Method for correcting the trajectories of a machining tool for machining a preformed blank and associated machining tool
The method corrects machining tool trajectories by integrating non-rigid matching and deformation algorithms to adapt to actual part shapes, addressing precision and complexity issues in machining complex geometries and partial datasets, enhancing machining efficiency and accuracy.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- FIVES MACHINING
- Filing Date
- 2024-12-18
- Publication Date
- 2026-06-19
AI Technical Summary
Existing machining algorithms fail to accurately adapt to the actual shape of pre-formed parts due to material deformation, leading to precision issues and limitations in handling complex geometries, partial datasets, and surface reconstruction errors, particularly with technologies like MAP, which are limited to simple parts and slow for high-density datasets.
A method involving data acquisition from theoretical and real models, generation of a point cloud, calculation of transformation functions through non-rigid matching under isometry constraint, and deformation of theoretical surface meshes to correct machining tool trajectories, allowing for precise adaptation to actual part shapes, even with pronounced curvatures and holes.
Enables accurate correction of machining tool trajectories, reducing computing power requirements and time, and enabling machining of complex parts with high precision, even with partial datasets, by minimizing information loss and modeling errors.
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Abstract
Description
Title of the invention: Method for correcting the trajectories of a machining tool for machining a pre-formed blank and associated machining tool. TECHNICAL FIELD OF THE INVENTION
[0001] The invention relates to a method for correcting the trajectories of a machining tool for machining a pre-formed raw part, and more particularly the correction of theoretical trajectories initially calculated on the basis of a theoretical 3D model of a pre-formed raw part. TECHNOLOGICAL BACKGROUND OF THE INVENTION
[0002] Many advances have been made in the field of programming machining machines, and more particularly in the programming of the trajectories and orientation of the machining tools of these machines.
[0003] The very operation of these machines is based on a mathematical algorithm. This algorithm gives the manufacturing means the ability to adapt the shape of the machining paths to the actual shape of the pre-formed parts.
[0004] Before machining, a raw part can be deformed to obtain a theoretical target shape. However, this deformation, due to the material used, the elasticity of the part, as well as many other parameters, becomes loose and is not identical to the theoretical target shape; the theoretical machining trajectories planned for the target shape are therefore no longer suitable, and it is therefore necessary to correct them to obtain a machined part conforming to the machining objectives.
[0005] Rigid to non-rigid type matching algorithms are known, allowing point matching in three dimensions for parts with complex geometry, as well as non-rigid isometric ICP algorithms.
[0006] These algorithms have the disadvantage of being incompatible with scaling, resulting in a significant loss of information, incompatible with precision objectives for a machining activity.
[0007] Furthermore, these algorithms only allow mesh-to-mesh matching, making them inoperable for applications where the dataset measured on a real part is partial and where surface reconstruction involves the introduction of potential errors.
[0008] We also know of a technology called MAP, which has replaced more polluting manufacturing processes, namely chemical machining.
[0009] This technology, and more particularly its implementation algorithm, has the disadvantage that it is only functional with geometrically and topologically simple parts.
[0010] In addition, MAP technology has many limitations, including: -Limitation of application to slightly curved parts only; -Limitation on parts with no holes or recesses prior to machining; -Limitation to the machining of pocket with constant thickness; -Limitation to machining of thin parts (< 30mm); -Limitation to normal machining at the reference surface (coaxial tool axes and support); and - Very slow implementation for datasets with high point density.
[0011] All its specific limits are additional functions to be added to the programming chain which each time bring specific complexities and constraints.
[0012] Algorithms such as those of MAP technology also have the drawback of causing too much information loss, preventing the proper processing of data from programming. We therefore propose to take advantage of our new computing resources to have a comprehensive MAP processing method capable of taking into account the limitations listed above.
[0013] The present invention remedies these drawbacks. Summary of the invention
[0014] The invention relates to a method for correcting the trajectories of a machining tool for machining a pre-formed blank.
