that a specific point in the representation corresponds to a specific point in the manufactured object O2, and that the proportion of a certain selected element in the (printed) representation is maintained.

[0070] Furthermore, in one particular embodiment, the objective function E also includes at least one term called an alignment term. Items, alignment items This allows the transformed textured mesh M2 to be adapted to the 3D points obtained on the manufacturing object O2.

[0071] In a preferred embodiment, alignment items Satisfy the following expression: in: - It can be used to control the influence of different points based on the corresponding reliability of those points; - It is a point The index of the corresponding point on the point cloud. (Used via the point cloud) The nearest neighbor is searched to identify the corresponding point. This nearest neighbor is represented as... ;as well as - At the corresponding point The unit normal to the target surface at that location. Using... The local regression calculation of the neighbors is used to calculate the target surface.

[0072] Then, item Measurement from to and The square distance between tangent planes.

[0073] Furthermore, in one particular embodiment, the objective function E also includes at least one smoothing term. .

[0074] Smoothing terms The goal is to force the distortion field to be smooth enough to avoid unnatural distortion shapes. "Regularity" refers to the assignment of regularity to two points that are close to each other. The affine transformations will have parameters that are close to each other.

[0075] For this purpose, smoothing terms Penalize adjacent points The differences between transformations on the same surface.

[0076] In a preferred embodiment, the smoothing term Satisfy the following expression: in: - It is the Frobenius norm; and - It refers to concatenates. and A 3 × 4 matrix.

[0077] Furthermore, in one particular embodiment, the objective function E also includes at least one rigid term. rigid items This makes the transformation of this set of affine transformations approximate a rigid transformation.

[0078] More specifically, the rigid item The goal is therefore to apply a transformation close to a rigid transformation (including rotation and translation) to each affine transformation.

[0079] In a preferred embodiment, the stiffness term Satisfy the following expression: In this expression, It is written as follows: Additionally, ,in .

[0080] In a preferred embodiment, the objective function E used in sub-step S2B satisfies the following expression: In this expression, , , , and These are weighting coefficients associated with different terms of the objective function E, which preferably satisfy the prior expression.

[0081] These weighting factors allow for adjustment of the importance assigned to each item. Preferably, the positional item... and shape retention items It is what I prefer.

[0082] Furthermore, in a preferred embodiment, in sub-step S2D, the computing unit 4D performs the following consecutive operations: - It calculates the objective function E with respect to the set of affine transformations. The gradient; - It determines the direction of adjustment based on this gradient; that is, in order to reduce the value of the objective function E, the parameters of the affine transformation set... The direction that should be adjusted; and It determines the new set of affine transformations along this adjustment direction, for example, by adding predetermined (or not predetermined) values ​​to all parameters of that set of affine transformations. .

[0083] In one particular embodiment, in substep S2D, computational element 4D uses a specialized nonlinear least squares (NLLS) solver, such as a Gauss-Newton or Lewenberg-Marquardt solver. Since the objective function E has the form of a sum of squares, convergence and optimization problems can be advantageously solved using such solvers to achieve superlinear convergence rates.

[0084] In addition, such as Figure 2 The computer device 1 described herein may also include: - At least one memory 8 (MEM) capable of storing data for data processing and computation implemented by the computing elements of computer device 1, such as, for example, an initial transformation set; and - Human-machine interface 9 (HMI) that allows the operator to supply data to computer device 1, such as, for example, the threshold V2 of objective function E.

[0085] Furthermore, the receiving unit 2 and the transmitting unit 3 can form part of a conventional communication system 10, which enables the computer device 1 to communicate with devices outside the computer device 1 via wired or wireless links.

[0086] The different computing elements and / or computing units of computer device 1 can correspond to any type of processor capable of performing the corresponding processing and computation. They can be grouped within a single computing unit.

[0087] Therefore, in the context of this invention, two similar types of meshes (with the same number of vertices and polygons) are provided, the first mesh corresponding to the tessellation of the designed object, and the second mesh being created as a copy of the first mesh, which is designed to fit the manufactured object (defined by the acquired point cloud).

[0088] Therefore, method P (using computer device 1) implements a non-rigid transformation that uses a distortion model (or set of transformations) to model the distortion of the manufactured object relative to the design object, aligning the initial textured mesh with the 3D points of the point cloud obtained on the manufactured object. This causes a slight displacement of the vertices of the created mesh (the transformed textured mesh) without changing the overall structure of the mesh (the same number of vertices and polygons, the regularity of the polygons, etc.). Thus, unlike rigid distortion where the entire mesh undergoes the same transformation to align with the point cloud, in this non-rigid transformation, different parts of the mesh may experience different distortions to account for non-rigid behavior, such as in the case of an aircraft, where the aircraft may experience non-homogeneous total distortion due to gravity and / or dimensional variations due to manufacturing tolerances.

[0089] As described above, method P and computer device 1 therefore have many advantages. In particular, they enable: - The transformed textured mesh is determined relatively simply (without complex filtering), and additionally, the mesh is particularly well-suited for analog printing; - Helps to achieve good fidelity of paint as if printed on a manufactured object relative to paint as if designed on a design object, especially when the geometry of the manufactured object does not perfectly correspond to the design object and its error is significantly greater than the required printing accuracy; - Ensure that a certain vertex corresponds precisely to a certain point on the manufactured object; and - Ensure the (geometric) proportion of certain elements in the maintained texture.

