Loop Subdivision Surface Mesh Approximation for CAD Surfaces
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing CAD-based modeling techniques are not feasible in all situations, necessitating a CAD-free surrogate that can efficiently approximate computer-aided design (CAD) surfaces, particularly in fields like vehicle design and endoscopic surgery, where CAD-based approaches are undesirable or unfeasible.
Innovation Solution
The use of Loop subdivision surfaces generated from an equilateral triangle mesh, where vertices are moved to create a control mesh with a limit surface that passes through all vertices, and local refinement is performed on regions with errors greater than a threshold, to closely approximate CAD surfaces, while parameterizing the mesh for a 2D representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional CAD-based modeling techniques are used, then design precision is maintained, but the approach becomes undesirable or unfeasible in certain fields
Solution Approach 1:
The patent creates a surrogate CAD surface by copying the essential geometric features of the original CAD model using subdivision surfaces. Instead of working with the original CAD data directly, it generates a mesh-based approximation that replicates the surface geometry, enabling use in fields where CAD systems are incompatible or undesired while maintaining geometric fidelity.
2Manufacturing precision
If iterative mesh refinement is performed to improve surface accuracy, then approximation quality increases, but processing time and computational resources increase
Solution Approach 1:
The patent performs preliminary actions by pre-computing the control mesh and limit surface before final surface generation. The control mesh is constructed with vertices strategically positioned to predict the final surface geometry, and the limit surface is pre-calculated to guide subsequent refinement steps, reducing the need for extensive iterative adjustments later.
Solution Approach 2:
The subdivision surface algorithm performs self-service by automatically refining the mesh and adjusting control points based on the inherent mathematical rules of the subdivision scheme. The limit surface computation self-corrects and converges to the final surface without requiring external intervention or manual adjustment, reducing processing overhead while maintaining accuracy.
3Manufacturing precision
If the control mesh is refined through multiple iterations, then the limit surface more closely approximates the target surface, but memory requirements increase
Solution Approach 1:
The patent segments the surface approximation process into distinct stages: control mesh generation, limit surface computation, and final surface refinement. Each stage operates on a different level of mesh detail, allowing memory-intensive operations to be performed only when necessary. The control mesh serves as a compact intermediate representation that requires less memory than fully refined meshes while still enabling accurate surface reconstruction.
4Manufacturing precision
If local refinement is applied to regions with high error, then surface accuracy in critical regions improves, but device complexity increases
Solution Approach 1:
The patent applies local quality by performing refinement operations selectively on specific regions of the mesh rather than uniformly across the entire surface. Error metrics are computed for different mesh regions, and refinement is applied only where the error exceeds a threshold, concentrating computational resources on critical areas while leaving low-error regions unchanged, thus reducing overall complexity.
Data Source
AI summary
Systems and methods are provided for generating a surface that approximates one or more CAD surfaces. An input that approximates the one or more CAD surfaces via a plurality of triangles is received. A mesh of equilateral triangles is generated on the input, with the mesh including vertices that lie on the input. Vertices of the mesh are moved to generate a control mesh, the control mesh having a corresponding limit surface that passes through all of the vertices of the mesh. A local refinement is performed on one or more regions of the control mesh that have an error that is greater than a threshold value, where the local refinement causes the limit surface of the control mesh to more closely approximate the one or more CAD surfaces. The mesh is parameterized to generate a two-dimensional (2D) representation of the mesh.