[0015] According to a general definition of the invention, the process comprises the following steps: - Acquisition of data from a theoretical 3D model of the preformed raw part to be machined including a theoretical surface mesh and associated theoretical machining trajectories of the machining tool; - Acquisition of data from a real model representative of the preformed raw part; - Generation of a point cloud from the data of the real model representing the actual preformed raw part thus acquired; - Calculation of transformation functions to be applied to the theoretical 3D model, including a calculation of non-rigid matching of the vertices of the theoretical 3D model with the points of the point cloud under isometry constraint, comprising a sub-step of assignment between the vertices and the points and a sub-step of deformation of the theoretical surface mesh according to a deformation algorithm chosen as a function of the result of the assignment sub-step, these sub-steps being repeated until a transformed theoretical model is obtained that is matched with a real model having a chosen matching score; - Calculation of corrected machining tool trajectories from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model are applied.
[0016] Advantageously, the method according to the invention makes it possible to obtain on the one hand a corrected locality of the points of the part, but also corrected normals to the surface.
[0017] This result makes it possible to correct the machining axis according to the corrected normal information, to precisely correct the trajectories of the machining tool and the potential associated support in path and inclination so that they are calibrated with respect to the actual surface of the pre-deformed part, thus making it possible to adapt the tool trajectory for parts with more pronounced curvatures, up to 90°, having holes or hollowing and to overcome the limitations of prior art algorithms.
[0018] In addition, the method according to the invention also allows for point cloud mesh matching without requiring surface reconstruction, and greatly limiting modeling errors.
[0019] In practice, the substep of assignment between vertices and points is implemented by nearest neighbor projection of the vertices of the theoretical surface mesh to the corresponding points of the point cloud or of the points of the point cloud to the corresponding vertices of the theoretical surface mesh.
[0020] Advantageously, this substep allows the implementation of the process, even if one of the acquired datasets is only partial, thus allowing the management of absences of points in the dataset, due for example to holes or hollows on the pre-deformed part.
[0021] In addition, the substep of deforming the theoretical surface mesh according to a chosen deformation algorithm further includes the following substeps: - construction of an orientation constraint for the vertices according to the result of the assignment substep; - deformation of the theoretical surface mesh by applying the calculated orientation constraints and obtaining a deformed theoretical surface mesh comprising a set of vertices.
[0022] According to an embodiment of the invention, the matching step further comprises the following substeps: -Calculation of a convergence score for the sum of the points in the point cloud and the vertices Si' of the deformed theoretical surface mesh assigned to the points; and -Comparison of the convergence score obtained to a chosen threshold: -if the convergence score is greater than or equal to the threshold then the trajectory calculation step is implemented; -if the convergence score is below the threshold then the step of calculating transformation functions is repeated, the non-rigid matching calculation under isometry constraint is implemented with the deformed theoretical surface mesh of the transformed theoretical model obtained in place of the theoretical surface mesh of the theoretical 3D model.
[0023] Advantageously, these steps allow, on the one hand, to maximize the accuracy of the calculated deformation, and on the other hand, to integrate specific deformation parameters, specific to the pre-deformed part(s) to be machined.
[0024] According to a particular embodiment of the invention, the data acquisition step of a theoretical 3D model of the preformed raw part to be machined comprising a theoretical surface mesh includes a hierarchical optimization substep in which the theoretical surface mesh comprising a first chosen vertex density is converted to a second chosen vertex density lower than the first density.
[0025] In practice, the assignment and deformation substeps are implemented iteratively on the basis of a theoretical 3D model whose theoretical surface mesh of second chosen vertex density serves as the basis for the calculations of transformation function until an intermediate convergence score is obtained, said substeps then being implemented iteratively on the basis of the theoretical surface mesh of second chosen vertex density greater than the first density until a convergence score is obtained.
