CAD Model Parametrization via Gradient Alignment
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Solution Overview
Problem
Current CAD systems lack an efficient method for parametrizing 3D models of mechanical parts with sweeps, particularly in manufacturing contexts, where natural direction alignment and robustness to noise and incomplete surfaces are essential.
Innovation Solution
A computed-implemented method that optimizes an objective function to align the gradient of a candidate parameter with vector fields representing the boundary and trajectory of a sweep, using a Poisson's problem formulation and discrete geometry representation to determine parameter distributions that follow natural directions and are robust to noise and incomplete surfaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional parameterization methods are used for CAD models with sweeps, then the parameterization can be computed, but it fails to align with natural directions and is sensitive to noise and incomplete surfaces
Solution Approach 1:
The patent transforms the parameterization problem from a geometric constraint satisfaction problem into an optimization problem by changing the parameters to be optimized (gradient alignment with vector fields) rather than directly computing parameter values. This allows the method to be robust to noise while maintaining alignment with natural directions through the objective function formulation.
Solution Approach 2:
The patent replaces traditional geometric processing mechanisms with an optimization-based mathematical approach. Instead of using geometric algorithms that are sensitive to input quality, it uses gradient-based optimization that can handle noisy and incomplete surfaces by finding the optimal parameter distribution that aligns with vector fields representing natural directions.
2Manufacturing precision
If optimization-based parameterization is used to align gradients with vector fields, then natural direction alignment is improved, but computational complexity increases
Solution Approach 1:
The patent formulates the parameterization as an optimization problem where the objective function measures gradient alignment with vector fields. By changing from direct geometric computation to optimization, it achieves better alignment with natural directions while managing computational complexity through efficient gradient computation and optimization algorithms.
Solution Approach 2:
The optimization process automatically adapts to the local geometry through the objective function formulation. The gradient alignment requirement causes the parameterization to naturally follow vector fields representing natural directions without requiring explicit geometric constraints, making the system self-adjusting and reducing the need for complex preprocessing.
3Manufacturing precision
If gradient alignment optimization is performed, then parameterization follows natural directions, but the method becomes more sensitive to initialization and optimization parameters
Solution Approach 1:
The objective function provides continuous feedback on gradient alignment quality during optimization. This feedback mechanism allows the algorithm to adjust parameters iteratively to improve alignment with natural directions while the structured formulation of the objective function helps guide the optimization toward reliable solutions regardless of initialization.
Solution Approach 2:
The patent uses a regularized objective function that may impose stronger alignment constraints than strictly necessary, ensuring robust convergence to good solutions. This excessive action in terms of optimization constraints helps overcome sensitivity to initialization by providing stronger guidance toward the optimal parameterization.
Data Source
AI summary
A computer-implemented method for parametrization of a computer-aided design 3D model of a mechanical part including a portion having a distribution of material arranged as a sweep. The sweep has a trajectory and a boundary. The method includes obtaining the 3D model, the 3D model including a skin portion representing an outer surface of the portion of the mechanical part, and one or more vector fields, each vector field representing the boundary and/or the trajectory. The method further includes, for each vector field, determining a distribution of values of a respective parameter of the skin portion by optimizing an objective function which rewards alignment of a gradient of a candidate parameter with the vector field.