Generative 3D Shape Optimization Without Singularities or Disconnection
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Solution Overview
Problem
Current CAD software struggles with singularities and disconnections in generative design processes, particularly when using boundary representation models, which can lead to optimization halts and suboptimal designs.
Innovation Solution
A method involving a computer-aided design program that iteratively modifies a generatively designed 3D shape using numerical simulations, computes shape change velocities, and updates level-set representations, while preventing singularities and disconnections by fitting polynomial functions and adjusting shape changes based on reference velocities and densities, ensuring convergence to a stable solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If boundary representation models are used for generative design, then manufacturing precision is improved, but singularities and disconnections occur causing optimization halts
Solution Approach 1:
The patent introduces an intermediary representation system that bridges boundary representation models and level-set methods. The B-Rep model provides precise manufacturing boundaries while the level-set function serves as a mediator that prevents singularities during optimization by representing geometry through a continuous scalar field rather than explicit surfaces. This intermediary approach allows the system to maintain B-Rep precision for final output while using level-sets for stable iterative optimization.
Solution Approach 2:
The patent transforms the geometric representation parameters from explicit boundary definitions to implicit level-set functions. By changing the parameterization method from direct surface coordinates to distance functions, the system eliminates singularities that occur in B-Rep models during topology changes. The level-set parameter φ(x) continuously evolves during optimization without creating discontinuities or singular points.
2Manufacturing precision
If shape optimization is pursued aggressively, then design quality improves, but disconnections and singularities prevent convergence
Solution Approach 1:
The patent ensures continuous geometric evolution by using level-set functions that maintain continuity throughout the optimization process. The level-set function φ(x) evolves continuously through advection equations, preventing sudden disconnections or singularities. This continuous representation allows the geometry to transform smoothly from initial to final states without breaking topological connectivity or creating numerical singularities.
Solution Approach 2:
The patent implements preventive measures by using level-set representations that inherently cushion against singularity formation. The implicit function representation provides a buffer zone around geometric features, allowing gradual evolution rather than abrupt changes. This beforehand cushioning prevents the formation of zero-curvature points and self-intersections that would otherwise cause optimization failure.
3Reliability
If level-set methods are used for shape optimization, then singularity prevention is improved, but computational complexity increases
Solution Approach 1:
The patent segments the computational domain into discrete grid cells and represents the level-set function on this structured grid. By segmenting the continuous space into manageable computational units, the system simplifies the calculation of shape derivatives and advection operations. The grid-based approach breaks down the complex PDE solving into discrete finite difference operations that are computationally efficient and easier to implement than continuous methods.
Data Source
AI summary
Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes. A method includes obtaining one or more load cases and one or more design criteria for a modeled object; iteratively modifying a three dimensional shape of the modeled object in accordance with the one or more design criteria and the one or more load cases, the iteratively modifying comprising regulating shape change velocities for an implicit surface representation of the three dimensional shape that exceed a reference velocity, where the reference velocity is set based on a mean and a standard deviation of a shape derivative on the implicit surface; and providing the three dimensional shape of the modeled object for use in manufacturing a physical structure corresponding to the modeled object using one or more computer-controlled manufacturing systems.