[0026] Advantageously, the hierarchical optimization substeps and the application of datasets of different densities make it possible to considerably reduce the computing power required to implement the process while reducing the computation time by a factor of ten to twenty, which is essential for an industrial-scale application.
[0027] By way of example, the deformation algorithm implemented in the matching step is of the ARAP (As-Rigid-As-Possible) type.
[0028] Furthermore, the step of calculating corrected machining tool trajectories from theoretical trajectories, onto which the transformation functions of the obtained transformed theoretical model are applied, further includes the following sub-steps: - analysis of the transformed theoretical model T obtained from the deformed theoretical surface mesh obtained; - calculation of new positions and normals from the vertices and transformation functions calculated to go from each vertex of the theoretical surface mesh to each vertex of the deformed theoretical surface mesh; and - calculation of new modified trajectories based on theoretical trajectories by applying the transformation functions obtained.
[0029] The term trajectory refers to the path and inclination of the machining tool, as well as its support.
[0030] By way of non-limiting example, the data acquisition step of a real model is implemented by laser scanner-type data acquisition means.
[0031] Advantageously, the method according to the invention allows on the one hand a matching between mesh and point cloud under isometry constraint, efficient on large datasets but compatible with a partial dataset, the method also allowing robustness of the matching and calculation of corrected trajectories even when using a noisy point cloud.
[0032] The invention also relates to a machining system for implementing the process according to the invention.
[0033] According to a second definition of the invention, the system comprises: -a machining tool comprising at least one tool tip configured to remove material from a preformed blank along a chosen trajectory in space and inclined along at least 5 axes to obtain a target machined part; -data acquisition means configured to allow the acquisition of data from a theoretical 3D model of the preformed workpiece to be machined, including a theoretical surface mesh and associated theoretical machining tool trajectories, and the acquisition of data from a representative real model of the preformed workpiece; and -processing methods configured for: -generate a point cloud from the data of the real model representing the actual preformed raw part thus acquired; - Calculate transformation functions to be applied to the theoretical 3D model including a calculation of non-rigid matching of the vertices of the theoretical 3D model with the points of the point cloud under isometry constraint including a sub-step of assignment between the vertices and the points and a sub-step of deformation of the theoretical surface mesh according to a deformation algorithm chosen as a function of the result of the assignment sub-step, these sub-steps being repeated until a transformed theoretical model is obtained that matches a real model with a chosen matching score; - Calculate corrected machining tool trajectories from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model are applied. BRIEF DESCRIPTION OF THE FIGURES
[0034] Other advantages and features of the invention will become apparent upon examination of the description and drawings in which: - [Fig-1] schematically represents the main steps of the process according to the invention; - [Fig.2] schematically represents a detailed view of the process according to the invention; - [Fig.3] schematically represents the sub-steps of the data acquisition step according to the invention; - [Fig.4] schematically represents the sub-steps of the step of calculating transformation functions to be applied to the theoretical 3D model of the process according to the invention; - [Fig.5] schematically represents the sub-steps of the step of calculating new trajectories of the process according to the invention; - [Fig.6] represents a three-dimensional view of the data obtained after acquisition and generation according to the process according to the invention; - [Fig. 7] represents a three-dimensional view of the data at different stages of the process according to the invention; and - [Fig.8] schematically represents a cross-sectional view of a machining tool before and after correction according to the invention. DETAILED DESCRIPTION
[0035] With reference to Figures 1a 8, the method according to the invention for correcting the trajectories of a machining tool for machining a preformed raw part, comprises a data acquisition step S0, configured to record the theoretical and actual data necessary for machining, a generation step SI of an NPR point cloud from actual data, a calculation step S2 of deformation functions configured to identify the deformation functions to be applied to the theoretical data to obtain the actual data, and a calculation step S3 of corrected trajectories on the basis of the calculated deformation functions.
