MCAD Model Deformation via 2-D Parametric Grid Extrapolation
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Solution Overview
Problem
Current MCAD technologies face challenges in reconstructing a deformed mesh model from a given deformed mesh, particularly in applying deformations to the original MCAD model while maintaining the same parameterization and handling arbitrary surfaces.
Innovation Solution
The method involves generating a deformed MCAD model by applying deformation to an undeformed MCAD model using a computer-aided engineering mesh model, where the deformation is extrapolated from a two-dimensional grid with a linear least squares minimization of spatial derivatives, ensuring smoothness criteria are met, and handling holes through interpolation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deformation is applied to an MCAD model using simulation data, then the accuracy of deformed geometry representation is improved, but the complexity of the modeling process increases
Solution Approach 1:
The patent introduces a 2-D parametric grid as an intermediary structure between the simulation mesh and the NURBS surface. This grid serves as a mediator that maps deformation data from the simulation onto the parametric surface, enabling accurate deformation application while maintaining a systematic and manageable workflow through structured intermediate representation
Solution Approach 2:
The patent replaces complex mechanical deformation modeling with a mathematical field-based approach using 2-D grids and parametric mappings. Instead of simulating physical deformation processes, the system uses mathematical interpolation and extrapolation on grid data to achieve accurate deformed geometry representation
2Stability of the object's composition
If deformation is extrapolated to grid points outside the face region, then the completeness of the deformed model is improved, but the difficulty of ensuring smoothness increases
Solution Approach 1:
The patent changes the parameter representation by using a 2-D parametric grid with specific smoothness constraints (minimizing second and third spatial derivatives). This parameter transformation allows the system to enforce smoothness mathematically through derivative minimization, making the smoothness requirement quantifiable and enforceable rather than qualitative
Solution Approach 2:
The patent creates a copied parametric representation of the deformation field on the 2-D grid, which can be independently processed and constrained for smoothness. This copied representation allows smoothness enforcement without directly modifying the original NURBS control points, separating the smoothness constraint application from the base geometry
3Adaptability or versatility
If a 2-D grid is generated from the MCAD surface and deformation is applied, then the adaptability to arbitrary surfaces is improved, but the device complexity increases
Solution Approach 1:
The patent creates a universal 2-D parametric grid framework that can handle arbitrary 3-D surfaces by mapping them to a common 2-D parameter space. This universal grid structure serves multiple functions: it can represent any surface topology, accommodate different deformation types, and work with various NURBS surface representations, making the system highly adaptable while maintaining a consistent underlying architecture
Data Source
AI summary
A mechanical computer-aided design (MCAD) model representing an object is received. The MCAD model contains a surface with a face defined therein. Deformation of the face is obtained in a simulation based on the MCAD model. The surface is defined by Non-Uniform Rational Basis Spline patches and mapped to a two-dimensional (2-D) parametric grid. The 2-D grid contains a first group of grid points representing the face and a second group of grid points representing outside of the face. The deformation of the face is applied to the first group of grid points. The deformation is extrapolated to the second group of grid points. An updated MCAD model representing a deformed object is generated using the 2-D grid associated with the applied deformation and the extrapolated deformation.