Medial Surface Construction via Tetrahedral Mesh Cuttings
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Solution Overview
Problem
Conventional methods for constructing medial surfaces of non-manifold connected solids are prone to inaccuracies due to decomposition into multiple manifold sub-problems, which complicates error-free modeling and computation.
Innovation Solution
A tetrahedral mesh is generated with nodes only on the boundary surfaces, and cuttings are created based on vertex coding templates to approximate the medial surface, allowing for efficient representation and computation of non-manifold geometries without interior nodes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional methods decompose non-manifold solids into multiple manifold sub-problems, then the modeling becomes easier to handle, but inaccuracies arise when connecting the sub-problems
Solution Approach 1:
The patent applies segmentation by dividing the non-manifold solid into multiple manifold sub-problems, where each sub-problem is processed independently to generate its own medial surface. This allows complex non-manifold geometries to be handled through simpler manifold components while maintaining overall accuracy through proper connection of the sub-problems.
2Shape
If tetrahedral mesh with interior nodes is used, then the mesh can represent complex geometries, but computational resources increase
Solution Approach 1:
The patent extracts and removes interior nodes from the tetrahedral mesh, keeping only boundary nodes that lie on the surface of the solid object. This reduction in node count significantly decreases computational resources required for medial surface construction while maintaining the ability to represent complex geometries through the boundary node configuration.
3Productivity
If boundary surfaces are identified and coded, then the construction process becomes more systematic, but the process complexity increases
Solution Approach 1:
The patent applies local quality by assigning different codes to boundary surfaces based on their geometric properties and relationships. Each boundary surface is analyzed and classified locally, allowing the construction process to adapt to specific geometric features while maintaining overall systematic organization. This localized classification improves construction efficiency by enabling targeted processing of different surface types.
Data Source
AI summary
Data is received that encapsulates a model of a solid object. The model includes a set of boundary surfaces that are approximately parallel to a medial surface of the solid object. Thereafter, a tetrahedral mesh is generated to represent an interior of the solid object with tetrahedral elements having nodes located on the boundary surfaces. Cuttings are generated for each tetrahedral element based on the nodes. These generated cuttings are used to construct a representation of the medial surface of the solid object. Related apparatus, systems, techniques and articles are also described.