[0036] The data acquisition step S0 comprises a first substep S0A of data acquisition DMT of a theoretical 3D model MT of the preformed raw part to be machined, the theoretical 3D model MT comprising a theoretical surface mesh ST and theoretical machining trajectories of the machining tool as well as its potential support associated. The theoretical 3D model MT also includes vertices Si associated with the theoretical surface mesh ST.
[0037] Vertex Si means the vertex of each cell of the theoretical surface mesh ST, a cell being a 3-dimensional surface delimited by a contour connecting at least 3 points distributed on said surface.
[0038] According to one embodiment of the invention, the SOA data acquisition step of a theoretical 3D model MT of the preformed raw part to be machined comprising a theoretical surface mesh ST includes a hierarchical optimization substep in which the theoretical surface mesh ST comprising a first chosen vertex density DI is converted to a second chosen vertex density D2 lower than the first density D1.
[0039] By way of non-limiting example, the conversion of the theoretical surface mesh ST from a first density D1 to the second density D2 can be carried out by applying an edge contraction simplification function.
[0040] Density is understood to mean the number of vertices of the theoretical 3D model MT.
[0041] The data acquisition step S0 then comprises a second sub-step S0B data acquisition of a real MR model representative of the preformed raw part.
[0042] By way of non-limiting example, the S0B data acquisition step of a real MR model is implemented by laser scanner-type data acquisition means, allowing the pre-deformed part to be machined to be scanned.
[0043] The method according to the invention then includes a step of generating SI of an NPR point cloud from the DMR data of the real MR model representative of the real preformed raw part thus acquired comprising a plurality of points Ti.
[0044] The method according to the invention then includes a calculation step S2 of transformation functions to be applied to the theoretical 3D model MT.
[0045] This calculation step S2 includes a non-rigid matching calculation of the vertices Si of the theoretical 3D model MT with the points Ti of the NPR point cloud under isometry constraint.
[0046] The term non-rigid matching under isometry constraint means a non-rigid matching that preserves geodetic distances.
[0047] The matching calculation comprising an assignment substep S21 between vertices Si and points Ti.
[0048] In practice, the assignment substep S21 between the vertices Si and the points Ti is implemented by projection according to a "nearest neighbor" function of the vertices Si of the theoretical surface mesh ST onto the corresponding points Ti of the cloud of NPR points or Ti points of the NPR point cloud to the corresponding vertices Si of the theoretical surface mesh ST.
[0049] Advantageously, the projection being able to be carried out in both directions makes it possible to carry out the assignment substep S21 even when dealing with a partial data set such as a hole or hollow.
[0050] A partial data set is understood to be a point cloud that does not represent the entirety of the theoretical part to be matched.
[0051] The calculation step S2 of transformation functions includes a second substep of deformation S22 of the theoretical surface mesh ST according to a deformation algorithm chosen as a function of the result of the assignment substep S21.
[0052] In practice, the S22 deformation substep of the theoretical surface mesh ST according to a chosen deformation algorithm further comprises the following substeps: - S23: construction of at least one constraint in orientation Mi for vertices Si according to the result of the assignment substep S21; - S24: deformation of the theoretical surface mesh ST by application of the calculated orientation constraint Mi and obtaining a deformed theoretical surface mesh STD comprising a set of vertices Si'.
[0053] By way of non-limiting example, the deformation algorithm implemented in the matching step S2 can be of the ARAP (As-Rigid-As-Possible, i.e. as rigid as possible) type or similar.
[0054] The assignment substeps S21 and deformation substeps S22 are repeated until a transformed theoretical model MTT is obtained, corresponding to the deformed theoretical surface mesh STD whose matching with the real model MR has a matching score SC greater than or equal to a chosen target threshold SE attesting to an identity of position between the theoretical model MTT and the real model MR.
[0055] After each iteration of the assignment steps S21 and deformation S22, it is checked whether the deformed theoretical model STD has the parameters required to be classified as a transformed theoretical model MTT.
