Parallel Mesh Simplification with Consistent Boundary Constraints
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Solution Overview
Problem
Existing mesh simplification techniques face challenges in ensuring that the boundaries of component meshes simplify identically during parallel mesh simplification, leading to artifacts and limited simplification when using standard algorithms, or result in non-manifold meshes when trying to preserve manifoldness.
Innovation Solution
The approach involves decomposing the input mesh into component meshes, calculating costs for candidate edge collapses, and interleaving boundary and interior edge collapses based on these costs, using a non-standard boundary edge collapse function that ensures the resulting vertex lies on the boundary plane independently of the interior mesh, and inserting geometry to preserve manifoldness if necessary.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If standard mesh simplification algorithms are applied to component meshes in parallel, then processing speed is improved, but boundary consistency deteriorates leading to artifacts and non-manifold meshes
Solution Approach 1:
The input mesh is decomposed into multiple component meshes that can be simplified in parallel. Each component mesh is processed independently by separate processing elements, enabling parallel computation while maintaining the ability to control boundary behavior through the decomposition structure
Solution Approach 2:
Different simplification strategies are applied to different parts of the mesh: boundary edges use a non-standard collapse function that ensures the resulting vertex lies on the boundary plane, while interior edges use standard collapse operations. This local differentiation ensures boundary consistency while maintaining simplification efficiency
2Manufacturing precision
If boundary edges are constrained to simplify identically in parallel component meshes, then boundary consistency is improved, but simplification freedom deteriorates limiting the number of possible collapses
Solution Approach 1:
The invention applies different collapse functions to different edge types: a non-standard boundary edge collapse function that constrains resulting vertices to the boundary plane, and a standard interior edge collapse function that provides full simplification freedom. This local differentiation resolves the contradiction by applying constraints only where necessary for consistency
Solution Approach 2:
The invention modifies the collapse function parameters for boundary edges specifically, requiring the resulting vertex to lie on the boundary plane rather than anywhere in space. This parameter change ensures boundary consistency while the rest of the mesh can use standard collapse parameters for maximum flexibility
3Manufacturing precision
If non-standard boundary edge collapse function is used to ensure vertices lie on boundary plane, then boundary consistency is improved, but computational complexity increases
Solution Approach 1:
The non-standard collapse function is applied only to boundary edges, not to interior edges. This localized application minimizes the increase in computational complexity by affecting only the subset of edges that require consistent boundary behavior, while interior edges use the simpler standard collapse function
Data Source
AI summary
An input mesh can be decomposed into component meshes that can be independently simplified. A computing device can calculate costs of performing candidate edge collapses for a component mesh. The candidate edge collapses can include boundary edge collapses and interior edge collapses. To simplify a component mesh, the execution of boundary edge collapses and the execution of interior edge collapses are interleaved in an order based on the costs of performing the candidate edge collapses. The position of a vertex resulting from a boundary edge collapse can be calculated independently of the interior of the component mesh. When component meshes are simplified in parallel, a boundary that is common to the component meshes can be simplified identically.