Boundary Continuity Constraints for Curve Network Surface Patches
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Solution Overview
Problem
Conventional CAD methods struggle to efficiently compute continuity constraints between surface patches in curve networks, failing to accurately reflect the intrinsic shape of input curve networks and often require solving large global systems.
Innovation Solution
The method determines boundary continuity constraints for each edge of a surface patch using local geometric information, evaluating derivatives of adjacent edges and blending them to create continuity constraints, allowing for independent computation of G0, G1, and G2 continuity between surface patches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If global methods are used to evaluate all surface patches in a curve network, then continuity constraints can be computed for the entire network, but the global system becomes too large to solve as the number of curves increases
Solution Approach 1:
The patent divides the global curve network into individual surface patches, each treated as a separate local problem. Continuity constraints are computed independently for each patch using its boundary curves, avoiding the need to solve a single large global system. This segmentation maintains continuity accuracy while dramatically reducing computational complexity.
Solution Approach 2:
The patent applies local quality by computing continuity constraints using only the local geometric information of each surface patch and its adjacent patches. Each patch's continuity constraints are determined based on its specific boundary curves and neighboring patches, rather than treating all patches uniformly in a global system. This local approach reduces the problem size while maintaining accuracy.
2Productivity
If local methods are used to construct surface patches independently for each face, then computational efficiency is improved, but the ability to specify continuity constraints that reflect the intrinsic shape of input curve networks is limited
Solution Approach 1:
The patent incorporates feedback by using the boundary curves of adjacent surface patches to determine continuity constraints. The continuity constraints for each patch are computed based on feedback from its neighbors' boundary geometries, ensuring that local computations reflect the global intrinsic shape of the curve network. This feedback mechanism maintains accuracy while preserving computational efficiency.
Solution Approach 2:
The patent changes parameters by computing continuity constraints in terms of boundary curve geometries and their derivatives. By expressing continuity constraints using the actual boundary curve parameters of each patch and its neighbors, the method adapts to the intrinsic shape of the input curve network while maintaining local computational efficiency.
3Ease of manufacture
If conventional methods are used to compute continuity constraints, then surface patches can be generated, but sharp and smooth features of the input curve network are not accurately reflected
Solution Approach 1:
The patent applies preliminary action by computing continuity constraints before generating surface patches. The continuity constraints are determined in advance based on the boundary curves of each patch and its neighbors, ensuring that sharp and smooth features are preserved from the beginning. This preliminary computation of constraints based on input curve geometry ensures shape fidelity throughout the surface generation process.
Data Source
AI summary
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for receiving data describing a model, the model describing a curve network; determining boundary continuity constraints for each edge, of each face, in the model; combining the determined boundary continuity constraints to determine respective boundary continuity for each face; and determining, using the respective boundary continuity constraints, a respective surface patch for each face.