[0056] This verification is implemented according to the sub-steps of calculating an S25 convergence score SC, comparing it with the SE threshold, and determining whether the step of calculating the transformation functions S2 should be completed or not.
[0057] In practice, the substep of calculating an S25 SC convergence score based on at least two criteria: -distance between each vertex Si of the theoretical MT model and the point of the associated NDP point cloud; -Isometry measurement between the mesh of the theoretical model MT and the obtained deformed theoretical surface mesh STD.
[0058] The comparison substep S26 of the convergence score SC obtained at a chosen threshold SE further includes determining the continuation of the process according to the comparison result; if the convergence score SC is greater than or equal to the threshold SE then the trajectory calculation step S3 is implemented; if, on the other hand, the convergence score SC is less than the threshold SE then the transformation function calculation step S2 is repeated via the assignment substep S21 and deformation substep S22.
[0059] According to one embodiment of the invention, the non-rigid matching calculation under isometry constraint, the assignment substeps S21 and deformation substeps S22 are implemented with the deformed theoretical surface mesh STD obtained via the previous iteration of the calculation step S2, instead of the theoretical surface mesh ST of the theoretical 3D model MT.
[0060] According to a particular embodiment of the invention, the assignment substeps S21 and deformation substeps S22 are implemented iteratively on the basis of a theoretical 3D model MT whose theoretical surface mesh ST of second density D2 of chosen vertex, called weak, serves as the basis for the calculations of transformation function until an intermediate convergence score chosen SCA is obtained.
[0061] Once the chosen intermediate convergence score SCA is reached, the result of the transformation function calculation is applied to the deformed theoretical surface mesh STD of second density D2, said deformed theoretical model STD being converted into a deformed theoretical model STD having a number of vertices according to the first chosen vertex density DI greater than the second vertex density D2.
[0062] Said sub-steps of assignment S21 and deformation S22 being then implemented iteratively on the basis of the theoretical surface mesh ST of second density D2 of vertex chosen greater than the first density DI until a chosen convergence score SC greater than or equal to the threshold SE is obtained.
[0063] Advantageously, this makes it possible to drastically reduce the number of iterations required to obtain a transformed MTT theoretical model, while minimizing the computing power required as well as the associated computing time.
[0064] The method further includes a step of calculating corrected machining tool trajectories S3 from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model MTT are applied.
[0065] In practice, the step of calculating corrected machining tool trajectories S3 from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model MTT are applied further includes several sub-steps.
[0066] The step of calculating corrected machining tool trajectories S3 includes a first sub-step of analysis S31 of the transformed theoretical model obtained MTT.
[0067] The step of calculating corrected machining tool trajectories S3 then includes a second sub-step of calculating new positions and normals S32 from the vertices Si' and the transformation functions calculated to go from each vertex Si of the theoretical surface mesh ST to each vertex Si' of the deformed theoretical surface mesh STD.
[0068] The step of calculating corrected machining tool trajectories S3 finally includes a third sub-step of calculating new trajectories S33 modified by applying the transformation functions obtained from the transformed theoretical model MTT applied to the theoretical trajectories of the theoretical model MT.
[0069] In practice the trajectory of the machining tool with respect to a support opposite to the machining tool normally has a coaxial component and follows a trajectory normal with respect to the surface to be machined.
[0070] The tool and support trajectories are generally of the form (x, y, z, i, j, k), where i, j and k represent the normal position of the tool or support relative to the surface to be machined.
[0071] The calculation of the S33 trajectories also allows, via the application of the transformed theoretical model MTT and its associated transformation functions, to correct the coordinates i, j and k representing the normal position of the tool or the support with respect to the surface to be machined.
[0072] Advantageously, this correction of the normal position of each point allows, for example, the implementation of a so-called non-standard machining, in that the position of the tool and the support opposite this tool for at least one given point of the surface to be machined each have coordinates i, j, k representing different normal positions, not coaxial with respect to each other, such that the tool has coordinates il, jl, kl and the support i2, j2, k2 different from il, jl, kl allowing, for example, the machining of parts of high curvature, of high thickness, or the implementation of non-normal machining.