Claims

1. A method for determining a transformed textured mesh (M2) of a three-dimensional manufactured object (O2) based on a textured mesh called an initial textured mesh (M1) of a three-dimensional design object (O1), the transformed textured mesh (M2) being intended for printing a two-dimensional texture (T) on the manufactured object (O2) corresponding to the design object (O1), the method (P) being implemented by a computer device (1) and comprising at least the following steps: - Receiving step (S1), for receiving a mesh representing the three-dimensional design object (O1) and an associated two-dimensional texture (T), and three-dimensional points (Pm) from a point cloud (NP) obtained on the manufactured object (O2), the mesh and the associated two-dimensional texture (T) forming the initial textured mesh (M1) including vertices; and - Determine step (S2) for determining the transformed textured mesh (M2) by taking into account at least some of the vertices and at least some of the three-dimensional points (Pm). The characteristic is that the determining step (S2) implements an iterative process to determine a set of affine transformations with personalized parameters, such that the value of an objective function can be minimized by taking into account the initial textured mesh (M1) and the 3D points (Pm) taken into account from the point cloud (NP), the objective function including at least one term that promotes a specific property involving the set of affine transformations, and therefore, the determined set of affine transformations is applied to the vertices taken into account by the initial textured mesh (M1) to obtain the transformed textured mesh (M2).

2. The method claimed in claim 1, Its features are, The determining step (S2) includes at least the following sequence (SE) of consecutive sub-steps, which are iteratively implemented: - First sub-step (S2A) for applying an affine transformation set to the vertices considered in the initial textured mesh (M1) to obtain the vertices of the textured mesh referred to as the computed textured mesh, the affine transformation set corresponding to a predetermined affine transformation set during the first iteration and corresponding to an affine transformation set determined in the previous iteration during each iteration of subsequent iterations; - Second sub-step (S2B) for calculating the value of the objective function based on the vertices included in the initial textured mesh (M1), the three-dimensional points (Pm) included in the point cloud (NP), and the vertices of the calculated textured mesh; - The third sub-step (S2C) is used to compare the calculated value of the objective function with a predetermined threshold, and is used to: • If the calculated value is less than the threshold, the determination step (S2) is stopped, taking into account that the transformed textured mesh (M2) corresponds to the textured mesh calculated in the first sub-step (S2A) of the current iteration; and • If the calculated value is greater than or equal to the threshold, then the determining step (S2) continues by implementing the fourth sub-step (S2D); and - Fourth sub-step (S2D): for determining a new set of affine transformations based on the objective function and the set of affine transformations, the new set of affine transformations being used in the first sub-step (S2A) of the subsequent iteration.

3. The method claimed according to any one of claims 1 and 2, Its features are, If necessary, the determination step (S2) is stopped when a predetermined number of iterations is reached, and the transformed textured mesh (M2) corresponds to the last calculated textured mesh.

4. The method claimed according to any one of the preceding claims, Its features are, The objective function includes at least one term that corresponds a certain vertex of the transformed textured mesh (M2) to a point of the manufactured object (O2) called the target point.

5. The method claimed according to any one of the preceding claims, Its features are, The objective function includes at least one term that ensures a predetermined distance is maintained between certain vertices of the transformed textured mesh (M2).

6. The method claimed according to any one of the preceding claims, Its features are, The objective function includes at least one of the following: - To adapt the transformed textured mesh (M2) to the items of the three-dimensional points obtained on the manufactured object (O2); - This causes the transformations generated by the set of affine transformations to force terms that undergo smoothing distortion; - Terms that make the transformations generated by the set of affine transformations approximate rigid transformations.

7. The method claimed in any one of claims 2 and 3, Its features are, The fourth sub-step (S2D) includes the following consecutive operations: - Calculate the gradient of the objective function with respect to the set of affine transformations; - Determine the adjustment direction based on the gradient; and - Determine a new set of affine transformations along the adjustment direction.

8. The method claimed according to any one of claims 2, 3 and 7, Its features are, The fourth sub-step (S2D) uses a specialized nonlinear least squares solver.

9. The method claimed according to any one of the preceding claims, Its features are, The method includes: - Calculation step (S4) for determining the initial set of affine transformations; and / or - Calculation step (S5) for determining the target point of the manufactured object (O2); and / or - Calculation step (S6) for determining at least one region of the two-dimensional texture (T), the proportion of the region must be maintained.

10. A computer device for determining a textured mesh called a transformed textured mesh (M2) of a three-dimensional manufactured object (O2) based on a textured mesh called an initial textured mesh (M1) of a three-dimensional design object (O1), the transformed textured mesh (M2) being intended for printing a two-dimensional texture (T) on the manufactured object (O2) corresponding to the design object (O1), the computer device (1) comprising at least: - A receiving unit (2) is configured to receive a mesh representing the three-dimensional design object (O1) and an associated two-dimensional texture (T), as well as three-dimensional points (Pm) from a point cloud (NP) obtained on the manufacturing object (O2), the mesh and the associated two-dimensional texture (T) forming the initial textured mesh (M1) including vertices. as well as - A calculation unit (4) is configured to take into account at least some of the vertices and at least some of the three-dimensional points (Pm) to determine the transformed textured mesh (M2). The computational unit (4) is characterized in that it comprises computational elements (4A, 4B, 4C, 4D) configured to perform iterative processing to determine a set of affine transformations with personalized parameters, such that the value of an objective function can be minimized by taking into account the initial textured mesh (M1) and the three-dimensional points (Pm) taken into account from the point cloud (NP), the objective function including at least one term that promotes a specific property involving the set of affine transformations, and thus the determined set of affine transformations is applied to the vertices taken into account by the initial textured mesh (M1) to obtain the transformed textured mesh (M2).

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