Triangular Mesh Slope Constraint Projection for Drainage Design
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Solution Overview
Problem
Existing methods for designing triangular meshes in three dimensions often fail to accurately represent drainage conditions and surface slope constraints, leading to suboptimal designs in applications like road grading and golf course design, where proper drainage and slope alignment are critical.
Innovation Solution
A method involving iterative projections onto geometric constraint sets, specifically using maximum slope constraints and proximity operators to adjust triangle vertices, ensuring that the triangular mesh converges to an optimal solution that meets design objectives such as drainage and slope requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional triangulation methods are used to generate terrain models, then the mesh generation is simple and fast, but the drainage representation is inaccurate and local minima/sharp slope changes occur that do not exist in reality
Solution Approach 1:
The patent applies preliminary action by pre-identifying drainage channels and constraints before final mesh generation. The method first detects drainage features and establishes constraints, then uses these pre-established constraints to guide the subsequent mesh optimization process, ensuring accurate drainage representation from the outset rather than correcting errors afterward.
Solution Approach 2:
The patent employs parameter changes by adjusting triangle surface parameters (vertices, edges, slopes) to smooth out grade changes and eliminate unrealistic local minima. The optimization process modifies geometric parameters of the mesh while maintaining drainage channel integrity, transforming the mesh from a simple triangulation to one that accurately represents real-world drainage conditions.
2Manufacturing precision
If heuristics are applied to generate higher order Delaunay triangulations, then drainage representation improves, but the method remains non-deterministic and may still produce suboptimal results
Solution Approach 1:
The patent implements feedback through an iterative optimization process that continuously evaluates mesh quality against drainage constraints. The method provides feedback loops where the mesh is adjusted based on constraint satisfaction, and the process repeats until optimal drainage representation is achieved, ensuring deterministic and reliable results rather than relying on non-deterministic heuristics.
Solution Approach 2:
The patent applies preliminary action by pre-establishing deterministic constraints based on identified drainage channels before optimization. These pre-defined constraints serve as a reliable foundation that guides the optimization process, ensuring consistent and reproducible results across different runs, unlike non-deterministic heuristic approaches.
3Manufacturing precision
If triangle surfaces are adjusted to smooth out grade changes and create drainage channels, then drainage accuracy improves, but the computational complexity and optimization challenge increase significantly
Solution Approach 1:
The patent applies segmentation by dividing the mesh optimization problem into manageable components: identifying drainage channels, establishing constraints for each channel, and optimizing triangle surfaces individually or in groups. This segmentation of the complex optimization problem into smaller sub-problems based on drainage features makes the overall process more tractable and computationally efficient.
Solution Approach 2:
The patent employs local quality by applying different optimization strategies to different regions of the mesh based on their functional requirements. Drainage channel regions receive specialized constraint-based optimization, while other regions may use different criteria, allowing localized adjustment of surface quality without requiring complete re-optimization of the entire mesh.
4Manufacturing precision
If constraints are imposed on triangle surfaces for drainage and slope requirements, then design accuracy improves, but the mathematical optimization becomes more challenging at large scale
Solution Approach 1:
The patent applies segmentation by dividing the large-scale mesh into smaller sub-meshes or processing regions based on drainage channels and constraint zones. This allows the optimization algorithm to handle constraints locally in manageable segments rather than attempting to optimize all triangles simultaneously across the entire large-scale mesh, reducing computational complexity while maintaining overall constraint satisfaction.
Data Source
AI summary
A method and system provide the ability to design a (land) surface. A triangular surface mesh representative of an existing surface is obtained. The mesh includes triangles that are connected by vertices and edges. Design constraint sets are determined based design constraints. The design constraints include a maximum slope constraint for a first triangle of the two or more triangles in the triangular surface mesh. The maximum slope constraint is a maximum angle between a normal vector of the first triangle and a reference vector. Heights of the vertices of the first triangle are projected onto the design constraint sets such that the normal vector satisfies all of the design constraints. The projecting includes modifying the heights by a minimum Euclidian distance. A design of the surface represented by the triangular surface mesh is generated based on the projecting.