[0073] The invention further relates to a machining system capable of implementing the process according to the invention.
[0074] The machining system includes at least one machining tool comprising at least one tool tip configured to remove material from a preformed blank along a chosen path in space and inclined along at least 5 axes to obtain a target machined part.
[0075] A machining tool means any tool, support and / or tool / support group.
[0076] The system according to the invention further comprises data acquisition means configured to allow the acquisition of DMT data from a theoretical 3D MT model of the preformed raw part to be machined comprising a surface mesh theoretical ST and associated theoretical machining tool trajectories and DMR data acquisition of a real MR model representative of the preformed raw part.
[0077] The system further includes processing means configured to implement the process according to the invention.
[0078] In practice, the processing means are configured to: - SI: generate an NPR point cloud from the data of the real MR model representative of the actual preformed raw part thus acquired; - S2: Calculate transformation functions to be applied to the theoretical 3D model MT including a calculation of non-rigid matching of the vertices Si of the theoretical 3D model MT with the points Ti of the point cloud NPR under isometry constraint including an assignment substep S21 between the vertices Si and the points Ti and a deformation substep S22 of the theoretical surface mesh ST according to a deformation algorithm chosen as a function of the result of the assignment substep S21, these substeps being repeated until a transformed theoretical model MTT is obtained that matches the real model MR with a chosen matching score SC; - S3: Calculate corrected machining tool trajectories from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model MTT are applied.
Claims
Demands
1. A method for correcting toolpaths for machining a preformed blank, comprising the following steps: -SOA: Acquisition of data from a theoretical 3D model (TM) of the preformed blank to be machined, including a theoretical surface mesh (ST) and associated theoretical machining toolpaths; -SOB: Acquisition of data from a real model (RM) representative of the preformed blank; -SI: Generation of a point cloud (NPR) from the data of the real model (RM) representative of the actual preformed blank thus acquired;- S2: Calculation of transformation functions to be applied to the theoretical 3D model (MT) including a calculation of non-rigid matching of the vertices Si of the theoretical 3D model (MT) with the points Ti of the point cloud (NPR) under isometry constraint including an assignment substep (S21) between the vertices (Si) and the points (Ti), and a deformation substep (S22) of the theoretical surface mesh (ST) according to a deformation algorithm chosen as a function of the result of the assignment substep (S21), these substeps being repeated until a transformed theoretical model (MTT) is obtained, which is matched with a real model (MR) having a chosen matching score (SC); - S3: Calculation of corrected machining tool trajectories from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model (MTT) are applied.
2. A method for correcting the trajectories of a machining tool according to claim 1, characterized in that the assignment substep (S21) between the vertices (Si) and the points (Ti) is implemented by nearest neighbor projection of the vertices (Si) of the theoretical surface mesh (ST) to the corresponding points (Ti) of the point cloud (NPR) or of the points (Ti) of the point cloud (NPR) to the corresponding vertices (Si) of the theoretical surface mesh (ST).
3. A method for correcting the trajectories of a machining tool according to claim 1 or 2, characterized in that the deformation substep (S22) of the theoretical surface mesh (ST) according to a The chosen deformation algorithm further includes the following substeps: - S23: construction of an orientation constraint (Mi) for the vertices (Si) according to the result of the assignment substep (S21); - S24: deformation of the theoretical surface mesh (ST) by application of the calculated orientation constraints (Mi) and obtaining a deformed theoretical surface mesh (STD) comprising a set of vertices (Si').
