3D Mesh Model Edge Collapse Using Length-Based Evaluation
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Solution Overview
Problem
Existing methods for reducing the number of meshes in three-dimensional mesh models, such as coronary artery models, often result in shape deviations and the generation of long, narrow meshes, which can lead to inaccuracies in simulations and computational inefficiencies, especially when thin portions are collapsed excessively.
Innovation Solution
A modeling apparatus that calculates an evaluation value for each edge based on its length and collapses edges in ascending order of this value, while adding new nodes at positions that minimize the quadric error metric (QEM) to maintain the original shape, and uses weights based on the thickness of blood vessels to prioritize edge collapse in thicker portions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the number of meshes is reduced by collapsing edges in ascending order of QEM, then the original shape is maintained as much as possible, but long narrow meshes are generated for long thin shapes like coronary arteries
Solution Approach 1:
The patent changes the parameter used for edge collapse ordering from QEM (quadric error metric) to edge length. By sorting edges in ascending order of length rather than QEM, the method prevents the generation of long narrow meshes while still maintaining shape accuracy through the use of a threshold value that controls the collapse process.
Solution Approach 2:
The patent applies preliminary anti-action by introducing a threshold value that prevents collapse of edges that would result in long narrow meshes. Before performing the collapse, the method evaluates whether the collapse would create problematic mesh geometry and blocks such collapses, thereby preventing the harmful effect of long narrow meshes from occurring in the first place.
2Manufacturing precision
If sufficiently small meshes are used to create a coronary artery model, then the original shape is accurately represented, but the number of meshes becomes excessively large
Solution Approach 1:
The patent applies partial action by performing edge collapse only on edges that meet specific criteria (ascending order of length and below a threshold value). Instead of collapsing all edges or using uniformly small meshes throughout, the method selectively collapses edges in regions where it is safe to do so, achieving mesh reduction while preserving shape accuracy in critical areas.
3Manufacturing precision
If edges are collapsed in ascending order of QEM, then the collapse process minimizes shape deviation, but the computational complexity increases
Solution Approach 1:
The patent simplifies the computational complexity by changing the ordering parameter from QEM to edge length. Calculating and sorting by edge length is computationally simpler than calculating QEM for each edge, while still achieving effective mesh reduction. The threshold value mechanism further simplifies the decision process compared to full QEM-based collapse.
Data Source
AI summary
A modeling apparatus calculates, with respect to edges in a three-dimensional mesh model, an evaluation value of each edge on the basis of the length of the edge, and selects the edges one by one as a first edge in ascending order of their evaluation value. In this connection, a lower evaluation value is calculated for a shorter edge. Then, if there is a specific node placement position where a value of a calculation formula using distances between the node placement position and each first face having either one of first nodes at both ends of the selected first edge as a vertex is lower than or equal to a threshold, the modeling apparatus removes the first edge, first nodes, and first faces from the three-dimensional mesh model, and adds a second node at the specific node placement position in the three-dimensional mesh model.