Parametric Surface Symmetry via Mesh Subdivision
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Solution Overview
Problem
Existing CAD systems face challenges in creating parametric surfaces that are symmetric with respect to a given symmetry operation, often resulting in insufficient curvature continuity, especially when symmetrizing initial subdivision surfaces, which can lead to discontinuities at junctions.
Innovation Solution
A method involving identifying a mesh pattern, creating a symmetric base mesh according to the symmetry operation, subdividing it, and forming a parametric surface from the subdivided mesh to ensure geometrical continuity, such as G1 or G2, using Catmull-Clark subdivision rules and adjusting vertices to maintain continuity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing CAD systems symmetrize initial subdivision surfaces, then a symmetric surface is obtained, but curvature continuity is insufficient and discontinuities occur at junctions
Solution Approach 1:
The patent applies preliminary action by creating a symmetric base mesh that inherently satisfies continuity requirements before performing subdivision. The mesh is constructed with vertices, edges, and faces arranged to ensure G1 or G2 continuity across symmetry planes, so that when Catmull-Clark subdivision is applied, the resulting parametric surface automatically maintains curvature continuity without requiring post-processing corrections at junctions.
Solution Approach 2:
The patent employs parameter changes by modifying the mesh structure parameters (vertex positions, edge connections, face configurations) to enforce symmetry constraints. By adjusting these discrete mesh parameters to satisfy continuity conditions, the method ensures that the continuous parametric surface derived from the mesh inherits the desired G1 or G2 curvature continuity properties.
2Manufacturing precision
If manual correction is used to fix continuity issues, then curvature continuity can be improved, but time and complexity increase
Solution Approach 1:
The patent implements self-service by designing a mesh construction process that automatically generates symmetric meshes with inherent continuity properties. The algorithmic approach to creating the base mesh and applying symmetry operations enables the system to self-correct potential continuity issues before subdivision, eliminating the need for manual intervention and reducing both time and computational complexity.
Solution Approach 2:
By performing preliminary mesh construction with built-in symmetry and continuity constraints, the patent prevents continuity problems from arising in the first place. This preliminary structuring of the mesh ensures that when parametric surfaces are generated through subdivision, they naturally satisfy G1 or G2 continuity requirements without requiring subsequent manual correction.
3Shape
If symmetry operation is applied to subdivision surfaces, then symmetric geometry is achieved, but discontinuities are introduced at the symmetry plane
Solution Approach 1:
The patent applies segmentation by dividing the mesh construction process into distinct phases: creating a base mesh with explicit symmetry constraints, applying the symmetry operation to generate the full symmetric mesh, and then performing subdivision. This segmentation allows continuity requirements to be satisfied in the discrete mesh domain before transitioning to the continuous parametric surface domain, preventing discontinuities at the symmetry plane.
Solution Approach 2:
The patent uses parameter changes to transform the mesh representation from an asymmetric base mesh to a fully symmetric mesh while maintaining continuity. By systematically adjusting mesh parameters (vertex coordinates, connectivity) to satisfy both symmetry and continuity constraints, the method ensures that the parametric surfaces generated from the symmetric mesh inherit smoothness across symmetry planes.
Data Source
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AI summary
The invention is directed to a method for creating a parametric surface symmetric with respect to a given symmetry operation (20), comprising steps of: - identifying a mesh pattern (15a); - creating a base mesh (15s) from the mesh pattern, according to said symmetry operation, said base mesh being symmetric with respect to said symmetry operation; - subdividing the base mesh, at a given order, into a subdivided mesh defining elementary faces; and - forming the parametric surface (16s) according to said faces. The invention further concerns computer program product and systems implementing the method according to the invention.