4. A method for correcting the trajectories of a machining tool according to claim 3, characterized in that the matching step (S2) further comprises the following substeps: S25: Calculation of a convergence score (SC) of the sum of the points (Ti) of the point cloud (NPR) and the vertices (Si') of the theoretical deformed surface mesh STD) assigned to the points (Ti); and - S26: Comparison of the convergence score (SC) obtained to a chosen threshold (SE): -if the convergence score (SC) is greater than or equal to the threshold (SE) then the trajectory calculation step (S3) is implemented;-if the convergence score (SC) is less than the threshold (SE) then the transformation function calculation step (S2) is repeated, the non-rigid matching calculation under isometry constraint is implemented with the deformed theoretical surface mesh (STD) of the transformed theoretical model (MTT) obtained in place of the theoretical surface mesh (ST) of the theoretical 3D model (MT).;
5. A method for correcting the trajectories of a machining tool according to any one of claims 1 to 4, characterized in that the SOA step of acquiring data from a theoretical 3D model (MT) of the preformed raw part to be machined comprising a theoretical surface mesh (ST) includes a hierarchical optimization substep in which the theoretical surface mesh (ST) comprising a first chosen vertex density (Dl) is converted to a second chosen vertex density (D2) lower than the first density (Dl).
6. A method for correcting the trajectories of a machining tool according to claim 5, characterized in that the substeps of assignment (S21) and deformation (S22) are implemented iteratively on the basis of a theoretical 3D model (MT) whose theoretical surface mesh (ST) of second density (D2) of chosen vertex serves as based on transformation function calculations until an intermediate convergence score (SCA) is obtained, said sub-steps then being implemented iteratively on the basis of the theoretical surface mesh (ST) of second density (D2) of vertex chosen greater than the first density (Dl) until a convergence score (SC) is obtained.
7. A method for correcting the trajectories of a machining tool according to any one of the preceding claims, characterized in that the step of calculating corrected machining tool trajectories (S3) from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model (MTT) are applied further comprises the following substeps: - S31: Analysis of the transformed theoretical model (MTT) obtained from the obtained deformed theoretical surface mesh (STD); - S32: Calculation of new positions and normals from the vertices (Si') and the transformation functions calculated to go from each vertex (Si) of the theoretical surface mesh (ST) to each vertex (Si') of the deformed theoretical surface mesh (STD); and - S33: Calculation of new modified trajectories on the basis of the theoretical trajectories by applying the transformation functions obtained.
8. Method for correcting the trajectories of a machining tool according to any one of the preceding claims, characterized in that the deformation algorithm implemented in the matching step (S2) is of the ARAP type.
9. A method for correcting the trajectories of a machining tool according to any one of the preceding claims, characterized in that the data acquisition step of a real model (RM) is implemented by laser scanner-type data acquisition means.
10. A machining system for a preformed blank for implementing the process according to any one of claims 1 to 9, comprising: - a machining tool comprising at least one tool tip configured to remove material from a preformed blank along a trajectory chosen in space and inclined along at least 5 axes to obtain a target machined part; - data acquisition means configured to allow the acquisition of data from a theoretical 3D model (TM) of the preformed blank to be machined, comprising a surface mesh theoretical (ST) and associated theoretical machining tool trajectories and data acquisition from a real model (MR) representative of the preformed blank; and - processing means configured for: -generate a point cloud (NPR) from the data of the real model (MR) representative of the actual preformed raw part thus acquired; - S2: Calculate transformation functions to be applied to the theoretical 3D model (MT) including a calculation of non-rigid matching of the vertices Si of the theoretical 3D model (MT) with the points Ti of the point cloud (NPR) under isometry constraint including an assignment substep (S21) between the vertices (Si) and the points (Ti) and a deformation substep (S22) of the theoretical surface mesh (ST) according to a deformation algorithm chosen as a function of the result of the assignment substep (S21), these substeps being repeated until a transformed theoretical model (MTT) is obtained that is matched with a real model (MR) having a chosen matching score (SC); - S3: Calculate corrected machining tool trajectories from theoretical trajectories on which the transformation functions of the obtained transformed theoretical model (MTT) are applied.