JP-7856484-B2 - Parameterization of CAD models

JP7856484B2JP 7856484 B2JP7856484 B2JP 7856484B2JP-7856484-B2

Inventors

ルーカスブリフォール

Assignees

ダッソーシステムズ

Dates

Publication Date: 20260511
Application Date: 20220518
Priority Date: 20210521

Claims (15)

A computer implementation method for parameterizing a computer-aided design (CAD) 3D model of a mechanical part, which includes a portion having a material distribution arranged as a sweep with a trajectory and boundary, - A 3D model including a skin portion representing the outer surface of the part of the machine component, - To provide one or more vector fields X , each representing the boundary and/or the trajectory, A computer implementation method comprising determining the value distribution of each parameter of the skin portion for each vector field X by optimizing an objective function that assigns a reward to the alignment of the gradient of a candidate parameter f with the vector field X.
The method according to claim 1, wherein the objective function rewards the alignment of the gradient of the candidate parameter f and the vector field X by imposing a penalty on the error between the gradient of the candidate parameter f and the vector field X.
The aforementioned error is the distance between the gradient df# of the candidate parameter f and the vector field X , as shown below: The method according to claim 2, wherein the distance is based on the metric tensor g .
The objective function is as follows: The method according to claim 3, wherein in this equation, M is the skin portion, X is the vector field X , f is the candidate parameter f , df# is the gradient of the candidate parameter f , ωg is the standard volume form of the skin portion with respect to the metric tensor g, and |df#-X|g2 is the distance between the gradient df# of the candidate parameter f with respect to the metric tensor g and the vector field X.
The candidate parameter f is in the following space The method according to claim 4, wherein H1(M) belongs to a space representing the following, and in this equation, H1 (M) is the Sobolev space of weakly differentiable functions on the skin portion M.
Optimizing the aforementioned objective function includes finding an approximation of the solution to the Poisson problem in H * 1 (M), as shown below. The method according to claim 5, in this equation, ∂M represents the boundary of the skin portion M, ∇ α X α is the divergence of the vector field X , and ιY(ω) is the inner product of n-forms ω∈Ω n (M) on M with respect to the vector field Y∈Γ(TM), where TM is the tangent bundle of M and Γ(TM) is the set of smooth tangent vector fields on the skin portion M.
The method according to claim 6, wherein the skin portion is represented by a 3D discrete geometric representation having discrete elements, and the approximation of the solution to the Poisson problem lies in a discrete space representing H * 1 (M).
The discrete space is as follows: The method according to claim 7, wherein in this equation, n is the number of discrete elements of the discrete geometric representation, and each φi is a continuous piecewise linear function on the skin portion M associated with the discrete element i.
The method according to claim 1, wherein the one or more vector fields X include a plurality of vector fields that are all aligned in the principal curvature direction of the skin portion.
The method according to claim 1, further comprising the material distribution being arranged as an extrusion, the computer implementation method providing the extrusion axis, and the one or more vector fields X include a vector field formed by the cross product of the extrusion axis and the normal of the skin portion.
The method according to claim 1, wherein the material distribution is arranged as a rotation, and the computer implementation method further includes providing a rotation axis, and the vector field X includes one or more vector fields formed by the cross product of the normal to the skin portion and a vector tangent to the skin portion along the trajectory.
The method according to claim 1, further comprising the computer implementation method calculating the contour of the sweep based on the determined value distribution.
A computer program including instructions for performing the computer implementation method described in any one of claims 1 to 12.
A computer-readable storage medium on which the computer program described in claim 13 is recorded.
A system comprising a processor connected to a memory storing the computer program described in claim 13.

Description

This disclosure relates to the field of computer programs and systems, and more specifically, to methods, systems, and programs for parameterizing computer-aided design (CAD) 3D models of mechanical parts. The market offers numerous systems and programs for the design, engineering, and manufacturing of objects. CAD stands for Computer-Aided Design, and refers to software solutions for designing objects, for example. CAE stands for Computer-Aided Engineering, and refers to software solutions for simulating the physical behavior of future products, for example. CAM stands for Computer-Aided Manufacturing, and refers to software solutions for defining manufacturing processes and operations, for example. In such computer-aided design systems, graphical user interfaces play a crucial role in terms of technical efficiency. These technologies can be integrated into Product Lifecycle Management (PLM) systems. PLM is a business strategy that helps companies share product data, apply common processing, and leverage enterprise knowledge to help develop products from concept to lifecycle, across the concept of an extended enterprise. Dassault Systèmes' PLM solutions (under the trademarks CATIA, ENOVIA, and DELMIA) provide an engineering hub for organizing product engineering knowledge, a manufacturing hub for managing manufacturing engineering knowledge, and an enterprise hub that enables enterprise integration and connectivity to the engineering and manufacturing hubs. Combined, this system provides an open object model that links products, processes, and resources to enable dynamic, knowledge-based product creation and decision support, facilitating product definition, manufacturing preparation, production, and service optimization. Some of these systems and programs offer functionality for processing CAD models of machine parts. In "Levy et al., “Least Squares Conformal Maps for Automatic Texture Atlas Generation”, ACM Transactions on Graphics (TOG), 21 (3), 2002, pp. 362-371," a quasi-conformal parameterization method based on the least-squares approximation of the Cauchy-Riemann equations is presented. The objective function defined in this way minimizes angular deformation. In "Mullen et al., “Spectral Conformal Parameterization”, Computer Graphics Forum, Wiley, 2008, 27 (5), 2008, pp. 1487-1494," a spectral procedure is described for automatically and efficiently performing discrete free-boundary conformal parameterization of triangular mesh patches without introducing artifacts frequently caused by vertex position constraints or excessive bias resulting from sampling irregularities. Advanced parameterization is calculated via constrained minimization of discrete-weighted conformal energies by finding the maximum values of eigenvalues/eigenvectors in a generalized eigenvalue problem involving symmetric sparse matrices. Refer to the attached diagram to illustrate a non-limiting example. This method is illustrated as an example.This method is illustrated as an example.This method is illustrated as an example.This method is illustrated as an example.An example of the graphical user interface for this system is shown.An example of this system is shown. This specification proposes a computer implementation method for parameterizing computer-aided design (CAD) 3D models of mechanical parts. The mechanical part includes a portion having a material distribution arranged as a sweep. The sweep has a trajectory and a boundary. The method includes providing a 3D model and one or more vector fields. The 3D model includes a skin portion representing the outer surface of the mechanical part. Each vector field represents the boundary and/or the trajectory. The method further includes determining the value distribution of each parameter of the skin portion for each vector field by optimizing an objective function. The objective function rewards alignment of the gradients of candidate parameters with the vector fields. This invention constitutes an improved solution for processing CAD 3D models of machine parts or parts thereof. In particular, the method provides parameterization of the skin portion of a CAD model representing the outer surface of a part of a machine part, having a material distribution arranged as a sweep. In other words, the method allows for the parameterization of the sweep of a machine part. "Providing parameterization of the skin portion" means determining the value distribution of one or more (e.g., two) parameters describing the geometry and/or topology of the skin portion. Parameterization of sweeps is particularly relevant to the CAD manufacturing field, as described below. Furthermore, this method not only allows the sweep to be parameterized, but also provides a natural parameterization, that is, a parameterization that is optimal with respect to the natural direction of the sweep. In fact, this method provides, as input, one or more vector fields, each representing the boundary and/or trajectory of t